C. Joshi- The Plasma Beat Wave Accelerator- Experiments

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THE PLASMA BEAT WAVE ACCELERATOR - EXPERIMENTS

C. Joshi

University of California, Los Angeles, CA 90024, U.S.A.

ABSTRACT

In th e Plasma Beat Wave Accelerator, acceleration is achieved by alongitudinal electrostat ic f ield produced as a resul t of charge separation

generated by a plasma wave traveling close to the speed of l ight . Theplasma wave in turn is produced by two colinear laser pulses whose f requency difference i s such that th e beat frequency matches the plasma frequency. Optical mixing and Raman forward scattering instabi l i ty p laya

crucial role in the growth and nonlinear saturation of such high phase

velocity plasma waves. In this paper we describe experiments that show,i) that long wavelength high phase velocity electron plasma waves can be

generated in a quasi-homogeneous plasma by opt ical mixing, i i ) re la t iv is

t ic part icles are indeed generated by the Raman forward instabi l i ty, andi i i ) with short wavelength lasers, potential exists for obtaining ul t ra

high electr ic f ields.

INTRODUCTION

Collective particle accelerators making use of th e high f ields asso

ciated with focused laser beams have received considerable attention inrecent years. Although the transverse electr ic f ields at th e focus can be

as high as 109-1010 volts per meter, a charged particle osci l lat ing in

such a field achieves no net acceleration at a l l since there i s no component of the electr ic field in the direction of propagation. To circumvent

this problem i t has been suggested that the electrostat ic f ield of a long

i tudinal plasma osci l lat ion set up by the electromagnetic wave can be used

to accelerate particles .

In a laboratory plasma with no external magnetic f ield there arebasically three processes which give r ise to high frequency plasma

osci l lat ions. The f i r s t is. a l inear mode conversion process, also knownas resonant absorption because i t occurs when the frequency of the laserl ight matches the local plasma frequency in an inhomogeneous plasma. Theenergy in the plasma wave is then coupled to plasma electrons by coll isional damping, Landau damping, electron trapping and wavebreaking. Since the

phase velocity of the resonant f ield propagates towards the lower densityregion, th e wave particle interaction preferentially accelerates electrons

down the density gradient. Although this process can produce very largeelectr ic fields (1010-1011 volts/em), the region of resonance i s very

narrow and consequently part icles are not accelerated to ul t ra-relat iv is t ic

energies.The second mechanism i s known as high frequency parametric instabi l

i t ies in which an electromagnetic wave propagating in an underdense plasma

undergoes a decay into an electron plasma wave and another electromagnetic

wave(Stimulated Raman Scattering), or an ion acoustic wave (Parametric

D e c , ~ y Instabi l i ty) or another electron plasma wave (Two-Plasmon Decay).

Whenever one of the decay products is an electron plasma wave, very large

electr ic fields in the direction of propagation can be produced. Poisson'sequation gives V'Ep = -4TIenl and the maximum amplitude of the electronplasma wave i s obtained when the level of density fluctuation nl/no = 1.

Thus kpEp = -4TIen and using wp = 4TInoe/m we obtain the elec t r ic f ieldo

-1 5



Ep = mWpvp/e and the wave potential e as m v where vp is the phase velocityof the wave. Fbr vp = c, e = ymc 2 . In the nonrelativistic case, a part ic le whose velocity Ve in th e direction of propagation of the wave is near

the phase velocity can be trapped and gain up to 4 m v ~ ( v e / v p ) ~ . In the rela t iv is t ic case vp c and the maximum energy gained i s theoretically upto ( w 2 / w ~ ) m c 2 .

