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TECHNICAL REPORT

Experiments on the Dynamics andHydrodynamic Instabilities of AblativelyAccelerated Targets

February 1983

Submitted to: Naval Research LaboratoryCode 47304555 Overlook Avenue, SWWashington, DC 20375

Attention: Dr. Barrett Ripin

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Copy.j MRC/WDC-R-050

TECHNICAL REPORT

Experiments on the Dynamics andHydrodynamic Instabilities of AblativelyAccelerated Targets

February 1983

Submitted to: Naval Research LaboratoryCode 47304555 Overlook Avenue, SWWashington, DC 20375

Attention: Dr. Barrett Ripin

MISSION RESEARCH CORPORATION5503 Cherokee Avenue, Suite 201Alexandria, Virginia 22312

(703) 750-3556

V .. i docuimbn h. 2e ,

TABLE OF CONTENTS

Page

INTRODUCTION 1

DOUBLE-FOIL AND NOTCHED-EDGE EXPERIMENTS 3

ABLATION-PLASMA ION MEASUREMENTS 3

ANALYSIS OF ION MEASUREMENTS 4

TRACER METHOD 5

TEKTRONIX DATA ACQUISITION SYSTEM AND SOFTWARE 6

TARGETS AND TRACERS FOR RAYLEIGH-TAYLOR EXPERIMENTS 6

EXPERIMENTAL METHODS FOR RAYLEIGH-TAYLOR MEASUREMENTS 7

LONG SCALELENGTH EXPERIMENTS 8

Accession Forr- GEA&I

TABe

_ _ _ _ _ _ _ _ _ _ _ _ _ _Dis

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INTROUCTIONI

The Laser-Plasma Interaction group at NRL is evaluating for the

Department of Energy the feasibility of using direct laser drive to

Implode fusion pellets.t Mission Research Corporation (MRC) has

contracted to support this experiment by using its best effort to perform

the tasks summarized below:

A parametric study shall be performed using the double foil

technique on actual laser-foil experiments. Design parameters, to

be varied as needed, include laser intensity, material and

thickness of the first foil, material and thickness of the second

foil, and the spacing between foils. Notched-edge configurations

will also be investigated.

In support of the above task, other diagnostic measurements will be

performed. Such diagnostics include calorimeters, Faraday cups, 1'and ballistic pendula.

0 Analytical techniques and methods analyzing the experimental data

will be developed and implemented on the existing PDP-11/10 system.

We will investigate whether the x-ray tracer technique ... is

suitable to track plasma flow from targets accelerated to high

velocities. We will also investigate whether this technique Is

suitable for the study of plasma hydrodynamic Instabilities. For

this purpose we will experiment with target and tracer materials

that are density matched and at the same time maintain a sufficient

tracer/target x-ray emission contrast. We will also use plasma

t B. I.. Ripin et al., Phys. Fluids 23(5), 1012 (1980); 24, 990 (E)

C

Ft1

calorimeters and ion collectors to investigate laser absorption in

long-density-scalelength plasmas. These studies will Include, as

needed, parametric variations of laser intensity, laser energy,

laser profile, target thickness, and target density. We will

operate and develop software for the 4052 Tektronix data

acquisition system If this becomes necessary for the above

experiments.

* Mission Research Corporation (MRC) will Interface existing NRL

x-ray detectors and particle detectors with digital data

acquisition systems which are owned by NRL. MRC will operate,

maintain, and upgrade these systems for the purpose of

Investigating the properties of laser Interaction with matter.

Software will be developed for these systems If necessary for the

above experiment.

0 The data obtained in the above tasks will be reduced and analyzed.

The following sections summarize our fulfillment of these

tasks. Details are provided In the appendices.

L2

L

.

DOUBLE-FOIL AND NOTCHED-EDGE EXPERIMENTS

Experiments using double-foils and notched-edge configurations

have been performed. In particular:

. The validity of the double-foil method was verified using clear

double-foils and x-ray backlighting methods.

0 A low density plasma traveling ahead of the accelerated target has

been identified and diagnosed.

. A triple-foil configuration was used to diagnose the impact foil.

. Target speeds up to 160 km/sec have been measured.

0 Target pressure has been measured using the double-foil technique.

These measurements verify earlier results obtained with ballistic

pendula, plasma calorimeters, and ion collectors.

. The relationship between Irradiance uniformity and target velocity

uniformity was measured.

* A notched double-foil configuration was used to diagnose shocks in

the impact foil.

Appendix A provides more details.

ABLATION-PLASMA ION MEASUREMENTS

Earlier experiments which inferred target pressure from

measurements on the ablation plasma were compared to more recent

experiments which Inferred target pressure from its acceleration as

measured with x-ray backlighting. Good agreement was found.

Appendices B an C provide more details.

3

.

ANALYSIS OF ION MEASUREMENTS

A program called MINCAL was written to analyze plasma

calorimeter data aquired by NRL's PDP-11/10-based data acquisition

system. MINCAL Is a flexible, user-oriented program with the following

features:

* Parameters are stored permanently on disk.

" The program provides options to list and/or change parameters.

" Energy and velocity data reduction Is possible.

" Plots are done on a line printer using a line printer graphics

(LPG) routine.

" Program stores all system constants (amplifier gain, etc.) and

automatically reduces data to absolute values.

* Program reduces plasma calorimeter data, Interpolates between data

points, and plots energy and velocity versus angle.

* Program outputs useful calculations for user: 81/2 (angle

containing half the mass, momentum versus angle, others as

specified by the user).

0 Program is designed to easily incorporate new data reduction

routines.

• Program is Implemented on the DEC-10 and the PDP-11/10.

Program Listing Is provided In Appendix D.

4

TRACER METHOD

The tracer method, coinvented by an MRC employee (3. Grun), has

been used to study the ablation plasma flow from planar targets irradiated

by uniform and perturbed laser beams. The experiment:

• Discovered that the ablating plasma flows away from the target as

if It were an Incompressible fluid.

0 Explained the angular distribution of ablation plasma momentum,

velocity, and mass as measured by diagnostics placed far from the

target.

. Provided qualitative evidence for velocity smoothing caused by

thermal conduction In the overdense ablation plasma.

Initial experiments to spectrally and spacially resolve the

emission from a planar target irradiated by a nonuniform laser beam have

been performed. From such measurements, the temperature and density of

the plasma along the target surface may be resolved and, thus, the "cloudy

day effect" may be quantitatively studied.

MRC has applied the tracer method to the study of

hydrodynamically unstable targets. This aspect of our work will be

discussed below.

MRC has also helped to use tracers to make local spectroscopic

measurements within laser-produced plasmas. This application of the

tracer method constitutes a major advance in plasma spectroscopy, since it

potentially eliminates problems of interpreting spectra originating from

regions of varying density and temperature In an inhomogeneous plasma and

reduces complications due to plasma opacity.

Appendices A, E, and F provide more detail.

5

TEKTRONIX DATA ACQUISITION SYSTEM AND SOFTWARE

MRC recommended the purchase of a data acquisition system

consisting of a Tektronix 4052 computer, 4907 disk drive, 7612D

digitizers, 4631 hard copy unit, and an HP-IB 37203A extender. The

Installation and operation of this system was overseen by MRC. This

system is being used to acquire Ion time-of-flight data and plasma

calorimeter data.

The data acquisition software for this system was custom built

by Tektronix to MRC specifications. Subsequently, the Tektronix program

was modified by MRC to help on-line analysis of the data. A listing of

this software is in Appendix G.

Other software written to aid analysis of the data includes two

programs to reduce focal spot size data (Appendix H) and a program used to

calculate the speed and the number of classical Rayleigh-Taylor e-foldings [of an ablatively-accelerated target (Appendix I).

TARGETS AND TRACERS FOR RAYLEIGH-TAYLOR EXPERIMENTS

MRC suggested that tracers embedded in perturbed targets be used

to study the ablation plasma flow characteristic of hydrodynamically

unstable targets. In our opinion these targets should have the following

characteristics - some of which are necessary, others desirable:

* Targets should have uniform density.

" Periodic structure should have a wavelength > lOm and perturbation

magnitude of 0-2.

" Tracer emission should be significantly larger than target emission

in the energy band being measured.

6

• Target perturbation period should be larger than the tracer period

for acceptable resolution.

0 Tracers should not perturb target areal density.

* Tracers should not perturb the dynamics of the ablation plasma (for

example pv2 should be the same for the target and the tracer).

. It is desirable that the tracer perlod match the perturbation

period for some experiments.

. It is desirable that the target manufacturing methods match the

capabilities of the target fabrication group at NRL. In particular

polystyrene targets are desirable since this group has had

extensive experience making them.

MRC has evaluated over 40 materials for their suitability and

has examined various manufacturing methods. We found that carbon targets

with silicon or aluminum tracers met all our criteria except the last. To

extend the capabilities of the NRL target fabrication group MRC located a

used, ion-mill machine which was purchased by NRL permitting the

manufacture of the above targets.

EXPERTMENTAL METHODS FOR RAYLEIGH-TAYLOR MEASUREMENTS

In addition to the tracer method as applied to the

Rayleigh-Taylor problem, MRC invented a magnesium-layer method that may

provide a measurement of the Rayleigh-Taylor growth rate.

The tracer and magnesium-layer methods and Initial experiments

are described in Appendix 3.

7

LONG SCALELENGTH EXPERIMENTS

NRC has participated In long scalelength experiments in support

of the NRL effort. Details are provided in Appendix K.

X-RAY DETECTORS

The existing NRL x-ray data acquisition system has been upgraded

and operated by tRC. In particular:

The detectors and their associated electronics have been

reconfigured (with the addition of several new components and

electrical shielding) in order to eliminate a pre-existing

electrical noise problem.

* The x-ray detectors have been operated in conjunction with the NRL Vlong-scalelength experiments.

MRC has maintained and upgraded the NRL's PDP-11/10 computer system

and software. This has included the purchase and installation of a

new RT-11 operating system, as well as streamlining the computer

interface for more reliable operation.

A program titled PADCAL has been written to facilitate calibration

of the x-ray detector system. This program has significantly

reduced both the time and effort previously required in the

performance of this task and allows calibrations to be performed

much more frequently in the course of an experiment.

MRC has Investigated available options towards the possibility of

integrating the Tektronix 4052 and PDP-11/1O data acquisition

systems Into a single, coherent system. These options will be

considered by NRL personnel for future Implementation.

APPEND~IX A

Ablative acceleration of planar targets to high velocitiesJ. Grun," S. P. Obenschain, B. H. Ripin, R. R. Whitlock, E. A. McLean, J. Gardner, M. J. Herbst,and J. A. StamperNaal Research Laboratory. Washington. . C 20375

(Received 8 January 1982; accepted 20 October 1982)

Laser irradiated targets are ablatively accelerated to velocities near those required for fusion pelletimplosions while remaining relatively cool and uniform. The target velocities and velocity profiles aremeasured using a double-foil method, which is described in detail. Also, the ablation plasma flow from thetarget surface is spatially resolved, and the scalings with absorbed irradiance of the ablation pressure,ablation velocity, and mass ablation rate are determined. Results are compared with hydrodynamic codecalculations.

1. INTRODUCTION m, f/6 aspheric lens. Such large diameter, quasinear fieldOne approach to inertial confinement fusion involves laser spots are used whenever possible to maximize irra-

the use of a multi-nanosecond, moderate-irradiance laser diance uniformity and to minimize focal-spot-edge ef-pulse to implode a hollow pellet containing DT fuel.' If this fects.2" ' Irradiance profiles, such as those shown in Fig. 1,concept is to succeed, the imploding pellet shell must be effi- are measured on each discharge in an equivalent target i:ciently and uniformly accelerated to a high velocity, and the plane.9 These profiles are fairly uniform with small and largeDT fuel must be kept cool. Only then will the pellet compress scale peak-to-valley variations of about + 35%. Unlessto densities sufficient for a high gain thermonuclear burn. otherwise stated, irradiance is varied by adjusting the laser

In this paper, we describe experiments which utilize ab- energy and not by changing the focal spot size. The laserlatively accelerated planar targets to model large pellet shells pulse duration is 3-5 nsec FWHM.early in the implosion phase. We have made detailed mea-surements of the motion of such targets 23'4 and of the abla-tion plasma that accelerates them.2" ' 6 These measurementsinclude: emitted light studies; visible light shadowgraphy 10and x-ray shadowgraphy on a novel target-impact foil (dou- 4 50% ENERGY CONTENT

ble-foil) configuration which is used to determine the mean 190% ENERGY CONTENT

velocities and velocity profiles of the dense part of the accel-erated target, to study irradiance symmetrization, and to TIME HISTORY

study double-foil interactions; diagnosis of the impact foilusing a triple-foil configuration; spatially resolved studies ofthe ablation plasma flow from uniformly and nonuniformly _

irradiated targets; as well as measurements of the ablation -plasma pressure, velocity, and mass ablation rate. The targetvelocity, velocity profiles, and the temperature of the target irear have been studied as a function of target thickness, irra- .

diance, and irradiance uniformity. We have accelerated rela-tively cool and uniform targets to velocities of 160 km/sec-a velocity which is above the minimum thought to be re-quired for laser fusion." Our experimental results are com- -

pared to hydrodynamic code calculations.The experimental arrangement is described in Sec. II.

Measurements on the accelerated target are described in Sec.II; and measurements of the ablation parameters are de-scribed in Sec. IV. Conclusions are offered in Sec. V.

II. EXPERIMENTAL ARRANGEMENT .01

These experiments are performed using the NRL 0RADIUS mml

Pharos I1 Nd:glass laser (A = 1.05/uml which has been de-scribed elsewhere.' The laser beam is typically focused to a FIG. I. Azimuthally averaged radial intensity profiles at the target plane.large diameter ( -- I mmi spot on the target surface by a 1.2 Focal-spot radius is vaned by moving the focusing lens. Arrows indicate

radii within which 50% or Q% of the energy is contained. Inserts show thetemporal behavior of the laser pulse and constant irradiance contours of a I-

* Present addre,.: .issimon Research Corporation. Alexandria. Virginia. mm diameter laser spot.

588 PhyS. FluidS 26 12), February 1983 0031-9171/83/020588-I1001 90 e 1983 American Institute of Physics 588

LASER the side using an x-ray backlighter, and (3) from the rear.- :

[ BEAM recording light emitted by the impact foil when it collidesSINGLE OR --" DIAGNOSTICS with the target (Fig. 2). The details of particular double-foil

DOUBLESTREAK TARGET V configurations depend on the intent of the specific experi-CAMERA ment and will be discussed in later sections.

DO Q LTemporally resolved temperature at the rear surface ofLONG the accelerated target is determined by comparing the abso-. Py-. oBEPROBE lute visible continuum emission from the target's rear to

L -black body emission.'" The continuum intensity is measuredFILTER SHORT PROBE at two different wavelengths using 3/4-m spectrographs

5270A rMINICALORIMETERS (ofl coupled to l-nsec risetime photomultipliers.I ION COLLECTORS I&)LPENDULA IUJ Ill. TARGET DYNAMICS

In earlier studies of ablative acceleration we inferred the

SPECTROGRAPH PMT target velocity from the velocity of its debris measured withtime-of-flight ion collectors, and from the velocity of its opti-cal shadow.' Each of these methods however, has limita-

FIG. 2. Sketch of the expenmental setup tions. Ion collectors, for example, measure properties of the

target very far from its acceleration region, while opticalshadowgraphs can not distinguish the high density part of

Figure 2 shows the experimental arrangement. The tar- the target from any low density plasma that may precede it.get normal is tilted 6" from the laser axis to make it experi- In the present work we use a double-foil technique" thatmentally accessible. Surrounding the target are arrays of discriminates against such a low density plasma, and permitsplasma calorimeters, in-situ calibrated ballistic pendula,2 temporally and spatially resolved diagnosis of the dense partand time-of-flight ion collectors which monitor the ablation of the target. Double foils may also be used to investigateplasma and target energies, momenta, and velocities, respec- hypervelocity impact phenomena such as the generation oftively. (In this long pulse regime ion collector t aces are nar- ultra high pressures 2 or to model double-shell fusion pellets.row and single peaked, making them ideal for time-of-flight With the double-foil method, the target velocity is de-measurements.) From the angular distributions of these termined from its flight time to the impact foil, placed aquantities we infer the ablation pressures, mass ablation known distance away. The flight time, in turn, is determinedrates, and ablation velocities. Although any two of the mea- by noting the moment at which the impact foil reacts to itssured quantities are sufficient to calculate the third, we mea- collision with the target. Such reaction includes any of thesure all three with independent diagnostics to verify the con- observable phenomena normally associated with colli-sistency and validity of the results. Spatially resolved sions-for example, spall or fluff from the rear of the impactpictures of the ablation plasma flow are also obtained using foil, movement or deformation of the impact foil, or visibletracer elements deposited in the target surface. light emission from its rear surface. The target position as a

Temporally and spatially resolved measurements of thetarget motion are made using a double-foil technique. Thismethod consists of placing a thin foil (impact foil) behind the 7 )m CHlaser accelerated target and observing the reaction of the )impact foil to its collision with the target (Fig. 3). We observethe two-foil interaction in three ways: (II from the side withoptical shadowgraphy or optical streaking (Fig. 2), (2) from

TARGET IMPACT LASER 1.3 nsec 3.8 nsecFOIL FOIL

LASERf . 4 Ey ~iJ

* 10 pm CH7 'm Al

ld) (e)

BEFORE ,APACT AFTER IMPACT FIG 4 Optical %hadowgraphs of a single ja.bc) and a double-foil Id.n.fl

larget irradiated at 5 × 10' W/cm: The times notes are relati e to Ihe peak

FIG 3 Schematic of the double-fot concept- Behavior of the laser acceler. of the laser pulse. Photographs b. c, and . fare taken during the same dis-

ated target is inferred from the response of the tmpaA;t foil to the collison. charge.

589 P"'ys ,uds vo. 26. No. 2. February 1983 Grun et al 589

function of time is measured by varying the initial target- graphy and interferometry diagnostics, but is discriminatedimpact foil spacing, thereby controlling the instant of colli- against with the double-foil method.sion. In this manner we can diagnose the target during as Another way to view the delayed reaction of the impactwell as after its acceleration phase. Also, the visible light foil is presented in Fig. 5, which shows the streak record of aemission from the rear of the impact foil gives spatial resolu- double-foil collision backlit by a 10-nsec, 5270-A lasertion along the target surface so that the relationship between probe. This one-dimensional, but temporally continuous,velocity and irradiance uniformity may be studied. shadowgraph shows the low density plasma advancing to-

The choice of the target and impact-foil material, their ward the impact foil, the low density plasma-impact foil col-dimensions, and the spacings between the two foils depend lision, and the reaction of the impact foil when the dense parton the purpose of the experiment. To infer target velocities, of the accelerated target finally strikes. The sudden reactionfor example, it is desirable that the impact foil be thin enough time ( 0.5 nsec) of the impact foil suggests a localized, denseso that the sound-transit-time through it is very short com- accelerated target. The time of the dense target-impact foilpared to the flight time of the target. In this case, the sound- collision is, therefore, a good marker for the target time-of-transit-time may be ignored, and the collision time of the flight.target with the front surface of the impact foil is directly We determine a target velocity by varying the initialrelated to the reaction of the impact foil's rear surface. target-impact foil separation and accumulating distance

The ability of the double-foil method to discriminate traveled versus time-of-travel data for many discharges.against a low density plasma preceding the dense part of the Such data for 7-/pm thick and 10-/pm thick CH targets irra-target is demonstrated in Fig. 4. Here, we compare shadows diated at 6 x 102 W/cm2 are shown in Fig. 6. For most ofcast by a single and a double-foil target that are temporally these cases, the target-impact foil separation is large enoughresolved by multiple-frame shadowgraphy using a 0.5 nsec, so that the collision occurs after the ablative acceleration5270-A laser probe flash. Both types of targets are photo- phase is nearly over. Therefore, the data for each targetgraphed before, as well as 1.3 nsec, and 3.8 nsec after the thickness lie on a straight line whose slope is the final targetpeak ofthe laser pulse. Figures 4(a), (b), and (c) show shadow- velocity. Velocities obtained in this way agree with predic-graphs of the single target which is a 7-pum thick CH foil. The tions based upon measurements of the ablation momentumshadow of this target moves with a velocity of 1.6X l0" cm/ (pressure), mass ablation rate (Sec. IV) and momentum con-sec and traverses a distance of about 400.pm in 2.5 nsec. servation, and with the predictions of a hydrodynamic codeFigures 4(d), (e), and (f) show a corresponding sequence for described below. However, they are significantly lower thanthe double foil which is composed of a 10-pum thick CH tar- the low density plasma velocities inferred from the motion ofget and a 7-pim thick aluminum impact foil. Note that al- the target's optical shadow in the double-foil streak pictures.though the target shadow has already reached the impact Averaged over many discharges, the ratio of the opticalfoil in Fig. 4(e), the impact foil itself does not react at this shadow velocity to dense target velocity is 2 ± 0.8, with thetime. In fact, the first indication of the impact foil's reaction spread mostly due to discharge-to-discharge variations inoccurs in Fig. 4(f)-more than 2.5 nsec after the optical shad- the low density plasma velocity. This ratio is consistent withow of the accelerated target reached the impact foil. Since the leading edge of the low density plasma being caused bythe shock-transit-time through the impact foil is less than 1.4 spall or fluff from the unloading of a shock at the target'snsec (sound speed in cold Al is 5 X 10 cm/sec), much of this rear surface.' 3

delay is caused by the material in the leading edge of the Like the target shadow, the impact-foil shadow is alsotarget shadow exerting insufficient pressure for the impact cast by low density material and not by the dense part of thefoil to react. Because the pressure exerted by a moving mass impact foil. Thus, the acceleration of the impact foil or theis proportional to its density, we conclude that the leadingedge of the accelerated target shadow is composed of low I I I 1 I I I I I

density material. This low density material obscures the 0.- TARGET-IMPACT FOIL

dense part of the accelerated target from optical shadow- 0 7im CH- 7pm Al-. 0 71dm CH - 0.Smm Al

E0.7 t0,m CH- 7wansAl

tot -lI (0I Z 6 10'2Wlcm

2 -1 10

7 cm/s

-Il a 0.5

-IMPACT 0.3

.TARG T REAC 0.1

MOTION 0 2 3 4 5 6 7 8 9 10TIME Insec)

360,.,- FIG. 6. A graph of target-impact foil separation versus the time Iith re-

spect to an arbitrary ongini at which the impact foil reacts to its collisionFIG 5. Streaked optical hadows of a target colliding with an impact foil: with the target. The slopes of lines drawn through points accumulated overra-before dicharge. and ibi-after discharge. The target is 7./m thick OfI many discharges give the dense target velocities. The laser pulse duration isand the impact foil I-, 7-Aim thick AL. 4-nsec FWHM

590 P(iys Ru:Cs. Vol. 26. No 2. Febru.ar, 1983 Grun et at 590

L .. ...... . .,

N r 10 _0_ ,

REACTIONd 14 2 nsc4 km, W

ii6 S "C

I;01-IMPACT

:177

10 I

0001 -2 -2-

0 I-- - - - - - ---------- ----

30$ 0mFIG. 9. Density profiles of a thin and a thick target accelerated to high

velocities. The laser is incident from the right; p,,,, is the critical electronFIG. 7. Triple-foil experiment: A third foil diagnoses the second foil. The dest.Tesmaio nitnsr:()16 ]0 Wm bord.2-laserdensity. The simulation conditions ar: (a) 1.6 x W/CM 2 absorbed. 2.6-thick C. respectively, is 3-im thick the impact foils 7-1un nsec pulse duration, 6.5-pum thick CHI target and (b) I X 10" W/cm2 ab-sorbed, 4-nsec pulse duration and 20-pum thick CH target.

pressure history in the collision cannot be gotten from mea- density. Thus, the figure shows that the dense, acceleratedsurements using optical probe light (Fig. 5). This is demon- target traversed most of the distance to the impact foil-astrated in Fig. 7 which shows that the leading edge of the distance 30 times its thickness-without noticeable breakup.impact foil shadow exerts insufficient pressure to cause a It is evident too that the impact foil does not react apprecia-third foil to react. bly before it is hit by the high density part of the target. These

Backlighting the double foils with x rays provides a way observations support our interpretation of results from theto directly measure the motion of the dense portion of both double-foil method. Also, velocities obtained by x-ray back-foils. An x-ray shadowgraph of a double foil photographed lighting agree with those obtained by the double-foil meth-using a J-nsec duration Al x-ray flash (K shell emission, od: velocities obtained with the two methods, on differentmostly at 1.6 keV; I mil Be filter on camera) as a backlighting shots, are the same to within 35%.source, is shown in Fig. 8." This figure is the x-ray shadow- It is also interesting to note that the accelerated target isgraph of a 7-1um thick carbon target irradiated with not "cut out" from the rest of the target foil, but is connected3.5 X 10"2 W/cm-, and moving at 3-4 X 106cm/sec before its to it with a near solid density bridge. The gap between thecollision with a 7-pum thick carbon impact foil. The shadows accelerated target and the target foil is thus effectively closedvisible in Fig. 8 are the unaccelerated foil, the accelerated so that front surface plasma cannot flow to the impact foiltarget, and the impact foil. Bright regions are due to the x- and disturb our measurements. This bridge, in addition, pre-ray flash and x-ray emission from the plasma corona on the vents front surface plasma from heating the rear of the tar-target's front surface. We estimate, from x-ray absorption get, and thereby spuriously increasing the rear surface tem-data in cold carbon and the observed path lengths, that the peratures measured in Ref. 10 and later in this paper.shadows are caused by material that is at least 3% of solid We have computed target velocities and density profiles

using a one-dimensional fluid code that has been describedelsewhere."' This code utilizes a sliding zone Eulerian gridIwith flux corrected transport (FCT). The physics included inthe code are: a single temperature fluid, classical transportphysics with Spitzer heat conduction, and the same temporalirradiance history as the experiment. Absorption in our< 10s' W/cm2 long pulse regime is assumed to be by inverse

bremsstrahlung in the underdense region with any remain-ing energy dumped smoothly into two zones surroundingthe critical surface. The only target preheating considered is

IMPACT FOIL by shocks. Examples of computed density profiles for thin,

- ~ ACCELERATED fast targets and thick, slow targets are shown in Fig. 9. BothTARGET the thick and thin target in the figure are compressed during

the acceleration phase. Afterwards they expand somewhatTARGET FOIL and develop a low density foot that precedes the dense target.

Such a low density foot in front of the dense target material isinferred in the experiment. The expansion rate of the dense

1 mm target is much smaller than its directed velocity. However,

FIG. S. The x-ray shadowgraph ofadouble foil before the target-impact foil the expansion rate and the length of the low density foot arecollision. The x-rjy flash is 4 nsec longand occurs 5 nsecafterthe peak of the probably underestimated in the calculation because preheatLaser pulse. Pinhole smeanng and time smeanng are about 20,um each. mechanisms other than shock heating are not included.

591 PIys Flutas, Vol. 26. No 2, February 1983 Grun e*t S91

In addition to measuring target velocity magnitude,measuring the velocity profile across the target is also impor-tant. This is because nonuniformly accelerated pellet shellswill not achieve high compression ratios and will therebyaegrade the pellet gain. Nonuniform target velocities couldarise from any number of sources such as hydrodynamicinstabilities, nonuniform targets or nonuniform irradiation.We now address the third issue, namely: Are target velocityprofiles and irradiance profiles directly related, or will amechanism such as thermal conduction in the ablation plas- IMPACT FOil.

ma smooth irradiance nonuniformities? Answers to thisquestion will influence the choice and design of lasers fordirect illumination pellet implosions.

