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Radiation Physics and Chemistry 70 (2004) 535–552

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Overview of future directions in high energy-density andhigh-field science using ultra-intense lasers

T. Ditmirea,*, S. Blessa, G. Dyera, A. Edensa, W. Grigsbya, G. Haysa,K. Madisona, A. Maltseva, J. Colvinb, M.J. Edwardsb, R.W. Leeb, P. Patelb,

D. Priceb, B.A. Remingtonb, R. Sheppherdb, A. Woottonb, J. Zweibackc,E. Liangd, K.A. Kieltyd

aDepartment of Physics, University of Texas at Austin, 1 University Station, Austin, TX 78712, USAbLawrence Livermore National Laboratory, Livermore, CA 94550, USA

c General Atomics, San Diego, CA 92121, USAd Rice University, Houston, TX, USA

Abstract

The increasing proliferation of 100TW class ultrashort pulse lasers and the near completion of a number of petawatt

class lasers world wide is opening many frontiers in laser science. Some of the most exciting frontiers rest in high energy-

density science and high field physics. A multi-TW laser can create heated matter with pressure in excess of a Gbar and

can create electric fields of ten to one hundred atomic units. In this paper some of the recent advances in high energy

density science and high field physics made using high intensity short pulse lasers will be reviewed with illustrative

examples from work performed at the University of Texas and Lawrence Livermore National Laboratory.

r 2004 Elsevier Ltd. All rights reserved.

1. Introduction

The increase in light intensity available in the

laboratory over the previous 20 years has been

astounding. Laser peak power has climbed from giga-

watts to petawatts in this time span, and accessible

focused intensity has increased by at least seven orders

of magnitude. Such a dramatic increase in light bright-

ness has accessed an entirely new set of phenomena.

High repetition rate table top lasers can routinely

produce intensity in excess of 1019 W/cm2, and inten-

sities of up to 1020 W/cm2 are possible with the latest

petawatt class systems (Mourou et al., 1998; Mourou

and Umstadter, 2002; Perry and Mourou, 1994). Light-

matter interactions with single atoms are strongly non-

perturbative and electron energies are relativistic. The

intrinsic energy density of these focused pulses is very

ing author. Tel.: +1-512-471-3296; fax: +1-

ess: [email protected] (T. Ditmire).

ee front matter r 2004 Elsevier Ltd. All rights reserv

dphyschem.2003.12.042

high, exceeding a gigajoule per cm3. The interactions of

such intense light with matter lead to dramatic effects,

such as high temperature plasma creation, bright X-ray

pulse generation, fusion plasma production, relativistic

particle acceleration, and highly charged ion production

(Mourou and Umstadter, 2002).

Such exotic laser–matter interactions have led to an

interesting set of applications in high field science, and

high energy density physics (HED physics). These

applications span basic science and extend into un-

expected new areas such as fusion energy development

and astrophysics. In this paper some of these new

applications will be reviewed. The topics covered here do

not represent a comprehensive list of applications made

possible with high intensity short pulse lasers, but they

do give a flavor of the diverse areas affected by the latest

laser technology. Most of the applications discussed here

are based on recent experiments using lasers with peak

power of 5–100 TW. How these experiments could be

extended with a petawatt class laser will also be

discussed.

ed.

ARTICLE IN PRESST. Ditmire et al. / Radiation Physics and Chemistry 70 (2004) 535–552536

1.1. State of the art in high intensity short pulse lasers

Many important leaps in laser technology have driven

the rapid advances in HED and high field science over

the last 15 years. The enabling advancement for this

technological progress was the invention of chirped

pulse amplification (CPA) lasers (Strickland and Mourou,

1985). This technique, first demonstrated by Strick-

land and Mourou in 1985 is illustrated in Fig. 1. A

broad bandwidth, mode-locked laser produces a low

power, ultrafast pulse of light, usually with duration of

20–500 fs. This short pulse is first stretched in time by a

factor of around ten thousand from its original duration

using diffraction gratings. This allows the pulses, now of

much lower peak power, to be safely amplified in the

laser, avoiding the deleterious nonlinear effects which

would occur if the pulses had higher peak power

(Koechner, 1996). These amplified pulses are, finally,

recompressed in time (again using gratings), in a manner

that preserves the phase relationship between the

component frequencies in the pulse. The CPA output

has a duration near that of the original pulse but with an

energy greater by the amplification factor. In high-

energy CPA systems, severe nonlinearities occurring

when the pulse propagates in air can be a major

problem, so the pulse must be recompressed in an

evacuated chamber.

The first generation of CPA lasers were based mainly

on flashlamp pumped Nd:glass amplifiers (Danson et al.,

1998; Kitagawa et al., 2002; Patterson and Perry, 1991;

Strickland and Mourou, 1985). These glass based lasers

are usually limited to pulse duration of greater than

about 300 fs because of gain narrowing in the amplifiers

(Blanchot et al., 1995). The most significant scaling of

this approach to CPA was demonstrated by the Petawatt

laser at Lawrence Livermore National Laboratory in the

Fig. 1. Illustration of how the technique of chirped pulse amplifica

late 1990s (Perry et al., 1999). This laser demonstrated

the production of 500 J per pulse energy with duration of

under 500 fs yielding over 1015 W of peak power. Since

this demonstration, a number of petawatt laser projects

have been undertaken around the world (Service, 2003).

The second common approach to CPA uses Ti:sap-

phire as the amplifier material. This material permits

amplification of much shorter pulse durations often

down to 30 fs. However, the short excited state lifetime

of Ti:sapphire (B3ms) requires that the material be

pumped by a second laser (usually a frequency doubled

Nd:YAG or Nd:glass laser). The inherent inefficiencies

of this two step pumping usually limit the output energy

of such a laser to under a few joules of energy per pulse.