The third mechanism is known as optical mixing in which two electromagnetic waves beat in a plasma to resonantly drive density fluctuations.The electrostat ic field of such a resonantly driven plasma wave can be

very large and be used to accelerate the plasma electrons or an injectedgroup of part ic les. One can think of the opt ical mixing process as Raman

scattering instabil i ty below threshold but with f ini te noise source, or

al ternat ively, nonlinear saturated l imit of Raman forward scattering.In this paper we shall discuss the optical mixing process and th e

stimulated Raman forward scattering ins tabi l i ty . In part icular , we shal l

examine the role of these in th e Plasma Beat Wave Accelerator. In th ePlasma Beat Wave Accelerator, acceleration is achieved by an electrostat icfield produced as a resul t of charge separation generated by a plasma wavetraveling close to the speed of l ight. The plasma wave in turn i s pro

duced by colinear two laser pulses whose amplitude is modulated so that

the beat frequency matches the plasma frequency. Experiments that showthat long wavelength and high phase velocity electron plasma waves can be

generated by the optical mixing process in a homogeneous plasma as wellas generation of ul t ra- re la t iv is t ic part ic les by the Raman instabil i tyare described.

OPTICAL MIX IN;

The nonlinear excitation of electron plasma waves (EPW) by beating twoelectromagnetic (EM) waves has been under considerable investigation latelybecause of i t s potential role in the laser-electron accelerator, 1 cascade

plasma heating,2 laser-fusion pellet preheat,3 and as a plasma density

diagnostic. 4 Basically, when two coherent EM waves, (wo,ko) and (WI' kl) ,

occupy the same volume the total intensity is modulated in space at ~ =k ± k l ' and in time at ~ = Wo ± WI. The ponderomotive force (E ) in ap£asma associated with this beat wave can resonantly drive l o n g i t ~ i n a l electron density fluctuations of wavenumber kp = ~ k i f wEPW = ~ w . WEPW, i s

the frequency of the electron plasma wave and i s related to the plasma frequency via the dispersion relation w ~ P W = w + 3 k ~ v ~ . This is the usualopt ical mixing process. I f the two EM waves are colinear as shown in Fig. 1,

then the phase velocity vp = wEPW/kp at which the density fluctuations propagate is nearly equal to th e group velocity of the EM waves, v = c(l w ~ / w ~ ) ~ , and the three waves are locked into synchronism over tRousands of

wavelengths i f w »w o • Also, since vp c there is l i t t l e Landau dampping and the EPW can grow to a very large amplitude.

The behavior of such large amplitude plasma waves driven by beating

of two laser beams has been studied by Rosenbluth and Liu. 5 They foundthat for Vole « 1, nIno « 1, the density fluctuations grow l inear ly withtime when wp = ~ w

n n 1 VO(O)- ( t ) = - (t=O) + - (1 )no no 4 c

Where nIno is th e EPW amplitude and Vo(O,l) = eE(O,l)/rnw(O,l) is the electron quiver velocity in the laser f ie lds. Wavebreaking is approached whennIno 1; however, to reach this l imit th e EPW must be exactly in

-196



BEATWAVE

.. - . . . . . . . - . . . . . . FNL

-+ PLAMA WAVE

W

,-,' . ' \ ,-,

-,N- " " " "en " , ( ' , " " , ' l ,-, I " I '·'\1 I ... 2D DENSITY" ~ " ~ I , I,r'd 1"'''1 1'[ ,lo l'\.,'II@II'' 'I, ~ III '"© FLUCTUAJ"fONS\ "" , ~ I \\.1: I Ih"\ '01,

.. , , , " , .. , I ... ,bI ' " " I,

a.. \/ \ ' I \

(J), ~ ' ..' .....' ...../

Fig. 1. Resonant excitation of an EPW (WEPW, kp) by beating two EM

waves (wo,ko) and (wI' kl) . Because of the f inite spot size,the density fluctuations are 2D with solid l ines (dotted l ines)representing contours of increasing (decreasing) density.

phase with the beat wave. As nIno 1, relat iv is t ic effect on the frequency mismatch becomes important and the EPW saturates at a lower amplitude given by

1 (v0(0)(fl/n ) (2)

a max 16 c

If vole i s 0(1) for one or both the beams, then the threshold for thestimulated Raman forward scattering (RFS) instabil i ty may be exceeded

in which case relat iv is t ic effects do not provide the saturation mechanismfor th e EPW.

