Pre-Ionization Controlled Laser Plasma AIAA-2010-4307

8/10/2019 Pre-Ionization Controlled Laser Plasma AIAA-2010-4307

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American Institute of Aeronautics and Astronautics

1

Pre-Ionization Controlled Laser Plasma Formation for

Ignition Applications

A.P. Yalin1, F. Loccisano2, S. Joshi3

Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA

Z. Zhang4Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville, TN, USA

and

M. Shneider5

Department of Mechanical & Aerospace Engineering, Princeton University, Princeton, NJ, USA

We present initial modeling and experimental results on the use of pre-ionizing pulses to

enhance and control laser plasma formation in gases. The approaches are based on use of an

initial pulse to achieve pre-ionization with a second pulse for generation of additional

ionization and energy addition. Experimental results using a pair of nanosecond duration

1064 nm pulses are presented. In the configuration studied, the first pulse provides

breakdown which also promotes additional energy deposition by the second pulse.

Maximum energy deposition occurs when the inter-pulse separation is approximately 20 - 40

ns. Modeling results examine a case where the first pulse provides pre-ionization (but not

breakdown) and shows that in the presence of pre-ionization, the effect of a second pulse is

to increase ionization and heat the gas. Non-intrusive microwave diagnostics for ionization

measurements are also presented.

Nomenclature

B = bandwidth of the detection sensor

= dissociative recombination rate coefficient

ii = ionion recombination coefficientCW = continuous wavec = speed of light

d = beam waist diameter

= skin depth

e = electron chargeE = pulse energy

EAI = electron avalanche ionization

EAL = energy addition leg

1

Associate Professor, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, AIAA

Member.2Graduate student, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO.3Post-doctoral researcher, Department of Mechanical Engineering, Colorado State University, Fort Collins, CO.4Assistant Professor, Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville,

TN, AIAA Member.5Senior Research Scientist, Department of Mechanical & Aerospace Engineering, Princeton University, Princeton,

NJ, AIAA Member.


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Ei = microwave electric field

E0 = electric field amplitude

0 = dielectric constant

e, = flux of the electrons

+, = flux of the positive ions

= flux of the negative ions

IL(r,t) = intensity of the infrared laser fieldIMW = incident microwave power

k = Boltzmann constant

kd = electron-detachment rateLIBS = laser induced breakdown spectroscopy

me = electron mass

N = total electron number in the plasma

Nd:YAG= neodymium-doped yttrium aluminum garnet laser

NO2 = density of oxygen moleculesne = electron number density

n- = density of negative ions

n+ = density of positive ions

a = electron attachment rate

c = coulomb collisional frequency

en = electron neutral collisional frequency

i = rate of cascade ionization by electrons oscillating in a laser field

O2 = oxygen atom

O2- = oxygen ion

L = radiation frequency

MW = incident microwave frequency

opt = optimum microwave frequency

p = plasma frequency

PD = thermal noise powerPL = preionization leg

r = radial coordinate

REMPI = resonance-enhanced multi-photon ionization

= conductivityph = cross section of electron photodetachement from

2O ions

T = plasma temperature

TD = temperature of the detection sensort = time variable

td = pulse duration

= total average power

V = volume of the plasma

x = displacement of electrons

x& = velocity of electrons

x&& = acceleration of electrons

I. IntroductionSoon after the advent of high-power ("giant) laser pulses in the 1960's it was observed that tightly focused laser

beams can be used to generate laser breakdown. Laser breakdown (spark formation) can be non-resonant such that

the laser electric field causes gas breakdown, or resonant, such that there is a resonant photoionization step. At

typical nanosecond laser conditions, for non-resonant breakdown, initiation of the breakdown process requires abreakdown threshold intensity of ~100-200 GW/cm2 for visible or near-infrared wavelengths in atmospheric

pressure air1-8with typical beam waists of ~10-30 m and pulse energies of 5-10 mJ. Ronney9has summarized

four modes of laser ignition: non-resonant and resonant breakdown (mentioned above), thermal ignition (in which

there is no breakdown, but the laser is used to heat the gas), and photo-chemical ignition (in which resonant

dissociation is employed, and no breakdown occurs).