A number of multi-terawatt lasers based on Ti:sapphire

now operate in many high intensity laser labs world wide

(Yamakawa et al., 1999; Walker et al., 1999; Patterson

et al., 1999). An example of a typical table top scale

multi-terawatt system is the laser we have constructed at

the University of Texas. This optical schematic of this

system, which delivers 0.75 J in 35 fs pulses at a 10 Hz

repetition rate, is illustrated in Fig. 2. To date, the

largest scaling of Ti:sapphire technology has been to the

100 TW power level (Yamakawa and Barty, 2000;

Patterson et al., 1999) with energy of up to 10 J per

pulse. Scaling of Ti:sapphire to the petawatt power level

is being pursued in Japan and will likely be achieved

within a year or so (Service, 2003).

The third major technology upon which a new

generation of high peak power CPA lasers is being

based is optical parametric chirped pulse amplification

(OPCPA) (Ross et al., 1997). In this approach,

amplification of the stretched pulses occurs not with

an energy storage medium like Nd:glass or Ti:sapphire

but via parametric interactions in a nonlinear crystal.

This approach is quite attractive because of the very

tion is used to amplify ultrashort pulses to high peak power.

ARTICLE IN PRESS

1.5J @ 10Hz YAG1.5J @ 10Hz YAG

1.5J @ 10Hz YAG1.5J @ 10Hz YAG

0.3J@ 10HzYAG

0.3J@ 10HzYAG

Regenerative amplifier (20 passes)Regenerative amplifier (20 passes)

4-pass amplifier

4-pass amplifier5-pass amplifier

Pulse stretcherPulse stretcher

VacuumPulse compressor

VacuumPulse compressor

30fs out-putto Target

35fs outputto Target

20 fs 1 nJ

600 ps

50 mJ pump

3 mJ out

15 mJ out

> 1.2 J out

130 mJpump

0.75 J out aftercompression

Fig. 2. Optical schematic of the Texas High Intensity Optical Research Laser which is based on standard Ti:sapphire CPA technology.

T. Ditmire et al. / Radiation Physics and Chemistry 70 (2004) 535–552 537

high gain per stage possible (often in excess of 104 per

pass) and the very broad gain bandwidth possible in

principal. To date, a number of CPA demonstrations

with OPCPA have been published (Ross et al., 2000;

Jovanovic et al., 2002; Leng et al., 2003). Though there

are still significant technological issues to be resolved

with OPCPA, this technique promises to lead to a new

generation of high peak power, femtosecond lasers.

1.2. Overview of high energy density and high field

physics with high intensity short pulse lasers

The physics accessible with this class of lasers is quite

extreme. The science applications made possible with

these extremes can be simply classified into two

categories. First, by temporally compressing the pulses

and focusing to spots of a few wavelengths in diameter,

these lasers concentrate energy in a very small volume. A

multi-TW laser focused to a few microns has an intrinsic

energy density of over 109 J/cm3. This corresponds to

about 10 keV of energy per atom in a material at solid

density. As a result, quite high temperatures can be

obtained. Such energy density corresponds to pressure in

excess of 10 Gbar. Many applications of ultraintense

lasers stem from the ability to concentrate energy to high

energy-density which can lead to quite extreme states of

matter.

The second class of applications arises from the high

field strengths associated with a very intense laser pulse.

At an intensity of over 1018 W/cm2, an intensity quite

easily achievable with modern table top terawatt lasers,

the electric field of the laser exceeds ten atomic units,

over 1010 V/cm. Consequently, the strong field rapidly

ionizes the atoms and molecules during a few laser

cycles. At intensity approaching 1021 W/cm2, the current

state of the art with petawatt class lasers, the electric

field is comparable to the field felt by a K-shell electron

in mid Z elements such as argon. The magnetic field is

nearly 1000T. An electron quivering in such a strong

electric field will be accelerated to many MeV of energy

in a single optical cycle. Such charged particles will

experience a very strong forward directed force resulting

from the Lorentz force.

The increase in laser intensity over the past twenty

years accesses new regimes in both high field and high

energy density physics. This is illustrated in Fig. 3, where

new thresholds in intensity and the applications they

enable are shown. In the following sections, we consider

various basic and applied science applications of such

intense laser pulses. Examples of physics at high energy

density will be considered first, and then a couple of

examples of the strong field of such intense pulses will be

discussed.

2. High energy density science with ultraintense ultrafast

lasers

2.1. Isochoric heating and probing of off-Hugoniot

equations of state

High peak power femtosecond lasers are unique in

their ability to concentrate energy in a small volume. A

dramatic consequence of this concentration of energy is

the ability to create matter at high temperature and

pressure. Matter with temperature and density near the

ARTICLE IN PRESS

Fig. 3. Plot of optical tunneling ionization thresholds of various ions as a function of laser peak intensity.

T. Ditmire et al. / Radiation Physics and Chemistry 70 (2004) 535–552538

center of dense stars can be created in the laboratory

with the latest high intensity lasers. For example, solid

density matter can be heated to temperature of over

10,000,000�C (>1 keV). Under these conditions, the

particle pressure inside the sample is over 1 billion

atmospheres, far higher than any other pressure found

naturally on or in the earth and approaches pressures

created in nuclear weapons and inertial confinement

fusion implosions.

Study of the properties of matter at these extreme

conditions, namely solid density (i.e. B1022 cm�3) or

higher in the temperature range of 1–1000 eV, is crucial

to understanding many diverse phenomenon, such as the

structure of planetary and stellar interiors or how

controlled nuclear fusion implosions (inertial confine-

ment fusion or ICF) evolve. Yet, despite the wide

technological and astrophysical applications, a true,

complete understanding of matter in this regime is not in

hand. A large obstacle is posed by the fact that

theoretical models of this kind of matter are difficult

to formulate. While the atoms in these warm and hot

dense plasmas are strongly ionized, the very strong

coupling of the plasma, and continuum lowering in the

plasma dramatically complicates traditional plasma

models which depend on two body collision kinetics

(Spitzer, 1967). Even the question of whether electrons

in this state are free or bound is not as clear cut as it is in

a diffuse plasma.