RAMAN FORWARD SCATTERING INSTABILITY

RFS instabil i ty is basically the decay of an incident EM wave into

a forward propagating EM wave and an EPW with the usual energy and momen

- l 7



tum conservation condition:

(3)

The threshold for th e RFS ins tabi l i ty is rather high in an inhomogeneousplasma6

17 2 -2 2> 5xlO (nc/n) (6n/nc) (A/6x) Wcm (4 )

where the density changes by 6n in a length 6x at an average density n.

However, once th is threshold i s exceeded, the long wavelength high phase

velocity EPW can grow rapidly. Relat ivist ic effects do not provide asaturation mechanism because the change in wp can be adjusted out by achange in th e frequency of the forwards scattered l ight ws. Thus in the

two beam case, the density fluctuations driven by optical mixing will act

as an enhanced noise source to vigouously drive RFS provided that th e

threshold intensity i s exceeded. The other one-dimensional ins tabi l i tycompeting with RFS is th e Raman backscatter (RBS). By solving the dispersion relation 7

1 - (5)

where Z' i s the Fried-Conte function and AD i s the electron Debye length,th e growth rate for th e two ins tabi l i t ies can be found. 8 This i s shownin Fig. 2. In a cold plasma, RBS dominates; however, in a hot underdense

plasma, the growth rates for the two ins tabi l i t ies become comparable. The

longitudinal E f ield associated with the high phase velocity EPW character

i s t ic of RFS can be very high and is responsible for accelerating ei therth e plasma electrons or externally injected part icles to ul t ra- re la t iv is

t ic energies. This mechanism, known as "trapping", can be more severe

y/wo

y/wo R B

0.02

0.015

0.01

0.005

R : ~ ~RFS

0.1 0.15 0.2 0.25

0.02

0.01

n./n.

T. 81 keV

0.1 0.15 0.2 0.25 n./ne

Fig. 2. The normalized growth rates for the RFS and RBS at differentdensit ies in a homogeneous plasma. Vole - 0.1 (Ref.8)

-198



than Landau damping. (Fig. 3) Landau damping is strong when vp is O(ve )because the slope of th e electron distribution function (3f/3v)ve has amaximum near th e thermal velocity. Landau damping results in the local

flattening of the distribution function in the vicini ty of vp thereby

producing a heated t a i l of (nonrelativistic) electrons. However, whenvp » v Landau damping is small. Furthermore, when the amplitude of such

a highephase velocity EPW is small, there are very few electrons in the

background thermal distribution which are near enough to the phase velocityto be trapped. However, as pointed out by Dawson and Shanny,9 electron

trapping is a nonlinear damping mechanism not local in velocity space. Asth e wave amplitude increases, th e number of particles that can interactwith the wave increases rapidly. Consequently, the damping can be muchlarger than that p r e d i c t e ~ by the l inear theory. The trapping widthlO is

given by Vt = ( 2 e E p v p / m w p ) ~ . Electrons or externally injected part ic leswith velocity close to th e phase velocity will be accelerated to = c.

Since v cannot exceed c, a small change in vic greatly increases the relat iv is t ic y = (1 - v 2 I c 2 ) - ~ so that particles with very large energies can

be produced.

The saturation mechanism for the EPW driven by RFS instabi l i ty is thusparticle trapping. Pump depletion should not be a problem since the

energy given to the forward scattered EM wave is much greater than thatto the EPW. This is dictated by the Manley-Rowe relation or the law of

conservation of wave action. Viz:

wo-= (6)

wo

where Wj • Njtw and Nj is the change in number of quanta of the j th wave.

21.".m - - - - + - - - - - = : ; . . - - + - - - = ~ I :""""" ' ; \ -" ' : :" : : :- - - , f- - - kx

I I Il IORCE ON I 1 . . - .

ELECTRON. xLONG X I . - I I +0-

f IELECTRON IVELOCITY I

RELATIVE TOWAVE

eVe - Vp )

UNTRAPPED

Fig. 3. Trapped part ic le orbits in an electron plasma wave. Theframe of reference is moving at vp along x.