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Benefits of laser sparks for ignition relative to conventional ("spark-plug") sparks can be owing to several factors.

First is the differences related to the physical configurations, e.g., the fact that conventional spark discharges require

the presence of adjacent electrodes which act as heat sinks and tend to quench the flame. However, the differing

plasma parameters (initial temperature, pressure, electron parameters etc.) also result in more fundamental

differences including flame propagation speeds. For example, in a study of laser ignition of propane-air mixtures theflame propagation speeds were evaluated from Schlieren images10. The experiments showed that at early times the

measured flame speeds exceed the laminar flame speed thereby providing a clear indication of plasma-assisted flame

propagation (a phenomenon which the authors term overdrive). Early flame speeds are particularly critical as thisis when flame kernels are most prone to extinction due to flame stretch. This is an example of differing plasma

parameters of laser created sparks that, along with the lack of electrodes and flexibility in the spark location, can

lead to combustion advantages in a range of applications, for example in large-bore reciprocating gas engines thatare used for power-generation, (e.g., distributed power generation at hospitals), for pumping and compression of

natural gas3,6,11-16, and for ignition of turbines used in power generation, and (military) aircraft engines 17,18. Finally,

we mention that there has been significant recent interest in use of atmospheric pressure plasmas (e.g., from

dielectric barrier discharges) for flame holding and flow control, and it is possible that laser plasmas could be of

interest in such applications owing to the ability to freely locate the plasmas within flows and boundary layerswithout the presence of perturbing electrodes.

The present contribution presents initial experimental and modeling results onnew approaches employing pre-

ionizing pulses, followed by energy addition pulses, to enhance and control laser plasma formation in gases. Byappropriately selecting laser pulse parameters (for example, wavelengths, pulse durations, pulse energies, pulse

separation etc.) it may be possible to achieve laser plasma parameters not readily achievable from single laserpulses. For example, a current challenge is to deliver combustion initiating pulses with sufficient energies through

fiber optics13,16, and the use of a combination of pre-ionizing and energy addition pulses may allow higher (total)energy delivery. Another potentially attractive configuration, as will be shown in the modeling presented in this

contribution, may be the ability to use multiple pulses to control the gas temperature in order to achieve thermal

ignition.

A key requirement for experimental characterization of pre-ionizing pulse configurations is appropriate

diagnostics. In this regard we present the results of an innovative diagnostic based on microwave scattering.Microwave absorption, reflection, scattering and interferometry methods have been used in various applications19,20.

Recently coherent microwave Rayleigh scattering has been used for the detection of laser-induced small-volume

plasmas21. The electric field of the Rayleigh scattering signal is approximately linearly proportional to the totalelectron number inside the plasma when the plasma frequency is much smaller than the microwave frequency. When

the microwave scattering method is used to detect the plasma selectively generated by Resonance-Enhanced Multi-

Photon Ionization (REMPI), a highly sensitive diagnostic method, Radar REMPI, can be used for trace speciesmeasurement

22, rotational temperature measurement

23 and plasma decay characterization

24 etc. The coherent

microwave Rayleigh scattering method is capable of time-accurate, highly sensitive and extremely selective

measurement of the small-volume plasma, even in cases when the plasma is not luminous. Such diagnostic

techniques are useful to obtain information needed for accurate modeling of plasmas in single pulse or double pulse

(pre-ionization followed by energy addition).The layout of this contribution is as follows. In Section II, we present the experiment setup used for studies of

energy addition to a pre-ionized plasma volume with nanosecond duration lasers. In Section III, we present the result

and discussion of the experiments. Modeling results on the use of pre-ionizing pulses are presented in Section IV. InSection V, we present the microwave diagnostic process for measuring the plasma conditions and finally in Section

VI, we present the conclusions.