Over the last 15 years, since the development of high

energy short pulse lasers, there have been a number of

experimental studies aimed at isochorically heating solid

density targets with a femtosecond laser pulse (Audebert

et al., 2002; Widmann et al., 2001). This class of

experiments uses a femtosecond pulse to heat, at solid

density, an inertially confined target on a time scale

much faster than the hot material can expand by

hydrodynamic pressure. This approach can be very

powerful. Not only can spectroscopic diagnostics be

implemented to derive information on the heated

material (such as ionization state) (Nantel et al., 1998)

but isochoric heating experiments can also enable laser

heated pump–probe experiments. Pump–probe experi-

ments can use an optical, or laser-generated X-ray pulse

to probe the material on a time scale before it can

expand. This yields, for example, conductivity informa-

tion through reflectivity and transmission probing

(Widmann et al., 2001), as well as XUV and X-ray

opacity if a short wavelength probe is employed

(Workman et al., 1997). The general experimental

technique used in these experiments is illustrated in

Fig. 4. The laser heats a thin slab of material, with

thickness usually comparable to or less than an optical

skin depth. Fig. 5 illustrates the parameter regime

accessible with short pulse laser heating. Here, the phase

space of aluminum is illustrated. When the material is

heated from its initially cold, solid state, the plasma will

be in the ‘‘strongly coupled’’ regime, denoted by the

state in which G > 1; even at temperature approaching

1 keV. Here G is the ratio of particle potential energy to

its kinetic energy.

The scheme depicted in Fig. 4 is that in which a laser

directly heats a sample, and the energy deposits within

an optical skin depth. Direct laser heating has draw-

backs. Because of the small depth of such a skin depth,

the expansion time of the sample is often only 100 or

200 fs. The few hundred fs release time of the heated

material is comparable to the electron–ion equilibration

time (Spitzer, 1967) and hampers interpretation of this

kind of experiment. Microsopically rough surface finish

of the very thin target often leads to a large uncertainty

in the initial density, complicating analysis of the data.

Consequently, it is desirable to explore mechanisms of

ARTICLE IN PRESST. Ditmire et al. / Radiation Physics and Chemistry 70 (2004) 535–552 539

heating larger volumes (i.e. thicker layers) of material.

One promising approach is to use fast bursts of

penetrating radiation, such as protons or X-rays, to

heat thicker layers of material than are possible with

direct optical heating. Use of X-rays to perform

Fig. 4. Cartoon of the isochoric heating technique in which a

short pulse laser heats a thin slab of solid density material and a

second pulse probes the material before it can expand.

Fig. 5. A density–temperature plot showing the parameter

space in aluminum in which a plasma is strongly coupled. The

parameter range accessed by isochoric heating with short pulse

lasers is also shown on this plot.

isochoric heating was first proposed by Lee et al. in

the context of X-ray free electron lasers sources (Lee

et al., 2002, 2003). A multi keV X-ray pulse can, for

example, penetrate many microns of material (depend-

ing on the wavelength and target Z). To explore the

advantages which may arise from X-ray heating we have

begun exploration of X-ray heating using high intensity

laser based sources.

One way to produce an intense, ultrafast burst of hard

X-rays for such an X-ray heating experiment is to use a

high peak power short pulse laser to produce Ka

radiation on a solid target, an idea shown in Fig. 6.

Such X-ray radiation is produced during the illumina-

tion of a solid target by intense pulse because fast

electrons are produced in the interactions. These elec-

trons travel into the cold target and create inner shell

excitations in the targets atoms. These X-rays have been

shown to exhibit pulse duration under 1 ps if ultrafast

laser illumination is employed. An experiment based on

the concept is illustrated in Fig. 6. In our experiment we

have chosen to study the heating of solid Al. To

maximize the X-ray heating for a given X-ray fluence, it

is desirable to chose a Ka source with photon energy just

above the K-absorption edge of the Al. This choice of

Ka X-rays maximizes absorption. Si Ka; with a photon

energy of 1.74 keV, is optimum for X-ray heating of Al.

If the Si X-ray yield is known, we can use the known

photo ionization cross sections to determine explicitly

the deposited energy density in the Al layer. In our

experiment, X-rays were generated in the Si layer by

irradiating it with an 800 nm laser pulse from a

Ti:sapphire laser. Shots were performed on the JanUSP

laser facility at Lawrence Livermore National Labora-

tory which delivers 100 fs pulses with energy up to 10 J

(Patterson et al., 1999).

To derive information on the heated Al layer, we

optically probe the target with a second 100 fs, 800 nm

Fig. 6. Cartoon showing how a laser based X-ray source can be

used to bulk heat a secondary target.

ARTICLE IN PRESS

Fig. 7. Schematic of the diagnostics used in the K-alpha X-ray

heating experiment.

Fig. 8. (a) Measured aluminum material motion as a function

of time on the back surface of the X-ray heated slab. (b)

Measured reflectivity of the X-ray heated slab as a function of

time.


pulse. This allows us to measure reflectivity of the

material after heating as well as the expansion of the

material along its release isentrope. Fig. 7 shows the

various diagnostics fielded in the first set of experiments.

Expansion of the heated aluminum layer is measured

with an interferometer. The same probe pulse can give

information about the heated target’s reflectivity. The

other diagnostics measure radiation emitted by the

target. An X-ray pinhole camera yielded an absolute

measure of X-ray energy radiated at photon energies

above B1 keV, as well as an approximate source size.

An X-ray CCD camera, positioned far from the target

was used in photon-counting mode to give an absolute

spectrum of X-rays passing through the aluminum layer.

A knife-edge close to the target was used to measure the

source size of X-ray radiation.

Interferometer data are presented in Fig. 8a. Expan-

sion of the heated aluminum was inferred from

interferometer fringe shifts and is plotted here as a

function of time. The material appears to expand

initially with a velocity of about 5� 104 m/s over a time

of B5 ps. For comparison, the expected expansion

velocity of a 5 and a 100 eV Al ideal gas are plotted in

Fig. 8a. The material expansion then seems to accelerate

5 ps after the initial expansion. This apparent increase in

temperature at later times may be attributed to fast

protons emitted from the back surface of the Si target.