To measure target velocity profiles we utilize the visiblelight which is emitted from the rear surface of the impact foil Iduring its collision with the target. The time of this emissioncorresponds closely to the time of the dense target-impact Ira TWW-foil collision as determined from double-foil streak shadow- ®'graphy (Fig. 10), making the emission a good time markerfrom which the target velocity may be derived. Now, if anonuniformly accelerated target collides with an impact foil E

Ethe regions of the impact foil struck by fast portions of the Itarget will emit first. Conversely, the regions of the impactfoil struck by slower portions of the target will emit later.Consequently, target velocity profiles may be determined FROM FROM

from differences in emission time across the impact foil's TARGET REAR IMPACT FOIL RE

surface.The relationship between a dense target-impact foil col- FIG. Ii. Two views of the collision between a nonuniformly accelerated

lision and the visible emission from the impact foil's rear target and an impact foil: (a) An x-ray shadowgraph taken after the targetand the impact foil collided. The x-ray flash and pinhole smearing condi-surface is graphically illustrated by Figs. I l(a)and I l(b. Fig- tions are the same as in Fig. a. (bJ Visibleemission from the rearofanonuni-

ure 11 (a) shows the x-ray shadowgraph of an impact foil after formly accelerated target and from the rear of an impact foil struck by thatit has collided with a nonuniformy accelerated target. Non- target.uniform acceleration was purposefully induced by a laserpulse whose spatial intensity profile was distorted with arectangular mask that blocked a portion of the laser beam regions of the target accelerate ahead of the shadowed regionthus casting a low-intensity shadow across the center of the and subsequently impress their shape on the impact foil.focal spot. Under these conditions, the directly irradiated Streaked emission from the rear of an impact foil struck by a

nonuniformly accelerated target is shown in Fig. 1 l(b). Inithis figure, we used a double-foil configuration in which the

.7 impact foil was transparent so that emission from the accel-Serating target rear and the impact foil rear could be recorded

7 jm C TARG T F on the same discharge. The temporal history of this emission? 7.im At IMPACT FOIL - is as follows: Before the collision, and while the impact foil is

E 01 ttransparent, only the emission from the target is seen. This/ emission emanates initially only from those target regions

4 €0- that are directly irradiated--as seen on the left of Fig. I l(b).As time goes on, however, the emitting region spreads in

a.3 0 space causing both the directly irradiated and shaded targetregions to appear luminous. Such spread may be caused in

0 "/c part by the expansion of the low density, luminous plasma2 that precedes the dense part of the target and, perhaps, in

part by shock heating of the shaded region of the target.I Whatever the mechanism, when the low density portion of

0 t 2 3 4 5 the target reaches the impact foil, the foil's optical opacity isTIME (n sec increased so that the target emission is no longer visible, and

FIG 10 Fed separation ,ersus collision time determined in two ways: III the middle of the streak record appears dark." Afterwards,

from double-fodstreik hadowgraphy dashed line . and 21from light emts- when the high density portion of the target finally collidesston at the rearofthe impact foil la. Light emission ismeasured at 1017 of with the impact foil, the impact foil's rear begins to emitthe full icale reading of the spectrograph photomultiplier. from two well defined lobes. These luminous lobes corre-

592 Pmys. Fus,. Vol. 26. No 2. February 1963 Grun oa1 592

spond to the two impact foil bulges in Fig. I l(a). Thus, we speed is consistent with the predictions of our hydrodynamichave further evidence that emission from the impact-foil rear code. The code, for example, predicts the measured targetis sensitive to velocity nonuniformities in the dense portion velocities at an absorbed irradiance of 1.6X 10I" W/cm 2

of the target. Target structure which may be obscured from (Fig. 9a), while the experiment utilizes an incident irradiancedirect view by a low density plasma is unmasked by the dou- of 2.9)X 10" W/cm 2 which-with 80% absorption'-isbit-foil method. equivalent to an absorbed irradiance of 2.3 X 10 " W/cm 2.through aluminum impact foils has been directly measured and small laser spot size of this measurement (600pm diame-The seed f th ligh emisionfrontpropgatig Fo al lsspot efs-e a the mesreiey highiradiance-

by using impact foils with a thickness step on their rear sur- ter) probably reduce the effective irradiance below 2.3 X 10"face and noting the time difference between emission from W/cm2 and bring it closer to the predicted value.the two sides of the step. We found that the emission front The fast moving targets in Fig. 12(a) exhibit a velocitywas supersonic (10' cm/sec) when the foils collided during nonuniformity (V,.. - V,,I)/Vj of only 15%, eventhe laser pulse, i.e., when the target was still accelerating; but though the peak-to-valley nonuniformities of our laser beamit was close to sonic if the collision occurred after the accel- are about 2 to 1 (Fig. 1). This smoothing of laser nonunifor-eration. The supersonic velocities are consistent with shock mities may be due to the so-called "cloudy day effect"' 6 in3 heating causing the rear-surface light emission. The lower, which laser radiation absorbed near the critical surface issonic velocities can be explained by assuming that de- thermally smoothed by the time it is transported to the abla-

4 compression of the target after acceleration cushions the col- tion surface, where most of the pressure is applied to thelision impact preventing the formation of a strong shock. target. We did, in fact, make measurements on the ablation

Figure 12(a) shows the velocity profiles of dense targets plasma which qualitatively support such a mechanism.accelerated to 160 km/sec-a velocity above the lower limit These measurements will be shown at the end of Sec. IV.thought to be required for laser fusion.' The rear-surface We have also conducted quantitative studies of the rela-brightness temperature of these targets is measured to be tionship between laser nonuniformities and target velocitybelow 10 eV throughout the acceleration [Fig. 12(b)]. Their nonuniformities s To simplify the analysis we used slowly

STREAK CAMERA LASER CONTOURS

ns, (0h4

E~ /

- 0.4 CAMERA

0 4t

0 T TIME- I mct: L ASER

0.2

0. 0.23 "

- .,: II r n m I

0 IM 2ncse

09 tc)

00.6

w 0.36-.

- -1 (3

0.2 0.4 0.6 0.8__ 1INTENSITY 1013 W/cm

2

-2 0 s 10 is 20 25 30

TIME Inciel FIG. 13. Velocity nonuniformiiesdecrease with irradiance: (at. Ibil Streakedemission from the rear surface of an impact foil struck by a target irradiated

FIG. 12. Velucsty profiles and positions (a). and rear surface temperatures with a structured laser profile. The mean irradiances are 1&$ 4 X 1O' W/cm"Ibi oftargets accelerated to 160 km/sec. The dashed line is a theoretical fit to and ibi 9/ 10Xo W/cm2

. Spatial resolution is 20om. Ic) Target velocity non-the data m ba.sed on the ablation pressure and mass ablation rate scaling uniformities graphed as functions of average irradiance for different dips inlawsdescribed in Sec. IV. The peak of the laser pulse in (bi is at 0 nsec. The the incident beam: 0I 1,,, =- 10. 220-ium FWHM4 dip; 121 I,..,/.targets are 6.5 im thick CH. the laser pulse length is 2.6 nsec, the laser-spot 140-fuin FWHM dip; 131 !,,, /1, nr2, 140-p m FWHM dip. Case 12l has thediameter is 6l lum, and the incident trradiance is 2.9 < tO W/ca. Veloc. laser focal-spot contours shown in the figure. Finite nsetime of the impacticy profiles are measured with the double-foil method. foil emission limits velocity nonuniformity resolution to approximately 5%.

593 Phys Ful.us Vol. 28. No. 2. February 1983 Grun etal. 593

moving foils accelerated to no more than 50 km/sec. Under that the observed smoothing of target velocity profiles is in-these conditions, the fraction of mass ablated from these foils deed caused by smoothing in the ablating plasma.is small so the velocity nonuniformities are expected to scale Both foils and disk targets are chosen for these studies.almost linearly with irradiance nonuniformities in the ab- Each type of target has its own advantage: Wide foils, forsence of smoothing, i.e., (V,/V,) 9../9 _ example, do not permit ablation plasma to flow around the

(J,/J )o.s, where the scaling of pressure with irra- foil edge and interfere with rear surface measurements. Diskdiance derived in Sec. IV is used. Velocity nonuniformities targets, on the other hand, can be irradiated relatively uni-below this scaling indicate the presence of a smoothing formly by using a focal-spot diameter larger than the diskmechanism. diameter, and, since the laser-target interaction area A is

Some velocity nonuniformity results are shown in Fig. fixed by the finite geometry, average irradiances as well as13. Figures 13(a) and (b) show the emission from impact foils ablation pressures (az momentum/area) and mass ablationstruck by targets irradiated with the spatially structured la- rates (cc mass/area) may be reliably calculated. Also, anyser beam shown in the inset at two different average irra- energy that escapes the interaction area is easily detected and

diances. Note how the velocity nonuniformities are marked- its effect on the results easily estimated. A small amount ofly reduced at the higher irradiance. In Fig. 13(c) velocity ablation plasma energy has indeed been measured at the rearnonuniformities for several laser irradiance profiles are plot- of disk targets with plasma calorimeters, but its effect is min-ted. In all cases there is an increase of irradiance profile imal in our experiments. For example, for 300-lim and 600-smoothing with higher average irradiance. At about 10'3 W/ pm diameter disks less than 20% of the total absorbed (plas-cm2, 140-pm FWHM dips in intensity are almost completely ma and target) energy is detected at the rear of the disk, whilesmoothed out but the 200-#m FWHM dips in intensity are for 1000-pm and 1200-pum diameter disks less than 5% ofimprinted on the target. Calculations 4 indicate that in this the absorbed energy flows rearward. At the irradiances em-irradiance regime the ablation to critical surface separation ployed in these experiments, this excess energy is probablyincreases with irradiance as Io7 and is about 100pim at 10" due to the flow of hot thermal plasma around the disk edges.W/cm2 . Therefore, these results are qualitatively consistent Very energetic suprathermal electrons observed in CO2 laserwith a thermal conduction mechanism which smoothes laser experiments" and at higher irradiance Nd laser experi-nonuniformities when the ablation surface to critical surface ments 9 are not the dominant mechanism here, as evidenceddistance is comparable to the nonuniformity scalelength. It by the low level of x-ray emission observed above 20 keV.2°

remains to be seen whether larger wavelength perturbations When a ballistic pendulum measurement2 is used, as itat somewhat higher irradiances are similarly smoothed out. is here, special care must be taken that events beyond theIf they are, then the 1 %-3% ablation pressure uniformities focal-spot periphery do not influence the experimental re-required for a high-gain pellet'7 may be achievable with real- sults. Such events, if significant, could not only complicateistic laser systems. interpretation of the results but could make them irrelevant

to laser fusion, since a fusion pellet surface has no edges. ForIV. ABLATION PLASMA STUDIES many diagnostics the finiteness of the laser spot is not a ma-

jor concern since the phenomenon investigated requires highIn this section we present measurements of ablation energies that exist only within the focal spot or the diagnostic

plasma properties relevant for the target velocity measure- has time or space resolution. But a pendulum is time andments described above. Also, using a tracer technique to spa- space integrating, and a small amount of energy can easilytially resolve the ablation plasma flow, we provide evidence heat large amounts of mass to produce a large momentum.

Small amounts of such extraneous energy may be providedby thermal conduction through the focal-spot periphery, byplasma flow along the target surface, or by radiation from

LASER4the plasma plume. The situation is further complicated since<i these heating mechanisms may vary with laser-spot size, en-

ergy, or irradiance. We have observed, in fact, that under

some circumstances the momentum of material from be-yond the focal-spot region is seven times as large as the mo-mentum from within the focal-spot region.2 For these rea-

MOMENTUM -sons we ordinarily use only disk targets with the pendulumIdynsisr20-measurement.

Angular distributions of the ablation plasma energy I.

E (0), momentum p(0 ), and velocity i(0 ) for an isolated diskVELOCITY target are shown in Fig. 14; ri is a mean velocity unfolded

~ Sris/ from ion-collector traces. 2 Angular distributions from var-ious disk (0.3 to 1.2 mm diameter) and wide foil targets havesimilar shapes. All detectors are in the plane of incidence andFIG 14. D,%inbutuoe of blowoff velocaty, energy, and momentum meta- idia ymtyaot h agtnra sasmd

sured with ttme-of-flight ion collectors, plasma calorimeters. and ballistic cylindrical symmetry about the target-normal is assumed.pendula respectovel). The target is a 1.2-mm diameter CH disk irradiated at From such angular distributions we determine the ablation3)e to' W/cm*. pressure 9, = P, /rA, mass ablation rate m = m./A-, and

594 Phys FlugS. Vol 26, No. 2. February 1983 Gru etal. 594

ablation velocity u, - P1/m. where m. is the ablated mass, Figure 15 also shows that the measured ablation param-r is the FWHM pulse duration, and P, is the normal compo- eters agree well with like quantities computed with our hy-nent of the total momentum P obtained by integrating p(19) drodynamic code. In this code, the time averaged ablationover all solid angles. The letter A in the definition of 9 , and parameters are calculated by computing the total mass andmh represents either the surface area of a disk target or, for a momentum moving away from the target late enough in thefoil target, the focal-spot area containing 90% of the laser run (-14 nsec) so that little further mass or momentum isenergy. In the latter case, the focal-spot diameters are chosen added to the plasma. This is done so that the computed quan-to be large (= I mm) so that extraneous focal-spot-edge ef- tities are nearly the same as the quantities measured experi-fects are minimized. mentally. The calculated scalings are: 9, m -o24,

Scaling of ablation pressure with absorbed irradiance and m cc In .9 c 1.0 is shown in Fig. 15(a).1' s Momentum (pressure) in Table I compares our ablation results to other pub-the case of disk targets is determined in two independent lished theories. All of these theories assume a steady or qua-ways: first directly, using the pendulum array and second, sisteady ablation plasma flow which is described by conser-indirectly, using the energy from plasma calorimeters and vation of mass, energy, and momentum: but they differ invelocity data from time-of-flight detectors; wide foil results other details. Some theories (Kidder, Caruso, and Grat-use the latter method only. Agreement between all these in- ton),2 1.22 which are in planar geometry, neglect details of thedependent measurements increases our confidence in the reabsorption and energy transport to the ablation layer. Theysuits. The scalings in the absorbed irradiance of the ablation also assume that all of the absorbed energy supports the ex-velocity u, c 10 2, and the mass ablation rate m c1j are pansion of the ablation plasma, and that the underdenseshown in Fig. 15(b). plasma expands with sonic velocity. Some theories assume

The momenta of the ablation plasma [Fig. 15(a)] and the sonic flow at the critical surface with (Manheimer et aL)23

momenta of the accelerated targets, inferred from the veloc- and without (Jarboe et al.)24 thermal conduction, and someity measurements in Sec. III, balance. For example, the tar- (Ahlborn et aL.)2 eliminate the sonic flow hypothesis alto-get momentum for the cases in Fig. 6 is about 0.7 of the gether. Divergent plasma flow from planar targets was in-ablation plasma momentum. Similar agreement was ob- cluded by Puell2 who treated plasma hydrodynamics intained on a few irradiations where the target velocities and planar geometry using a model similar to Refs. 21 and 22,

* the ablation plasma momenta were simultaneously mea- but considered plasma expansion when calculating absorp-sured. tion of laser light and the temperature at the sonic radius.

Scalings of ablation parameters with irradiance in sphericalgeometry were determined by Nemchinov 2'1 who neglectedthermal transport. Scaling of the mass ablation rate was de-

0. .termined by Gitomer et al.i who included thermal trans--7 .2ii "W port but assumed that the sonic radius does not vary with

a* 0.6 e . / irradiance. The effects of inhibited thermal conductivity in1 z,&A 03I_WIDE FOILS ICHI o a spherical geometry (at irradiances higher than ours) upon

Id aw WIablation was considered by Max et al.29v I r a 7 Our results agree with all the theories except that of

Max et at. which assumes strongly inhibited thermal trans-

0.1 . . . .l . . . . J "TABLE l1. Comparison ofexperiment to theoreticlscaling laws. Tableetn-tries are the exponents b ofy a .where y is an ablation parameter, and/o.the absorbed irradiance. The theories may be found in Refs. 21-29.

1 0 , -& 03 18"t 0.6WIDE FOILS ICH|)f~llU. -

I: Kidder 0.75 0.25 0.50

log 8e Caruso 0.75 0.25 0.50Ahlborn 0.78 ° 0.22' 0.56'Jarboe 0.66* 0.33' 0.33'

0Z Manheimer 0.66 0.33 0.33S-VM u02 Puell 0.78 0.22 0.560 <- Nemchinov 0.78 0.22 0.56

5 U 0 Gitomer 0.56< 1011 .1012 1013 1014 Max 0.57 0.09 0.45

ABSORBED IRRADIANCE l. (Wlcm 2 ) Experiment 0.8 0.2 0.6

FIG I Ahlation pre iure al massablation rate and ablation velocity (b) *it'"', il" in Ahlborn's epreaukme have been treated as constants, i is%erus aborhed I.,er irradiance for disks and wide foil targets. The data 0. the absorption fraction.U. A are inferred u'ong momenta meaured with ballistic pendula. The data 'arboe et a/. explicitly derive a relation for uI, only. To get the other two(L, z.,a are obtained uing calorimeter and time-of-flight measurements. quanties we used the relations ) a II, ItI and m i,[ n, u, implied by his

The laser pulse duration is 4-nsec FWHM. theory; n, is the critical density.

595 Pnys Fluids. Vol. 26, No. 2. February 1983 Grun e at 595

C AGET,, ,

AI OOTS. 1-•Ia)

LASER (b)LIGHT CONE

X-RAYPINHOLE CAMERA

(-

FIG. 16. Experimental setup 1a) to spatially resolve plasma flow (b) near thetarget surface. The five images are from five pinholes in the camera. FIG. 17. Ablation plasma flow from thick CH targets irradiated by a struc-

tured laser profile. The irradiance conditions are: (al Mean irradiance of3 x 101

2 W/cm-, l_/I_. =8, 220-Mm FWHM dip. (b) Mean irradiance of6X 10 W/cm2, 1,_./1,. -C6 140-jum FWHM dip. Mean irradiance is

port, and that of Jarboe et al. and Manheimer et al. who fix changed here by reducing the laser spot diameter.

the sonic flow point at critical density and do not let theexhaust density vare with irradiance. than expected given the irradiance nonuniformity. We sur-

Untilrnow, we have discussed measurements of ablation mised that these smoother velocity profiles resulted fromplasma parameters far from the target surface, i.e., after the ablation pressures which were themselves smoothed by a-parameters reached their asymptotic values. It is, of course, teral heat flow in the ablation plasma. Such smoothing in thedesirable to also know the hydrodynamic development of ablation plasma is also observed using the tracer technique.these quantities as the plasma flows away from the target. In Figure 17(a) shows spatially resolved plasma flow from aparticular, if the results ofou,, experiments are -w be extrapo- Fick i a) irraially a las m fsorom alate tospheica gemetr, ten te dffeencebeteen thick CH target irradiated by a laser beam distorted as inl ted to spherical geom etry , then the difference between F g 1 h v r g r a i n ei o l W C 2plasma flow from our planar targets and spherical pellets Fig. 11. The average irradiance is 3 x 1012 W/cm, the non-

must be taken into account. Toward this end, we have devel- uniformity depth I. /1.i . is about 8, and the nonunifor-oped a tracer technique that lets us spatially resolve the plas- mity width is 2 20-pum FWHM. Under these conditions no

ma flow from a target surface.6 Using this method we can significant ablation smoothing is expected and none is seenalso track plasma flow from nonuniformly irradiated targets here. However, smoothing is expected and seen in Fig. 17(b)so that smoothing effects may be studied. where the average irradiance is raised by a factor of 2, the

The arrangement for this experiment is shown in Fig. nonuniformity depth is reduced to about 6, and the nonuni-

16(a). An x-ray pinhole camera is placed to view edge-on a formity width is reduced to 140-/im FWHM. Under thesepolystyrene (CH) target with a row ofsmall Al dots (0.5/pm conditions, lateral energy flow from the directly irradiated

thick, 25-pum diameter, spaced 50/pm apart) imbedded in it. regions into the central shaded region ablates the target sur-When the target is irradiated both the aluminum and the face there and causes distinct streamlines of plasma to eman-polystyrene ablate from its surface. However, since the alu- ate from the shaded region. These streamlines are com-minum is a much stronger emitter of x rays in the spectral pressed only slightly by the surrounding plasma which

band of the pinhole camera (> I keV) than polystyrene, the indicates that the pressures in the shaded and unshaded re-

presence ofaluminum ions in the plasma flow is identified by gions are comparable, and qualitatively confirms the pre-

the presence of strong x-ray emission. We assume that the vious results. Quantitative measurements of plasma condi-

perturbation of the flow pattern by the aluminum tracer is tions in the shaded region are the subject of a future study.

small. This assumption is reasonable since for a given elec-tron density n, in the ablation plasma the fully ionized ion V. CONCLUSIONmass density p, for Al and CH targets differ only by 12%(p, = nM /Q, where Q and M are the ion charge and mass, In this work we used ablatively accelerated planar tar-respectively). Also, the speed of Al and CH target ions, mea- gets to model the dynamics of large, hollow, ablatively driv-si-red with time-of-flight ion collectors, is the same. en fusion pellets. The velocities and velocity profiles of the

Figure 16(b) is a photograph of the plasma flow from a dense regions of highly accelerated planar targets were mea-target irradiated by a nonperturbed laser beam. The five im- sured. Despite two-to-one laser nonuniformities, we did ac-ages in the figure result from a five pinhole array (5-55 psm) celerate thin, relatively uniform, and cool targets to 160 km/through which the target was photographed. It is evident sec. We have also measured an increase in irradiance profilefrom Fig. 16lbl that the ablation plasma flow is reminiscent smoothing with increasing laser irradiance. This is encour-of a steady state fluid flow from a circular orifice. Note that aging for laser fusion. However, the behavior of targets withthe plasma flow is planar near the target surface, and that multimillimeter density and nonuniformity scalelengthsdistinct regions of the target map into distinct solid angles. that are typical of fusion scenarios is not yet known.

In Sec. III it was shown that the velocity profiles of We also made simultaneous measurements of the abla-accelerated targets %%ere, under certain conditions, smoother tion pressure P ,, ablation rate m, and ablation velocity u,.

59 Pys Flu,es. Vol 26, No. 2, FOruary 1983 Grunetal 596

...... ....

In these measurements we utilized large laser spots and disk 99. H. Ripin. NRL Memorandum Report No. 3315. edited by S. E. Dodnertargets so that our results are not sensitive to focal-spot-edge (August 1976), Chap. 11.

effects. We found that .9. o:I.0-, ih cc1.0-, and u, a: 10.2 "'.A. McLean. S. H.- Gold. J..A. Stamper. ft. R. Whitlock, H. R. Griem, S.P. Obenschain. B. H. Ripin. S. E. Bodner. M. 3. Herbst, S. J. Gitosner, and

where 1. is the absorbed irradiance. Also, the ablation plas- M. K. Matzen, Phys. Rev. Lett. 45, 124611980).ma momenta and the momenta of ablatively accelerated tar- "B. H. Ripan. S. E. Bodner. S. H. Gold. H. ft. Gniem. 3. Grun. M. J. Herbac,gets balance. These results agree with a planar geometry flu- ft. H. Lehimberg, E. A. McLean, J. M. McMahon. S. P. Obenschain. J. A.id code that uses classical transport physics. Stamper. R. R. Whitlock, and F. C. Young. presented at the CLEOS/ICF

80 Topical Meecing on Inertial Confinement Fusion, 27 February 1980.San Diego, CA.

ACKNOWLEDGMENTS "R. 3. Trainor. H. C. Graboske. K. S. Long, and 3. W. Shaner, LawrenceLivermore National Laboratory Memorandum Report No. UCRL-52562

We acknowledge useful discussions with S. Bodner, H. (1978); Rt. J. Harrach and A. Szoke, Lawrence Livermore National Labor-Griem, and R. Lehmberg. The technical assistance of M. atory Report No. IJCRL-86798 (198 11.Fink, N. Nocerino, L. Seymour, and E. Turbyfill is greatly "Ya. B. Zei'dovich and Y. P. Raizer, Physics of Shack Waves and High-

apprecated.Tcmpenlure Hydrodynamic Phenomena jAcademic. New York, 1966).apprciaed."J. H. Gardner and S. E. Bodner, Phys. Rev. Lett. 47, 1137 (198 11.

This work was supported by the Department of Energy "5One of the authors has also observed an increase of opacity in an initiallyand the Office of Naval Research. transparent single target irradiated by a laser. S. Gold and E. A. McLean,

J. AppI. Phys. S3,1784)j2982)."J. H. Nuckolls, L. Wood, A. Thiessen, and G. Zimmerman, Nacure 239.

193 (1912).'J. H. Nuckolls, Rt. 0. Bangerter. J. D. Lindi, W. C. Mead, and Y. L. Pan, "S. E. Bodner. J. Fusion Energy 1)(3), 221 (19821).European Conference on Laser Interaction with Matter, Oxford, Eng. "N. A. Ebrahim, C. Joshi, D. M. Villeneuve, N. H. Burnett, and M. C.land, September 1977. Richardson, Phys. Rev. Lett. 43, 1996 (1979).3J. Grun, Naval Research Laboratory Memorandum Report No. 4491 "'C. M. Armstrong, B. H. Ripin, F. C. Young, ft. Decoste, Rt. Rt. Whitlock,(1981). and S. E. Bodner, J. Appl. Phys. 50, 5233 (1979).'S. P. Obenachain, J. Grun, B. H. Ripin, and E. A. McLean, Phys. Rev. 2SM. 3. Herbst, Rt. Rt. Whitlock, and F. C. Young, Phys. Rev. Lett. 47, 91Lett. ". 1402 (198 1). (198 1); 47, 1568 fE) (198 1).

'ft. ft. Whitlock, S. P. Obenschain, 3. Grun. J. McMahon, and B. H. Ripin, 2Rt. E. Kidder, NucI. Fusion 8, 3 (1968).in Proceedings a/the Topical Conference on Symmetry Aspects of Inerfial 12A. Caruso and ft. Gratton, Plasma Phys. 10. 867 (1968).Fusion Implosions, 27-29 May 1981, Naval Research Laboratory, Wash. 3W. M. Manheimer, D. G. Colonibant, and 1. H. Gardner, Phys. Fluids 25,ington, D. C. 1644(1982).

3J. Grun, Rt. Decoste,B. H. Ripin, and J. H. Gardner, App). Phys. Lett. 39, 24T. ft. Jarboe, W. B. Kunkel, and A. F. Lietzke, Phys. Fluids 19, 130154511981). (1976).

'M. J. Herbst and 3. Grun. Phys. Fluids 24, 1917 (198 1). 23B. Ahlborn and M. H. Key, U. of British Columbia Lab. Report No. 73'3. M. McMahon, ft. P. Bumns, T. H. Deftieux, ft. A. Hunsicker, and ft. H. (1980).Lehmberg, IEEE J. Quantum Electron. QE-17, 2629)(19821). 'H. Puell, Z. Naturforsch 25s, 1807)(1970).'ft. Decoste, S. E. Bodner. B. H. Ripin, E. A. McLean, S. P. Obenschain, "I. V. Neinchinov, J. AppI. Math. Mech. 31, 320 (1967).and C. M.. Armstrong, Phys. Rev. Lett. 42, 1673 (1979); B. H. Ripin, R. laS. J. Gitoener, Rt. L. Morse and B. S. Newberger, Phys. Fluids 20, 234Decoste, S. P. Obenschain. S. E. Bodner, E. A. McLean, F. C. Young, ft. (1977); Scaling ef the mass ablation rate may be determined from this pa-ft. Whitlock, C. M. Armstrong, J. Grun, J. A. Stamper, S. H. Gold, D. J. per if r, (the sonic radius) is assumed constant--S. 3. Gitomer (privateNagel, Rt. H. Lehmberg, and J. M. McMahon, Phys. fluids 23, 1022 communication).(1980); 24,990(JE) (1981). 55C. E. Max, C. F. McKee. and W. C. Mead, Phys. Rev. Lett. 45,28)(1980).

507 "s~ Fluds. Vol. 26.14o. 2. February 1983 Grun et at 597

APPENDIX B

Characteristics of ablation plasma from planar, laser-driven targetsJ. Grun, " R. Decoste, 1) B. H. Ripin, and J. GardnerNaval Research Laboratory Washington D. C. 203 75

(Received 20 March 1981; accepted for publication 21 July 1981)

The momentum, energy, and velocity characteristics of plasma ablating from planar targetsirradiated by long Nd-laser pulses (4 ns, < 101

4 W/cm2) are measured and the dependence ofablation parameters upon absorbed irradiance is determined. Large laser spots are used in theseexperiments so that the results are not sensitive to boundary effects.