II. Experimental Setup

Here we present the experimental setup used to investigate a dual pulse approach based on an initial pulse toachieve pre-ionization with a second pulse for generation of additional ionization and energy addition. In this study

both pulses are from Q-switched Nd:YAG lasers with 1064 nm radiation and pulse durations of nanoseconds. Figure

1 shows the experimental setups used both of which are based on overlapped collinear beams. In Figure 1a), both

pulses were from the same laser source - Big Sky CFR Model. The P- polarized beam was split into two legs. A thinfilm plate polarizer was used to convert one of the P-Polarized legs into a S-polarized leg. The P-Polarized leg

formed a pre-ionizing leg (PL) that made the spark or pre-ionized volume and the S-Polarized leg formed an

energy addition leg (EAL) that added additional energy into the spark.


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Figure 1.Schematic of the experimental setup. 1) 1064 nm Nd:YAG laser - Big Sky CFR Model, 2) 50/50

Beam Splitter, 3) Telescope, 4) Half Wave Plate, 5) Thin Film Plate Polarizer, 6) Recombiner, 7) Mirror, 8)

Focusing Lens, 9) Spark Location, 10) Detector, 11) Collimating Lens, 12) 1064 nm Nd:YAG laser -

Continuum Powerlite 8000 Model, 13) Beam Dump. The star indicates the location where the two beams are

focused.

The beam diameters for the PL and EAL are controlled with telescopes in their respective legs. The two beamswere combined into a final beam via a recombiner (which let P polarized beam through and reflected S polarized

beam). The final beam was focused by a plano-convex lens with a focal length of 20 mm. A careful alignment

procedure using IR beam cards and a beam profiling camera (Spiricon) ensured a high degree of spatial overlap

between the two beams. Due to the limited space, this experimental setup provided a maximum inter-pulseseparation of 40 nanoseconds between the two pulses in the two legs. Figure 1b) shows a similar experimental setup

but one in which the two different lasers were used. The reason to use two beams was to be able to achieve more

flexibility in the pulse delay (separation) since in this case the time delay was controlled electronically via a pulse

delay generator. The resulting timing jitter due to internal laser circuitry was ~10 ns. In this case, a 1064 nm

Nd:YAG - Big Sky CFR Model with P polarized beam and a 1064 nm Nd:YAG - Continuum Powerlite 8000Modelwith S polarized beam were used as the two legs. The beam qualities (M 2) of the two lasers were 1.8 and 3.7

respectively. Similar to the first experimental setup, the two beams with two different polarizations were combined

into one final beam using a beam recombiner.In both experimental setups, the energy transmitted through the plasma was measured using an energy meter.

Each leg had a variable attenuator formed by a combination of a half wave plate and a polarizer. The energy

absorbed by the plasma was found as the difference between the input energy and the transmitted energy. Thisprocedure neglected any beam scattering or reflection. A thin film plate polarizer was placed after the spark in setup

1b) so that the transmitted beam could be split into two beams corresponding to their polarization. This allowed for

accurate measurement of the energy deposited in the spark by each individual leg. Other parameters, such as spot

sizes are provided within the following section.

III. Results and DiscussionAs a baseline, we have first investigated the amount of energy that a spark from a single pulse would absorb at

100% sparking condition. Figure 2 shows the fraction of energy that is absorbed by the spark at varying input energy

levels. (We term this as the PL spark though in case there is a single spark.) For this experimental configuration, the

waist diameter was d=15 m, the pulse duration was td=9.6 ns, and the input laser energy at the spark threshold (i.e.,

Single

Laser

Scheme

Dual

Laser

Scheme


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intermittent sparking) was 5.5 mJ. The trend line in Fig. 2 shows that the fraction of energy absorbed by the spark

remains nearly constant at ~0.5. This is consistent with other results which show that the fraction of energy absorbed

by the spark grows linearly at energy levels just above the spark threshold and then remains constant at higher input

energy levels25.