We also measure the material reflectivity as a function of

time. These data are shown in Fig. 8b. We derived

reflectivity changes from the that of cold Al by

examining the spatially imaged optical probe on the

surface and comparing average pixel value in the center

of the heated region to that in a region just outside in a

region of cold Al. A transient increase in reflectance is

seen a few picoseconds after main pulse arrival. The

reflectivity of the heated aluminum raises by 70% over

the cold Al within 5 ps after heating. We can attribute

this to an increased free electron density caused by a

cascade of Auger processes following the initial photo-

ionization of Al K-shells by the X-rays.

A quantitative result from this approach will require

improvement of the technique. In particular, it will be

desirable to increase the X-ray yield, increasing the

attainable temperature and the spatial scale of the

heated target. Such X-ray flux increase should be

possible with the use of a petawatt class laser to produce

the X-rays. Assuming a 10�4 X-ray conversion effi-

ciency, X-ray fluxes of >100mJ/cm2 should be possible

with a few hundred J, frequency doubled petawatt laser.

Such intensity is one to two orders of magnitude higher

than that demonstrated in our first experiments and

would likely heat a target to nearly 100 eV.

2.2. Ultrafast dynamics in shocked materials

Another class of high energy density experiments

using high intensity short pulse lasers involves the study


of materials under shock compression. Equilibrium

studies of shock compressed materials are often con-

ducted with gas guns or explosives. However, the

development of high power pulsed lasers opened

the potential to study shock compression at much

higher pressure and higher strain rate (Moshe et al.,

2000). The laser pulse ablates the surface of a target

and the material blow-off acts as a rocket engine

which drives a shock into the underlying cold material.

Because of the fast rise of such a laser shock drive,

quite high strain rates, >107 s�1 can be driven in a

material. Furthermore, using ultrafast, high energy

lasers as shock drivers permits time resolved pump–

probe style experiments. This has the advantage of

allowing study of shock dynamics on the microscopic

scale. Such experiments require sufficient energy to

drive a shock over an area large enough for effective

probing. Multi-joule short pulse lasers can provide such

a shock drive.

High power lasers can access much higher shock

pressures, up to 1 to 10Mbar, than are obtainable with

gas guns or easily derived with small to mid-scale

explosive experiments (Trainor et al., 1979). More

important, however, is the fact that an intense laser

can produce a probing pulse, synchronized to the shock

driving pulse, to examine the dynamics of the material.

This probe can be optical, and can probe the surface

properties (like conductivity through reflectivity) with

high time resolution. In addition, an intense laser can

produce a bright burst of X-rays (via mechanisms

discussed in the last section) that can probe the

dynamics of the materials on the lattice level. This

approach can, in principle, begin to examine atomic

motion behind the shock (and around defects) (Wark

et al., 1989), a possibility which could yield unprece-

dented information on deformation mechanisms and

defect generation.

Despite the vast number of previous shock compres-

sion studies, a detailed understanding on a lattice level

of shocks is still lacking. This is particularly true at very

high strain rates (>108 s�1) since conventional deforma-

tion mechanisms are not valid and limited data exist. It

is known, for example, that currently accepted consti-

Fig. 9. Illustration of the manner in which microscopic d

tutive models are quite speculative in this strain rate

regime. The issues surrounding high strain rate shock

dynamics are illustrated in Fig. 9.

Fundamental to shock propagation in a crystal is the

formation, and propagation, of defects and dislocations

(Asay and Shahinpoor, 1993). For example, when a

crystal is shocked beyond its elastic limit, it is well

known that plastic flow takes place. In the extreme limit

of a strong shock the material behaves hydrostatically;

the material strength is negligible, and the crystal lattice

is compressed equally in all three directions. This plastic

flow normally occurs at shock pressure above the

Hugoniot Elastic Limit (HEL) which rests at pressure

of a few tens of kbar for most materials. For the plastic

flow to occur, dislocations must be present at the

interface between the compressed and uncompressed

lattice. This can be seen in the illustration of Fig. 9,

where the dislocations shown schematically at the shock

front allow the unit cells to be compressed equally in all

directions. Only recently have these dynamics, such as

density and type of dislocation production, come under

study, mainly using molecular dynamics simulations

(Holian and Lomdahl, 1998), and there are only limited

experimental studies to corroborate these calculations.

Another important phenomenon with complications at

the lattice scale occurs when the material is shocked to

high enough pressure that it melts. The transition from

crystalline solid to amorphous melting on the ultrafast

time scale is also not well studied.

Ultrafast optical probes can shed light on these

dynamics. The principle behind these experiments is

illustrated in Fig. 10. It is possible to use the fact that the

linear and nonlinear optical properties of a material

differ when the solid becomes a liquid. This means that

the material reflectivity will change as it undergoes a

phase transition to a liquid and its nonlinear optical

properties can change. The later fact can be exploited if

second or third harmonic is generated off the back

of a target that is shocked and the harmonic intensity

is monitored via pump–probe techniques. This ap-

proach has been used in the study of femtosecond laser

induced melting in semiconductors such as silicon

(Shank et al., 1983).

efects get generated in a plastic shock deformation.

ARTICLE IN PRESS

Fig. 10. Cartoon of the probing of a shock induced lattice

change by optical or nonlinear optical probing.

Fig. 11. Schematic of the shock induced melting experiment in

a tin slab.

Fig. 12. Data showing the drop in reflectivity observed on the

back of a tin slab 2 ns after the shock driver laser pulse

irradiated the sample.

Fig. 13. Measured tin reflectivity as a function of time showing

the drop in reflectivity coincident with the shock break out.


To illustrate the possibilities in optical time resolved

probing of laser produced shocks, we have performed

the experiment illustrated in Fig. 11. We use the

University of Texas THOR Ti:sapphire laser illustrated

in Fig. 2. The uncompressed, 600 ps pulse from THOR

drives a shock in a thin sample, which is a slab of tin

4mm thick in our initial proof of principle experiments

(chosen to match the shock transit time driven by our

600 ps pulse). This shock is driven by about 1 J of light

focused to a 0.4mm spot. This slab is probed on the

back side with part of the laser that has been split from

the shock driver laser and compressed to 40 fs time

duration. In this way, the ultrafast probe pulse is well

synchronized to the shock driver. A CCD camera images

the reflection off the back surface of the tin slab. The

probe pulse is itself split and sent through an inter-

ferometer to derive simultaneous information on the

amount of shock driven expansion on every shot.