PACS numbers: 52.50.Jm, 52.70.Nc, 52.30. + r

Considerable effort is underway to study the feasibility plosion. Accurate measurements of these ablation param-of imploding moderate aspect ratio, high-gain fusion pellets. eters are, therefore, basic to the calibration of computationalIn this concept, long duration laser or ion beam pulses ablate codes used to design fusion pellets, and are basic to thepellet surface material whose rapid evaporation creates a search for an irradiance regime consistent with a stable andpressure that implodes the pellet walls. This pressure, and efficient implosion.' Measurements of ablation pressures onthe speed of the ablated material or the mass ablation rate, planar targets using small-diameter laser spots and theoreti-help determine the velocity of the imploding walls, their rate cal estimates of the effective laser-target interaction areaof acceleration. and the hydrodynamic efficiency of the im- have been previously reported.2 In this letter we present si-

rultaneous measurements of the ablation pressure, the mass* Present address: Mission Reearch Corporation. Alexandria. VA. Work ablation depth ( a mass ablation rate), and the ablation veloc-perlormed in pan, whilt associated with the Dept. of Physics. University of ity. We also use large-diameter laser spots and uniformlyMar) land. College Park. MD'Preent address Institut de Recherche d'Hydro-Quebec Varennes. Que- irradiated disks, so that the results are not sensitive to focal-

bec, JOL :PO. Canada Work performed in part while associated with the spot edge effects associated with energy flow through theSa.hih freeman Corporation. focal-spot periphery. The laser-target interaction area is ex-

545 A0o' P'Ys. Lent 39t7). 1 Octocer 1981 0003-69S1/81, 190545-03S00.50 e 1981 American Insttte of Physics 54S

perimentally determined. We utilize redundant measure- diances, the energy observed behind the target is probably

ments and diagnostics to verify the validity and self-consis- due to the flow of hot thermal plasma around the disk edges:

tency of these results. Very energetic suprathermal electrons' are not the dominant

Configuration of the experiment is similar to one pre- mechanism as evidenced by the low level x-ray emission ob-

viously described.' Polystyrene (CH) targets are irradiated served above 20 keV.'by a 1.05-pm wavelength, 4-ns FWHM duration laser pulse We note that the angular distributions of energy, veloc-focused through anf/6 aspheric lens to an average irradi- ity, and momentum from various diameter (0.3-1.2 mmlance < 10'" W/cm2 . This pulse length is long enough so that disks and wide foils irradiated by various diameter laserstationary ablation physics dominate the laser plasma inter- spots (0.3-2 mm) are similar. The momentum angular distn-action." Ablation pressure e;, =P lr-A, mass ablation bution, for example, is characterized by a half-cone angledepth d =-m, IpA, and ablation velocity u. =P, /m, are de- cos- (P IP) = 40* for both the disk and wide foil cases.termined from angular distributions of the ablation plasma Figure (a) shows the scaling of ablation pressure withenergy E (0), momentum P (0), and velocity E(6) measured absorbed irradiance to be e, a I o for disks and wide foilwith arrays of plasma calorimeters, ballistic pendula, and targets. Momentum in the case of disk targets is determined

time-of-flight ion collectors arranged around the target. (In in two independent ways: first directly, using the pendulumthe long-pulse regime ion collector traces are narrow and array (dark markers) and second indirectly, using energy andsingle peaked, making them ideal for time-of-flight measure- velocity data (open markers); wide foil results (X) use thements.) The quantities r, A, andp are the pulse duration, the latter method only. Agreement between the two methodslaser-target interaction area, and the target density, respec- increases our confidence in the results. The scalings withtively; P is the normal component of the total momentum P absorbed irradiance of the ablation velocity u, cc I 2 and thecalculated by integrating the momentum distribution P (9) or mass ablation depth dc 1a are shown in Fig. 1(b).the distribution 2E/9over all solid angles; m, is the ablated We also verified that these pressures, determined frommass. Although any two of the measured quantities would asymptotic measurements, are the same (within 30%) as thehave been sufficient, we measured all three with independent ablation pressures deduced from measurements of targetdiagnostics to verify the self-consistency and validity of our acceleration.'results. The measured ablation parameters agree well with like

The pendula employed here were tested and calibrated quantities calculated using a one-dimensional (planar geom-in situ.5 In particular, we verified that pendulum recoil is etry), single-temperature hydrodynamic code (Fig. 1). Thiscaused by plasma impact only and that the pendulum array code is a sliding-zone Eulerian FCT code that requires nobalances blowoff plasma and recoiling target momenta (to artificial viscosities, utilizes classical thermal transportwithin 30%). We found, however, that material reflected orsputtered from a pendulum surface affects its absolute cali-bration. To determine the contribution of material reflection _0__........___........___......

or sputter to the pendulum response and to thereby calibrate I s I

it absolutely, we built a double-pendulum device.' It consists o ofIBe 06

of a primary pendulum directly facing the blowoff plasma & L , 03 --WIDEOISIH .and a secondary pendulum oriented to detect most of the _ ., t,,,, 10.8

material reflected or sputtered from the primary pendulum TH EOR

but shielded from the blowoff plasma. This in-situ calibra- Dtion showed that the pendula in these experiments are2.4 ± 0.6 more sensitive then their bench calibration would L 1a)

indicate. o. , . .. i -11. 0-

To model the surface of large spherical pellets we utilize 10 10

wide foil targets irradiated by large, I-mm diam laser spots. DS f

The targets are sufficiently thick, so that their motion has 1 0 "little effect on the measurements. In some cases we also use WIDE OIL.S ICl , 1.0.

uniformly irradiated disks." These disks have two advan- 108 '0

tages over foil targets: first, the laser-target interaction area THEORYZ -

.A that enters into calculations of absorbed irradiance, abla- 2 . -

tion pressure, and mass ablation depth is experimentally de- ,termined; second, any energy that escapes the interaction < 1b)

area is easily measured with plasma calorimeters so that its 0i 1012 o1 0

effect on the results can beestimated. A small loss of ablation ABSORBED IRRADIANCE I. IWcm?)plasma energy to the rear of disk targets does in fact occur,but this has minimal effect on the ablation parameters. For FIG. 1.taAblation pressurevsabsorbedlaserirradiancefordisksandwide

example. for 300- and btAW-Mm diam disks less than 20% of foil targets. The data denoted by U. 0. and A are inferred using momenta

the total absorbed energy reached the rear disk surface, measured with hallistic pendula. The data C. 0. and A are obtained using,Ahtle for 1000- and 100-pum diam disks less than 5% of the calorimeter and time-of-flight meaurements. The symtx)l 7 denote% theo-

retical result,.. iN Ma%, ablation depth d and normal ablaton velocity u v

ab,,orbed energy reached the rear disk surface. At our irra- aborbcd trradiance I,

5S6 Aro, Prys Let.. Voi 39. No. 7. 1 Octer 1981 Grun etai. 546

physics with no ad-hoc inhibition, and uses the same irradi- ;ance profile as the experiment. Absorption is by inverse 3- 3

bremsstrahlung in the underdense region with any remain- 0ing laser energy dumped smoothly into two zones surround- E 25 -

ing the critical surface. To make a direct comparison with 00 2 / 4,sec.lM 1

our data, we calculate the momentum and mass of all plasma 5moving toward the laser after these quantities reach their

0.5 1 1.5 2asymptotic values (14 ns after the laser pulse peak), and de- INTERACTION-AREA DIAMETER Imm)

termine the temporally averaged ablation parameters? ,du, in the same manner as the experiment. (Peak calcu- FIG. 2. Ablation .elocity u. vs interaction.area diameter for ,,tde fol tar-

lated pressures which occur near the ablation surface are gets. !Interaction area isdefined as the area that contains 90%c of the mci-

only 20% higher than the temporally averaged calculated dent laser energy.

pressures.) The good agreement between measured and cal-culated ablation parameters supports the view that basicconservation laws without any transport inhibition govern irradiance, both these phenomena may contribute to the ve-

laser-target interaction physics in this irradiance and laser- locity variation in Fig. 2. Lateral heat flow especially could

pulse length regime. shift energy from a higher to a lower portion of the effective

Since the flow characteristics of ablation plasma from irradiance profile and increase the fraction of low velocity

planar targets are set by its nozzlelike expansion from the ions. Large spot sizes, with a relatively uniform and flat-

target surface, plasmas from planar targets are not truly one topped illumination, have a smaller fraction of absorbed en-

dimensional. The good agreement between our experiment ergy escaping through their edges and, therefore, behave

and a one-dimensional, planar geometry code may be ex- somewhat independently of spot-size diameter.

plained, however, if the final nature of the ablation param- In summary, we studied the ablation characteristics of

eters is determined near the target surface, when the plasma plasma from planar, laser-driven targets. We found that ab-

flow is still planar. This picture is born out by the code which lation pressure, ablation velocity, and mass ablation depth

shows that most of the ablation plasma acceleration occurs scale as the 0.8, 0.2, and 0.6 power of the absorbed irradi-

between the ablation surface and a few times the distance ance. Our results agree well with a one-dimensional hydro-

from the ablation surface to the critical surface. This abla- dynamic code that uses classical transport physics. Pres-

tion surface to critical surface separation is about 100pm at sures of 10 Mbar exist at about 5 X 10" W/cm2.

I X 10" W/cm2 (and less at lower irradiance), which is Hydrodynamically efficient comm ession of moderate aspect

smaller than the laser-spot diameters or the diskidiameters in ratio pellets at this or slightly higher irradiance may thus be

the experiment. One-dimensional, spherical calculations possible. We also found that due to edge-effects ablation ve-

with a large ratio of pellet radius (0.5 cm) to ablation to criti- locity varies with laser-spot size, but the variations are small

cal-surface distance gave irradiance scaling laws similar to for sufficiently large spots.

those in planar geometry. We thank S. P. Obenschain, S. E. Bodner, C. Manka,

Studies using planar targets are subject to criticism that and H. Griem for valuable discussions. The technical assis-

phenomena at the focal-spot periphery distort effects as- tance of N. Nocerino, E. Turbyfill, M. Fink, L. Seymour,

cribed to the spot as a whole, so that the results do not ex- and R. McGill is greatly appreciated. This work was sup-

trapolate to spherical geometry pellets. Such phenomena ported by the U.S. Department of Energy and Office of Na-

may include energy leakage laterally across the focal-spot val Research.

edge, which alters the irradiance distribution, and extrane-ous plasma from target areas outside the focal spot, whichcontributes to the measured results. To check for these ef-fects we placed planar targets in the near field of the focusinglens and varied the spot size by aperturing the laser beamwhile monitoring the ablation velocity. Because of laser en-ergy limitations, this experiment used an average irradianceof I X 10'2 W/cm2 . But even at this low irradiance, the abla-tion velocity does vary with spot size(Fig. 2). The variation is iS. E. Bodner. J. Fusion Energy to he publishedi.

small, however, if the laser spot diameter is sufficiently large 'B. Arad. S. Eliezer. Y. Gazit. H. M Loehenstein. A. Zigler. H. Zmora. and

i ;1 mIni. That is why experiments on foils reported here S. Zs~eigenhaum, J. Appl. Phy,. 50. 6817 (1979.

utilize large laser .pots. even though this lowers the maxi- B. If. Ripin. R. Decoste, S. P. Obenschain. S. E Bo.ner. E. A. McLean. Fmum irradiance achiesable with our laser. It is also clear that C. Young. R. R. Whitlock. C M. Armstrong, J. Grun. J. A Stamper. S. H.

Gold. D J Nagel. R. H. Lehmberg. and J M McMahon. Phys. Fluds 23.

cuntrolling irradiance by changing the focal-spot size, as is 1 19801

often done. may lead to misleading results. "M. K. Matzen and R. L. Morse Phy% Fluid% 22. 654 (19791.

T%4o parameters A hich may change the effectie spot 'J. Grun. NRL Memo 4491, 191 junpubhlihedi.size are the spatial prohle of the incident irradiance and the "lntenstty vanatmmns are 50%.

'N A Ehrahim. C. Joshi. D M, Villeneuse. N I. Burnett. and M Clateral heat Plos, throuih the focal spot periphery. Since the Richardson. Phss Rev. Lett, 43, 1995 119791

nrl"er of ,n, at a Farn,.u:,ar elocit, depends on absorbed F. Young private ommunication,

a' , , . s 1 .3 .,, 7 C:,.et '4,1 Grunetal 547

APPENDIX C

Flash x radiography of laser-accelerated targetsR. R. Whitlock, S. P. Obenschain, and J. Grun "

U. S. Na Research Laboratory. Washington. D. C. 2)3 "5

(Received 22 April 1982; accepted for publication I I June 19821

Flash x radiography ofablatively accelerated planar foils has provided quantitativemeasurements and qualitative observations regarding several parameters of critical interest todirect illumination laser fusion. A 1.05-j, 3.3-ns drioer beam was focused onto carbon foils in alarge (0.7-1-mm diameterl spot to reduce edge effects. From image-, produced by a backlighting x-ray flash, we have measured overall coupling efficiency. smoothing of laser nonuniformities,target velocity, and ablation pressure. The high velocity targets maintain a localized, high density( > 3% ofsolid). In contrast to other workers' recent measurement of pressure from x-ray imaging.our x-radiographic results, including pressure, are in general agreement with earlier NRL studies.Our results have also provided further insights into double foil interactions and planar targetpreheat measurements.

PACS numbers: 52.50.Jm, 52.25.Ps, 52.25.Fi

Direct illumination of spherical pellet shells by laser achieved. The carbon C) foils were accelerated by NRL'slight in a moderate intensity regime somewhat above 10t" Pharos 11 laser operating at 1.05p with 3.3-nsI + 10%)driv-W/cm2 may permit inertial confinement fusion to be er pulses focused to 0.7-1.0-mm diameter. The x-ray sourceachieved.' To that end, studies at NRL 2' have been direct- was approximately half that diameter. For some shots, aed to the physics of the laser-pellet interaction and of the double foil targeta-s'NIii was used, in which an impact foil,efficient acceleration of pellet shells to fusionlike velocities.' located behind the irradiated first foil (see Fig. 1), serves as aTo experimentally model spherical pellets early in the implo- diagnostic of the motion of the first foil.sion phase, we use planar targets and large focal spots. These The source must be properly placed and timed to flashexperiments have shown that the moderate intensity, direct when the accelerated foil target moves into the view axis. Aillumination approach scales favorably in several areas of complication arises since the foil is also an x-ray emitter;physics which have been identified as critical elements for therefore, we chose to radiograph the accelerated foil after itlaser fusion,2 and that, therefore, furth,.r extension of these had ceased to emit. i.e., at a time 4-5 ns after the peak of theexperimental studies to a regime closer to reactor conditions main (driver pulse. An x radiograph of a C foil irradiated atis warranted. In the present work, we used a flash x-ray 6.5 X 1012 W/cm2 is shown in Fig. 2(a). The backlightingprobe to temporally resolve the position of the dense region source's :mission is imaged on the left and the foil's emissionof accelerated foils; from this, we quantitatively measured is imaged on the right. Furthest to the right, x rays emittedthe ablation pressure, the target velocity, and the uniformity by the C blowoff plasma are imaged. Since the C foil is widerof target velocity. We also gained further insights into dou- than the laser's focus, only the central, irradiated portion ofble foil interactions and target preheat measurements. the foil is accelerated, leaving the rest of the foil behind. The

In earlier work,' visible probes, operating within limi- shadow of this stationary margin may be seen in the image oftations imposed by absorption and refraction, have beenused to image ablatively accelerated targets. Flash x radiog-raphy - " is applied here to planar target geometry to extendthe probing photon energy by about 10' beyond the visible,thereby gaining simultaneous access to the front and rear, as SOURCE (Al SLABO)

well as the dense middle, of accelerated, high velocity tar-get%. The experimental setup is diagrammed in Fig. 1. A I I _ MAIN LASER BEAM

pinhole camera using photographic film recorded the image aofan x-|ay source, an aluminum plasma produced by a 20-J, OBJECT (C FOIL IU

0.6-,t 1.iser pulse.' ' The object to be radiographed was 'plebctsseen the source and the pinhole; source x rays 2nd FOL .lrNabsorbed by the object result in a shadow image of the object PINOLE c== / ==m WATA

on the film. The objects radiographed were planar foil tar- VOLTS I

gets of p) rol5 tic graphite having areal densities in the range qof 1.0-1.5 mg/cm:. i'he backlighting x-ray flash was shortenough that, for these targets, the travel distance during the IMAGE ,90 FILM PACK) -5 0 .w

flash i.e., the velocit) smearing) was comparable to the pin- FIG I Setup fmr flash x radiography ino Io ,scale, angles arc correctly

hole camera resolution labout 2011 for a 10-p* pinhole, mag- drawni The 1 It la, ser beams,,were focused through an'./, lens onto

niticition 1.4.., thus enabling good image contrast to be %eparatelaritets A n;+sorption radiograph ofihe hack lit object% areco.rd -ed on x-ry him hs a pinhole camera. Single or double carbon frotl %ere

emploedij,)hects Inset scope trace shows temprx'al shape (f the mainAlso , t ission Reserarch C,,rpora:,.)n. Ale tindria. VA li,,cr beam peak it t .= O and delay of the hackighter's laser pulse 5 n,,.

429 Acl P' s Let! 41f5) I September 1982 00C3.651, 82,0S0429-C3S 1 00 c. 1982 American insittute of Physcs 429

2 1 nique are in similar agreement with the value obtained here.However, our pressure results do not agree with the

recently reported" 1.0 Mbar (at increased irradiance,-. .3.6 X 10" W/cm2 ) which was found to be 5-10 x lower than

cited measurements on ablation plasma. 4 In that work, aE r ,smaller spot size (200 X 300/pm 2), a shorter driver pulse J0.8E 0 ns), and a longer probe pulse (0.8 ns) were employed. At ourR 0 3-ns pulse length, lateral energy flow within the blowoff

extends as far as 140u at about 1 x 10" W/cm2 ; therefore,we have used focal spot diameters several times this length toavoid a reduction in pressure due to lateral flow of energy toregions outside the focal spot. Also the longer pulse lengths

(al 4 3 1b achieve a more predominately steady state ablative accelera-tion. However, the actual source of the discrepancy noted in

FIG. 2. (a) Flash x radiograph ofa single, 1.3-mg/cm'. carbon foil moving at Ref. 14 remains unresolved.3 I l0 cm/s: I. C plasma emission. 2. Al source emission, 3. shadow ofunaccelerated C foil. 4. shadow of accelerated C foil, (bl Intensity contour A further measurement of the image in Fig. 2 showsprofile of the main laser beam's focal spot. The middle contour level is that the on-axis thickness of the shadow of the moving foil isdrawn in thicker lines fot companion with la). Incident irradiance was about 35-70,p. Pinhole resolution (20p, velocity smearing6.5 x 10" W/cml. with 90% ofthe laser energy in a 0.7-mm-diam spot. The (about 20-30/z), and geometric factors including parallax,peaks of the two laser pulses were 4 9 ns apart. Shot 81-10636.

foil rotation, and foil curvature, make the 70y an upperbound for the axial extent of this highly absorbing foil. It is

the foil's own emission, i.e., as a self-radiograph [see Fig. estimated from the x-ray attenuation of un-ionized C that2(a)]. Since the accelerated portion of the C foil moves se- the observed absorption images (measured to be mostly 1.6-veral foil thicknesses while radiating, some of the self-emis- keV photons, taking a 1/4-mm photon path) represent, as asion occurs to the left of the stationary foil's shadow. After lower bound, a density ofabout 3% of solid. Shorter paththe driver laser pulse shuts off, the accelerated portion ceases lengths, higher photon energies, and increased ionizationto radiate but continues to fly to the rear (left). The flash x- would raise this estimate. Since the x-ray range at 1.6 keV isray source was positioned just to the left of the stationary only 8/u, there were at most a few solid bodies, if any, of thisfoil's shadow, but extended several hundred microns further size or larger outside the shadow region of the acceleratedto the left than the self-emission. Within this several hundred foil; the high-density region was therefore localized to withinmicrons, the shadow of the moving foil is clearly seen and the shadow.appears connected to the stationary margin. Several interest- The observation of a connecting structure of the shad-ing measurements can be made from this representative im- ow [Fig. 2(a)] strengthens the validity of both the double foilage. technique and the measurements of low preheat obtained for

Using the stationary foil's shadow as a fiducial of the thin, planar targets.6 One might intuitively expect that anoriginal position and taking the accelerated foil's shadow as accelerated disc would part from the unilluminated foil,the final position, an average velocity v = s/7- may be com- leaving a break, through which plasma could flow and heatputed, with rd the delay of the x-ray flash. The result is the rear of the foil. Double foil collisions would then be in-3x 10x cm/s for this shot, for an energy density of 5 X 10'J/ fluenced by such spurious preheat. Previous investigationg on the axis of the driver laser. The energy in the accelerated using optical6 and double foil' techniques showed no evi-

foil was E, = (1/2Ap. v2, where A is the area and p. is the dence of such a plasma flow (see Fig. I in Ref. 6). The con-areal density. The initial 1.3 mg/cm2 may be taken asp., necting structure observed in Fig. 2(a) evidently isolates thesince other measurements ' indicate that less than 20% of cool, rear surface from a hot plasma flow from the laser side.the thickness would ablate by the time of observation. This Thus, the x radiographs explain how low rear surface tem-leads to an estimate of total kinetic energy in the target of peraturcs' of below 8 eV are maintained.E, = (l/2)mv= 1.5 J. The incident laser energy FL was 76. Looking at the finer details in Fig. 2(a), there is an evi-J, from which the coupling efficiency, one of the critical ele- dent waviness to both front and rear sides of the acceleratedmerits,2 was 71= E,/E,. / 100 = 2%; higher values are foil's shadow. However, neither the source emission nor Cachieved when a larger fraction ofthe target is ablated. This foils, ofthe type used, have nonuniformities of the amplitudeefficiency combines laser absorption and hydrodynamic ac- and wavelength needed to explain the waviness.' On theceleration processes. other hand, irradiance nonuniformities are known to exist

Ablation pressure may also be obtained from these and to influence target motion. The laser's focal spot distri-data, using P = p0 L'/7 1 , where 1L is the full width at half- bution was taken on the same shot and shows illuminationmaximum ofthe main laser. This leads toa pressure estimate nonuniformities of about 3:1, with a spatial wavelength ofof 1.4 Mbar, at an incident irradiance of 6.5 X 10" W/cm 2. about 7 5-100p. The waviness in Fig. 2(a), which may beThis is in good agreement with pressures inferred from mena- quantified as about 25% of the distance travelled, representssurements on ablation plasma," which showed a value of a lateral profile of nonuniformities in the target's velocity.1.7 -- 0.3 Mbar at an absorbed irradiance of 6.5 X 10'". The The relationship between velocity nonuniformities and irra-pressure and velocities obtained using the double foil tech- diance nonuniformities has been investigated previously and

430 Appi P"v$ Lett.. Vol 41. No, 5. 1 September 1982 WhittOck. Obensca,n. and Grun 430

APPENIX D

PROGRAM LASERCC THIS PROGRAM WRIlTEN BY W. MICHAEL BOLLENi MISSIONC RESLARCH CORP~kAlluN FOR THE LASER I'HYSICS E:RAHNC ATC liHE NAVAL RE' 'AhlU LABORATORY.

C

INTEGER CHAR ,CINDLOMtiON CLASER I ADL (72) NCHAR , CNAR , CMND ,Ni , N2, NZ, N4, IGOT,

COVEN W(UIT=iYA7LE='LASERl). DA')P1 AD( ) VAR,VARR, ILCLOSE(UNIT~l)VARR (3)=-a

HO WRITE(S,1i0)110 FORdMAW( )",)L READS A STRING

CALL ADEINQ(GQT,-&ADL)NCUiAR~i I!CALL NXTCH.R

1"0 FORMAT(X,3120)Il" CHAR.-GE. 6 5 AN'D. CHAR .LE.90)01O TO 400

310 ruRMAWt U14INTELLIGABLE INPUT -TRY AGAIN.')Go 10 0

C DECODE COIMMANDC400 CMND zC HA R-4

CALL NXTCH:RNI: 0N21 0

IF0'JHAR.GT.IGOTfi)GO TO 500CriLL NU~IiR(Ni)II (UL.!AR.JIE.44)GO TO 500CALL 'lXTCHRCALL NUlr.BR(N2)lF(CNAR.NE.4)(, TO 500CLL NXTCHRCALL NUMBR(N3)iF(CHAR.flE.44)GO TO S00CALL NIXTCK.CALL NJUMDR(W4

500 CALL EXCL'TEIHIOT.EQ.-?9)GU TO 600

GO TO "DO&00 %CoffI NUL

UPEN4(UN]IT'iF!LE='LASEO'RR.DAl')WRITE i )'AR ,'AR, ,ILLRITE(5,6iO)

LID FORMA1I(X)'PROGRAM LASER TERM1NAILD')CLOCE(UNIT~i)sl OilEND

SULDROUTINE NXTCft

C GET NEXT CHARACTER FROM INPUT STRING (IGNORINU SPACES)C

INTEGER CHAR., CMNDCOMM/CLAERI ADL (72) ,NCHAR LEWA, LMN, NI, )N2,)W, N4, 1GOT,

H0 CHWRIADE(NCHAR)NCIHAR:NCIAR iIIF(CHiAR.EQ.32) GO IL) 10

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SUl.:NOUTINE NUME!W(NUM)

C GET A NUMBER FRO" THE U. l INPUT SIRINU IF THERE IS ONLC V 7:i,.RE IS NO0 NWtIER RETURN WTJI NUM40

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40 MFCHAR.LT.40.0 CHlAR.GT.5M)U 10 20IL QCA P,.GT I 1T 11)GO TO C,

CC ADD A NEW DIGI'!C

NUM=NUr'.*i 0+ (CHAR-48)CHAR= IADE (NC: AR)NCIIARWNHARPI

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10 FOR M A I( 72'RCC THIS READ AND DECODE IS PARTICULAR TO THE DEC-10C IN CouDER 10 USE UN THE Wi OR THE 11/03 IT M~C BE MODMIED. MHE IMPUT ARRAY ELLMENr MUST BE MASK 17DC SUCH THAT THE RIG4HI MOST E CONTAIN THE ASCII CODEL ANDi IHL RESI OF THL WORD IS CILLL11 WI(H ZEROS.CCC rIND THE END UF tH LINEt

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CC EXLCUTE A COM1MANDiCC - - -~CMNBOK:

CINT ECER CHAR ,CMND

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GO 10 600

,00 GO TO S000

L C HANUIE

300 CONTINUE110i.LE.0)CO TO 51000IF(Ni.GT.'0)CGJ TO S000U

lF(N2.GT.0)GO TO 0'GO TO 309

305 ITEMPzN2GO0 TO0 33 35

309 CONTINUEWRITE(5,310O)

310 FORMAT(' THE PRESENT VALUES AkE:')

3030 FORMAT(' WHAT VALUE DO YOU WISH '10 CHANGE?',)PEAD(S,*)ITEMP

WRITE(5,340)1.40 FORMAI(' WHAT IS IME NEW VALUL?',$)

IF(IQ1.LQ.2)GO TO39Rl AD(5,*)VAR(Ni,N2)

345 WRIIE(5,350)VAR(Ni,i)I3S UOCRjA'KX,'TO CHANGE MORE VALUES FOR DET#',F3.fj,

'ENI1ER VAR C(IF NUT ENTER~ e):'$)kLAD(5,*EIT[MP

IFr(IllTMP.EQ.0UG0 TO 390V0~ T 0 '035

39 WRITE(5,395)

795 IORMAT( THE NEW VALUES ARE:')4RI lE(5, 2i0)WRIIE(ct220) (VAk(NiJ),J=i,7)GO TO 6000

3'10 READ(S,398)VAR(Ni,2)398 FURMAT(RS)

60 'O 345CC DC400 LODNl NUE

GO TU S000CC ECSO0 CONTINUE

CALL ENERGYGO T) 6000

C

600 CONTINUECU TO 5000

C

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CC HCg00 CONTINUE

GO TO S000CC IC

900 CONTINUECO TU S00

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i200 CONI INUEI]F(Ni. LI .0)GO TO 127 0WPITE (S, I2'i

MO1 FORMAT(X,/,' DET$'X'TYPE'2X'ANC (TfD'2X'ANGPQ)'9X'R,~3 X'CAL'7Xv'GAIN')

IF(NI.CT.0)GO TO 1'255DO 125l 01:1,30lWRI'iL(S,,1220) (VAR(1,J), J=1,7)

1220 FHA(,52X~b22,F 2~ F.,X2~i.,)125 0 CONTINUE

GO iO 1260s255 WRIl £(5,1220) (VAR(Ni,J) 3=1,7)1- 0 0 TO o 000

1270 IF(Ni.L.T.-i)r.0 TO 12'80IF(N2.CT.0 AND. N'21.EO)CO TO IL'76W~lTL(5,127i)VARRM1

12 71 1ORMAIC(' (i )-INCIILNT LASER ENERUY (J) ',FiO.3)WRI (E(S, 1272)VARR(2)

1272 FOkMA'I(' (2)-TARGEl ANGLE MCIs) ',Fi0.3)URI fLr',273)VARR(J)

1'273 FORMWN~ (3)-SHOT s',io.3)DO 1277 1=4,10

1 277 C UNT INUZGO '10 000

127 6 1=N2WRIFE(5,1278)N2,VARR(N2)

12"77 FORMWtA( VARR('12') =',Fi0.1w)GO (0 6000

1,280 CONTINUE

IF(TIL().EQ.0)GO 10 1281WRlTE(S,,1282)I,IL(I)

12032 FC!:t AWXPART DLT4'Idl' SAME AS LIGHT DEIV'1)12301 CONTINUE

rn 1D 6,000

L M

1300 CONTINUE

C N

c~400 CONTINUE

GO TO S0OCc 0C1500 CONJTINUE

c pCU~03 COINTIIN UE

O Oo 00Cc;C0100 C0fITINUE

GO TO 50130CC RC

OO CONT INUEGO1 lo 5000

cL SCIM0 CONlINUE

GO TO 5000OCC TER~MINATE PROr*RA.1C2 U 00 CONI INUE

N~O :'-9VGO -10 6000

Co uC2i00 CONTINUE

GO TO 5000Ct: vC

p20CONT I.NUE

CALL Vi.lI

GU W U63

GO T13 SOUD

C AC2'400 CONTINU;E

GO TO SOUG

C yC2500 CONIIINUE

GO TO 5000

C

C2600 CONT INUE

GO TO 5000S000 IJRITE(5,5010)5010 F 0 RMAH' I TNVALID C"OMMAND')sol0 Go TO 6000

601 RETURNEND

SUBNOUTINE ENERGY'

C TflS vUtRn!UTl:! .ANDLES EHE7RGY CILCUILATIONC BS'D ON INJPUT CALORIMET~rC ihUL ROgAL~~wl

INTEnCER C4AR r-IND

E Q UIVAL EN CE !- AIS 'A R R i) E P. NVANR3)

s WIR ITLU(5, 0)a 0 FO;RMAT(' WHAT 15 THE SHOT t

11 (ERkN.GT..)G0 TO 20

ii FORMIAT' THE SNOT # MUST LE CxEAIIBR TXAN ZERL'. '

L, 0CON" NUE

.00 ORMAT( WHAI IS THE INCIDENT LASR ENERGYI (3) J SRrAD (c *EADS

90 rU:,,4T (v., 'WHA'T IS THE TARGET Atk,'LE (DEG)?' )

OVEN iUNIT1, , F'LE='l F-Ml .IIP)

110 FG0RIM AT( W E11 ULL DO0 F 0 R"A "" ANGL FIRS T.t;. L z AL (E rL ,LFP , I

T ITE (S, a20120 FORMAT' NOW WE WILL DO THE ~IAAD ANGLES.'