10 12 14 16 18

0.0

0.2

0.4

0.6

0.8

1.0

Frac

tiono

fEnergy

Absorbe

d(PL)

Energy Input (PL) (mJ)

PL

td= 9.6 ns

d= 15 m

Figure 2. Fraction of energy absorbed by plasma for single laser pulse (PL).

Figure 3 considers a dual pulse case with a PL followed after some delay by EAL. Two pulse delay times, 5 and

40 ns, were examined. The ordinate shows the fraction of energy in the EAL that was absorbed. In this case the two

beams have similar waists and pulse durations, i.e., d=15 m and td=9.6 ns. The energy in the PL was held constant

at 10 mJ whereas the energy in EAL was varied. At pulse delay of 5 ns, the spark (initially created by the PL)absorbs approximately 70% of the energy in the EAL. However, at 40 ns pulse delay, within the measurement

uncertainty, the spark completely absorbs the energy in the EAL. This occurs for cases where the EAL is (on its

own) sparking or not sparking, i.e., right of left of the arrow in Fig. 3. Clearly, the energy in the EAL can couple tothe ionization of the PL. Figure 4 shows photographs of the visible spark emission from the PL (left) and

combination of PL and EAL (right). The latter image has a larger spark containing more energy.

0 4 8 12

0.0

0.2

0.4

0.6

0.8

1.0

Frac

tiono

fEnergy

Absorbe

d(EAL)

Energy Input (EAL) (mJ)

5 ns Delay

40 ns Delay

PL:

E = 10 mJ

td= 9.6 ns

d= 15 mEAL:

td= 9.6 ns

d= 15 m

Figure 3. Fraction of energy absorbed from the EAL. The EAL arrives at the focal volume at delay times of 5

and 40 ns relative to the PL. The arrow at 5.5 mJ shows the threshold for the EAL to spark (on its own).


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Figure 4. Photographs of laser sparks. Left: PL. Right: PL and EAL. The two images have same spatial scale

and exposure conditions and show the spark due to PL and EAL to be larger than that from PL alone.

We have also measured the effect of increasing the focal spot size of the EAL beam relative to the PL beam. The

beam in the PL is focused to a waist 15 m whereas the beam in the EAL is focused to a waist diameter of 24 m.In this case the threshold for the EAL to spark (on its own) was 12mJ. Figure 5 shows the absorption of the EAL fordelay time of 40 ns. Again, even though the EAL has larger focal spot, essentially all of its energy is absorbed by the

PL. This may be explained by the fact that the initial spark (created by the PL) will have grown to a size of ~1mm

after the 40 ns delay26and hence has a larger absorption cross-sectional area. This configuration could correspond toa situation where the PL is delivered through the core of a double clad fiber (high beam quality) while the EAL is

delivered through the (inner) clad with lower beam quality.

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

Frac

tiono

fEnergy

Absorbe

d(EAL)

Energy Input (EAL) (mJ)

EALPL:

E = 10 mJ

td= 9.6 ns

d= 15 mEAL:

td= 9.6 ns

d= 24 m

Figure 5. Fraction of energy absorbed from the EAL. The EAL arrives at the focal volume at delay time of 40

ns relative to the PL.

Another experiment used the setup of Fig. 1b) to investigate the effect of varying the pulse delay between the PLand EAL. Additionally, the final polarizer used in this setup allowed for separate measurement of the energy

absorption of both legs. Figure 6 shows the fraction of energy absorbed by the plasma for both PL and EAL. Asshown in the legend, the two legs had similar waists and pulse durations. The energies in the PL and the EAL were

held constant at 13 and 16 mJ respectively. For short delay times (20 ns) the presence of the partially overlapping

EAL influences the PL and increases its absorption. For larger delay times the PL is unaffected by the EAL (whicharrives later) and has absorption of ~40% (similar to Fig. 2). The peak absorption of the EAL occurs at delay times

of ~20-40 ns after the PL and shows greater than ~90% absorption. The behavior of the EAL for larger delay times

is more complex. There is an interesting effect whereby for delay times of ~200 ns - ~20 s, there is zero absorption


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of the EAL, even though it has enough energy that it does breakdown the air (and have absorbed energy) on its own.