Typical data are shown in Fig. 12 where the reflectivity

of the slab 2 ns after the drive pulse begins irradiating

the surface is shown. As can be seen, a well defined

region of the tin, where the shock has broken out on the

back side, has dropped in the reflectivity.

A measurement of the reflectivity in the center of the

shocked region as a function of time is plotted in Fig. 13.


We observe a quick (o200 ps) drop of the reflectivity to

90% once the shock breaks out from the target surface.

A slower, further fall of the reflectivity follows this rapid

drop. The dynamics leading to this behavior are still not

understood but the early time drop may result from

shock melting while the later reflectivity fall may derive

from some microscopic break-up of the surface. The

implementation of nonlinear optical probing in the

future will help to remove this ambiguity. Future work

will benefit from shocking at higher pressure over

thicker target slabs using higher energy laser pulses.

2.3. Astrophysics and radiative hydrodynamics

Another area of shock physics which can be studied

with high intensity lasers is that of strong shocks in

gases. Such shock studies have some relevance to

astrophysical phenomena. Astrophysical shocks play

an important role in the evolution of the inter-stellar

medium providing an energy source, and triggering a

variety of phenomena including star formation (McKee

and Draine, 1991). On galactic time-scales, supernovae

are a frequent source of such shock waves, which expand

into the surrounding medium sweeping up material into

a thin, dense shell. If the circumstellar medium is

sufficiently dense, radiation can play an important role

in the energy transport dynamics of the supernova

remnant blast wave (Bartel et al., 2000). It is also

believed that various shock instabilities associated with

these radiative shocks, including the well known

Vishniac overstability, have an important effect on the

structure of interstellar matter (Vishniac, 1983). Because

of the complicated dynamics associated with these

astrophysical phenomena, there is a strong motivation

to produce radiative blast waves in the laboratory. A

radiative blast wave can occur over a wide range of

temperatures and densities in astrophysical shocks but is

more difficult to achieve in the laboratory. Nonetheless,

high Mach number, laser driven blast waves in certain

dense gases can reach the high temperatures needed to

enter the radiative regime (Grun et al., 1991).

To create a laser driven radiative blast wave, it is

necessary to produce a localized, high temperature

plasma in a modest density gas without perturbing the

surrounding medium with the incoming laser. One way

to do this is to utilize the now well characterized high

absorption efficiency of high intensity femtosecond

lasers in gases containing large clusters (Ditmire et al.,

2000; Shigemori et al., 2000). An intense laser focused

into a strongly absorbing cluster gas will produce a hot,

elongated filament which will subsequently develop into

a cylindrical shock (Ditmire et al., 1997a).

How this is done with a short pulse laser and

how these blast waves can be probed is demonstrated

in Fig. 14. This figure illustrates a specific experiment on

blast waves conducted at LLNL using the 35 fs Falcon

Ti:sapphire laser (Edwards et al., 2001). The blast waves

were produced by focusing 0.1 J, 35 fs laser pulses with

an f/15 lens into a gas jet expelling a plume of neon,

argon or xenon gas. A cylindrical plasma filament

B50 mm in diameter stretching across the 4mm width of

the gas jet resulted from the irradiation. The evolution

of the blast wave in the gas was probed by splitting a

small portion of the laser energy and passing it

perpendicular across the plasma filament. Two probing

techniques examined the blast wave: interferometry,

which yielded information about the electron density

profile, and dark field imaging, which gave images

sensitive to gradients in the electron density. The time

history of a shock was found by varying the temporal

delay of the probe pulse with respect to the driving

pulse.

From the interferograms, we observed the clear

formation of a blast wave produced by the explosion

of the heated cluster plasma. Characteristic interfero-

grams and deconvolved electron density profiles of blast

waves produced in argon and xenon are illustrated in

Fig. 15a. In the case of argon, a weak shock is formed in

the weakly absorbing gas and a clean shock front is

observed. The xenon profile also exhibits a well formed,

sharp shock front, however, we also observed significant

ionization of gas ahead of the shock front. This indicates

an ionization precursor formed by radiation emitted

from the hot plasma and deposited in the otherwise

undisturbed ambient gas. Such a radiative precursor is

one of the classic signs that an exploding plasma is

driving a radiative shock wave. Interestingly, we also

observed an increasing rate of deceleration of the Xe

shock which suggested that radiative energy loss played

a significant role in the evolution of the blast wave

(Edwards et al., 2001).

These experiments also examined how this radiative

flow dynamic affected the blast wave stability. The

presence of instability growth was sought experimentally

by examining ‘‘dark field’’ imaging. We examined all

gases in our experiments (Ne, Ar and Xe), though we

expected potential instability growth only in the case of

the strongly radiating Xe. Dark field images of a Xe

blast wave at times 4, 30 and 110 ns are shown in

Fig. 15b. The shock front is located at the thin bright

region which appears extremely smooth down to the

scale of the instrument resolution, B10mm, even at

the latest time. These data suggest that no radiative

instabilities were present in these experiments, or at least

were not growing fast enough to be significant on the

time scale of this experiment.

Further studies on these short pulse laser produced

radiative shock systems will benefit immensely if shocks

can be created which persist for longer and retain a high

mach number to greater radius than in this initial

experiment. Once again, the use of a petawatt class laser

will make such larger scale experiments possible. For the

ARTICLE IN PRESS

Fig. 14. Schematic of the radiative blast wave experiment illustrating how the blast wave is created by irradiation of a cluster jet with a

femtosecond pulse and then is diagnosed by a delayed optical probe pulse.

Fig. 15. Data showing the formation of a blast wave in the gas jet. (a) Deconvolved electron density profiles of shocks in argon and

xenon gas 6 ns after irradiation. A UV radiative ionization precursor is clearly seen in the xenon shock data. (b) Dark field images of

the shock evolving in xenon showing the evolution of a smooth shock front out to 110 ns.



self similar blast waves studied here, the shock velocity

(the parameter most important to determining if the

shock is radiative) scales with the initial deposited laser

energy, E; as E1=2 for a constant radius. So an increase

of laser energy from the 0.1 J used in our experiment on

Falcon to a 100–1 kJ short pulse laser will enable high

Mach number experiments to be conducted in a

clustering gas with radii extending out to over 1 cm, an

improvement of two orders of magnitude in size. With

this test bed, it should be possible to study many of the

details of radiative shock propagation in the lab.