CALL ECAL(EKL, 17p')CLUSE(UN!l)CALL ETOT(lElL, .EFL)CALL ETOT(EFP,[EFP)r'LL :T0T(EDlL, I'flL)

CALL ETOT(EBP,TEl',P)F PEi,= E'P ' U( EPP :T EFP)PLP ( TEDP+TEFP)/EABiS

30FO:;'.AT (X, 'UERGY IN LIGHT "FORWARD" EVERY S D

WkITE(SJ,13i)(FL()* j7)

'31 FCP 'T (X, 'NER GY I N PA RT I CLS F F1!AR D EVltk Y 1. 11 r')U:,'I TE (S, 23±(UP (I). I= t,'5

1 HI7,TE(S 15j12)22 FORMA1 (X,'ENLRG,? IN LIONT r:LALKL VR Y I D EC'

WH ITE(S) 1331343 1 UPMAT (X, 4J C EN E A'~ :R G, INK FER CT 'LCL

L~T 25,211) (EP 2r ~ , 01 ' 91,)

WROTE5,200flEF-L,TEFP,TESL ,TED FEE2 "R F1h~ TOTA FIWH EEY FPEB L PEP JUE,~~JJUE

TO T1ALFO AL 9 OR.W1AHGU L4 110, H , "'

* I TOTAL BJACKWAN'D ENRG INLUL:,I.5 OLE'LTOTA BAKWR -EEGY I N Ir A N'JULE>S' FIS, J OUL ES',/

* ~ ~~~ 1:A T1r OF i'RI±LL r~iZLk.Mf~ ~ 1

& /I ' TAL PARTICLE ENERGY/EINERY ACPE'FRIES 3 05,EL 'N, V ARR(2

WN I TE U5,303)303 FO!"A(X ,/I DL]jI'XITNPUT'X'CLNV IP'X'TYPE '2X'ANG(TH)'2y,

I9X JA/CM') 1 'I'',E~,. M'A 30A 1=,2

UPLAD(UN = FZILEJT32 MP.

IF (TJ.En.0.)GO TO 300,JRTES,02IJJ2(VAR(J )J=2,))

DO 40 0 T1,2RCAD(i 3n0i) TJ,TJ2IF(TJ.EQ.0.)GO T 0WI TL(, 2ITJOf32VARIJd;

400 LGr r7 UC

305 LOMT/,JX ThE SHOT $ i:',LS.0/,30rX ,TTHE (A!NGT ANGLE !I:

END

CI

t: 7, T S 0 0Y

DD.I TO I,2)

i A '.L 2):U

C Nf I h L~h E PATT I T INiNIS S

R0 I2d( HC'AYLT EE S~J 12 0 1 E

READ(5 *)-

iF ( IE LT O '0 TO -reCALL E EL - -r ," i

c 5E 4 0 1 n nJ ,1 E 3 ) '2J-

,..0, FO3A I ' IO[J ~4 Pi )1CS ~ Z

1. DO "rt.~ = rtO3E

WP "I If 1 0 ,- ' 1? 97 EC 1 1% S 2

ILL EX-(EP ,IE,"E. -C ' T (SA0):C L E4 E S ES I

F CO RT I U....EF

C C "TT"J,,r, .,

SUE p U T IN'E E EE -1 7T Y , E L A CC =C;),>'.... A ;; ''"}'O " " "- }

CINTEGER CHAR, CMD

COMON/LA~R/ID~(2) NC~ ,C:ARC~D ,~i N,,14,ICOT,C

L-

... ,ICS I E, 2 (, ,. 2 ETRE 'I , LI nr FU ~ RCE LA' '01 CAN'T llrP ICI1LY D1'1 re:

;AEOVE 2IEJI~SLI~liT # IIlU:l PAIRTICLES Tb U0.. ....J,, A ' ,

* x m ~ , , . 9

I S L(SIFC4, 32

INI.DET.LE.0)CC TO S'N

EDET)IdE1EP

WX WI T CS, 1S)J , ES:( I ET 4

C O..TOEA LU WJTS AN Dr ET A l L E OF D ETC TC1;r

I

IF (FLAG LT .0)GO TO 3010DO 2"' J=4 ,IE

MUET 2) E i 71 P(J)Z,0 DaJ1R(,13 VR'

UO O TO 3 = RI v

300- DO 253 J~i.,IE

D, L T 2 1L 'LET)LE( ,J ='III51P 1,4')/ ( IDET 7) T E T2,' /V F iCT y-))

L"(1HI 2)=E r ET)

2, DE. J =VAR IDCT 3 VhiR (2)

C ADD E=O AT 90l DEC AS A POINT

17 'ITf E9.2)DE",( lk)=270 .

V (AL.'LE lDEG)NDEG=Q -I

:ALL RINT(ETE ,1,L,DET,JITY, (DLCu)

E ND

SUBDOUT INE E f n. ( E, TCTD I IEN' ION E(A)

L TkISi PROCRA- USES I .HL T NTERPOLATED VALUES 0C EC TO CALrLTE TOTAL ENERGY ASEUMING Nil SYMENY "INDL SYMLTRY ADMT 1I!L LI.NE NORMAL 10 TWEr TARET

Pl=3.1415?26'AXmllNG=F'l13O

-.. XAtlr~i DlESRE,,.RIM=0

CL, INT.RATE r'Y T4,APIZUIDAL RULEc

RT4O1*YNG

C USE ~AS EETMES STEP SECT SN00AD

2 E TUR NEIND

SjUrt:%:UT TNE VELCC TIS S'UEROUTINEj D.CLS THE V~ELOCI TY CAILCULATT I,

CN T EG ER C HAR C N D

C 11MONCLASER I D1- 72 ) ,NM!AR , CHAR , IMND N14 , N2, N. 1N4, 1 GOT ,

EQUIVALENCE A',)R(a.1)ThEISION FPF(90i),B?(q)

C VF !'S- AN ARRAY COUNTAINING 1HE FORWARD VELOCITYL VPB IS AN ARRAY CMNIA1INING THE BAC:WAPD 'XLOfCI;YC RMF IS AN ARRAY C1UNTAINING T7IE F07WAI'L MASSL R.M.L I AN ARRAY LON4AINING 1HE BACKWARD MALS

C i.Q0f I33 THlE TOJAL IORWARE' MAS$C TRME IS THE TOTAL BACKWARD MASSC ALL ARRAYS HAV~E ML TETA VALUES SPACED i DECC L I T 1NG AT 0 (CIL, AN GON u 1 20

IFkYARR(3).GT. OGOV TO ±0

F~ FOR~IMAI YOU MUICOMPUTE ENLRGY FIRST! !)

GO 10 Soo10 WRITE(S,i.)VARR:3)

ia okMAT( ' WE ARE CUING EXPLERIMENIAL SH:OT t' )F 0.)VRI1T(1,0)VARR(2)

YG' FORMA11' TEE 1ARGLT ANGLE IS"F/.2' DE4REESw')URI-T(ss,lio)

i i'0 FO;.,MAT(' WE "JILL Do FORWARD ANGLL FIPST.')CALL VCAL ( VF, 4CALL MCAL(ThF,V XLL,EFP,1,±PPF)WR ITE ('1, 120)F2 CR AT( NOW WE 1flLL DO THE PACYWAIRD ANGLES.)CALL VCAL M, u')

CALL MTOT(PMF,TRMF,i)CALL .-TOT(RMBi,TRMF,2)CA LL 'P R11F ,VF,TRM4F,V'F, 1)

CALL ::ilPQMF.T RMF, TH'fF, I)CALL T:!xi(k MB, 7Rh,4T: 8, 1)C'ALL ^TOT-'RPF,TRPF,TRPPF,1±)

CALL PTQT(RPB,TuP,TRPPF,2.

U; 1 ?E s 1 202)

'100

201 FDn4T!X,' "FORWARD" VELOCITY EVERY S DEC' ) q2 02 0 i' Ai/ "F.WMD- MASS EVERT S3 DEC:')2 B F OR ATU/,' ''0-tARVD' 10MENTU. EV --F Y ca D EC)204 F QT/,h 1ACKWAdRD" VELOCITY EVERY 5 DEC')

F 0K FFMA 1u,' "BACKI4AlD" oAASS EVERY DEC')206 F CmR M(A , A CWA I"D " OM' E NT.U 11 E V L Ryr L. E G

T H =T H4H 18~!?TES,4o)VF,~rTP~FTRBFIF THHIE,I RPF, TRPPlF, TRP, Tr,,PPB

400J FUMAT(X,'FORWA4;D 'ARALLEL VLiiY'F.5'E7CM/E',,,'& X,'BACKWARD PARALLLL VELOClfY=' ,IJ O .5,C--l~~'/

',TOTAL MASS IN OdADACL',i.C L7C,'

X,'1DTAL MASS IN BVACKWARD ANGLES=' ,F142. CS, 'E-7 G1 ,1).1 X,'M=0.c TUTAL MASIC (FORWA1R1D) Af' ,F12 .c5,' DEC' ,")

,'TOTAL FCRt4 fU) MONlENTUMl' ,Fi*.S,' DYt4E-LSU', A'. PAIRALLEL FfjRV~ARD ~U1NL~ F~''DYNE~~~

& -,'TUTAL DACK Ll~~U~ ii2.S, DYNE-SEECU/kx,,roTAL P'ACF, PAR.ALL-L61 ~ IN'~i., DYNE 3EC')

END

SUflROUTINE VCAL (V flTY)

C INUMi IS TH~E rJuih~R I.- INT POINIS

I~D PO~nAT 11 OW MANY YLLOCIlYINUS.)READ(j,*) IEIfU(I .O.)GO TU YJ.OCALL VEX(VIEITY)

350 R E ". URNEND

f E~I NE VEXV ,I L ,ITY)

INTEGER ANDUUI.MUN / CL A ':R/ Il TADL 7) NCHAR , rHA[" , LMND', N' , N",Ni.. ,IGO&VA R(32, 7 V A R( I U

DIN~NSIO I 'Ji ,EM(i0 ),DET('n.)C THE AOV DIMENSIOrN3 LIMIT t INPLT IPAPRT'CLEZ [0 10

DO i'.0 J=i,IE

ISO F"NMA T (' ENTER (~*FEOIY k

R EA DS, ~I"ET ,CTE1 r(Ir'J)1 DLT =1DE T+2 0IF( IDLT.LE,20 )CO TO SOOIF(lIEIcT.GT.*.)L TO SOO)DET (J1) FLOAi (.1LI)

i3 0 -4DTIr4UE

C CO"N'EIRT 10 REAL 'UNITS AND GET ANVLE OF DETEC40l2

DO 200 J='AIEIDET=1VET(J)

200 :crcJ=VMr(IDT)-AW(2~ ,),*',(DT

L IL~RP CLATE

c IEC:2CALL RIN.,,TCETE 4lP,IL,DLT,J,ITY,NDLU)

SUDr.OpUTY"E M1TOT(RhT1) ,iATY)

D]MILNSION RMiWiC

C THIS CALCULATES TXL TOTAL (A% I !ER FOT'L'AWD IIY=iL OR BACKWARD -ITT =2).

P1:- 3. 14i1S9 2 6-S 4XANQPI/'i8O

u I.L. XA.NG=i DEPRX E

C 11ING!ATE BY TRAPI'LOIDAL RULEc

TO T I= )2 . 14

J"1=RI+XANC10IV' TOIl=TSCT4S I t(.RI )* M('I)

L NOW MIULTIP'LY TIML5 STEPSZ

TO! =TOT*XANGTUT=2. O*PI*TO f

C UISE HAS BEEN M.ADE OF THE FACI THAT SIN(0)4O ANDC SN(7O)=i.0

RE""U RNEND

A.; U ,r~ THl!(Ri1TRti.,THH,iTY)

CCc THi I NDS "THE AIIOL- AT WHICI, !:ALI OF THE TUWAL hIIA4S ISC ACCUUNIED FOR

D I MLPI ION R M~'31=7 . 14ir?"Ir4XAN=Pl/10.r.HThOM= 0.5c*T R MTCT-0.0

C 11.1( 5)=ORI=O.

to 1=1:tRI tR I XANG101I =TGT *SI(RI )* IM)*XANC*2. 01PIL~ 1, OT.GE.fli.)G0 TO 100JfHI LE.90)CO TO t0

4 '

i THHIF LOAT(-i)RETUR~NE ND

..... ]...

DIMENSION PhU(i,(A),ELci)EP(i),: Pli)Dli ice~ I~i 9iIt OR .) .EQ. 0. )Q TO iceTU*'=2. 0*(LP(I))(IR.'(I) =f EMP

ice C 0.4T I UEC Wk1TCh(S,200)(RM(J)J,JiJ,5)200 FORMA f(X,SF12.':)

END

SU UINE YPr (I'M, , TRM1 ,TOT, ITDIJMEN S ION R M ()IV' \I)PI,=3. 14ic"9'16;,4

C I.E. XM'NG~i DECREL

C IITEGCRATE B:Y TRAPIZIOIDAL RULEC

DO 1l0I29RP'RIIXANC

100 TOT=TOTC)SIrJiRIr) Crwzc RI)*nm(I)*11cI)

C

TOT=TOTUxANCI DTZ:2. 0*PI1*TO1(0l =TOT !TR

u USE HAS LEEN MADE OF' THE FACT THAI SIAN(0)=0 AN DC SINl(7O)zi .1; USE HAS LEEN MADE Of O9)=.

R ETUP N

C;

C THIS CALCIULATES THE TOTAL Mnl rCIT'flR POPUARD TiY~j

c GPZ OlAC1uVARD-TY2) kBOTH4 TOT ANID TOT PAALL

P17=3.114iS2654X AN =I i/1 0

c XL AN G= 1 DEGREL

C INTEGIRATE BY TRAPIZOIDn"L RULEC

TOTP=0.0

N( HI0 1=,90R I =Rl XANGTr0.P=OIN(R7A)*RP(I)TOTF=TOTP+1..COS(R 1)*,'TE.M

IUD TOTzTOT4TEOP

L NOW MULTIPLY TIMES STEP 'SIZEC

rOT7TDT*XANQ'u(DIP l=TOTP.*XANC14I(0i=2. 0PIOTT OT=T OT PC2 .0 VUSC HAS BEEN MADE 01* THE FACT THAI SIN(O)=0 AND

END

TtjOTnER TE~h I.C , TE ANE T T

C EtrCnP IS YnAMNIAY

c I1.1 IS THE NO U T,Cn L " Th ME OUTPUJT NJC,41RPOLATED ARk~AY0 1i Y TELLS Ir FOADOf. D'ACY

DO A J~i,±0c

CALL CC,'EF(.A,Da,,.T T QNECaE)

10 lFO~ltAT(X,?,F±0v.3)IF(ITY.E..)NrL-117( ITY .Er4. 2)ANCLEi/,DO 1300C J~i,9A

FO=1.0

loo IF'(I.rE.D'EC)GO TU 2o0

R'.1N IT=A (1+ i) *FNLI: .:PTT

r.0 TO "U1rlr

END

C N 1S II NU1,11E. OF INFUT PI)~

LT;:,"' COM1PUTES ML INIIERPOLATI.WoL L'F A)Bi,IQ"

0!LvIPPD=FL';AT(. N)Do lcoI= I,NX.FrRODXFP'ROD.'X(l

AM'

10 f YF.F:SD=YFrlROD+Y (1)A Ii )zY; PROD/ FLO AT (IN)): I)=XFPRD/F)ILO AT -I IN

c F IiL; C AL CUL AT E F 2

DO L~n0 i~i't(

C CALCULATE A ).a)(I

2 il IF (Y,. ST.I)GO TO "001.

'f FPRfl 0 1

tpC CumPIUTE it4NER ?I*:UDUjLTSDO A49,0 1=1, NYFH0'DYFRODirY(.I) NEW(TAIjI

.C'

- i

F;,prrD=FFPrl':;'O P'40C X I :U=F R0+ X LY Q

A K)~PRODTF~F."0D11 (1.E10i1)C0O 'Iei"990

CC CALCULAT E CHIF FUJ K-UTH ORTAHC IVLYc

Pi (.' 1) =XFPRODI/I FP""CD"2(.11 i " FFPI)ODIOLDPPD

DO SOO l~i,'NFHOLDh=FNEW(I)

F0 FcD I )F HOL D

GO 10 2104v.D RE NR

END

I APPENDIX E

Fluid flow of ablated plasma from planar targetsM. J. Herbst and J. Grun)

Natal Research Laboratorv. Washington D C 20375(Recelsed 12 January 1981; accepted 15 July 19811

Using a novel diagnostic technique, the streamlines of the flow of plasma from a laser-irradiated target areobserved for the first time Implicaions for far-field Ion measuremnents and similarity to a simple fluid floware ioted.

Although laser fusion will use spherical pellets, many tational flow of a nonviscous compressible fluid from alaser-matter interaction experiments are performed circularor,fice.3 Near the target surface, the observedon flat targets. If the results of planar experiments are streamlines curve away from the target normal at a rateto be scaled to spherical geometry, the effect on plas- which is greatest for streamlines whose source pointsma profiles of differences in material flow from the at the target surface are nearest the edge of the fluidtarget must be taken into account. The one-dimensional source. Beyond Z - r.. where Z is the distance fromspherically divergent flow from a uniformly irradiated the target surface and r. is the fluid source radius, thepellet affects plasma profiles at distances from the curvature is negligible and material flows outward in atarget which scale with the pellet radius. While it has straight path. The dearth of published multidimensionallong been recognized that the more complex multidi- code results showing the fluid flow pattern leads us tomensional flow from a finite focal spot on a planar make an interesting comparison between the data andtarget must diverge at distances from the target sur- the aforementioned potential flow. The latter, at leastface which scale with the focal spot radius.' the first for low Mach numbers (nearly incompressible flow) andpublished results of multidimensional calculations which nearly paraxial streamlines, is well approximated byshow-. the fluid flow pattern are only to appear soon. I the solution to Laplace's equation subject to the boundaryIn thE present work, a new diagnostic technique allows conditions at the source [see Fig. 2fb)]. To quantifythe first ex'pcrrmental identification of the fluid flow the comparison, we consider the streamline angles 0lines from a planar target. relative to the target normal, which depend upon Z and

upon the source position r of the streamline ir, the tar-As shown in Fig, I. foil targets are irradiated in the get plane. Fixing Z =r 0 /3, where e- is the orifice ra-

near field o' an. f 6 lens at a 6' angle of incidence b:. diusfor the Laplacian flow andthe observedfluid source100-50C J of Nd laser (P,= 1.054-pm) radiation. With radiusforthe x-ray data, the dependences of e upon r roan incident pulse length of 3.5 nsec. and an irradiated are displayed in Fig. 2(c); thesimilaritvofthetwocasesisspot diameter d_90 t energy content) of 1.4 mm. aver- striking. Of course, the model chosen does not accu-age irradiances within d,, are 1.5-8 TW cm'. The rately represent the case of the laser-ablated target.focal-intensit.,' distribution, as determined by equivalent where fluid emerges at low velocity from the solid sur-focal-plane cameras, is relatively flat-topped, with ap- face and is subsequently accelerated to sonic or super-proximately 2:1 intensity nitdulation across the central sonic speeds (where the flow is highly compressible).region. A camera with an array of pinholes is used to Nevertheless, the resemblance of the data to the La-obtain time-integrated images of x-ray emission at 90' placian does suggest that some form of steady jet flowto the taret normal. The 15-pm beryllium filters is present. Here. jet flow is meant to denote the fluidused onthe cameraallow imaging of photons withenergy expansion, as opposed to the collisionless expansionhv I I keV. of material from a circular orifice.

A linear array of aluminum spots. 25 pm in diameter The fluid nature of the flow is not surprising, sinceand I0 P.m thick, are embedded as tracer material in the plasma radius r, -850 pm is much greater than the300 "m thick polystyrene (C) target foils, which are ion-ion collision mean-free-path ( -1 pm at 0.1 criticalthen alig.'ned so that Ute spots fall along a diameter of density with T --400 eV as determined from x-ray spec-the laser-irradiated region. Since aluminum line emis- tra). One wouldalso expect steady flow, sincethelasersion is more int. nsp than the CH continuum emission pulse-length (3. 5 nsec FWHM) is greater than the soundin the sp-ctral band of the pinhole camera, stream- transit time (- 2 nsec) across r,. Experimental evi-lines (if inattrial flowing from the aluminum spots are dence that the flow is steady, at least for a large frac-

identifiable by the tracks of stron, x-ray emission tion of the duration of x-ray emission, is obtained from15._. Fig. 2t.)*. The p,'rturbation of the flow p.ttern streak photugraphyofiniages of3 2,,emissionfromthedue to tho addition of a ; econd material should be mini- n, '4 surface. The position along the laser axis of thismal bec;iuse: (I , the full-., ionized mass densities for AI surface appears stationary for the duration of the 3 '2,oand Cli dffer br only 12 , at a given electron density emission, a period of up to 3 nsec near the time ofin the blr, pl.sma. and 12) the average velocity, of peak laser intensity.

ablated tons as determined by Faraday cups is the same The fluid flow affects the far-field particle diagnrsticsfhefrudthewafettwoe fr-feltpatileiaalosi.for the two mat-:rials, such as ion collectors or plasma calorimeters; we be-

The -bs,.r d f ,w pattern resembles that of the irro- lieve that these effects have not been previously n,,ted.

1''7 P $ . ,2 C'-!a.er 19 t G0351917' 101 317 022S0090 ,. 1931 Amercri Is.t,-le of Phys5Ls 1917

CH TARGET 1nn

Al DOTS

LASERLIGHT CONE .'X

X-RAY PINHOLE CAMERA 02 04 " "

FIG. 1. Schematic illustration of experimental apparatus. (a) (bi c)

FIG. 2. Comparison of observed flow and simple fluid model.(a) Three x-ray images corresponding to pinhole diameters of

First, the angular distribution of ablated mass observed 13, ?, and 54mm. withlaser incident from right. (b) PatternofLaplacian flow from circular orifice. Dotted lines are con-

bye iostics may be solely determined by the stant velocitv-potential surfaces and solid lines are fluidflow. Due to the shape of the jet near the target sur- streamlines. (c) Dependence ofstreamline angle 6atZ zrO/3 up-face, a fluid velocity direction is imparted to each on source position r in the target plane. Solid curve is forfluid element. As the density decreases away from the Laplacian flow pattern fz m bi, and points (x ) with errortarget, the flow eventually becomes collisionless, and bars are data from x-ray images such as (a).the material drifting in the direction set by the jet ex-pands due to random thermal motion. Since directedablation velocities are generally significantly greater effects on the shape of this flow. Detailed comparisonsthan ion thermal velocities, the thermal expansion will should then be possible with the results of multidimen-not greatly increase the angular range of material flow sional hydrodynamics calculations, which are more ap-set by the jet. Indeed, charge collector and plasma propriate to the problem than the simple model pre-calorimeter measurements indicate that half of the sented here. In the present study, streamlines wereablated mass appears in a cone about the target normal identified by introducing localized sources at the targetwith a 40' half-angle'; this is consistent with the angu- surface: it should be noted that the same phenomenonlar spread observed in the x-ray images, as well as may be observed if localized sources arise due to unin-with that given by the simple model of Fig. 2(b). tentional effects, such as filamentation of the incident

Ion detectors are further affected because the jet, ex- laser beam. 6

cept for any smearing due to thermal expansion after The authors acknowledge valuable discussions withthe flow becomes collisionless. maps regions of target R.R. Whitlock. S.P. Obenschain. R. H. Lehmberg.surface into space. Since each point on the target sur- B. H. Ripin. and C. K. Manka as well as the expertface feeds mass into a specific solid angle, a single ion technical assistance ofM. Fink. N. Nocerino.detector far from the target samples only a portion of L. Seymour, and E. Turbyfill.the irradiated region. To measure the parameters This work was supported by the U.S. Departmentaveraged over the focal spot, then. one should use an of wr k ad the U.S eparh.

array of detectors at a range of angles. The error of Energy and tte Office of Naval Research.that may result if too few detectors are used dependsupon the uniformity of the laser illumination at the tar-get. the ratio of the directe,! ablation velocity to theplasma thermal velocity. and the solid angle subtended aiPresent address: Mission Research Corporation, Alexandria,by the detectors used. Virginia 22312.

In conclusion, a new diagnostic technique allows the tG. J. Pert, Plasma Phys. 16, 1019 (1974) and referencesfirst experimental observation of the streamlines of contained therein.material flow from the surface of a laser-irradiated 2M. K. Matzen, R. L. McCrorv, R. L. Morse, and C. P.target. Knowledge of the flow is required if the results Verdon (private communication).of planar experiment, are to be properly scaled to the 31L. 1). Landau and F. M. Lifshitz, Fluid Mcchanics ( Perga-spherical laser fusion problem. Implications of the mon, London. 1959). Chaps. I and Nil.fluid nature of the flow on far-field ion diagnostics in 6M. J. Ierbst. J. A. Stamper, It. R. Whitlock. It. II. Lehm-

herg. and S. If. Itipin, Phys. Rev. Lett. 46, 32, t 19 1 I.p~l~inar experintents are noted, as is a resemblance of sJ. (Grun, It. Dvecoste. II. II. Itipin, and 3. Gardner, Appi.the observed flow pattern to a very simple fluid flow. Phs. Lett. (to be published).Futurt. studis will include parameteric variation of 6M. J. lierbst. It. It. Whitlock. and F. C. Young. Phys. Rev.laser intensity and spot size. to assess the possible Lutt. 47. 91 (19,1).