In other words, for these delays, there is some residual effect of the earlier PL that precludes energy coupling from

the EAL. As shown in Fig. 6b, for much larger delay times (40 s), the absorption of the EAL recovers to its valueof ~0.4 (as expected when it is on its own).

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

FractionofEnergyAbsorbed

Pulse Delay (ns)

EAL

PLPL:

E = 13 mJ

td= 9.6 ns

d= 15 mEAL:

E = 16 mJ

td= 9.6 ns

d= 15 m

6a)

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4


Pulse Delay (s)

EAL

PL

6b)

Figure 6. Fraction of energy absorbed from the EAL and PL as function of delay times. 6a and 6b are for the

same conditions and differ only in their scales.

A final experiment has investigated the effect of pulse delay on the laser-plasma energy coupling when the EALhas longer pulse duration than the PL. Conditions are given in the legend of Fig. 7. Also of interest is that in this

case is that the EAL does not spark on its own for the delivered energy of 25 mJ (since the longer pulse duration

gives intensity below breakdown). The presence of the PL plasma still leads to absorption of the EAL and the resultsare generally similar to those of Fig. 6.

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0


Pulse Delay (ns)

EAL

PL

PL:

E = 13 mJ

td

= 9.6 ns

d= 15 mEAL:

E = 25 mJ

td= 43 ns

d= 15 m

Figure 7. Fraction of energy absorbed from the EAL and PL as function of delay times. The pulse duration of

PL is longer than EAL.

IV. Modeling of Dual Laser PulsesHere, we present preliminary modeling results on dual pulses for laser induced plasmas. We consider a case in

which the first pulse partially ionizes the gas but does not provide breakdown, e.g., as could be achieved with afemtosecond laser pulse. After some delay, a second pulse, of nanosecond duration, passes through the partially

ionized region. The modeling presented here examines the temporal dependences of the electron number density and

temperature during the second pulse. It is found, for example, that the second pulse can elevate the temperature to

levels of several thousand degree Kelvin which could provide an ignition source. In this work, thermal ionization ofthe second pulse is not considered.


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The modeling approach followed here is similar to that employed in past work27. Because the laser spark at the

focal region of the beam represents an extended ellipsoid, we simplify the plasma evolution and radial expansion as

the 1D time-dependent diffusion-drift equations for the weakly-ionized plasma in air. The model is based on the

continuity equations for a three-component plasma consisting of electrons and positive and negative ions. These

equations are solved self-consistently in our model with the Poisson equation for the field potential, axially

symmetric NavierStokes equations for gas flow parameters, equations for energy transfer to molecular vibrations,

and heat conduction equation. The flow field properties of the initial laser pulse are used to set the initial values forthe second pulse. Effects related to the influence of the second laser pulse are included in our model through the

terms accounting for the photodetachement of electrons from2O ions in the kinetic equations and through the Joule

heat term in the electron heat conduction equation. The intensity of the second laser pulse is assumed to be too lowto induce any noticeable ionization effects. (This is in contrast to the experiments described in Section III.)