2.4. Neutron generation and time resolved radiation

damage dynamics

The use of high intensity short pulse lasers to produce

short bursts of X-rays is a well known application of

these lasers (Wharton et al., 2001; Gauthier, 1994). The

high temperature plasmas created by a focused ultrafast

pulse can emit a pulse of X-rays in the 1 keV to 1MeV

range, depending up on the laser intensity and focal

conditions. Such X-ray production has been utilized by

a number of groups in ultrafast X-ray probing experi-

ments (Siders et al., 1999; Von der Linde et al., 2001).

With the increase in the laser energy and peak power

available, the generation of other sources of radiation is

now being investigated.

One interesting radiation source is laser produced

fusion neutrons. The production of a high flux burst of

fusion neutrons could be of considerable importance to

the study of radiation induced damage in materials

(Averback and Rubia, 1998). The manner in which

neutrons damage materials is an area of active study,

particularly in the context of developing future fusion

reactor wall materials (Perkins et al., 2000). However,

high flux sources of clean fusion neutrons are not widely

available. A laser produced source could enable such

damage studies. In addition, the short duration inherent

in laser driven radiation sources could allow time

resolved studies of neutron damage. A laser driven

source of neutrons might also serve as a source for fast

neutron radiography where the small source size could

lead to high spatial resolution.

Using intense femtosecond lasers to produce high

fluxes of fusion neutrons may now be possible by

exploiting interactions of intense lasers with atomic

clusters. There have been a wide variety of experiments

in recent years which have shown that when an intense

laser interacts with a cluster of atoms or molecules of a

few hundred to a few thousand atoms, the cluster

explodes quite violently, ejecting ions of high kinetic

energy (Perkins et al., 2000; Ditmire et al., 1997b; Lezius

et al., 1998). How this happens is illustrated in Fig. 16,

which shows the results of a particle dynamics simula-

tion of a small (55 atom) Ar cluster irradiated by a 50 fs

laser pulse at modest intensity (1016 W/cm2) (Ditmire,

1998). Because of the rapid rise time of the pulse, tunnel

ionized electrons from the Ar atoms in the cluster are

heated and ejected by the laser field on a time scale faster

than the argon ions can move. The space charge forces

created by this ejection of electrons leads to a radial

explosion of the cluster. The laser cluster interactions are

quite efficient at converting laser energy to ion energy.

These exploding clusters can drive nuclear fusion

under the right conditions (Balcou et al., 2001; Ditmire

et al., 1999; Zweiback et al., 2000). Here, ions released

from energetic explosions of deuterium clusters irra-

diated with femtosecond laser pulses drive DD fusion.

Neutrons are released in the DD fusion by the well

known reaction D+D-He3+n (+3.3MeV of excess

energy). In this experiment, a high intensity, focused

ultrafast laser pulse traverses a gas of deuterium clusters

and rapidly heats them. These clusters subsequently

explode, ejecting deuterium ions with energies of many

keV. This process creates a plasma filament with a

diameter roughly that of the laser focus and a length

comparable to the extent of the gas jet plume (B2mm).

The fast deuterium ions ejected from the exploding

clusters can then collide with ions ejected from other

clusters in the plasma.

Initial experiments on this system indicated that

fusion yields of up to 104 neutrons/shot were possible

using 100mJ, 35 fs laser pulses (Zweiback et al., 2002).

Estimates for the needed neutron flux to induce

sufficient damage to be observable by optical or X-ray

pump probe techniques indicate that at least 109 n/shot

will be necessary, so a large scaling in yield is still

necessary before a usable laser based source can be

realized. To examine the feasibility of a laser based

fusion neutron source using exploding clusters, we have

studied the neutron yield scaling quite carefully. The

yield will be dependent on a number of parameters, the

ion energy from the exploding clusters (since the fusion

cross section is strongly dependent on ion energy), the

deuteron density, and the heated plasma volume. If

more energetic cluster explosions can be generated at

higher average gas density, it seems likely that sufficient

neutron flux can be obtained for some applications.

The results of recent experiments studying the fusion

yield scaling of a femtosecond laser irradiated deuterium

gas jet are shown in Fig. 17. The gas plume was

irradiated by a single pulse of 800 nm light from the

Lawrence Livermore National Laboratory JanUSP

laser. The laser energy was varied to a maximum pulse

energy of 10 J and we varied the duration of the

compressed pulse from 100 fs to 1 ps by varying the

grating spacing in the pulse compressor. After recom-

pression this pulse was focused into the gas plume by a

300 mm focal length off-axis parabolic mirror producing

a vacuum focal spot diameter of B10mm yielding a peak

intensity of 2� 1020 W/cm2 in vacuum, an intensity

sufficient to fully strip the 5–10 nm D2 clusters in our jet

ARTICLE IN PRESS

Fig. 16. Particle dynamic simulation of an exploding argon cluster irradiated by a 50 fs laser pulse. The blue spheres are argon ions and

the red spheres are electrons.

Fig. 17. Measured fusion neutron yield in a deuterium cluster

plasma as a function of incident laser energy. Data for three

different pulse durations (35 fs, 100 fs and 1 ps) are shown.


target. The neutrons were detected with scintillating

plastic detectors coupled to photomultiplier tubes. We

find that the fusion yield scales nearly as the square of

the laser energy, a finding which holds true both for

100 fs and 1 ps laser pulses. This yield scaling is also

consistent with earlier data taken with a lower energy,

35 fs Ti:sapphire laser (also shown in Fig. 17). At laser

energy over 5 J, roughly 106 neutrons per shot were

observed. This scaling can be simply explained by the

volume increase of the plasma at higher laser energy.