1918 P'YS F u.,Js. Vo. 24. %0i 10. October 1931 Research ,%o:, 1918

APPENDIX F

. ... ... ...... ..... ....

Spot spectroscopy: Local spectroscopicmeasurements within laser-produced plasmas

M. J. Herbst, P. G. Burkhalter, J. Grun," R. R. Whitlock, and M. Fink'

Nawal Research Laboratory. Washington. D. C 203 75

(Received 8 March 1982; accepted for publication 7 May 1982)

Use of a locally embedded tracer in laser-irradiated solid targets yields a localized source ofdiagnostic x-ray line radiation in the blowoff plasma. This technique potentially eliminatesproblems of chord integration over regions of varying density and temperature in aninhomogeneous plasma, and reduces complications due to plasma opacity effects in theinterpretation of spectra. Spectra obtained in an experimental test of this new technique are of aquality superior to those obtained from standard laser-produced plasmas, and should provide thebest tests to date of spectroscopic models for these plasma conditions.

PACS numbers: 52.50.Jm, 52.25.Ps

INTRODUCTION target; this yields a source of diagnostic lines which islocalized within the blowoff plasma. In Sec. I, we explain

Density and temperature profiles are directly related to the target fabrication procedure and describe a methodenergy absorption and transport processes in plasmas for in situ measurement of the spectrograph magnifi-produced by laser irradiation of solid targets. Therefore, cation. Data obtained with the new technique are com-measurements of these plasma parameters play a central catio and w e w tec are cpared with standard spectroscopic data in Sec. 11, whichrole in experiments addressing the physics relevant to also contains a discussion of caveats and remaining ques-laser-driven nuclear fusion.' At the densities and tem- tions. Finally. we assess the new technique in Sec. IIl.peratures of interest, x-ray spectroscopy provides oneviable method for performing these measurements. '3

There are two major drawbacks to the use of standard I. EXPERIMENTAL TECHNIQUESspectroscopic techniques in these plasmas. First, the mea- A. Target fabricationsurements are integrated along a diagnostic line of sightthrough an inhomogeneous plasma. Second, effects of For the proof-of-principle experiment, we choose poly-plasma opacity on the radiation exiting the plasma are styrene targets with embedded aluminum tracers. Thenon-negligible at the higher densities of interest.4" One tracer is so chosen because collisional radiative equilib-could use straightforward inversion techniques to obtain rium (CRE) computer models suggest the utility of alu-spatially resolved emissivities from the chord-integrated minum lines for measurement of temperatures and den-data if the plasmas were optically thin and axisym- sities of interest.9 The polystyrene is chosen because itmetric,3 but the additional complication of spatially vary- is a common and easily fabricated target material. Also,ing opacity makes inversion much more difficult. More its lower atomic number Z increases the ratio of thetypically, one predicts the plasma profile using a hydro- aluminum tracer emission to the surrounding plasmadynamics computer code and compares the experimen- emission and reduces the opacity of the surroundingtally observed spectrum with those calculated for chord plasma to the tracer emission.integrations across the inhomogeneous plasma.6' One is A two-step process is used to fabricate these targets.dependent in that case upon the correctness of the hy- The first step is the evaporation of the tracer materialdrodynamics model as well as the atomic physics model; onto a soaped-glass substrate using the standard tech-one Aould obviously prefer to make direct determinations nique of vacuum evaporation from a hot filament source.of density and temperature, independently of the hydro- The thin film of TEEPOL 610 detergent"0 on the glassdynamics. prevents the aluminum from adhering better to the glass

In the present work. a new spectroscopic method is than it will to the polystyrene. To achieve local depositiondescribed which circumvents the problem of plasma in- of the aluminum, bimetal masks into which the desiredhomogeneity and reduces the effects of plasma opacity. patterns have been chemically etched are magneticallySpot spectroscopy, the new technique, differs from stan- clamped in intimate contact with the glass substrate; fordard spectroscopic techniques in that the source of di- the present experiment, these patterns are circular spotsagnostic radiation is locally embedded into the solid tar- of various diameters. In the second step of the process,get before laser irradiation. As recently demonstrated." polystyrene dissolved in butyl acetate is cast over thethe tracer material shich is ablated by the laser can be aluminum-coated glass substrate. When dry, the com-confined collisionally in the hydrodynamic flow from the posite is lifted and the aluminum is embedded in the

1418 Rev. Set. Inutrum. 53(9, Sept. 1982 0034-6748 82 091418-05S01.30 , 1982 American Institute of Physics 1418

polystyrene; the surface of the tracer is flush with thatof the plastic. EMBEDDED Al SPOT

B. The proof-of-principle experiment

Except for the presence of the tracer in the target, theexperimental arrangement for the new technique is muchthe same as for standard x-ray spectroscopy. As shownin Fig. 1, the targets are irradiated with 50-250J of Nd IMAGINGlaser radiation (1.054/pm wavelength) in a 4-5-ns pulse. SPECTROGRAPHWe choose to operate at two focal conditions for thisexperiment. First, at the best focus of our 1/6 input lens,we use focal diameters (90% laser energy content) near100 um, and spatially averaged irradiances up to 5X 10'' W/cm2 . Because larger focal diameters are re-

quired to minimize edge effects in planar experiments, FIG. I. Experimental configuration for spot spectroscopy.targets are also placed in the quasinear field of the fo-cusing lens; intensities between 102 and 10" W/cm2 areobtained with focal diameters of 800-1000 pm. special double target. An aluminum foil is placed in the

The aluminum line radiation in the 5-8 A spectral usual target position, mounted to a glass substrate to

region is detected using an x-ray crystal spectrograph prevent target bowing. A few hundred microns in front

with a viewing axis parallel to the target surface. Spectral of the Al foil, toward the laser, a foil of copper backed

dispersion is achieved through use of a PET crystal, and by glass is mounted. The foils are aligned so that part

spatial resolution in the direction on the film which is of the incident laser beam strikes the edge of the Cu foil,

orthogonal to the spectral dispersion is accomplished with producing Cu line emission, while the rest misses the Cu

an entrance slit. As shown in Fig. 1, the slit is oriented and propagates the additional distance to the Al surface.to yield spatial resolution in the direction along the laser The spectrograph image then contains Cu and Al lines,

axis; resolution in the other two spatial dimensions results but the Al lines extend beyond the end of the Cu lines

from the knowledge of the position of the localized tracer by a distance L' = ML corresponding to the distance L

within the focal spot. The slit is located 4-5 mm from between the two target foils multiplied by the spectro-the target, which represents a tradeoff between light col- graph magnification M. As L may be accurately mea-

lection efficiency and slit survivability; even at this dis- sured under a microscope, M is experimentally deter-

tance, the 25-pum-thick nickel slit substrate is occasionally mined by the measurement of L'.

destroyed by target debris during a laser shot. Another One potential complication with this procedure arises

compromise must often be made between spatial reso- unless the spectrograph axis is closely aligned with the

lution and detectability of relevant spectral lines. To im- target surface; if it is not, the observed separation be-

prove spatial resolution along the laser axis, one must tween the Cu and Al may be lessened due to geometrical

reduce the slit width, sacrificing spectral intensity; to foreshortening. To assure that this is not a problem, we

recover the spectral intensity, one may choose to increase add a flag to the target, a 2-mm-wide and 125-pm-thick

the implanted spot diameter, reducing spatial resolution glass strip on the side between the irradiated target and

in the other two dimensions. For the purposes of this the spectrograph slit. This flag is offset toward the laser

study, slit widths between 4 and 30 pm and tracer spot from the Cu surface and is mounted with its broad face

diameters between 40 and 250 pm are used. The spectra parallel to the Cu and Al target surfaces. Given its lo-

arc recorded on Kodak No-Screen film, for which a film cation, it casts a shadow on the spectrograph; this shadow

model"i based upon an absolute calibration 2 is available, is observed on the spectrum as a gap in the Al and Cu

A beryllium filter of nominally 15 Im thickness protects spectral lines. By comparing the dimension of this gapthe film from visible exposure. with the thickness of the flag, the angle at which the flagand, therefore, the targets are viewed can be determined:

C. In situ measurements of spectrograph any angular misalignment causes an increase in the

magnification shadow dimension which depends on the known flagwidth.

In principle, one may use the measured slit-to-film andslit-to-source distances to calculate the magnification of II. RESULTS AND DISCUSSION.the spectrograph. Ilowevcr. given the uncertainties with A. Results of experiment and comparison ofwhich the exact paths of diffracted rays of various wave-lengths can he measured, we prefer a direct in situ mena- techniquessurement of the spectrograph magnification. To allow a comparison to be made between spot spec-

To measure the magnitication in situ. we devised a troscop and standard spectroscopic techniques we use

1419 Rev. Sc¢ Instrum.. Vol. S3, No. 9. September 1982 Spot spectroscopy 1419

(a) (b)

A(A) 6 7 8I I ,2

lmmI .,l 50/2

(C) (d)

FIG. 2. Qualitative comparison between data obtained with an Al foil target and d, acquired using a CH plastic target locally embedded withAl. The vertical axis for (a) through (d) corresponds to the laser axis, with the laser z.'cident from above and the target surface at bottom. (a)is obtained with Kodak 3490 film, and (b) through (d) are on Kodak No-Screen Film. (a) x-ray pinhole camera images, obtained with an arra%of pinholes (5-55 pm diameter), for an Al foil target. Laser intensity /o = 3 X 10': W/cm:, due to 100 J focused to I I00-Mm-diam spot ,90energy content). (b) Spectrum obtained for Al foil target at Io = 8 X 10"2 W/cm;. witi: 110 J focused to 600-pm-diam spot. (c) Pinhole imagesas in (a). but for a Cli target embedded with 180-pm-diam Al spot. 225 J of laser energy focused to 900-mm-diam spot yields 1 = 8 x 10:W/cm. (d) Spectrum from same shot as (c).

both simple Al foil targets and CH targets with embed- be significantly reduced through the use of a CH targetded Al spots. A pinhole camera filtered to detect photons with an embedded Al spot. As expected on the basis ofwith energy hv Z I keV looks at the blowoff plasma along Ref. 8, a collisionally confined channel of aluminum flowthe same axis but from a position diametrically opposite from the embedded tracer can be identified as the trackthe spectrograph. of stronger x-ray emissivity in the images of Fig. 2(c).

Typical images of an aluminum foil plasma, obtained This is a much smaller source volume than the aluminumwith a pentagonal array of pinholes with diameters be- foil plasma in Fig. 2(a) [the 20% difference in laser focaltween 5 and 55 um, are shown in Fig. 2(a). An x-ray spot diameter between Figs. 2(a) and 2(c) is not a majorspectrum obtained with an aluminum foil target can be factor in this reduction]. Even larger reductions in sourceseen in Fig. 2(b), although for somewhat different con- size are observed when smaller embedded spots are used.ditions than apply for Fig. 2(a). The horizontal edge at To date, we have embedded spots as small as 25 pm inthe bottom of the spectrum is the target surface, from diameter,' a limit imposed by the availability of maskswhich regions of strong line emission extend over dis- for tracer evaporation. In principle, the ultimate limit istances of several hundred microns. set by the ability of the plasma to collisionally confine

The x-ray pinhole images and spectrum for a CH tar- the tracer; as ion-ion mean free paths are estimated toget with embedded Al can be seen in Figs. 2(c) and 2(d), be less than I pm even at electron densities down to 10%respectively; this data is analogous to that shown in Figs. of critical density for the incident laser, there is consid-2(a) and 2(b) for an aluminum foil target. Note that erable room for further source reduction.Figs. 2(c) and 2(d) are obtained on the same data shot, A dramatic improvement in spectral resolution resultsbut that the conditions of this shot do not exactly cor- from the reduction in source volume. With an Al foilrcspond with those of either Fig. 2(a) or 2(b). The com- target, as in Fig. 2(b), the spectral widths of the linesparison between the techniques, therefore, is qualitative near the target surface are quite broad, the widths exceedrather than quantitative, those expected for other broadetaing mechanisms, and

Inspection of the pinhole camera images reveals that. reflect source broadening due to the large Al plasma ex-indeed, the source volume for the Al x-ray emission can tent transverse to the laser axis. In contrast, line widths

1420 Nev. Sol. Instrum., Vol. 53, No. 9. September 1982 Spot spectroscopy 1420

near the target surface are much narrower, as in Fig. localization requires a collisional plasma. This restriction2(d), when a CH target with embedded Al is used. Sev- may prevent use of the technique at much higher lasereral sets of lines which appear to the naked eye to be intensities or at much longer laser wavelengths, wheretotally unresolved in Fig. 2(b) are clearly isolated in Fig. higher plasma temperatures and the generation of su-2(d). These data are obtained with the larger focal spot; prathermal ions produce longer ion-ion mean free paths,a similar effect is observed at the smaller focal spot. destroying the confinement of the embedded tracer. Of

Two other important results of the reduced source vol- course, spot spectroscopy is not limited to laser-producedume are that the effects of plasma inhomogeneity can be plasmas; any method such as ion-beam irradiation orvirtually eliminated and that the effect of plasma opacity electrical discharge which creates collisional plasma fromcan be greatly reduced. Without embedded tracers, one an initially solid target may be used to generate the spec-might try to minimize inhomogeneity and opacity effects troscopic source.by reducing the size of the plasma to be studied. For A second caveat concerns the ability of the techniquelaser-produced plasmas, this would be accomplished by to serve as a plasma diagnostic. If we are to regard theminimizing the laser focal diameter. One could not ex- plasma flowing from the embedded tracer as a local spec-pect, however, to approach the small plasma sizes which troscopic probe for density and temperature measure-seem possible with embedded tracers. Even if one could ments, then we want to be certain that conditions in thelocalize the laser energy to micron scales, lateral trans- tracer plasma correspond to those in the surroundingport of energy by plasma processes would tend to broaden plasma. Certainly, the visualizations of the hydrody-the spectroscopic source, increasing the effect of plasma namic flow pattern, as shown in Ref. 8, strongly suggestopacity. Additionally, this source would still have prob- that there is pressure equilibrium between Al tracers andlems due to its inhomogeneity, one would still be sampling CH plasmas. In the future we will determine by corn-regions of widely different density and/or temperature. parison with other diagnostics when there is also densityWith the plasma resulting from an embedded tracer, one and temperature equilibration.can hope to obtain not only very small source-plasma Even if equilibration is shown for the present data,diameter, minimizing opacity effects, but also a nearly spectroscopic models show that each tracer element mayhomogeneous source, since the embedded spot diameter be used only within limited ranges of density and tem-can be made much smaller than the irradiated focal di- perature'; to diagnose a wide range of parameters, oneameter. The reduction in opacity, of course, is realized must use a variety of tracer materials.' 3 The requiredonly if the tracer is embedded in a target material with equilibration must be demonstrated for each of theselower opacity than the tracer at the wavelengths of in- diagnostic elements.terest. Another issue is the effect of time integration upon the

Given that the source volume for emission is much data. Much as with chord integration, time integrationsmaller with the embedded Al tracer than for an Al foil, can complicate interpretation of the spectra if plasmaone might have anticipated greater problems with de- parameters are varying during the x-ray emission. In thetectability of the spectrum than were actually encoun- present experiments, we believe that the laser pulse istered. In Fig. 2(d), the spectral lines are detectable sev- varying sufficiently slowly so that the plasma profiles areeral hundred microns from the target surface, just as far nearly in a steady state during the x-ray emission. Ex-as they are in the spectrum shown for the pure Al target perimental evidence 4 for this is provided by streak pho-(though under somewhat different conditions) in Fig. tography of imaged 112 wo emission (where wo is the in-2(b). In fact, even continuum emission is detectable near cident laser frequency), which indicates that the locationthe target surface in Fig. 2(d); this continuum is not of the nJ/4 surface, and, therefore, all higher densityobservable when plastic targets without the embedded surfaces, is nearly steady for a few nanoseconds aroundspots are irradiated, indicating that the source of the the peak of the laser pulse (when the x-ray emission iscontinuum is the Al tracer material. For the stronger observed to occur"5 ). Even though we believe time-inte-lines in the spectrum, such as the heliumlike and hydro- gration effects to be minimal for our case, one can hopegenlike resonance lines (I s' 'So-lIs2p'Pi and I s-2p, re- to obtain time resolution with spot spectroscopy in onespectively) and the helium-like intercombination line (Is' of two ways. First, one may replace the film with an x-'So-ls2p'P,), exposures near the target surface tend to ray streak camera to obtain a time history on a singlesaturate the film except on shots where smaller embedded shot, though one cannot simultaneously obtain the com-spots (40 ,m diameter) and narrower slits (4 pm wide) plete spectrum of wavelengths X for all positions : relativeare used. Weaker spectral lines such as the higher Ryd- to the target surface. An alternative method is to deposit

berg members are lost in this limit. Spot spectroscopy a tracer of lesser thickness at a prescribed depth beneathdoes appear to be practicable, then, at least with laser the surface of the target (this involves a more difficult,energies comparable to ours, though realizable, target fabrication procedure). By

varying the depth d and thickness t of the tracer, oneB. Caveats and remaining questions controls the time interval during which tracer emission

Spot spectroscopy has advantages over standard spec- occurs. On a single shot, then, one obtains informationtroscoptc techniques in laser produced plasmas; however, for all X and :, but at only a single time; I and d arethere are a few caveats to he mentioned. First, source varied on a shot-to-shot basis to generate a time history.

1421 Rev. Se,. Instrunt., Vol. 53, No. g. September 1982 Spot spectroscopy 1421

I.: .. ., , " ' t. . .

Ill. CONCLUSIONS L. Seymour, and E. Turbyfill is also greatly appreciated.The advantages of the new technique are clear for This work was supported by the U.S. Department of

measurements of density and temperature profiles in Energy and the Office of Naval Research.plasmas created by Nd-laser interaction with solid tar-gets. Localization of the source of line radiation allows ' Mission Research Corporation, Alexandria. Virginia 22312.

bt Sachs Freeman Associates, Bowie, Maryland 20715.spectroscopic measurements to be made with three d ' J. Nuckolls. L. Wood, A. Thiessen, and G. Zimmerman, Naturemensions of spatial resolution. Since this alleviates the 239, 139 (1972).problem of chord integration over regions of widely vary- W. Lochte-Holtgreven, in Plasma Diagnostics. edited by W.

Lochte-Holtgreven (Wiley lnterscience. New York, 1968), pp.ing density and temperature, one generally will not need 190 ff.

to account for the profile along which one is integrating 'H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York.1964).in order to obtain agreement with spectroscopic models. ' D. Duston and J. Davis, Phys. Rev. 21 A, 932 (1980).

Therefore, the new technique also provides improved 'J. P. Apruzese, P. C. Kepple, K. G. Whitney, J. Davis, and D.

checks of spectroscopic models. As added bonuses: (1) Duston, Phys. Rev. 24 A, 1001 (1981).' D. Duston, J. Davis, and P. C. Kepple, Phys. Rev. 24 A. 1505

the reduced source broadening improves spectral reso- (1981).lution in the data obtained, and (2) the interpretational 'K. G. Whitney and P. C. Kepple, J. Quant. Spectrosc. Radiat.

Transfer 27, 281 (1982).problems raised by opacity effects in the plasma are much 'M. J. Herbst and J. Grun, Phys. Fluids 24, 1917 (1981).

reduced, especially if the surrounding target material has 'D. Duston and J. Davis, Phys. Rev. 21 A, 1664 (1980).much lower Z than the tracer. ' Manufactured by Shell Oil Co. Reference to a company or productname does not imply approval or recommendation of the product

The present work represents a significant step toward by the U.S. Naval Research Laboratory or its contractors to theobtaining improved measurements of density and tem- exclusion of others that may be suitable.

D. B. Brown, J. W. Criss, and L. S. Birks, J. Appl. Phys. 47, 3722perature in laser-produced plasmas. Detailed analysis of (1976).the present data, including extensive comparisons with "C. M. Dozier, D. B. Brown, L. S. Birks, P. B. Lyons, and R. F.

spectroscopic models, is the subject of a future work. Benjamin, J. Appl. Phys. 47, 3732 (1976).V. A. Boiko, S. A. Pikuz, and A. Ya Faenov, J. Phys. B 12, 1889

Further experiments are also required to fully answer all (1979).

of the questions raised in Sec. 1IB. 'M. J. Herbst, J. A. Stamper, R. H. Lehmberg. R. R. Whitlock,F. C. Young, J. Grun, and B. H. Ripin. to appear in Proceedingsof the 1981 Topical Conference on Symmetry Aspects of Inertial

IV. ACKNOWLEDGMENTS Fusion Implosions, edited by S. Bodner, NRL."B. H. Ripin, R. Decoste, S. P. Obenschain, S. E. Bodner, E. A.

Valuable discussions are acknowledged with Dr. D. McLean, F. C. Young, R. R. Whitlock, C. M. Armstrong, J.Duston, Dr. D. Matthews, Dr. B. H. Ripin, and Dr. H. Grun, J. A. Stamper, S. H. Gold, D. J. Nagel, R. H. Lehmberg,

and J. M. McMahon, Phys. Fluids 23, 1012 (1980); and 24, 990Griem. The expert technical assistance of N. Nocerino, (1981).

1

S1422 Rev. Sc'. Inetrum.. vol. 53, No. 9. September 1982 Spot speetroscopy 1422

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AD-A130 408 EXPERIMENTS ON THE DYNAMICS AND HYDRODYNAMIC c/INSTABILITIES OF ABLATIVELY ACCELERATED TARGETS(U) kMISSION RESEARCH CORP ALEXANDRIA VA FEB 83

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APPENDIX 3

NRL Memorandum Report 4896

EXPERIMENTAL METHODS FOR STUDYING THE RAYLEIGH-TAYLOR

INSTABILITY OF ABLATIVELY ACCELERATED TARGETS*

J.Grun,+ M. H. Emery, M.J. Herbst, E.A. McLean

S.P. Obenschain, B.H. Ripin, J.A. Stamper and R.R. Whitlock

We describe new diagnostic methods for the study of hydrodynamic

instabilities in ablatively accelerated targets. These methods include face-

on x-ray backlighting that does not require a backlighting laser beam (for

growth rate measurement), and a tracer dot technique (for tracking ablation

plasma flow). The targets in our experiments are periodically perturbed to

provide initial conditions for the growth of the Rayleigh-Taylor instability.

*This memorandum report is based on presentations to the 12th Annual Anomalous

Absorption Conference in Sante Fe, h% (May 10-13, 1982) and the 24th Annual

Meeting of the APS Division of Plasma Physics in New Orleans, LA (November 1-

5, 1982).

Our work is sponsored by the Department of Energy, the Office of Naval

Research, and the Defense Nuclear Agency.

+.1ission Research Corporation, Alexandria, VA

INTRODUCTION

Designs of hollow, directly irradiated inertial fusion pellets are

constrained by the growth rates of the Rayleigh-Taylor (R-T) instability in

the ablation region. During the past few years we have used nonperturbed

planar targets to model the dynamics of such fusion pellets early in the

implosion phase, before spherical convergence effects become dominant. 2- 5 We

have successfully accelerated these targets up to 160 km/sec while keeping the

target relatively cool (< 10 eV) and uniform (15,.). 3 The target velocities

were consistent with ablation pressures and ablation rates measured on the

thrust (laser) side of the target. 3'5 Moreover, target nonuniformities

observed in these experiments were shown to be related to nonuniformities in

the irradiance profile: 3 '4 We have not as yet observed any nonuniformities of

accelerated nonperturbed targets that could be definitely ascribed to a

hydrodynamic instability.6

To study the development of hydrodynamic instabilities such as the R-T

during the ablation phase we have initiated experiments using F4*leratCtf

periodically-perturbed targets. 7- 10 Using perturbed targets 11,12 for R-T

studies has these advantages:

By seeding the instability with well-defined initial conditions

experiment and theory may be compared more directly than is otherwise

possible.

The known periodicity makes it easier to differentiate between R-T

effects which result from the initial periodic perturbation and other

effects which are not related to the perturbation.

2

By varying the wavelength and amplitude of the initial perturbation we

control the linear growth rate and the number of e-foldings necessary

to reach the nonlinear regime. Consequently, the linear and nonlinear

evolution of the instability is easier to study.

Our targets fall into two classes (Fig. 1), targets that are corrugated

(wiggly) with a constant areal mass density and targets that have a

periodically varying mass per unit area. The first type of target has an

initial amplitude perturbation only. The second type of target develops both

an ainplitude and velocity perturbation early in the laser pulse due to the

differential acceleration across the target surface. Also, in the second

target type changes in the areal mass density across the target surface - and

hence the instability growth rate - may be more easily related to the initial

target perturbations.

To get measurable growth rates we accelerate the targets to 107 cm/sec

with a 5 nsec FSrnM, 1.06 jim laser pulse. Under these conditions about 23

classical e-foldings (f ,/kg dt ) are expected for perturbation periods of

10 Jim: Perturbations with periods as large as 300 pm are expected to grow

with about 4 classical e-foldings (Fig. 1). Thus, even if actual R-T growth

rates are reduced from /kg by a factor of 2 or 3 as some predict, 13- 1 5

measurable growth rates can still be achieved in our parameter regime.

The following sections describe proof-of-principle tests 9 ,10 of two

experimental methods designed to study the linear and nonlinear evolution of

the R-T instability. The first method is a face-on x-ray backlighting

technique with which we hope to measure areal mass nonuniformity development

and, hence, the linear growth rates of the instability. The unique feature of

this technique is that it does not require a separate x-ray source or a

separate backlighting laser beam. The second method uses x-ray emission from

tracer dotsl 6 to map out the ablation plasma flow from accelerated perturbed

targets. This method may be capable of detecting the vortex shedding 17 and

Kelvin-Helmholtz like rollup that are predicted to occur on the ablation side

18of unstable targets.

[ FACE-ON X-RAY BACKLIGHTING

The R-T instability in a periodically perturbed target causes mass to

flow laterally near the ablation surface from the thinner to the thicker parts

of the target. Consequently, measurements of areal mass across the target

surface at some known time into the laser pulse, or measurements of the rate-

of-change of areal mass density across the target surface, can be related to

the instability growth rates.

We deduce areal mass variations from the attenuation of an x-ray pulse

that has passed through the spike and bubble structure in a target predicted

to be R-T unstable. These x rays originate from a thin layer of magnesium

that has been buried within a periodically perturbed target made of carbon.

In these initial experiments the depth at which magnesium is buried is chosen

so that the 5 nsec FWrH laser pulse burns through to the magnesium at 2.5 nsec

past the peak laser intensity. The sequence of events is as shown in Fig.

2: First, the outer carbon layer is heated and ablates, accelerating the

target but emitting relatively few x rays above 1 KeV. Once the outer carbon

layer is depleted (and hopefully the R-T is well developed) the thin magnesium

layer rapidly heats up emitting the short burst of > 1 KeV x rays that are

used to radiograph the target.

Figure 3 shows the experimental setup. The C/Mg/C perturbed target is

viewed by three pinhole cameras and a PIN-diode all filtered with 1/2 mil

4

beryllium. (An x-ray streak camera may also be used in the future.) One of

the two pinhole cameras on the laser side of the target provides a two-

dimensional image of the x-ray flash source; the second, with a carbon step

filter in front, provides a calibration of the film density as a function of

the carbon areal mass that the x rays pass through. The third camera, at the

* target rear, records the radiograph of the target. The diode is used to

measure the duration of the Mg x-ray pulse and its timing.

This face-on x-ray backlighting method has some very nice features: No

*separate backlighting laser beam is needed; alignment of diagnostics is easier

than in a comparable experiment with a separate backlighting source; the

diagnostics are simple, and the system is self-calibrating on each shot. It

* is also possible to account for x-ray source nonuniformities during data

reduction by comparing the x-ray source photograph with the radiograph. On

the other hand, the target is somewhat complicated and there may be some space

versus time distortion due to possible non-simultanelty of the Mg emission

across the target.

Our first experiments tested whether the magnesium pulse was sufficiently

brighter than the less intense but longer duration carbon x rays, whether the

x-ray film density is a sufficiently sensitive function of the carbon target

*areal mass density, and whether the magnesium x-ray pulse is sufficiently

short to make a meaningful growth rate measurement with a pinhole camera. To

check the ratio of magnesium to carbon x-ray emission we shot a perturbed

target in which the buried magnesium layer and the overlaying carbon had the

shape of a disk of about the same diameter as the laser focal spot. The laser

focal spot was offset with respect to this disk so that a part of the beam was

incident on pure carbon, exciting carbon x rays only, and a part was incident

on the C/Mg/C layer. The laser irradiance and thicknesses of C/Mg layers were

chosen so that the magnesium would light up at about 2 nsec past the peak of

the pulse and deplete 1/2 nsec later. Figure 4 describes the experimental

parameters and shows photographs of the x-ray source as well as the resulting

radiograph. The radiograph shows a clear picture of the perturbed target.