With an assumption of a cylindrical geometry of plasma decay, the continuity equations for the electron density,

ne, and the densities of positive and negative ions, +n and n are written as

+ ++=

+

n]

)t,r(I[nNknnnn

r

)r(

r

1

t

n

L

Lph2Odeaeei

ee

h (1)

+++ =

+

nnnnn

r

)r(

r

1

t

neiieei

(2)

+=

+

n]

)t,r(I[nNknnn

r

)r(

r

1

t

n

LLph2Odeiiea

h. (3)

where, tis the time variable, ris the radial coordinate,e, +, and are fluxes of the corresponding species,is the

dissociative recombination rate coefficient, a is the electron attachment rate, ii is the ionion recombinationcoefficient, kdis the electron-detachment rate,IL(r,t)is the intensity of the infrared laser field, Lis the frequency of

the laser radiation, NO2 is the density of oxygen molecules, phis the cross section of electron photodetachement

from2O ions in the atmosphere through the )()(

3

2

4

2

++ ggL OeOh process28, and i is the rate of

cascade ionization by electrons oscillating in a laser field. Details on the rate coefficients can be found in past

work27. Initial conditions (corresponding to the end of the first pulse) are taken asne=n+=1023m-3, with n-=0. Figure

8 shows the temporal dependence of these parameters as time evolves. The plasma quickly recombines, primarily bydissociative recombination, with the electron and positive ion number densities dropping by more than two orders of

magnitude in 20 ns. The number density of negative ions rises to greater than 1019m-3owing to electron attachment

to molecular oxygen.

0 10 20 30 40 50

1019

1020

1021

1022

1023

1024

n-

ne,n+,n-

(r=

0)(1/m

3)

t (ns)

no 2nd pulse

n+ne

initial conditions:

ne(0)=n

+(0)=10

231/m

3; n

-(0)=0

Figure 8. Time dependence ofnefor three different laser inter pulse delays.

Figures 9a and 9b show the effect of adding a second laser pulse of nanosecond duration. The pulse is assumed to

have duration of 10 ns, focused radius of 7.5 m, and pulse energy of 5 mJ. A wavelength of 1064 nm

corresponding to a neodymium laser is used. We consider three different delays between the end of the first pulse


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(t=0) and the arrival of the second energy adding pulse. These delays times are 10, 25, and 40 ns, which we specify

as the arrival time of the peak of the laser intensity. Figure 9a shows the evolution of the electron number density (at

r=0 on the laser axis) for the three delay cases. In each case, prior to arrival of the second pulse, nedecays as in Fig.

8. The effect of each pulse is to increase the electron number density owing to cascade ionization. As shown in Fig.

9, the gas temperature also increases due to arrival of each laser pulse. The energy from the laser beam is coupled tothe electrons by Joule heating and quickly transferred to the neutrals. The transfer is directly to the translational

modes as well as by vibrational excitation which in turn transfers to translational modes. For the pulse delays of 10

and 25 ns, the gas temperatures exceed 4000 K and 3000 K respectively. An attractive feature of such approach isthat these volumes of elevated gas temperature may be able to provide ignition sources (even in the absence of fully

ionized plasmas). It is important to note that we do not model thermal ionization which would result in further gas

heating and increases in electron density. Therefore, the second maxima of electron number density and temperature(i.e., the maxima that roughly coincide with the peaks of the laser pulses) may not occur in reality since the thermal

ionization will further increase the electron number density and temperature. Examination of the density profiles

(not plotted), shows that for the case of the 10 ns delay there is a shock wave present with the gas radial velocity

reaching 550 m/s, while in the 40 ns delay case the flow is almost acoustic with peak sound speed of 370 m/s.

0 10 20 30 40 50

1018

1019

1020

1021

1022

1023

1024

ne

(r=0)(m-3)

t (ns)

No 2nd Pulse

With 2nd Pulse

9a)

0 10 20 30 40 50

500

1000

1500

2000

2500

3000

3500

4000

T(0)(K)

t (ns)

With 2nd Pulse

No 2nd

Pulse

9b)

Figure 9. Time dependence of plasma parameters for different laser pulse delays. 9a): Time dependence of

electron density (ne), 9b): Time dependence of temperature (T).