These data indicate that fusion yield increases

strongly with laser energy. With a petawatt class laser

delivering >100 J, we might expect that, if this yield

scaling is maintained, nearly 109 n/shot might be

possible. This would result in a fluence near the target

of nearly 1011 n/cm2 per shot. Such high fluxes will

significantly damage a material and would lend them-

selves to time resolved neutron damage studies. Pre-

sently, the ion energies achievable in the cluster

explosion tend to be limited by the size of the clusters.

As a result, higher intensity pulses do not lead to any

significant increase in ion energy (Madison et al., 2003).

However, further improvements in the target jet could

lead to larger cluster production in deuterium and even

higher fusion efficiency.

3. High field physics with ultraintense ultrafast lasers

Each of the applications in the previous section relied

on the high energy density concentration possible with

an intense short pulse laser. Of course, at the high

intensity reachable, the field strength of these laser

systems is quite large (over 10 atomic units). This has

lead to a number of unique possibilities in high field

research.

3.1. Relativistic nonlinear optics

The most straightforward consequence of these strong

optical fields is manifested in the interaction of the field

with free electrons. At an intensity in which

the normalized vector potential of the laser field,


a0 ¼ eE=meco; approaches 1, (where E is the peak

electric field of the light) the electron oscillation motion

becomes relativistic during the course of a single laser

oscillation. In a laser field with wavelength around 1mm,

this relativistic regime is reached at intensity around

1� 1018 W/cm2. The relativistic quiver velocity of an

electron at this intensity has two consequences. The

electron mass in the lab frame increases and the electron

motion becomes anharmonic. The v � B Lorentz force

also becomes important. This leads to free electron

trajectories in the laser field which deviate significantly

from the simple, harmonic motion in non-relativistic

fields. This is illustrated in Fig. 18 which shows the

motion of a classical electron is a plane wave at an

intensity of 3� 1019 W/cm2 ða0E4Þ after it has been

tunnel ionized from an atom located at the origin. The

motion of the electron is very anharmonic and the

Lorentz force drives the electron in a trajectory that is

directed to a large extent along the laser k vector.

The relativistic motion of the electron has a number of

consequences in the interactions of single electrons with

intense laser fields. The anharmonic motion of the

electron can lead to the re-emission of high order

harmonics of the laser field (Lau et al., 2003; Banerjee

et al., 2002). This could enable a very bright, femtose-

cond soft X-ray source. The mass shift of the electrons

also affects the properties of a plasma. For example, the

mass increase increases the effective plasma frequency of

an irradiated plasma, so critical density plasma becomes

effectively underdense (Vshivkov et al., 1998). This is

known as relativistic transparency of a plasma (though

this effect has not yet been observed experimentally).

The relativistic shift of the plasma frequency has been

observed in channeling of an intense laser beam in an

underdense plasma. The increasing of the plasma

frequency at higher intensity can create a focusing effect

for a focused laser beam with an intensity profile peaked

on axis. Such relativistic self focusing is now well

established in experiments (Najmudin et al., 2000;

Fig. 18. Calculated trajectory of an electron liberated by

ionization near the electric field peak in a plane laser field at

intensity of 3� 1019 W/cm2.

Malka et al., 2000) and is well studied by simulations

(Sentoku et al., 2000; Feit et al., 2001; Naumova et al.,

2002).

3.2. Strong field ionization and ATI in super strong fields

Another consequence of the strong field Lorentz

acceleration described above is the ionization of single

atoms or ions at these very high intensities. When an

intense laser field of sufficiently long wavelength

illuminates an atom, the ionization can be described

by tunnel ionization. This process is illustrated in

Fig. 19a and occurs when the well known Keldysh

parameterffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIp=2Up

pis less than one, (where Ip is the

ionization potential of the ion in question and Up is

the ponderomotive or quiver energy of a free electron in

the laser.) In the quasistatic regime (i.e. when the

Keldysh parameter is o1), the ionization can be

described by the distortion of the ion’s binding potential

by the strong incident electric field (as pictured in

Fig. 19a). The electron can then tunnel through the

binding barrier. This tunnel ionization rate has a very

strongly nonlinear increase with increasing laser inten-

sity and therefore exhibits a threshold like behavior. The

thresholds for various ions are shown in Fig. 19b. This

figure illustrates that at the intensities likely achievable

in the near future with petawatt class lasers, high Z ions

can be fully stripped by this tunnel ionization.

Strong field tunnel ionization also has an interesting

consequence in that it effectively ejects a free electron

into the laser field at a well defined phase of the field,

with ionization occurring predominantly at the peak of

the field where the ionization rate is highest. The

electron then acquires some drift energy from the field.

This kinetic energy is often termed above threshold

ionization energy (or the ATI energy) (Agostini et al.,

1987).

In quasi-classical ATI at sub-relativistic intensities,

the tunnel ionized electron picks up a drift velocity that

is related to the phase in the laser oscillation at which it

is ionized (Burnett and Corkum, 1989). In sub-relativis-

tic (linearly polarized) fields, the electrons are ejected

predominately in the plane of the laser polarization and

the electrons drift is directed radially out of the laser

focus. As the intensity is increased toward 1018 W/cm2

(where the normalized vector potential of the laser field,

a0; approaches one), v� B forces start to affect the

trajectories of the electrons and the electrons begin to be

ejected in a direction forward of the polarization axis.

In a strongly relativistic field, these dynamics will be

different. Ionization of a very highly charged ion

effectively ‘‘injects’’ a free electron into the field at

phase near the field peak. When the laser field a0b1; the

v� B force curves the trajectory of the electron along

the laser propagation direction in a small fraction of the

field cycle. The electron with vsBc can then ‘‘surf’’ along

ARTICLE IN PRESS

Fig. 19. (a) Illustration of how strong field tunnel ionization of an ion occurs. (b) Plot of the laser intensity ionization threshold for a

number of different ions with different ionization potentials.

Fig. 20. Calculated electron distribution of energies as a

function of ejection angle. The angle of ejected electrons based

on a pure plane wave irradiation is also shown (which

corresponds to the line labeled tan2 y ¼ 2=ðg� 1Þ which denotes

the simple conservation of momentum in a laser field).


with the field, acquiring energy from the electric field. In

an infinite plane field, the electron has velocity slightly

smaller than c; and will fall out of phase with the field.