The exposure levels caused by x rays from the layered C/Mg/C region were about

6 times greater than exposures from the pure C region for a pinhole diameter

of 6-8 im and a pinhole camera magnification of 2.5. The signal/noise ratio

in this experiment is therefore adequate.

It is interesting to note that the radiograph in Fig. 4 shows some large-

scale nonuniformities that are not correlated with the initial target

perturbation. Some of these nonuniformities appear in the x-ray source photo

as well and are probably related to imperfections in the carbon/magnesium

coatings. These types of nonuniformities can be accounted for in data

reduction; also, improvements in the fabrication of the layered targets can be

made. Other small-scale nonuniformities appear in the radiograph but not in

the x-ray source. These may be caused by the instability mechanism itself or,

perhaps, by variations in target thickness caused by a nonuniform laser

beam. In either case, two-dimensional pinhole pictures will be necessary to

monitor and understand the phenomenon.

The functional relationship between the film density and the areal

density of carbon that the x rays passed through depends on the location of

the film's H-D curve - or equivalently on the source intensity, spectrum,

duration, the amount of intervening carbon, pinhole diameter, camera

magnification and so on. Because so many variables affect the result, in the

future we intend to take in situ calibration measurements on each shot through

an arrdy of pinholes.

For this experiment calibration was done on separate shots. An exarple

6

of a film density versus carbon areal density curve for an 8 jim diameter

pinhole, camera magnification of 2 and other conditions similar to Fig. 4 is

shown in Fig. 5. Under these conditions the useful range of film density

corresponded to areal mass density less than 1.5 mg/cM . The ratio of C/1g

layer to C x-ray induced density (signal/noise) was high. A larger, 13 Pmdiameter, pinhole showed reduced signal/noise but carbon thicknesses up to 2

mg/cm2 were easily distinguishable.

We measured the duration of the magnesium x-ray pulse using a filtered

MRD-500 photodiode, which has a 1/2 nsec rise time. However, since this

measurement is spatially integrating, nonuniformities in the laser pulse which

ablate the target at different rates as well as imperfections in the

carbon/magnesium layers broaden the diode pulse; the result is an upper limit

on the x-ray pulse duration for a given location on the target. This upper

limit was measured to be 2 nsec FWH.M. In future experiments we will deposit

the magnesium layer locally within the focal spot, improve the quality of our

targets, and improve the temporal resolution so as to measure the actual x-ray

pulse duration.

What if the magnesium x-ray pulse is not significantly shorter than 2

nsec - can meaningful measurements still be made? The answer is yes -

although the flexibility of this backlighting method would be reduced. For

example, during the latter part of the laser pulse the number of classical

integrated R-T growth periods ( J t 1g dt) changes by only 20% since the

laser power, and therefore, target acceleration are falling rapidly (Fig.

2). A measurement of such a slowly varying quantity is possible with a 2 nsec

x-ray pulse. But a 2 nsec NTIM x-ray pulse is too long to allow multiple

flash experiments where laterally offset magnesium layers are buried at

varying depths in the target to temporally and spatially resolve the evolution

t7

of areal mass perturbations with pinhole camera diagnostics. An x-ray streak

camera would have to be used under such circumstances.

TRACER METHOD FOR FLOW VISUALIZATION

The ablation plasma flow from a R-T stable and R-T unstable target is

predicted to be very different. If a R-T stable target is irradiated by a

relatively uniform laser beam the ablation plasma flows in a fan pattern which

resembles that of an incompressible fluid squirting from a circular

nozzle. 16 In a linearly unstable R-T target, however, non-colinear pressure

and density profiles in the ablation plasma are thought to generate vorticity

near the ablation surface causing the ablating plasma to be shed from the• • 17

target in a circulating pattern resembling that of a Karman vortex street.

In nonlinearly unstable R-T targets the vorticity is thought to be advected up

the sides of R-T spikes producing a Kelvin-Helmholtz-like rollup of the spike

tips. 1 5,18 The degree of rollup may depend on the delails of initial

perturbation (square vs sinusoidal), 15 and the wavelength of the

perturbation.'8 These phenomena may be responsible for the reduction of the

linear R-T growth rates below classical (/kg) and for the eventual saturation

of the instability.17'18

Figure 6 shows the nonlinear Kelvin-Helmholtz-like rollup of the spike

tips of a strongly perturbed R-T unstable target as predicted by the NRL FAST

2D simulation. |8 The corresponding flow pattern is shown in Fig. 7.

We are attempting to apply tracer methods used successfully in other

experiments ,16,19 to detect the above phenomena in periodically perturbed

targets predicted to be R-T unstable. The experimental arrangement is shown

in Fig. 8. A row of alum-inum or silicon tracer dots is embedded into or

deposited on the surface of a periodically-perturbed polystyrene (0i) or

8

carbon target. (For the experiments below the tracer material was aluminum

deposited on a carbon surface.) When the target is irradiated the tracers and

the target surface heat-up and ablate away. Since the tracers are. much

stronger emitters of x rays in the spectral band of the pinhole camera (> I

keV) than either carbon or polystyrene, the location of tracer ions in the

ablation plasma flow is identified through their emission. We assume that the

tracers do not significantly perturb the dynamics of the ablation plasma

flow. This assumption is reasonable since the speed of Al, Si, and CH or C

target ions, measured with time-of-flight ion collectors, is the same. Also

for a uniform electron density in the ablation plasma the fully-ionized ion

mass density for Al and CH (C) targets differ by only 12% (4%): Si and C

fully-ionized ion mass densities differ only by 0.2%. Embedded Si tracers

should not perturb the target dynamics significantly either since Si and C

densities are about equal (2.32 vs 2.25 gm/cm3).

Examples of the targets we use are shown in Fig. 8. The target types

are: wiggly C1 targets with Al dot tracers, areal mass perturbed carbon

targets with Al dot tracers, and areal mass perturbed carbon targets with

rectangular aluminum tracers that lie only on the thicker parts of the target

and have, therefore, the same periodicity as the target perturbations.

For the experiments described below the targets were viewed edge-on with

a pinhole camera. Since this gives no time resolution the expected circular

plasma motion will show up as a smearing of the tracer image. In the future

we intend to also use an x-ray streak camera to get the desired temporal

resolution and spatially two-dimensional information.

Our experiments show that the plasma flow from perturbed and nonperturbed

targets can indeed be very different. In the nonperturbed case each tracer

dot raps into a distinct flux tube as the Loris flow away from the target (Fig.

9

I.l

8,9). In contrast, flux tubes from perturbed targets merge together

indicating that lateral plasma flow occurs. This is seen most clearly in Fig.

9 which resolves the flow from a 200 Vm period, 2:1 areal mass perturbed

target using six tracer dots per period. A similar target with a 50 Pm period

(Fig. 10) shows such a merging of flux tubes also but with poorer resolution

(2 tracer dots/period). The lateral plasma flow deduced from these figures

resembles that expected from R-T unstable targets, but more mundane mechanisms

associated with dynamic breakup of these heavily perturbed targets cannot be

excluded. Future experiments with improved time resolution and more extensive

parameter variation will differentiate between the possible flow mechanisms.

I t is interesting to note that the x-ray emission from the thicker

portions of the heavily perturbed target in the edge-on photos of Fig'. 9 and

Fig. 10 is greater than the emission from the thinner portions. The same

phenomenon is seen in Fig. 11 which shows a frontal view of the emission from

a heavily perturbed carbon target. Since the height of the initial

perturbation step in all these targets is much smaller than the critical to

ablation distance, these brightness variations appear to be due to phenomena

occurring during the target acceleration. For example, similar phenomena

caused by a R-T spike shielding a R-T bubble from laser radiation have been

observed in numerical simulations.'4 Effects not related to the R-T may also

explain our observations: For instance, !f the thinner part of the target

accelerates ahead of the thicker part, the critical to ablation distance may

be smaller near the thicker part than near the thinner part. If this were so,

laser energy would transport preferentially to the thicker part causing it to

emit more brightly. In any case care must be taken experimentally that the

target self emission, which can acquire the periodicity of the imposed

perturbations, does not distort areal mass measurements. Cases in which the

10

ratio of backlighter to target x-ray emission is not very large or the

contrast of the backlighter x rays as they pass through the thicker and

thinner parts of the target is not very large require special care.

Very interesting and unexpected plasma flow patterns were seen in a few

cases. The most interesting 9f these is shown in Fig. 12. Here the target

was an areal mass perturbed type with tracers that were in phase with the

150 Um perturbation period. The plasma flow from most of this target exhibits

the lateral expansion that has been observed in Fig. 9 and Fig. 10. But the

flow from one location behaves very differently: The plasma near the target

surface in this location is compressed and is dimmer than plasma from other

comparable regions of the target. Further from the target surface a dramatic

decompression occurs and coincidently the plasma emission increases. Still

further from the target surface the plasma becomes compressed and dimmer but

this time the compression ratio is much smaller. (The second compression

cycle is seen on the negative though it may not be clearly visible on the

figure.) This phenomena is all the more amazing since it is seen in a time-

integrated pinhole picture. The flow pattern, therefore, resembles a

standing-wave-like phenomenon.

CONCLUSION

We are developing methods to measure the growth rate and ablation

characteristics of hydrodynamically unstable targets. In our experiments

perturbations which may seed the instability are purposely introduced in the

targets. The first experiments using a face-on x-ray backlighting method and

a tracer-dot method have been described. Both methods show promise.

Parametric studies will be attempted in the near future.

11

ACKNOWLEDGMENTS

The authors acknowledge helpful discussions with Dr. Steve Bodner. The

assistance of Dr. M. Peckerar, Mrs. Eva Austin, Mr. M. Fink, Mr. E. Turbyfill,

Mr. N. Nocerino, Mr. J. Kosakowski, and Mrs. B. Sands is very much

appreciated.

REFERENCES

1. G. Taylor, Proc. Roy. Soc. A201, 192 (1950).

2. B.H. Ripin, R. Decoste, S.P. Obenschain, S.E. Bodner, E.A. McLean, F.C.

Young, R.R. Whitlock, C.M. Armstrong, J. Grun, J.A. Stamper, S.H. Gold,

D.J. Nagel, R.H. Lehmberg, J.M. McIlahon, Phys. Fluids 23(5), 1012 (1980);

24, 990(E) (1981); J. Grun, Naval Research Laboratory Memorandum Report

4491, 1981; R.R. Whitlock, S.P. Obenschain, J. Grun, Appl. Phys. Lett. 41,

429 (1982).

3. J. Grun, S.P. Obenschain, B.H. Ripin, R.R. Whitlock, E.A. McLean, J.

Gardner, M.J. Herbst, J.A. Stamper, Naval Research Laboratory Memorandum

Report Number 4747, 1982 (accepted for publication in Physics of Fluids).

4. S.P. Obenschain, J. Grun, B.H. Ripin, E.A. McLean, Phys. Rev. Lett. 46,

1402 (1981); 48, 709(E) (1982).

5. J. Grun, R. Decoste, B.H. Ripin, J. Gardner, Appl. Phys. Lett. 39, 545

(1981i).

12

6. Other authors have also looked for the Rayleigh-Taylor instability in

ablatively accelerated targets: J.D. Kilkenny, J.D. Hayes, C.S. Lewis,

K and P.T. Rurasby, J. Phys. D: Appl. Phys. 13, L123 (1980); A. Raven, H.

Azechi, T. Yamanaka, and C. Yamanaka, Phys. Rev. Lett. 47, 1049 (1981).

7. B.H. Ripin, S.P. Obenschain, J. Grun, C.K. Kanka, M.J. Herbst, E.A.

McLean, J.A. Stamper, R.R. W~hitlock, J.M. McMahon, S.E. Bodner, Bull. Am.

Phys. Soc. 25, 946 (1980).

8. J. Grun, S.P. Obenschain, R.R. Whitlock, M.J. Herbst, B.H. Ripin, E.A.

McLean, N.H. Emery, J. Gardner, Bull. Am. Phys. Soc. 26, 1023 (1981).

9. J. Grun, IM.J. Herbst, E.A. McLean, S.P. Obenschain, B.H. Ripin, J.A.

Staraper, R.R. Whitlock, F. Young, Abstract of the 12th Annual Conference

on the Anomalous Absorption of Elect romagnetic Waves in Sante Fe, NH1

(1982).

L 10. J. Grun, S.P. Obenschain, N.J. Herbst, M. Emery, R.R. Whitlock, B.H.

Ripin, J.A. Stamper, Bull. Am. Phys. Soc. 27, 1028 (1982).

11. Perturbed targets were also used in electron beam driven experiments by

M.A. Sweeny, F.C. Perry, J. Appi. Phys. 52, 4487 (1981).

12. Other laboratories now using or planning to use perturbed targets in

Rayleigh-Taylor experiments include Rutherford Appleton Laboratory and

Lawrence Livermore National Laboratory: Ruciicrfor' Annual Report to the

Laser Facility Committee 1982; Karnig 0. Ni'ikaelian (private

13

communication).

13. R.L. McCrory, L. 1X-ontierth, R.L. Morse, and C.P. Verdon, Phys. Rev. Lett.

46., 336 (1931).

14. N.H. Emery, J.H. Gardner, J.P. Boris, Phys. Rev. Lett. 48, 677 (1982).

15. R.G. Evans, A.J. Bennett, G.J. Pert, Phys. Rev. Lett. 49, 1639 (1982).

16. N.J. Herbst, J. Grun, Phys. Fluids 24, 1917 (1981).

17. N.H. Emery et al., 9th International Conference on Plasma Physics and

Controlled Nuclear Fusion Research, Paper W9, Baltimore, ND (September 1-

8, 1982). M.H. Emery, J.H. Gardner, and J.P. Boris, Bull. Am. Phys. Soc.

27-, 1042 (1982). (Submitted to Phys. Rev. Lett.)

* 18. N.H. Emery, J.H. Gardner, J.P. Boris, Appl. Phys. Lett. 41, 808 (1982).

19. N.J. Herbst, P.G. Burkhalter, J. Grun, R.R. Whitlock, N. Fink, Rev. Sci.

Instr. 53, 1418 (1982).

14

FIGURE CAPTIONS

Fig. 1 Hydrodynamic instabilities are studied using accelerated,

periodically perturbed targets. Amplitude modulated targets with

constant areal mass and areal mass modulated targets are

illustrated. The number of classical Rayleigh-Taylor e-foldings

during the laser pulse is shown as a function of final target speed

to illustrate where measurable growth rates may be achieved in the

experiment. A is the wavelength of the Rayleigh-Taylor mode.

Fig. 2 Schematic of the temporal behavior of the laser pulse, magnesium x-; t

ray flash, and f /kg dt integrated over the laser pulse. The

exact duration of the x-ray flash is uncertain as indicated by the

dashed lines. If the x-ray flash is bright and of short duration

the instability growth may be temporally resolved using pinhole

cameras.

Fig. 3 Setup of the face-on x-ray backlighting experiment. The function

of each diagnostic is described in the text. The arrow indicates

the incident laser direction.

Fig. 4 Radiograph of a perturbed target and an image of the x-ray

source. On this shot the buried magnesium layer, which has the

shape of a disk, is offset with respect to the focal spot. The

oval brighter images are caused by the x rays emitted by the

magnesium layer. The dimmer part of the image is caused by the

emission of carbon x rays only. The parameters of this shot are-

target perturbation period = 50 Wm with peak (valley) thickness

( 8.7 um (5.4 Wm), upper carbon over layer thickness = 1 uIn, and :g-

15

layer thickness = 0.1 Wm; average irradiance = 1 x 1013 W/cm 2 .

Fig. 5 Optical density of x-ray film as a function of the areal density of

a cold carbon filter for an 8 Wm pinhole and a camera magnification

of 2. The irradiance and C/Mg layer thicknesses were similar to

those of Fig. 4. The Mg/C x-ray source curve and the C x-ray

source curve were obtained on separate shots.

Fig. 6 Density contours of a nonlinearly unstable Rayleigh-Taylor target

predicted by the NRL Fast 2D code. The target parameters and time

of the "snapshot" are shown in the figure.

Flg. 7 Predicted ablation plasma flow patterns for the same conditions as

in in Fig. 6.

Fig. 8 Experimental arrangement and targets used to visualize the ablation

plasma flow from periodically perturbed targets. Upper left: the

experimental arrangement. Lower left: fan-like plasma flow from

an accelerated planar target. Upper right: corrugated plastic

target with aluminum tracer dots. Lower right: carbon targets

with perturbed areal mass and tracer dots. Target dimensions are

exaggarated for clarity in these sketches.

Fig. 9 Plasia flow from a flat (left) and a perturbed target (right). The

perturbation period is 200 Wm with an areal mass ratio (thick/thin)

of 2. There are approximately 6 tracer dots per perturbation

period. Unlike the flat target case where flux tubes of individual

tracer dots are visible, the individual flux tubes in the perturbed

case are not distinguishable. The perturbed target photos were

taken on the same shot through three different diameter pinholes.

The smallest pinhole photo is on the bottom; the largcst pinhole

photo on the top.

16

Fig. 10 Plasma flow from a target perturbed with a 50 pm period. The

photographs of the perturbed target were taken on the same shot

through three different diameter pinholes. The smallest pinhole

photo is on the bottom; the largest pinhole photo on the top.

There are about two tracer dots per perturbation period.

Fig. 11 Pinhole photograph of > 1 KeV x-ray emission taken from the laser

side of a heavily perturbed carbon target.

Fig. 12 Unusual plasma flow from a perturbed target diagnosed with aluminum

tracers matched to the perturbation period. Note the coupression

and expansion of ablation plasma on the right laser side of the

photograph.

17

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APPE3NDIX K

SECURITY CLASSIFICATION OF TIS PAIIE ,W1eln Do,. L-nter-d,

READ INSTRUCT:ONS

REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

REPRT N-jMbER 2 GOVT ACCESSION No. 3 RECiPIENT' CATALOG NUmbER


4 TITLE (. d Sob tiI.) 3 TYPE OF REPORT & PERIOC COVERED

MEASUREMENTS OF LASER COUPLING AND PLASMAPROFILES IN LONGER-SCALELENGTII PLASMAS

6 PERFORMNG ORG REPORT NuMBER

- AUT..OR(.j 0 CONTRACT OR GRANT NkMBER'.)

M.J. Herbst, P.G. Burkhalter, J. Grun,* S.P. Obenschain,J.A. Stamper, F.C. Young, E.A. McLean, B.l. Ripin, and

R.R. Whitlock9. PERFORMiNG OR ANIZATION NAME AND ADDRESS 0 PCRAM E EMENT PROJECT TASK

AREA 1 WORK U NT NUMBERSNaval Research Laboratory DPE A108-79DP 40092(172)

Washington, D.C. 20375 47-0859-0-2

II. CONTROLLING OFFICE NAME AND ADDRESS 12 REPORT DATE

U.S. Department of Energy September 30, 1982Washington, D.C. 20545 13 NUMBER OF PAGES

14 MONITORING AGENCY NAME & ADO RESSfIt dilter-nI from Co trPo ~Ilna 0111.c ) 15 SECURITY CLASS. f of IhI. ep.,I)

UNCLASSIFIED15 OECLASSIFICATION DOWNGRADING

SCH EDJLE

IA OISTRIBUTION STATEMENT (o1 hI. RoporeJ

Approved for public release; distribution unlimited.

17 DISTRIBUTION STATEMENT (OI rho ob tl~rct enterd In Block 20. If difer nt It. R.pot)

B8 SUPPLEMENTARY NOTES

"Present Address: Mission Research Corp., Alexandria, VA 22312

19 , K E Y W C R O S (C on tin ue on - - 0 . tid. If ..c .. ry - Id ntify by blo ck n m b r)

Laser-matter interactionPlasma instabilitiesX-ray spectroscopyPlasma diagnostics

20 ABSTRACT fContf- m oes* sld. It noc eo.er y a d Identify by block numb r)

Novel configuration of our two-beam laser allows laser-coupling experiments to be performed in

longer-scalelength plasmas (Ln 250-600 mm at n/lIO), which better simulate reactor-sized pelletplasmas. Preliminary observations show increased backscatter, as expected, but also reveal large re-

ductions in 2(j and high-energy x-ray emissions. The latter may indicate lessened importance of

resonance asorption in longer-scalelength plasmas. Measurements of plasma profiles are at least as

Important as coupling measurements in these experiments and we show new diagnostic techniques

(Continued)

DD , , 1473 Eo,,,o, op I NoV 65 Is oesoLErES/4 0102"014"6601 SECuRITY CLA.SIFICATON OF TmIS PAGE (Ph., Da.t. aifored)

SEC u kiTV CL &S$i I CAT. ON OV TIS PeGr t When Dot* E11611d)

20 ASSTRACT (Continued)

based upon tracer-dot methods. These include the first techniques available for velocity profile mea-surement, as well as an improved x-ray spectroscopic method for density and temperature profilemeasurement.

Ste!.JIITY CLASSIFICATION Of

TNIS PAGV*¢%on Dofl Zntoroll

ii

CONTENTS

I. INTRODUCTION........................................................................ I

II. PRELIMINARY LONG ER-SCA LELENGTII EXPERIMENTS ................... 2

Ill. PLASMA PROFILE MEASUREMENTS .............................................. 3

IV. STATUS REPORT ....................................................................... 5

V. ACKNOWLEDGMENTS................................................................ 5

REFERENCES..................................................................................... 5

...... -----

MEASUREMENTS OF LASER COUPLING AND

PLASMA PROFILES IN LONGER-SCALELENGTH PLASMAS

I. INTRODUCTION

To maximize applicability of current laser-plasma coupling experiments to high-gain laser fusion,these experiments should include three very important characteristics. First, laser-target coupling stu-dies should be performed in plasmas with longer density, temperature, and velocity scalelengths tominimize the extrapolation which must be made from present experiments to the multimillimeter-scalelength plasmas anticipated for high-gain pellets. Second, measurements should be made over awide range of scalelengths to provide a number of benchmarks for the plasma and hydrodynamics codeswhich are used to make the extrapolation. This is important because the absorption physics in long-scalelength plasmas may be qualitatively (as well as quantitatively) different from that in short-scalelength plasmas: the various processes which determine absorption efficiency depend differently onplasma scalelengths, and the processes which determine the absorption efficiency in short-scalelengthplasmas might not be the same processes which are most important in long-scalelength plasmas.Finally, it is important that a complete set of plasma scalelength measurements be made in these exper-iments. If one measures absorption or scattered light and does not specify the scalelengths, free param-eters are available which may be used in a hydro-code calculation to fit the measurements: for example,the flux limiter may be varied (which alters the plasma profiles) to obtain agreement with the experi-ment. In this case, the physics assumptions in the calculation are not being properly tested, and noconfidence is developed in the ability of the hydro-code to predict laser-target coupling in reactor-sizedplasmas.

Standard measurements of laser coupling with solid targets exhibit weaknesses on all three points.As illustrated in Fig. 1, these generally involve focusing the laser to a small spot in order to obtain thehigher intensities of interest for high-gain scenarios. Planar geometry, rather than spherical, is com-monly used because somewhat longer plasma scalelengths can be produced with fixed laser power andintensity. Even so, scalelengths produced by a small focal spot are still much shorter than reactorscalelengths because of the divergent flow of plasma from the finite planar spot. Moreover, variationsof laser intensity and plasma scalelength cannot be made independently. If the laser power is varied tochange the irradiance at constant spot size, the plasma scalelength varies also, if laser spot size is variedto control plasma scalelength, laser irradiance and focal quality change as well. Measurements of den-sit), and temperature profiles have not been made routinely in these experiments, and techniques forvelocity profile measurement have not been developed.

Signilant physics results have been obtained in previous experinlents designed to address lasercoupling in longer scalelength plasmas: these experiments have also had limitations. Using underdensegas targets to eliminate complicating effects due to the presence of' a critical surface. inestigators havemade positi,,e identifications of stimulated Brillouin backscatter I and sidescatter5 and of stimulatedRaman scat ~r 1hey have also observed the saturation of Brillouin hackscatter and sidescatter.)MleasLrement-, ,nd calculations' suggest that coupling to these plasmas is dependent upon thed n.imlics of' oni/ation and heating waves, as %%ell as upon the hydrodynamic expansion lateral to the

%.~ ,.~~ ",m:Ic,.d J: hi 2'. 1I'4

laser axis, thus, the dynamics of the gas target plasmas are as complicated as the dynamics of solid tar-get plasmas but are less similar to the dynamics of reactor pellet plasmas. Furthermore, thescalelengths in these underdense gas targets are often so long that they can be treated by the theory ofparametric instabilities in homogeneous plasmas: therefore, one does not check the inhomogeneoustheory of relevance to reactor pellets. More recent experiments with inhomogeneous, overdense gastargets 12

-14 overcome this latter problem. However, the important effect of the flow velocity gradient

along the laser axis is still not present.

At NRL, longer-scalelength solid-target experiments in progress are designed to include effects offlow velocity gradients while overcoming the abovementioned deficiencies of standard solid-targetexperiments. To produce longer scalelength plasmas, two separate beams from our Nd laser (X = 1.054Mrm) may be focused in different planes, as shown in Fig. 2. One beam, operating with up to 250 J in a3-5 ns pulse, is brought to a large diameter (z I mm) spot at the target to produce plasmas with densityscalelengths L, -- n/7n of 250-600 m at n,./10. The second beam is tightly focused inside the first togive the high intensities of interest for laser-plasma coupling experiments. By reducing the pulse dura-tion of the second beam to r < 0.5 ns (with laser energies as high as 25 J), we can minimize the per-turbation to the long-scalelength hydrodynamic flow of the first beam that is caused by this higherintensity region. Both 1ig,- intensity and long scalelength can be achieved in these experiments, andthe two parameters may be varied independently since the scalelength is determined by the larger spotsize and the intensity by the smaller spot size. This new method for performing longer-scalelength cou-pling experiments has evolved from prepulse techniques pioneered by NRL in the mid-1970"s.15 As %%illbe discussed later in this paper, we are developing new plasma diagnostic techniques to make improvedmeasurements of density and temperature profiles, as well as the first measurements of velocityprofiles.

11. PRELIMINARY LONGER-SCALELEN fH EXPERIMENTS

Preliminary observations of laser-plasma couplJing have been made using this two-beamconfiguration to produce longer scalelengths. As indicated in Fig. 3, a significant increase in backscatterthrough the lens is observed when the large-focus be,'m is combined with the tightly focused beam: thisoccurs both for long pulselength and short pulselength operation of the higher intensity beam, althoughthe maximum intensity achievable in the former case is io.ver due to laser protection considerations.Despite the large increase observed in backscatter from the carbon targets used in these experiments,the maximum backscatter is 10 percent- thus, the backscatter accounts for only a small fraction of theincident energy. Mcasurements of scattered light at other angles, which have not yet been reduced.may alter this picture.

While the increase in backscatter in these preliminary longer-scalelength experiments %as entirelypredictable from parametric instability theory, (6 two other observations are more surprising. Time-integrated images of second-harmonic emission, taken at 90' to the incident laser axis, are sho%'n inFig. 4. When a single high-intensity beam is focused on a carbon target, as in the left hand image, alocalized region of copious 2wj, emission is observed. When this same high-intensity beam is incidentupon the longer scalelength plasma set up by the large-focus beam, the intensity of the 2w0 emission isnot detectable, as in the right-hand image.

The second surprising observation is in the x-ray emission. Time integrated spectra of I-SO keVx-rays are ohtaincd ,,ith arrays of PIN diodes and lphotonmuhiplier-scintillaor detectors. With the singlehigh-intensity beam incident upon a carbon target, x rays in the 10-50 kCV spectral range are easil%detected, as ind k:atcd in Vig. 5. llowe ,er, witi tihe same high-intensi . beam incident upon the longerscalelengili pl.isna, the intcnsity of x rays in this spectral region falls helo%% detection thresholds (sc;Fig 5). Ilh upper bounds on the x-ray flu\ at 50 and 20 keV represent reductions from the sinw h.-beam c .se hy factors of at least 3) and 1000. respecti\cl\ I hese reductions are consistent % itl ohr-vattons nmade in lnger-,.'lelength gas-jet targets at K.\IS."