V. Microwave DiagnosticsIn this section, we present a diagnostic method that we intend to employ to measure the plasma conditions in

double pulse configuration. This method of measuring electron number density in the plasma is based on coherentmicrowave Rayleigh scattering. When a fixed-frequency Continuous Wave (CW) microwave source is used to

illuminate the laser-induced plasma, movement of electrons in the plasma is modeled by a classical dynamic

equation21.

ei2pcen m/eExx)(x =+++ &&& (4)

Where e and me are electron charge and mass respectively, x, x& and x&& are the displacement, velocity and

acceleration of electrons, respectively, en is electron neutral collisional frequency, c is Coulomb collisional

frequency ande0e

2

p

m/ne = is the plasma frequency, 0 is dielectric constant, for a CW microwave

source, tcosEE MW0i = is the microwave electric field, E0 is the electric field amplitude and MW is themicrowave frequency.

When skin depth, MW2/c = , where conductivity )(m/ne2en

2MWeene

2 += , at microwavefrequency is larger than the size of the plasma, coherent microwave Rayleigh scattering occurs. The whole plasma

region is transparent to the microwave field. When the skin depth at the microwave frequency is smaller than the

size of the plasma only electrons within the skin depth oscillate in response to the microwave field, which


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corresponds to a general Mie scattering.29For Rayleigh scattering, the total averaged power scattered by the

plasma can be expressed as21

2MWcen

22MW

2p

4MW2

MW2MWcen

22MW

2p

4MW

4p

2MW

4))(()(

NI))(()(

VI

c6

1

++

++= (5)

whereIMWis incident microwave power, cis the speed of light, neis the electron number density, Vis the volume of

the plasma, andNthe total electron number in the plasma, = dVenN .The equation (4) and (5) are applicable not only to coherent microwave Rayleigh scattering but also to incoherentand coherent Thompson scattering. When electrons are collisionless, electron neutral collision, Coulomb collisionsand the electron plasma frequency are negligible. The microwave scattering becomes a classical Thompson

scattering. When the microwave wavelength is much larger than the plasma dimensions, the microwave scattering

becomes a coherent Thompson scattering.Based on the equation (5), the electric field and intensity of microwave scattering are functions of the electron

number density in the plasma. Relative electron number measurement in the plasma can be made since the

microwave loss and reflections due to the surroundings are not easily calibrated. As an approximation, when the

second term in the denominator is much greater than the first term 2)2MW2p(

2)MW)cen(( >>+, the

denominator can be regarded as independent of electron number density such that the total microwave scattering

power is proportional to the square of the total electron number inside the plasma, i.e., 2N . As an extension

to the equation (4), the electric field of the microwave signal is proportional to the total electron number, NE

which is the case for the homodyne detection used in the experiments22-24,30,31. The approximation is valid for the

experiments in the given references. However when the two terms in the denominator are

comparable, 22

MW2p

2MWcen )(~))(( + , the denominator in the equation (4) cannot be omitted completely

such that the scattered microwave intensity does not followN2and the electric field does not followN. Instead, they

are complex functions of the total electron number inside the plasma32.

Absolute electron number density measurement can be obtained from equation (5), i.e., maximum microwave

scattering occurs when the fraction of ]))(()/[( 2MWcen22

MW2p

4MW

4p ++ becomes maximum. Since the

plasma parameters, ne, N andpare to be measured, the only parameter in the fraction that can be varied is the

microwave frequency. Microwave scattering can reach its maximum when the microwave frequency is swept. In

such case the method can be referred to as resonant coherent microwave scattering. A simple mathematical

manipulation of equation (5) shows that the resonant effect, i.e., maximum microwave scattering occurs at themicrowave frequency:

2cen

2p

4p

opt)(2

2

+= (6)