Consequently the electron will be decelerated in the

following E-field half cycle. The finite extent of a focused

laser beam, however, can allow some electrons to exit

the region of high field before this phase reversal occurs,

and the ejected electron will acquire quite substantial

energy from the laser. This phenomenon was described

in detail in Hu and Starace (2002). Hu and Starace

found that electrons ionized from V22+ by 8� 1021

W/cm2 pulses would be ejected with energy up to 2 GeV.

To examine these dynamics in more detail we have

performed numerical simulations of ATI in a strongly

focused, relativistic intensity femtosecond laser pulse

(Maltsev and Ditmire, 2003). Our simulation solves the

ionization rate equations for atoms at randomly selected

points in the focus. We use ADK rates (Ammosov et al.,

1986) for ionization, using Monte Carlo techniques to

determine the ionization time of a given ionization state.

Ionized electrons are born with zero energy and their

trajectory is then calculated using the relativistic

equations of motion. We use the full equations describ-

ing the electric field at a Gaussian focus, including the

longitudinal components of the electric field. These

longitudinal components actually play an important role

in the relativistic electron dynamics (Quesnel and Mora,

1998).

We calculated ionization of Ar17+ ions by an 800 nm,

30 fs laser focused to a spot size radius of 5mm and

an intensity of 5� 1021 W/cm2. These results appear in

Fig. 20. Here the ejected electron energies and the

electrons’ ejection angles with respect to the laser

propagation direction are plotted for an array of test

ARTICLE IN PRESS

Fig. 21. Cartoon illustrating how an electron positron pair

plasma could be created with a pair of petawatt laser beams.

T. Ditmire et al. / Radiation Physics and Chemistry 70 (2004) 535–552 549

electrons. These electrons emerge from the focus in a

narrow cone along the laser propagation axis and

exhibit energies up to 0.7GeV. This is a dramatic

departure from the usual, sub relativistic ATI behavior

which is well known from strong field ionization

experiments. The longitudinal ponderomotive force is

responsible for the forward directed electrons seen in

this simulation. These kinds of strongly relativistic

dynamics will be observable with the new generation

of petawatt lasers.

3.3. Pair plasma production

Finally, we remark on one particularly speculative

application of the strong fields and high oscillation

energies associated with ultraintense lasers. When a

plasma, such as that produced by irradiation of a solid

target, is driven by a relativistic intensity, the oscillating

electrons in the plasma have average energy exceeding

twice the rest mass of the electron. This begins to mimic

a ‘‘relativistic plasma’’, i.e. a plasma in which the

temperature is high enough that most of the electrons

have relativistic energy. Such relativistic plasmas are

believed to exist near black holes and probably play a

major role in the production of gamma ray bursts

(Crider and Liang, 2000).

Gamma ray bursts are among the most enigmatic

phenomena in the universe. A number of theories have

been advanced to explain the very large energy release

and hard X-ray spectrum resulting from these gamma

ray bursts. Most theories rest on the belief that plasmas

near a black hole are so hot that matter and anti-matter

(electrons and positrons) exist in equilibrium with each

other (Crider and Liang, 2000). The dynamics of these

extremely exotic plasmas are not well understood and no

terrestrial experiment has yet been able to access such

extreme conditions.

Such matter-antimatter plasmas, however, might now

be created in a laboratory with a petawatt class laser.

How this might occur is illustrated in Fig. 21. The

development of petawatt-class lasers opens the door to

the study of this new frontier in plasma physics and a

new state of matter in the laboratory, high-density,

relativistic e+e� plasmas. A laser with intensity exceed-

ing B2� 1018 W cm�2 has a sufficiently strong electric

field to couple most of the field energy to superthermal

electrons with temperature kT > mec2 (where me is the

electron rest mass and c is light speed). Positrons are

created when the relativistic electrons interact with high-

Z target ions via the trident process and in a secondary

manner by producing energetic photons which them-

selves produce a pair upon scattering from a nucleus.

Gigagauss magnetic fields are also present, which help to

confine the electrons. Using particle-in-cell (PIC) plasma

simulations Liang et al. (1998) estimated the e+

production rate for a thin (Bfew mm) gold foil and

found that petawatt-class lasers with sufficient pulse

length can, in principle, achieve in-situ e+ densities as

high as B10�3 of the background electron density, or

approximately 1022 cm�3 for solid gold targets, far

exceeding any other laboratory source of positrons.

Detailed numerical simulations by other groups (Naka-

shima and Takabe) confirm this prediction (Nakashima

and Takabe, 2002). Such experiments will require the

construction of the next generation of petawatt lasers

but hold the promise to study some of the most exotic

matter in the universe in the laboratory.

4. Conclusion

In this paper we have reviewed some of the recent and

potential applications of high intensity short pulse

lasers. Examples of many of these applications have

been illustrated using results from our group. The kinds

of experiments described here leverage the rapid

advances in laser technology that now make possible

table top lasers with 10–100 TW and larger scale systems

with power exceeding 1PW.

The applications of these lasers tend to fall into two

categories: those experiments relying on the ability of a

high intensity short pulse laser to concentrate energy in a

small volume, and those applications which use the very

high electric and magnetic fields which are produced in a

tightly focused high intensity laser. The former category

leads to interesting high energy density experiments;

experiments which probe the state of matter at pressures

approaching 1 Gbar or which study the dynamics of

strong shock wave propagating though matter. Many of

these applications have relevance to astrophysics as they

represent the only way known to access some of the

exotic states of matter found in astrophysical objects in a

terrestrial laboratory.


The second category of experiments uses the large

field strengths that accompany the high focused laser

intensity. These high field experiments are presently

centered on understanding the consequences of the

relativistic motion of electrons in such a field. These

relativistic effects lead to an entire range of nonlinear

optical phenomena, harmonic generation, etc. and could

lead to quite energetic electron production in strong field

ionization. The next generation of petawatt lasers will

certainly lead to an even greater, unexplored range of

applications in both high energy density and high field

physics.

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