2

At least two explanations might be offered to account for the observations of 2w0 and energetic xray emission. First, a longer scalelength near critical density may directly reduce the importance ofresonance absorption: this could explain the disappearance of both 2 0 emission and high-energy x-rays, and would indicate that the experimental conditions are such that the relative importance of vari-ous absorption processes is changing. The observations may also be explained by a reduced laser inten-sity at the critical surface, due to increased inverse Bremsstrahlung absorption or Brillouin scatter in theunderdense plasma. The increased reflectivity through the lens in these preliminary experiments isinsufficient to account for this, but measurements of scattered light at other angles, which have not yetbeen reduced, may alter the picture.

1I1. PLASMA PROFILE MEASUREMENTS

As mentioned above, measurements of plasma density, temperature, and velocity profiles are atleast as important in these experiments as measurements of absorbed energy, scattered light, and xrays. Without these measurements, scalelengths in hydrocodes may be varied to fit the experimentalobservations, and our confidence in the ability of these codes to extrapolate the physics correctly toreactor conditions is not increased.

To overcome the deficiency of previous coupling experiments. NRL is developing new methodsfor measurement of plasma profiles. All of these new methods have evolved from a techniquepresented at the 1981 Anomalous Absorption Meeting, which allowed the first visualizations of materia]flovlines froni laser-irradiated targets. 17 We use a special target, as shorn in Fig. 6. which has Al tracerdots embedded within a polystyrene (CH) substrate. Here, the dots are 25 Mim in diameter and arespaced by 50 j.tm center-to-center. Regions of Al flow from each of the dots are easily identified astracks of stronger emissivity in pinhole-camera images of x-ray emission abo'e I keV, because the Alline emission in this spectral region is much stronger than either the C" or I contiuum emission.

Examples of flow visualizations obtained in this wa) are shown in F-i. 7. These three images.obtained with different-sized pinholes on a single shot, show tracks of stronger %olume emissisit\resulting from the Al dots. Images obtained with smaller pinholes prooide better spatial resolution.while those obtained with larger pinholes give greater sen,,i'it and , Ih %isuaih/ation of the flow,further from the target. A more thorough treatment of the flow pattern., ma) he found in Ref. 17: theone property relevant to the present discussion is the distinctness of the streamlines. Since these x-ra%images are time-integrated over the 4-nsec x-ray pulsewidth (WNII\), the absence of smearing of thestreamlines suggests that we are in a nearly steady flow regime. Furthei experimental evidence for thisflow condition is obtained from streaked images of 3 w/j 2 emission, which imp]\ a nearly stationary n,/4surface.

i5

If we are, in fact, in a stcady flow regime, we may use the flow , isualli/ations in conjunction "itha measured density profile to infer the fluid velocity profile in the plasma. As indicated in Fig. 8. themethod relies upon the steady-state mass conservation equation, which tells us that the product of thedensity i in a streamtube, the cross-sectional arca A of the streamtube, and the fluid velocity v in thestreamtube is a constant. C. If we measure the density profile by interferometry or some other tech-nique, and %-e obtain the area A from the flow visuali/alions, %ke need only to eval~ate the constant Cin order to obtain absolute values for the vclociy. (Reclati ye values may he obtained \without ()F '"perinmenlall.. %e may obtain C b) imposing a boundary condition far from tle target %%here the xheli-cit) has reached a constant value: in this region, we equate the %elocity with that measured fadr from thetarget by tinie-of-Ilight ion detectors.

I)a. t lomon .i proof-of-principle experiment hi\,e been reduced using this model, as shown in Iw9 T'h, dnsit profile obtained interferonmetricall. shows a I/:2 delcndencc Of' the dcnsity moth diN-tince : f.it froll the tir .t boitinr of Fig 9) In this sane rcgion. the flow ,isuli/ations shrik jsphcr..dll di~c rvcn lflow. gisinv .1 prop ori onil to :2. Since the p1oduct ofl densit% and area is colnstntin thi. rc on. tie modcl of Iig. X inplies that the flow% ,colt\it. is constant (lop i(f I ig. '4), it is in this

3

........... ........ ~~... -.... ....................... -....... ....... I .................. llf

region that we equate the velocity to that measured in the far field by ion detectors. In closer to thetarget, the density variation changes and we begin to infer a change of the flow velocity from its far-field value. Interestingly, the region of nearly constant velocity extends inward approximately to then1lO surface. This could explain the fact that 13rillouin scatter from solid targets often seems toemanate from this lower density region s, velocity gradients may stabilize the Brillouin process at higherdensity. To infer the velocity profile for higher densities than 0.3 n, the limit of the 3 u inter-ferometric probe under these conditions, a technique for measuring the higher densities closer to thetarget is needed.

To access higher densities, we are developing an improved x-ray spectroscopic method, as illus-trated in Fig. I0.19 Ilere, a polystyrene target with a single embedded Al spot is used, but now the Alis serving as a localized source of x-ray line emission for spectroscopic diagnosis. The Al line radiationis collected by an imaging spectrograph with the entrance slit oriented to give spatial resolution alongthe laser axis. This technique has three major advantages over standard laser-plasma spectroscopy(where the target is entirely Al). First, emission is obtained only from a known volume within theplasma, rather than by integrating along the diagnostic line-of-sight through regions of differing densityand temperature; thus, local measurements are made directly, without the need for deconvolution.Second, effects of plasma reabsorption of the emitted radiation are greatly reduced, particularly if ahigher Z spot is embedded in a lower Z target, this simplifies interpretation of measured spectra.Third, the reduced size of the emitter leads to better spectral resolution because source broadening ofthe detected radiation is reduced.

To demonstrate this third point, data obtained with this new technique are compared with stan-dard spectroscopic data in Fig. 11. In Fig. I IA, a set of pinhole images from an Al target show that alarge volume of plasma participates in the x-ray emission, as one would expect. In contrast, pinholeimages from a single-spot target show a well-confined channel of Al line emission within a larger-diameter region of plastic continuum emission, as seen in Fig. I IC. The result of this reduced emitterdiameter is that better spectral resolution is seen in the spectrum obtained with a spotted target, in Fig.l I D, than is seen in the standard spectrum of Fig. II B. More details on this new technique may befound in Ref. 19.

With this improved spectral resolution, one expects that better comparisons between data andspectroscopic models will be made and that these will lead to improved density and temperature meas-urements. 20 A standard technique for plasma density measurement relies upon the ratio betw een thelie-like intercombination line (fie 23P) and the lie-like resonance line (He-) 21; the measured varia-tion of this ratio with distance : from the target is shown in the left-hand graph of Fig. 12. Collisional-radiative equilibrium mode's indicate that this ratio should fall monotonically with increasing densityexcept for plasma opacity effects very near to the target. 22 For z > 200 im, this expected behavior isobserved and leads to the solid portion of the density profile curve in the right-hand graph of Fig. 12.this yields densities up to 0.5 n,.. For - < 200 Am, we observe an apparent levelling off or even anincrease in the Ile 23Pllle- ratio. At this time, we believe that this is due to interfering spectral lineswhich nearly underlie the lie 23P line and increase relative to it as the density increases. In previousexperiments, the spectral resolution was not sufficient to distinguish these from the intercombinationline: with our greater spectral resolution, we are on the verge of resolving these lines. Were we tonai.cly apply previous models to the apparently saturated line ratio, we would obtain a density shelf at5 x I02" elcctrons/cm3 for z < 200gim. In fact, we believe the lie 2'P/llIc-a ratio continues to

decrease, as indicated by the speculative dashed curve. This would imply higher densities, as shown hythe dashed cure in the right-hand graph of Fig. 12; densities up to 2n, should he accessible With thistechnique. We are currently working on eliminating the prohlem by using a more detailed model.which should i :sult in reliahle measurement of these higher densities.

For tinipcrature determinations, We rel. upon intensity ratios bet ,en lle-like and Il-like R.d-berg lincs. lntlslt. a.iriations of three of the stronger lines With distance from the target are sho , n inthe left-hand side oif l:-. 12. and temperatures inferred from the ratios of these line-, are shown in the

4

right-hand graph of the same figure. For < 200 .m, the temperatures are speculative because theinferred temperatures are dependent upon the inferred densities which are speculative at this region. asdiscussed above.

One final note concerns a new, untested idea to improve the velocity profile measurement. Themethod described earlier in Figs. 8 and 9 suffered from three drawbacks: (I) it required the assump-tion of steady state, (2) it required simultaneous measurement of the density profile, and (3) it ga',eonly a time-averaged velocity profile. To overcome all three of these problems, we propose the use oflayered tracer dots, as shown in Fig. 13. By making the tracer dot from alternating layers of twomaterials which hae distinguishable x-ray emissivit), we should obtain a direct measure of the velocity

profile with time resolution. We may follow the front of each of these layers as it transits the blowoffplasma by imaging the x rays onto the slit of a streak camera, the resultant z. t curve of the frontdirectly measures the velocity profile. The time evolution of this profile is obtained from the multiplelayers, each interface gives us the velocity profile at one time.

IN'. STATUS REPORT

To summarize, studies of laser coupling in longer-scalelength plasmas which better simulate reac-tor plasmas are under,.ay at NRL, as indicated in Fig. 14. Preliminary observations do show increasedbackscatter. as expected. The concomitant decrease in second-harmonic and high-energy x-ray emis-sions may indicate that we are entering a new physics regime where longer scalelengths are reducing therelative importance of resonance absorption.

Because we realize that these experiments are best used to benchmark the codes that are used forscaling to reactor-sized plasmas, we believe that measurements of plasma profiles are at least as impor-tant as measurements of laser-target coupling. We have demonstrated one technique and proposed asecond improved technique for velocity profile measurement, these are the first techniques available formeasurement of the velocity profile, which is important in evaluating parametric instability mechan-isms. In addition, we have demonstrated an improved method for x-ray spectroscopic measurements,and we are d'velnping the necessary improved models for extraction of plasma density and tempera-ture. We hope to make more definitive statements on laser-coupling and profile measurements inlonger-scalelength plasmas in the near future.

V. ACKNOWLEDGMENTS

The dcvelcpment of x-ray spectroscopy as described in Sec. III would not have been possiblewithout the computational support of Dr. ). Duston. We also wish to acknowledge the expert technicalassistance of M. Fink, N. Noccrino, and I. Turbyfill. This work was supported by the U.S. Department

.of lFnerg) and Ollice of Na',al Research.

REFERENCES

I. J.J. Turechek and F.F. Chen, Ph)s. Rev. Lett. 36, 720 (1976).

2. R. .,. K. Bcrggren. and Z.A. Pietr,k, Phys. Rev. Lett. 36, 963 (1976)

3. A.A Oflcnherger. M.R. Cervenan, A.M. Yam, and A.W. Pasternak, J. Appl Ph.s. 47, 1451(1976

4. N II Burncit. II \ Ilald,,G.). Enright, M.C. P :hardson. and P II C rk um, J Appl Ph\s 48.1 , 1 19'"

5 \I J ll\ rh-t. C I (I.,tin. ind F.F. Chen. J. Appl. Ph.s 51. 408() ( lLM(1)

5

6. R.G. Watt, RD. Brooks, and Z.A. Pietrz~k, Phys. Rev. Lett. 41, 170 (1978).

7. A. Ng, L. Pitt, D. Salzmnann. and A.A. Offcnberger, Phys. Rev. Lett. 42. 307 (1979).

8. NU. Ilerbst, C.E. Clayton, and F.F. Chen, Phys. Rev. Lett. 43, 1591 (1979).

9. Z.A. Pietrzyk and T.N. Carlstrorn, App. Phys. Lett. 35. 681 (1979).

10. M.J. Herbst, C.E. Clayton, W.A. Peebles, and F.F. Chen, Phys. Fluids 23. 1319 (1980).

11. N.H. Burnett and A.A. OfTenberger, J. AppI. Phys. 45. 2155 (1974),

12. F.J. Mayer, G.E. Busch, C.M. Kinzer, and K.G. Estabrook, Phys. Rev. Lett. 44, 1498 (1980).

13. A.A. Otfenberger and A. Ng, Phys. Rev. Lett. 45, 1189 (1980).

14. l.A. Tarvin, F.J. Mayer, D.C. Slater, G.E. Busch. G. Charatis, T.R. Pattinson, RiJ. Schroeder.and D. Sullivan, Phys. Rev. Lett. 48, 256 (1982).

15. B.11. Ripin and E.A. McLean. AppI. Phys. Lett. 34. 809 (1979) and references contained therein.

16. C.S. Liu, M.N. Rosenbluth, and R.B. White, Phvs. Fluids 17, 1211I (1974).

17. MiJ. Herbst and J. Grun, Phys. Fluids 24. 1917 (1981)

18, MiJ. Hecrbst,. IA. Stamper, R.H. Lehrnberg. R.R Whitlock, F.C. Young. J. Grun. and B.11. Ripin.to appear in Proceedings of the 1981 Topical Conference on Symmetry Aspects of lnertial FusionImplosions, ed. by S. Bodner, NRL.

19. NIT. Ilerhst, P.G. Burkhalter, R.R. Whitlock, J. Grun, and M. Fink, NRL Memorandum Report4812, 1982 (to appear in Rev. Sci. Inst.).

20. P.G. Blurkhalter. %U. Ilerbst. D. Duston. R.R. Whitlock, and 1. Grun. Proceedings of 1982 IEFEInternational Conference on Plasma Science and NRL Memorandum Report (to be published),

21. V.A. Boiko, S.A. Pikuz, and A. Ya. Faenov. J. Phys. B 12, 1889 (1979).

22. 1). 1)uston and J. Davis, Phys. Rev. 21A, 1664 (1980).

6

tI

E K< 250Jt = 3-5 nsf /6, d50 ~ 801Am

I < 1015 W/cm 2

Ln (nC/10)< 200pimI it I - St.indird arrangement for laser-coupling experiments uses a tightlh focused beam to achievehigh intensii. At NRI.. a single hern v.ith 250 J in 3-5 ns can be focused to 80 Acm diameter spot (50',.energ) content) h, an r/ lens. gi, ing incident intensities up to 101' % /cm2 . In this case. piasmas can begenerated siih d.'nsilt gradient scalelengths at nI10 which just exceed 200 j.m

I '

Fig. 2 -Nose) configuration of two-beam laser allowsproduction of longer-scalelength plasmas for couplingexperiments. One beam with 3-5 nsec pulselength isbrought to large focai diameter ( mm) to producelonger scalelengths (L, 250-600 jAm at n,110

),

while a second beam is tighti) focused within the firstto produce higher intens;ties of interest The pul-selength of the high-intensity beam may be shortenedto minimiwe its perturbation to the Iong-scl kkngthflow.

3-7 FOLD BACKSCATTER INCREASES

AT MID-1013 (5 ns) AND MID-1014 (<0.5 ns)

WHEN LARGE-FOCUS BEAM PRESENTFig, 3 - Sumimary of preliminary baickscattcr ik)ers Jtiiins

a

2 coo IMAGES:STANDARD vs. LONGER SCALELENGTH

g1 mm

(11938) (11940)

STANDARD LONGERTL < 0.5ns SCALELENGTH

At = 5.4nsFig 4 - Comparison of time -intkgratd images ofr second harmonic emission for to modes oroperJtion 1 le Ilser is incident from he eli and the m.age% ire negatices V, ti a single high-intensity heam, the imce on the left %hows copious 2.,0 emission Ahen the same high-intensit,beim is focused into ai longer-sclelength pl.sma. ,i hown in Fig 2. the

2I. 0 emission disappeair%

1 he del.iv of the shori-pulse. high jntensii hearn is 5 4 nsec after the peak of the longer pulse

E9

HIGH-ENERGY X-RAYS:STANDARD vs. LONGER SCALELENGTH

10 \Zk

X.

STANDARD

MID-1014 W/CM 2

r _L < 0.5 nsLU 111938

X 10- 3

_j

1o- 5LONGER SCALELENGTH

At = 5.4 ns1 (1194011

0 20 40 60X-RAY ENERGY (keV)

I ig 5 - Cuni rtson of high-energ xra specir i Cor two fllodC' (Cf 'Ix'r.iun Aith a mngle. shori-JpUhe, hth lnmit

bicjn. ijn %-rau juL, Lrre~pndne to 7,, -7 kcV is obscrced This ii [all hclo [li dclection threshold hirj tie

',cLiclength i 'n).g I lie dcI% , (it' th hori-iuikc. hei-ntn i m isrn~ 4 ncc hlwr the lc.jk (It Ilc hkmer pulK'

CH TARGET

Al DOTS

LASERLIGHT CONE

X-RAY PINHOLE CAMERAFig 6 -Sthcrnmitic: rilustration of the experintlI arrangzcrent for ',isujhzl~dion of h.%drodynamic flows.

Fig 7 -Tirnc integrjoed miages of x-ray enliivo obtairnci for single laser shot wit 13 28, ind 54 m diameterplh:' User is inuint front left, aind or.Igcs dre rice,,toc Camra fitler is noininjik Is A ni thick fie 23~0 J oitijser ertcrg) is fusdto 940) umi diantcer spot Of) energy content) to gij e 1, p 8 )i l 'A~ /crn on O ' ni thik 1OfI tartmc

12

STEADY-STATE MASS CONSERVATION

n A v = constant, C

CV -

nA

BOUNDARY CONDITION:v,,,, FROM TIME-OF-FLIGHT DETECTORS

Fig. 8 - Model for inferring fluid velocity profile.

13

Io

I

DENSITY AND FLOW VELOCITYPROFILES BELOW 0.3 nc

EL = 35J d0 650m 19O 2 x 1012 W/cm 2 dplasma 620m

5 x 107

> .L

• 'E 3x107

L) 2x 1070U.

1 x107

3 x10 20

I

z- 1 x 1020

U)w E

o .-0

M.I •1 1x1020

Lu

II I I

0 100 200 300 400 500 600 700

SHOT 10837 DISTANCE FROM TARGET (mim)lig 9 - Sample of data rcduc cd using model of Fig 8. Density profile is obtained interfcrometricall)

wilh short-pulse (r L < 0 5 ns) 3w0 probing beamin

14

EMBEDDED Al SPOT

SPECTROG RAPH

LASER FOCAL SPOTI ig 10 E Ixperimental irrangemcflt fr spot spciro)%opy

15

(A) (B)

)IA) 6 8

MM LJ Ii

(C) (D)

Fig. II - Qualitative comparison between data obtained with Al foil target and data acquired using C plastic target locallyembcdded with Al. the vertical axis for (A) through ()) corresponds to the laser axis, with the laser incident from above andthe target surface at bottom. (A) is obtained wiih Kodak 3490 film, and (B) through (D) are on Kodak No-Screen Film. (AlX-ray pinhole camera images, obtained with an array of pinholes (5-55 Mm diameter), for an Al foil target. Laser intensity/0 = 3 x 10l \,'/ Cm2

. due to 100 J focused to 1100 Mm diameter spot (90'Yo energy content). (B) Spectrum obtained for Al foiltarget at I) - 8 x 102 W/cm2. with 110 J focused to 600 Mm diameter spot. (C) Pinhole images as in (A), but for CH target

embedded with 180 Am diameter Al spot. 225 J of laser encrgy focused to 9 0 0 Mum diameter spot yields 10 - 8 x 1212 W/cm

2 .(D) Spectrum from same shot as (C).

16I.

n8 AND T. FROM Al-SPOT SPECTROSCOPY

10- 10 -

He (3 p) /He a

0- >

0~ He0.5 0

He3 0-0.3-

Ha

___ ___ __if_ 00.1 200 400 600 0.1 200 400 600

z (P~m) z (P.m)

Io=7.3 x 1012W/CM 2 d~o 1mm E =273J TL = 4ns 1115061

Fig. 12 - Preliminary reduction of spot spectroscopy data. Left-hand graph shows spatial variation of intensities of He-like aand ai lines and of11l-like a line, as well as of ratio of Hec-like inlercombination to resonance lines. Right-hand graph showAsdensityv and temperature information extracted from line ratios within spectrum. Note that dotted portions of density and tern-pcraturc proliles are based upon speculative extrapolation of lie 3P/IHea ratio shown in graph at left

17

rLASER FOCAL SPOT

Fig. 13 - New idcj for Iinmc-resolved measurement of velocity profile. Illusitrdtion ati left shows that we use laterally localizedtrdccr. as per spot %pctroictp) technique. Cross-section of target at right, however, shows that embedded spot is nov% madeof ;altcrnating layers of two mitcrials. which abldte sequentially in time during liscr irradiation.

18

STATUS REPORT

I. LONGER-SCALELENGTH EXPTS.UNDERWAY

" INCREASED BACKSCATTER" DECREASED 2 coo & HIGH-ENERGY

X-RAYS

1I. DIAGNOSTIC DEVELOPMENTCONTINUING

" FIRST TECHNIQUES FOR V PROFILE

" SPOT SPECTROSCOPY FOR n, TH-g 14- Summaryof worklo-dat

'9

APPENDIX L

S E C u R I T Y C L A S S I F C A T I O f O f T IS P G E ( h e n D a t a L t e r e d )I

REPORT DOCUMENTATION PAGE BEORD INSTRUCTIONSFORMI REPAT NUMBER 2 GOVT ACCESSION NO. I RECIPiEkT'S CATAL.OG NUMBER


4 TITLE (-t )S TYPE OF REPORT 6 PERIOD COVERED

NEW MEASUREMENT TECHNIQUES USING TRACERS Interim report on a continuingWITHIN LASER-PRODUCED PLASMAS NRL problem.

6 PERFORMING ORG REPORT NUMBER

7. AUTM4OR(,j B CCNTRACT OR GRANT NUMBER(.)M.J. Herbst, P.G. Burkhalter, D. Duston, M. Emery,

J. Gardner, J. Grun*, S.P. Obenschain, B.H. Ripin, R.R. Whitlock,J.P. Apruzese and J. Davis

I. PERFORMING ORGANIZATION NAME AND ADDRESS 10 PROGRIAM ELEMENT, PROJECT, TASK

AREA 6 WORK UNIT NUMBERSNaval Research Laboratory DOE AI08-79DP 40092(172);Washington, DC 20375 47-0859-0-3; DNA 62715H;

47-1606-0-3I'. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

U. S. Department of Energy January 6, 1983Washington, DC 20545 If NUMBIER OF PAGES

3514. MONITORING AGENCY NAME A ADDRESSNII dIlle-I from Controlling Ofiier) IS. SECURITY CLASS. (o tis report)

UNCLASSIFIEDIS.. DECLASSIFICATION, DOWNGRADING

SC.EDULE

1b. DISTRIBUTION STATEMENT (ol tli Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the Abstracl oIteod In Block 20, It different from Report)

1I. SUPPLEMENTARY NOTES

*Present address: Mission Research Corporation, Alexandria, VAThis work is supported by the U.S. Department of Energy, Office of Naval Research andDefense Nuclear Agency under Subtask I25BMXIO, work unit 00015, and work unit title"Laser Plasma HIANE Simulation Experiment." (Continues)

I1. KEY WORDS (Continue on to--e00 aide It neco."oo y and Identfy by block n.be,)

Plasma diagnostics Fluid flow visualizationLaser-plasma interactions Rayleigh-Taylor instabilityX-ray spectroscopy

20, ABSTRACT (Conlil.. , ,or*@. Ids It necessary ad Idenllfy by block ntumb.)

The use of locally embedded tracers within laser-irradiated solid targets has led to a new class of diag-nostic methods for laser-produced plasmas. Demonstrated uses of tracers include the first visualizationsof hydrodynamic flow of laser-ablated material and improved spectroscopic measurements of plasmadensity and temperature profiles; comparisons with a two-dimensional hydrodynamics computer codeare shown. Proposed future uses of tracers include the first measurements of fluid velocity profiles andimproved dcterminations of mass ablation rates.

DD O, 1473 EOITON O 1 NOVA IS OBSOLETE

$/T 01C CA014-6.01SErCuRITY CLASSIFICATION OFf T.IS PAGE (eo om Dore &now"*(*)

18. Supplementary Notes (Continued)

This paper was prepared for presentation at the Sixth International Workshop on Laser Interaction

and Related Plasma Phenomena held in Monterey, CA on October 25-29, 1982.

S907UMNIY CL ASSIICA1,ON OF TI..S PACE(Wh. D.c. E1.19'*)

CONTENTS

I. INT RO D U CT IO N ..................................................... 1

II. FLUID FLOW VISUALIZATIONS AND THEIR USES ......................... 1

A. Shape of the Visualized Flows ....................................... 3

B. Sizes of Visualized Flows ........................................... 8C. Flow Visualizations with Intentionally Perturbed Laser Intensity Distributions ... 10

D. Detection of the Rayleigh-Taylor Instability ............................. 10

III. SPOT SPECTROSCOPY: IMPROVED DENSITY ANDTEMPERATURE MEASUREMENTS ..................................... 12

A. The Experiment ................................................... 12B. Density and Temperature Profiles ..................................... 14

C. Caveats and Future W ork ........................................... 18

IV. LAYERED TRACERS: VELOCITY PROFILE ANDABLATION RATE MEASUREMENTS ................................... 19

V . SU M M A R Y ........................................................... 19

VI. ACKNOW LEDGEMENTS ............................................... 21

R EFER EN CES .... ................................................... 22

iii

NEW MEASUIEMENT TECIINIQUES USING TRACEIS

WITHIN LASER-PRODUCED PLASMAS

i. IPT OOUCT Iu,',

Many of tne physical processes einich are important to tne ablatlve-coi,dression approach to laser-pellet fusion are intinately relatec tcplas,,ia density, temperature, and velocity profiles. Inverse hremsstran -nabsorption and parametric instabilities are closely coupled with underg '3eplasma profiles. Similarly, energy transport Detween the critical dersitsurface ana the ablation surface is interrelated with overaense plas.aproriles. Therefore, laser-plasma interaction experiments can betteraddress these physics issues if they include measurements of tre plasi;,:,profiles. If experiments are pertormed in pVanar rather than sphericalgeometry, tne problem becomes two-dimensional since the plasma profiles ancthe above-mentioned physical processes are affected by lateral flow ofenergy out of the finite focal spot. Une then desires measurements of thearea over which the absorbeo energy is distrinuted and, if possible, ofboth axial and lateral profiles.

A new genre of diagnostic methods is being developed at the NavalResearch Laboratory to address these and other problems. The uniquefeature of tnese new methods is the use of tracer materials which arelocally ernedded into the solid target to be irradiated. Tracers which arelocalized within the focal region remain localized within the blowoffplasma, due to the collisional or fluid nature of the flow of materialablated from the target. By imaging characteristic radiation from a lineararray of such tracer dots, we have demonstrated the first visualizat ions ofthe hydrodynamic flow of material within laser produced plasmas; thistecnnique and its applications are discussed in Sec. II. As described inSec. I1, improved measurements of plasma density and temperature profileshave also been demonstrated, by sinq the tracer dots as local sources ofspectroscopic diagnostic lines. Comparisons witn these measurementsprovide the most direct calibration of hydrodynamics computer codes,because plasma protiles are the experimental observables most closelycoupled to mechanisms of energy absorption and transport in laser-producedplasmas. Tnerefore, comparisons betaeen experiments and the Naval ResearchLaboratory nydro-codes are found throughout Secs. II and III. In Sec. IV,the use of layered tracer spots is proposed for time-resolved reasurementsof fluid velocity profiles and for improved measurements of mass ablationrates.

II. FLUID FLU' VISUALIZATIONS AND THEIR USES

The simplest use of tracer dots is for visualization of thehydrodynamic flow of material from the laser irradiated target, for whichthe experimental arrangement is as shown in Fig. 1. The distinguishingfeature of this configuration is the target: thicK polystyrene [(Ch)>]with a linear array of 25 wm diameter, aluminum tracer dots. These dotsare embedded So that their initial surfaces are flush with that of the

surrour,.inj tdrjet, and their thicknesses are chosen to exceed tnu expectedablation deptn on any given shot. itn the tracer spots alignel to tallaIon,; dia'.;meter ot the laser-irradiated region, between 10 dnd bOO J ot

d-l aser enrJy $. = 1.054 pim) is brouut onto the target in a 3-5 nsecpulse. A calnera with an array ot pinholes is used to obtaln time-

M.inu,.'rp) ippru, .d [).c.mb-r 9. 1 9 '2.

--- J ll N • nminili /i nli ll 1

t

CH TARGET

LASERLIGHT CONE

X-RAY PINHOLE CAMERAFig. 1 Experimental configuration for visualization of hydrodynamic flow.