Quantitative measurement of average electron number density in a plasma can be conducted by tuning the

microwave frequency around the resonant conditions of the coherent microwave Rayleigh scattering. For the knownbuffer gas at a given pressure, the maximum microwave scattering signal occurring at a certain frequency can be

used to determine the plasma frequency and averaged electron number density within the plasma. If an evolving

plasma can repetitively generated at same conditions, such as laser-induced plasma, average electron number density

at various phases can be determined by maximizing the microwave signal at those periods.The minimal electron number density measurable by the resonant microwave scattering can be estimated. The

thermal noise level sets the lowest limit for the microwave detection. The thermal noise power (PD) can be

calculated as:BkTP DD = (7)

where k is Boltzmann constant, TD is the temperature and B is the bandwidth of the detection sensor. For themeasurement of 1 nanosecond resolution at room temperature, 1 gigahertz bandwidth for the microwave detection is

required which results in the minimum microwave power of 410-12W.

Under the resonant microwave Rayleigh scattering condition, by substituting equations (5) and (6) into equation(7), the detection limit of electron number density is about 3109~ 11010cm-3for the microwave source at a few

milliwatts when the microwave source is 30cm from the plasma. With such a low power, heating effect is essentially


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negligible on the plasma. Thus a non-intrusive and quantitative measurement of electron number density inside a

plasma can be conducted by the coherent microwave scattering at the resonant condition.

10a) 10b)

Figure 10. Normalized backward scattered microwave signal for a uniform plasma sphere. 10a):ne=1010

cm-3

and a radius of 100 m, with a buffer gas of 0.5 Torr Argon. 10b): ne=5x1010

cm-3

and a radius of 100 m,

with a buffer gas of 0.5 Torr Argon.

In order to take account of collisional frequency, a preliminary numerical approach has been conducted. Based on

the resonant coherent microwave scattering theory of equation (4) and (5) and a general Mie scattering calculation33,

the normalized backward scattering is shown in Figure 10a and 10b for a uniform plasma sphere of 11010 cm-3and51010 cm-3 at radius of 100 m in 0.5 Torr Argon, respectively. The plots show that the resonant coherent

microwave scattering occurs at 6.1 GHz for the plasma sphere of 11010cm-3and 12.74 GHz for the plasma sphere of

51010cm-3with a buffer gas of 0.5 Torr Argon (for collisional frequency m=2.65109s-1).

VI. ConclusionsIn this contribution, we have shown results from initial investigations on the use of pre-ionizing pulses to enhance

and control laser plasma formation in gases. The approaches were based on the use of an initial pulse to achieve pre-ionization and a second pulse for generation of additional ionization and energy addition. In the configurations that

we employed, the first pulse provides breakdown which promotes additional energy deposition by the second pulse.

We explored the energy coupling between a pair of 1064 nm beam. Different experimental configurations such as

different interpulse delays (separation) and different focal diameters and pulse durations of the second pulse in theenergy addition leg were explored. We found maximum energy deposition to occur when the interpulse separation

between the preionizing and energy adding pulse was approximately 20 - 40 ns and absorption was almost 100%.

The variation in the focused spot sizes of the two beams didnt show any significant effect nor did the longer pulse

width of the second energy addition pulse. However, compared to the case when two short pulses (~10 ns) were

used, we did observe that when the pulse in the energy addition leg had a longer pulse width, the spark absorbedlower fraction of energy from both the preionizing leg as well as the energy addition leg.

We have also modeled a case where the first pulse provides pre-ionization (but not breakdown) and showed that

in the presence of pre-ionization, the effect of a second pulse is to increase ionization and heat the gas. The model isbased on the continuity equations for a three-component plasma consisting of electrons and positive and negative

ions. These equations were solved self-consistently in the model with the Poisson equation for the field potential,

axially symmetric NavierStokes equations for gas flow parameters, equations for energy transfer to molecularvibrations, and heat conduction equation. We also presented a non-intrusive microwave diagnostic technique tomeasure the electron densities in plasma. Our future plans include modeling the specific cases that we have explored

in our experiments and comparing the modeled data with the measurements from the microwave diagnostics. Thiswould aid us to better understand the laser-plasma energy coupling for various configurations.

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