2

integrated images of x-ray emission at 900 to the target normal. The 15 wmberyllium filter used on the camera allows imaging of photons with energyhv > 1 keV. Since aluminum line emission is more intense than carbon orhydrogen continuum emission in the spectral band of the pinhole camera,streamlines of material flowing from the aluminumn spots are identifiable astracks of strong x-ray emission in the images (see Fig. 2).

Flow visualization experiments have been performed at a variety oflaser focal conditions with incident inten5ities 190 (av raged 2within the90% energy-content diameter d90 ) between 10 and 2 x 10

shot, a series of laser isointensity 4patterns is recorded in an equivalentfocal plane to that of the target, with a factor of 2.2 in intensitybetween successive patterns. From these records, we may plot focalintensity distributions, such as those shown in Fig. 3. (These one-dimensional profiles represent azimuthal averages of the real two-dimensional profiles of the laser; these are used as input to the hydro-codes.) Note that the focal distribution near best focus of our f/6 lensis qualitatively different from that in the quasi-near field. The mostobvious difference is near the center of the distribution, where largefocal spots tend to exhibit local minima in intensity. Equally important,however, are differences in the wings of the distributions, as will bediscussed in Sec. 11.8. It should also be noted that intensities 15?(averaged over 50% energy content diameter d- ) and I (peak intensitytend to be higher than 190 by factors of 2 and 4, respectively.

While we have not conclusively demonstrated that the presence of thetracers does not perturb the visualized flow, there is some evidence thatthe perturbation should be minimal. First, the fully ionized massdensities for Al and (CH) differ by only 12% at a given electron densityin the blowoff plasma. moreover, the average velocity of ablated ions asdetermined by Faraday cups is the same for the two materials.

In the following sections, the various physics issues that may beaddressed by flow visualization methods are discussed. The shape of thevisualized flows, as shown in Sec. II.A, is related to the outwardhydrodynamic flow of plasma, and provides a valuable check for thehydrodynamics codes. In Sec. II.B, we present the observed sizes of thefluid sources under various irradiation conditions; this should indicatethe degree to which absorbed laser energy spreads laterally as it flowsinward from the absorption region to the ablation region near the edges ofthe focal spot. Lateral energy transport can also be important near thecenter of the focal spot if the irradiation there is nonuniform.b '° Flowvisualizations obtained with intentionally perturbed laser beamsqualitatively show this effect,6 as described in Sec. II.C. Anotherproposed application for these flo%, visualizations, outline in the finalsection, is for diagnosis ot the Rayleigh-Taylor instability.

A. Shape of the Visualized Flows

While the size of the observed fluid source varies with laserintensity and spot size, the shape of the flow pattern seems to beremarKably constant. As shown in-Fi-. 2, streamlines curve away from the

3

TI

Fig. 2 Five flow visualizations obtained on a single shot with 5, 9, 13, 28,and 54 jim diameter pinholes. The laser is incident from the rig,and the target surface is to the left. 190 3.2 x 10

d o 1470 pam, and the laser energy is 212 J.

4

... 4

1 05

BEST FOCUS

1 04

103~

1 mm SPOT

Zx x

10-

-900 -600 -300 0 300 600 900RADIUS (lpm)

Fig. 3 Azimnuthally averayed laser energy profiles for best focus of our f/6lens and position in the quasi-near field where d go 1075 Pm.

5

target normal at a rate which depends upon r/r^, where r is thedisplacement of a given streamline from the center of the fluid source andro is the radius of the fluid source. Each streamline attains a constantdirection within a distance z = r from the target surface; beyond z = ro,all streamlines are following straight-line paths corresponding to a far-field, spherically diverging flow.

The shape of the visualized flows is in good agreement with NRL's two-dimensional hydrodynamics codes. As shown in Fig. 4, the measuredstreamline angles 6 relative to the target normal are well predicted by acylindrical (r and z) hydrodynamics simulation of the Sxperiment. Thecomputer model, described elsewhere in these proceedings, uses a sliding-grid Eulerian mesh with flux-corrected transport, classical T5/2 thermalccnduction, and inverse bremsstrahlung absorption. The calculation usesthe measured laser pulse duration and an azimuthal average of the measuredlaser focal distribution (such as those in Fig. 3). The slight asymmetryof the experimental data about r = 0 is a gentle reminder that real laserprofiles are not perfectly symmetric, but prohibitively expensive, three-dimensional codes would be required to accurately simulate such focalnonuniformities. While Fig. 4 shows agreement at one distance z from thetarget, sets of such plots at varying z convince us that the code iscorrectly calculating the shape of the flow.

The fluid nature of the flow is not surprising, since the plasma radiiare much greater than the ion-ion collision mean free path. The fact thattime-integrated flow visualizations compare well with snapshots of thecode, as in Fig. 4, suggests that we may also have a nearly steady flow;this is not entirely unreasonable, since the laser pulse length exceeds theacoustic transit time across a plasma radius. Experimental evidence thatthe flow is nearly steady, at least during the period of maximal x-rayemission, is obtained from streak photography of images of 3/2wo emissionfrom the n /4 surface . The position along the laser axis of this surfaceappears reiatively stationary for the duration of the 3/2wo emission, aperiod of up to 3 nsec near the time of peak laser intensity.

The shape of the flow affects far-field particle diagnostics such asion collectors or plasma calorimeters. First, the angular distribution ofablated mass observed by these diagnostics may be determined by thecollisional flow near the target, which imparts a fluid velocity directionto each fluid element. As the material drifts through the collisionlessregion further from the target, some lateral spreading of material resultsfrom random thermal motions; sinc- directed ablation velocities aregenerally much greater than ion thermal velocities, this should not greatlyincrease the angular range set by the fluid flow. Indeed, charge collectorand plasma calorimeter measurements indicate that half of the ableted massappears in a cone about the target normal with a 40' half-angle; this isconsistent with the angular spread inferred from flow visualizations.

Ion detectors are further affected because the flow, except for anysmearing due to thermal expansion in the collisionless region, mapsdifferent regions of target surface into different diagnostic solidangles. A single ion detector at a specific angle far from the target then

6

VECTOR FLUID FLOW AT Z 85/um2-D CODE vs EXPERIMENT

500

4Q00

2-D CODE

3Q0T

eI

2000-4q

, ,10 0

II

-350 -175 0 +175 +350

RADIUS (Lm)

Fig. 4 Comparison between measured and calculated streamline angles 0relative to the target normal as functions of the radial displacementfrom the center of the flow. Values are taken at one distance z =85 pm from the target surface. Th? calculation uses measuredexperimental conditions: 190 2 x 10 W/cm', d90 650 v laserenergy is 35 J.

7

samples only a portion of the irradiated region. To measure parametersaveraged over the focal spot, one should use an array of detectors at arange of angles. The error that may result if too few detectors are useddepends upon the uniformity of the laser illumination at the target, theratio of the directed ablation velocity to the ion thermal velocities, andthe solid angle subtended by the detectors used.

B. Sizes of the Visualized Flows

The sizes of the visualized flows are well-defined and usefulobservables. From the flow visualizations, we define the fluid source sizeto be the diameter of the region at the target surface from whichstreamlines are seen to emanate. This quantity does have physicalsignificance; as discussed below, it most likely reflects the diameterwithin which the plasma temperature is high enough for excitation of Al K-lines. It is also a well-defined quantity, in the sense that it is notextremely sensitive to the size of pinhole used to detect the x-rays. Asseen in Fig. 2, the same number of streamlines is observed in the threelargest pinhole images, despite a factor of 17 variation in pinholecollection efficiency. This may indicate the rapidity with which thetemperature is falling at the edge of the x-ray images. The advantage ofthis observable over the size of standard pinhole images lies mainly in theease of observation. The size of standard images is usually sensitive topinhole size. In order to define a plasma size, one must densitometer theimages, deconvolve the pinhole size, and invert the data to obtainisointensity contours of x-ray emission.

The observed fluid source diameter do varies with laser intensity andspot size. As indicated in Fig. 5, do increases with laser energy at fixedspot size and increases with spot size at fixed laser energy. Oneinteresting observation is that the sensitivity of do to laser energy isgreater for the smaller focal spot sizes. Several possible explanationsexist for such an observation: there is the potential effect of higherlateral thermal conductivity, which could result from higher plasmatemperatures at the higher intensities, as well as the possibility ofincreased lateral flow due to fast electrons. A closer look at the shapesof the wings of the laser focal distributions in Fig. 3 suggests anotherexplanation. By locating the position within the focal distributions atwhich a given intensity occurs and plotting the variation of that positionwith increasing laser energy, we generate curves such as shown in Fig. 5.Within experimental uncertainty (approximately a factor of 3)' theintensity for both curves shown in Fig. 5 is 2 x 101 W/cm Thecorrelation with the data points suggests that the edge of the fluid sourceconsistently occurs at that particular intensity in the wings of the laserfocal distribution. This could be explained by the existence of athreshold intensity for heating to a temperature at which th' Al K-linesare excited; this heating could be directly due to laser energy depositionor could be due to laser heating to a temperature at which the thermalconductivity allows lateral transport of energy from higher intensityregions. It is not likely that intensity thresholds for ionization of thetarget play any role in determining the fluid source size, since the two-dimensional hydrodynamics codes calculate the flow pattern correctly (see

8K

1500I~ mm

SPOT

w 00

Ucr-:)0W BEST

oFOCUS

- 500-

0

N

0 I50 100 150 200 250

LASER ENERGY (J)

Fig. 5 Variation of fluid source diameter (data points) with laser energy forthe two laser focal conditions shown in Fig. 3. Curves show thelocation of 2 x 10" ' W/cm intensity in the wings of the focal profileas function of laser energy for these same two focal conditions.

9

Fig. 4) while assuming initial ionization everywhere on the target.

If the fluid source size is entirely determined by the shape of newings of the laser focal distribution, one might infer that the effects oflateral energy transport at the edges of the focal spot are minimal or trn!the lateral energy flow does not result in a high plasma temperature at trefocal periphery. This empirical observation may be purely coincidental,however. Furtner comparisons should be made between the experiment andcode at a variety of intensities and focal spot sizes before such aconclusion can be drawn.

C. Flow Visualizations with Intentionally Perturbed Laser Intensi .yDistributions

Lateral energy transport between absorption ana ablation surfaces canalso be addressed by flow visualizations in the presence of intentionallyimposed laser nonuniformities. This diagnostic complements targetacceleration experiments, where velocity modulations Av/v hgv? beenmeasured as a function of imposed intensity modulations L 5II;5 , , l withthe tracer technique one hopes to access the modulation in ablationpressure AP/P which couples Av/v to 41/1.

The idea is qualitatively illustrated in Fig. 6, where two flowvisualizations are compared. The upper image is obtained with a deeper andwider intensity minimum imposed into the center of the focaldistribution. Under these conditions, target acceleration resultsindicate little smoothing of the intensity modulation by lateral thermaltransport between absorption and ablation surfaces. Indeed, the flo.wvisualization shows two seemingly independent fluid sources, with nodetectable ablation from the central region where the intensity is low. Incontrast, the lower image is obtained at higher average irradiance, with ashallower and narrower intensity minimum in the center of the beam; underthese conditions, smoothing %f the intensity modulation is observed in thetarget acceleration studies. Flow is now seen from the center of thefocal region, although compression of this region due to inward flow ofsurrounding streamlines indicates that there is residual pressuremodulation. More quantitative analysis of pressure modulations requirescomparisons of flow visualizations with the code or development of newtechniques discussed in Sec. III.C.

D. Detection of the Rayleigh-Taylor Instability

Another potential use of the flow visualization method is for7observation of hydrodynamic instability of accelerating targets. Two-

dinensional hydrodynamic simulations of foils unstable to Rayleigh-Taylorgrowth have shown that nonuniform ablation fr? the target surfaceaccompanies the nonlinear state of the instability. In the extreme limitof bubnle-and-spike formation, these computer calculations show that all oftne plasma flowing from the target can be emanating from the tips of thespi kes, while none flows from the target surface in the regions of thebubnles. Preliminary flow visualizatin experiments have been performed tolou< for this nonuniform ablation, using targets with periodically

10

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.4 4- -4 4 r

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perturbed Is eal densities to seed instability growth at gi venwavelengths. The use of these perturbed targets also allows one toselectively deposit the tracers at locations which are expected to developinto the spikes of the unstable target; one can then look for the tracermaterial to appear everywhere in the blowoff, signifying the expectednonuniformity in ablation. These preliminary experiments have producedflow patterns which show qualitative1 deviations from the usual patterns,but they are not yet fully explained.

III. SPOT SPECTROSCOPY: IMPROVED DENSITY AND TEMPERATURE MEASUREMENTS

A natural extension of tphe tracer technique is into the area ofspectroscopic plasma diagnosis. As pointed out in Sec. II, it is thestrong line emission from the ablated tracer material which allowsvisualization of 25 p m diameter streamlines within 1 mn diameter plasmas.These emitted lines can Nso serve for spectroscopic measurements of plasmadensity and temperature. The new technique, spot spectroscopy, has threemajor advantages over standard spectroscopic methods. Standardspectroscopic measurements are integrated along a diagnostic line of sightthrough an inhomogeneous plasma. One could use straightforward inversiontechniques to obtain spatially resolved emissivites from the chord-integrated data if the plasmas were optically thin,1 4 but effects of plasmaopacity on the radiation exiip the plasma are non-negligible at thehigher densities of interest. ' , A more complicated inversion technique

might also account for the spatially varying opacity; however, the moretypical . procedure has been to predict the plasma profile with ahydrodynamics computer code and to compare the experimentally observed

spectrum with those clculated for chord integrations across theinhomogeneous plasma. In that case, one is dependent upon thecorrectness of the hydrodynamics model as well as the atomic physics model,and one would obviously prefer to make more direct determinations ofdensity and temperature. Two of the three advantages of spot spectroscopyalleviate these problems of standard spectroscopy: 1) the localized source

of spectroscopic lines should eliminate chord integration across aninhomogeneous plasma, arid 2) the smaller source size also reducescomplicating effects due to plasma opacity. The third advantage of spotspectroscopy is that better spectral resolution can be realized, sincespectral resolution with standard x-ray spectroscopy is usually limited bysource broadening due to finite plasma size.

A. The Experiment

Except for the presence of the tracer in the target, the experimentalarrangement for the new technique is much the same as for standard x-rayspectroscopy. As shown in the illustration of Fig. 7, the target has asingle aluminum tracer spot embedded in the center of the focal region; thevariety of laser irradiation conditions used are the same as those used forthe flow visualization technique (see Sec. Ii). Aluminum line radiation inthe 5-8 A spectral region is collected by an x-ray crystal spectrographwitr, a viewiny axis parallel to the target surface. The spectrograph slitis oriented to yield spatial resolution in ne direction along the laser

12

EE

-L

V4- .0 < >~ --

__ 0a E .

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13

axis; resolution in tine otner teio spa ial imension s res:is frcknovaledge of tne position of tre l]calizeo tracer witnir tre focal s--;.The spectra are recorded on Kocja No-Sc-reen fi ir, tr wnicn a *i1l m;ccc "ibased upon an aosolute calibraic S i va ile. A beryiu fiternominally 15 um thickness procects tre film trom viSiDle exposcr_.

More specific conoitions depend upon tne goals of tne paric experiment. As witn standarI x-ray spectroscopy , one may va r the cr-type and geometry, the spectrc,.racpn slit wictn and magnification, ar -reslit-to-target distance in oroer to acnieve tne optimal traceott ee ,spectral resolution, spatial resolution along the laser axis, 8r:sensitivity. An additional variazle availatle with spot specrosc.-.-r isthe diameter of tne embedoed tracer; this allows one to specify sa aresolution in tne direction lateral to the laser axis, but it also impacsacnievable spectral resoljtion ano sensitivity. Tne specific choice ofparameters for the present ','orK are the sa!-e as those listed in Ref. 2.

Data obtained witn tne re,. tecnnicue do show the expectec improve:-ein spectral resolution. ).itn an a3jminun foil target, as sno , n in Fig. 7,the spectral widths of tne lines near tne target surface are quite orca:;the widths exceed those expected for other broadening mechanisms, arcreflect source broadening due to the large Al plasma extent transverse tothe laser axis. Also show.in in Fig. 7 is a spectrum obtained using a (C.'target with an embedded Al oct. Line widths near the target surface aremuch narrower, and sets of lines are clearly resolved that are not resol'eicin the Al foil spectrum.

B. Density and Temperature Profiles

Several features of the experimental spectra may be used indeterminations of plasma density and temperature. In the present work, .,eextract temperatures from intensity ratios of various helium-li~e (Al X":1ionic lines to nydrogen-liKe (Al XIII) ionic lines. ThEse ratios arecompared with calculated ratios from a cylindrical plasma/atomic physi-smodel of a finite, homogeneous plasma with diameter equal to the measuredtracer plasma diameter. 2 1 At least four methods exist for dens, -.determination: 1) the often-used technique based up22 the ratio bet,,eenthe helium-like resonance and intercombination lines, 22) a Wiethoo baseiupon the r~tio between t o helium-like satellite lines (ls2s -S 2s2p Pand is2p P - 2p )p) 3) Stark profile analysis of higher kydtergmembers, and 4) profile analysis of opacity-broadened lines near the tar-etsurface. To date, we nave exploited the first two methods, though we havediscovered a need to modify the first inethod wh'en comparing witn tneexperiment; preliminary work is underway on the two remaining techniques.

A problem with pr - ious models for density measurement is identifiedduring data reduction. Variations of intensity of various spectralfeatures with distance froii the target are plotted in Fig. 8. Plots aresno,n of the three strongest helium-like and hydrogen-like lines used indetermining temperature, but tne more important curve in the figure sroGstne /ar ation ot the ratio of tne helium-like intercomoination (He-P) anresonance (He ,) lines. As m entioned above, this ratio is routinely used

14

10-

He (3 P)/He a

,,oHe

He/3

H a

0.1 I

200 400 600z (/.tm)

190 7.3 x 1012W/cm 2 d90 =1 mm E = 273J TL = 4ns (11505)

Fig. 8 Variation of spectra' intensities of helium-like a and B and hydrogen-like x Rydberg lines with distance z from target. Also shown is thevariation of the ratio of the helium-like intercombinatior line to tneresonance line. The tart is LCH) with a 65 pm diameter, embeddedAl spot. 1 - 7.3 x 10 W/cm within dg- I mm and the laserenergy is2M J.

15

.A

AD-A130 408 EXPERIMENTS ON THE.0 NAMICs AND H ODRODYNAMICINSTABILITIES OF ABLA TIV ELY ACCELERATED TA RGETS UM SSION RESEARCH CORP ALEXANDRIA VA FEB 83

UNCLASSIFIED MRC/WDC-N 050 SBI-AD EOl 441 F 24 NL

MENOMONEE lK

IL2

1.8

MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS -I963-A

for density measurement. Collisional-radiative equilibrium (CHE) modelsindicate that this ratio should fall monotonically with increping densityexcept for plasma opacity effects very near to the target. For z >200 um, this expected behavior is observed and leads directly to measureddensities up to 0.5 nc . For z < 200 urm, however, we observe an apparentlevelling off or even an increase in the line ratio; were we to naivelyapply previous models to this data, we would infer a density shelf of n =0.5 nc for z < 200 urm. With our improved spectral resolution, we canalmost resolve-satellite lines which nearly underlie the long-wavelengthside of the intercombination line, and interfere with the intercombinationintensity measyreyent. These linss, identified ais the lithium-like s,tsatellites [Is2s S -/ s(2s2p'P) P3./2 and Is2s SI/? + Is(2s2p P) Pare seen in the CR' calculations to increase in intensity relative to tleintercombination line as the density increases. When the sum of thecalculated intercombination and satellite intensities is compared with thedata, mesured densities continue to increase for z < 200 urm, as shown inFig. 9." The densities measured in this way are then in reasonableagreement with those measured for z < 100 um using technique (2) of theprevious paragraph; for z > 100 urm, no -such comparison is possible, becauseof insufficient intensity in the helium-like satellite lines.

The density and temperature profiles measured in this way are in fairagreement with those calculated using the two-dimensional hydrodynamicscode. Error bars on measured densities are shown only for z < 100 urn,where they reflect the range of values from the two methods avaTlable inthat region; error bars for z > 100 um are not necessarily any smaller, butare more difficult to estimate. Even without these experimentaluncertainties at the lower densities, agreement in Fig. 9 is seen to begood. Agreement is not quite as good between the calculated and measuredtemperature profiles in Fig. 9. Temperatures near the target (z < 100 Vm)and beyond the point of peak temperature (z > 400 um) are-in goodagreement, but the details of the intermediate rej-on reveal discrepanciesas large as 35%; further comparisons between experiments and calculationswill be required to resolve these differences.

To demonstrate that this agreement is sensitive to details of thephysics contained in the code, we also show profiles in Fig. 9 fromcalculations without inverse bremsstrahlung absorption included. Using asimple dump of laser energy at the critical surface, the underdense densityand temperature profiles are greatly changed and they no longer agree withthe measured profiles. It is interesting to note that the overdenseprofiles obtained with inverse bremsstrahlung are very similar to thoseobtained with the critical dump, indicating that overdense profiles are notsensitive to details of the underdense absorption physics.

Comparisons such as these provide the most direct calibration ofhydrodynamics codes. Density, temperature, and velocity profiles are theexperimental observables most closely coupled to mechanisms of energyabsorption and transport in laser-produced plasmas. The ability toreproduce measured profiles is, therefore, a severe test of the ability ofthe code to treat these physical processes.

16

DETAILS OF ABSORPTION PHYSICS GREATLY AFFECT DENSITY ANDTEMPERATURE PROFILES

* 1000

4W a

fl/n6 To IsV)

10-2 100

200 400 Go 110 low0 200 400 GO0 800 1000Z (jMI Z pamI

O 6%im Al DOT (115051IOa7x Q /W -2-0) CODE. INVERSE SREMSSTRAHLUNGo) 115jmm At DOT I112441 1-mm-2-D CODE. CRITICAL DUMP

Fig. 9 Data points show density and temperature profiles from spotspectroscopy with 65 uzm (o) and 115 mm (q) diameter Al dots.Experimental conditions are 10 7 x 1012 W/cm2 within d90 1 mm.2-D code calculations for the same conditions are shown by the Solidcurve. The sensitivity of the agreement between code and experimentto details of the code physics is shown by the dotted curve, generatedwith the 2-D code altered to neglect inverse bremsstrahlung and todump all energy at critical density.

17

C. Caveats and Future Work

At least two sets of caveats regarding this work should be pointedout. First, there are three assumptions which we make when reducing thedata regarding the spatial qualities of the spectroscopic information. As

6 pointed out in Sec. II.B, the plasma/atomic physics model with which thedata are compared simulates a homogeneous cylinder of plasma; the implicitassumption here is that the Al tracer plasma is nearly homogeneous in theradial direction. We also assume that the Al tracer plasma equilibrateswith the surrounding CH plasma if tracer spot diameters are keptsufficiently small. This allows us to compare the spectroscopicmeasurements of density and temperature (which reflect conditions withinthe Al tracer plasma) with the results of the hydro-code (which simulates aCH target with no Al tracer ) in Fig. 9. These first two assumptions seemto be supported by the measured profiles in Fig. 9, where reduced data fromtwo shots with different tracer diameters are shown to agree. A thirdassumption is that the spectrum emitted at a given distance z from thetarget is determined by the density and temperature at that position, withnegligible effects due to photon pumping from higher density tracer plasmacloser to the target. This assumption will be tested using the above-mentioned plasma/atomic physics model.

A second set of caveats concerns the temporal qualities of thespectroscopic information. The present data is time-integrated; in makingthe comparison in Fig. 9 with an instantaneous profile from the hydro-code(at a time near the peak of the laser pulse), we are implicitly assumingthat the hydrodynamics is nearly in steady state. It is appropriate torecall the experimental inferences discussed in Sec. II.A, which supportthis assumption. By comparing the measurements with a CRE model, we arealso making assumptions regarding the steadiness of the atomic physics. Asthe plasma flows through a given volume at a distance z from the target, weassume that its residence time in that volume is sufficiently long thatstates of ionization and excitation approach the equilibrium conditionsappropriate for n(z) and T(z). This assumption is weakest far from thetarget surface, where relaxation times increase with decreasing plasmadensity. In this case, the state of plasma ionization and excitationbecomes dependent upon conditions that exist upstream in the hydrodynamicflow, and the temperature determined by spot spectroscopy may reflect anionization temperature rather than the local electron temperature.

In future work, time-resolved measurements of the profiles shouldprovide a more direct answer to this second set of questions. Thesemeasurements, as pointed out in Ref. 2, might be obtained by replacing thefilm with an x-ray streak camera. An alternative approach is to bury atracer spot of thickness t at a depth d within the target. By varying thedepth d and thickness t of the tracer on a shot-by-shot basis, one may varythe tim. interval during which the tracer emission occurs.

Future work may also allow us to satisfy the need for measurements oflateral profiles. As mentioned in the introduction, the use of finitefocal spots on planar targets causes the problem to become two-dimensional,and simultaneous measurement of axial and lateral profiles is desirable.

18

66 I

By changing the orientation of the spectrograph, one can take fulladvantage of its two-dimensional imaging capability. Then, using a targetidentical to those used in flow visualizations (Fig. 1), one obtains animage of the visualized flow in each spectral line detected by the

* spectrograph. In principle, this technique should allow determination ofthe desired profiles. Quantitative studies of lateral variations in plasmapressure, as discussed in Sec. II.C, may then be feasible.

IV. LAYERED TRACERS: VELOCITY PROFILE AND ABLATION RATE MEASUREMENTS

Further applications of tracers become available with the use oflayered tracer spots. Layered-tArget methods, suggested originally by G.Dah'.backa and developed by NRL, faciitated studies of axial transportthrough measurements of mass ablation. Here, we propose the marriage oflayered-target techniques with our new tracer methods for measurements offluid velocity profiles and improved measurements of mass ablation rates.

Use of a layered tracer spot should allow direct and time-resolvedmeasurement of fluid velocity profiles. Before tracers, velocity profilesof the fluid were not measured, despite their importance for interpretingstimulated Brillouin scattering observations. In Ref. 3, we demonstratedan indirect method for inferring time-averaged profiles, but tracers alsoallow a direct and time-resolved measurement. As shown in Fig. 10, one canfabricate a tracer spot from alternating layers of two materials withdistinguishable x-ray emissivities. As each successive layer ablates fromthe target, the progress through the blowoff plasma of the interfacebetween layers may be observed with an x-ray streak camera; the camera slitis oriented to give spatial resolution along the laser axis. The z(t)curves generated by the multiple interfaces may be inverted to give thev':Iccity profiles u(z) with time resolution.

The above data also yields the ablation rate through each layer ofthe tracer spot. This is an nimprovement over the original layered-targetmeasurement of ablation rate,2 b because localization of the layers withinthe tracer spot alleviates complications due to variations in laserintensity across the irradiated region.

V. SUrMM4ARY

With tracer methods still in their infancy, we see several newtechniques which are capable of addressing a variety of interesting andimportant physics issues. The measurements of density and temperatureprofiles shown in Sec. II and the proposed measurement of velocity profilediscussed in Sec. IV are an important adjunct to experiments related tolaser absorption in the underdense plasma. If overdense profiles can bemeasured with sufficient precision, issues of axial transport of energyinward from the absorption region may be treated; the applicability of thetime-resolved ablation rate measurement to this problem is also clear. Wehave alreadiy begun to apply the flow visualization technique to questionsof lateral energy spread due to finite focal spot size or due to laser

19

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nonuniformities, and proposed spectroscopic methods can make this morequantitative. Experiments are also underway to test the use of traeers fordetection of Rayleigh-Taylor instability. Many of these measurementsprovide valuable data for calibration of the hydrodynamics codes upon whichwe rely for predictions of high-gain target performance. As many of thecurrent ideas for use of tracers are proven and as new ideas continue tosurface, we anticipate an expanding role for these methods in experimentsrelated to the physics of laser-matter interaction and to inertialconfinement fusion.

VI. ACKNOWLEDGEMENTS

The authors wish to acknowledge useful discussions with Dr. S.E.Bodner, Dr. C.K. Manka, Dr. R.H. Lehmberg, and Dr. H.R. Griem. Invaluabletechnical support has also been received from M. Fink, E. Turbyfill, N.Noce-ino, and J. Kosakowski. This work is supported by the U.S. Departmentof Energy, Office of Naval Research, and Defense Nuclear Agency.

21

-- i

References

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