-1



Since repeated k matching is possible for the RFS instabi l i ty i t can be

argued that pump depletion i s only important when the original EM wavehas cascaded down by multiple RFS to waves near wp ' The other saturationmechanism such as harmonic generation, wave-wave coupling, ion dynamics

and mainbody heating followed by increased Landau damping may also be

significant. In rea l i s t ic experimental situations Raman sidescattering,filamentation, self-generated B f ields due to the electron beam anddensity inhomogeneities may also influence the RFS ins tabi l i ty . Computersimulations using re la t iv is t ic electromagnetic particle codes 11,12 i s

th e only readily available tool to investigate these competing phenomena.

EXAMPLE

The 10.6 and 10.27 l ines of the C02 laser can beat in a plasma toresonantly couple with a plasma density of -1016 cm-3 which i s 0.1% of thecr i t i ca l density (nIne - 10 -3) . The laser l ight group velocity is

-(1 - ~ w ~ / w 2 ) c . This equals the phase velocity of the plasma wave. Inthe wave f r ~ e a trapped electron travelling with vp thus has a re la t iv is-

t ic a = 1 - w ~ / 2 w ~ . I t s relat iv is t ic y i s equal to (1 - a 2 ) - ~ = wolwp'However, transforming the energy of the trapped electron from the wave

2to the laboratory frame we find that the maximum energy gained is 2y mc2 =(2w 2/w2)mc 2 which i s about one GeV. The length to reach this energy is

approxrmately ( 2 w 2 I w ~ ) ( c / w p ) which is about 10 em. This places a rathersevere requirement on the aensity homogeneity of th e plasma source andthe focusing of the two laser beams, but both can be achieved usingpresent day technology. The level of density fluctuations required toobtain an accelerating electr ic f ield of 10 GeV per meter can be estimated

using the Poissons equation and the optical mixing formula in the re la t i -

vis t ic l imi t given by equation (2) i s then used to roughly calculate thelaser intensity required. This leads to 10 = I I = 1.4 x 1016 Wcm-2 or

vo(l) /c = vo(O)/c 1. Incidentally, this intensity wi l l exceed theinhomogeneous RFS ins tabi l i ty threshold even i f we assume a 10% density

ripple per em.

EXPERIMENTS

Although simple in principle, optical mixing i s not straight-forwardin practice. In fact , unt i l very recently there had been only one experi

mentl3 in which resonantly driven density fluctuations using two laserfrequencies were diagnosed using a probe beam to Thomson scatter of the

density fluctuations. In any case, the signal to noise rat io of ' th e

Thomson scattered l ight was only about 3. Diagnosing th e EPW driven bycolinear laser beams with the condition wp « 00

0is a tremendously diff i -

cult problem because of the short kp ' Also, one must have either a well

controlled multi l ine laser or a tunable laser and a homogeneous, tunabledensity plasma source. By insert ing a 10 em long SF6 cel l inside a gainswitched TEA C02 laser oscil lator and varying the SF6 pressure i t is

possible to obtain controlled multiline operation mainly on 10.6 l inesin the P(20) band, 10.27 l ines in the R(16) band and the 9.6 l ines inthe P(20) band. Each band contains 3 to 5 l ines each -40 GHz apart of

roughly the same intensity (within a factor of 5). This is shown inFig. 4. The frequency difference between the 9.6 and 10.27 gives

wp = 1.35 x 1013 Hz corresponding to ne = 5.7 x 1016 cm-3•For a tunable density source one can ei ther use a e pinch or a pulsed

arc plasma. Density homogeneity required can be obtained in a e pinch in

a fully ionized HZ or He plasma whereas one has to use a heavy gas such

-200



100·1)-(02'01PIl61-P1241

o •.15,...A 'O.t....• '0 .• • ,. .

RESOlUTIONLlms

SINGLE::.t"-

GRATING

10- ok---!-.-,.l.o-*'",-----f.20-----.;z',

loo·II-CIO"OI

111141-11(22)

(b) I l ~ ll60 64 68 72 7& 80 1040 44 48 :lZ 60

lIIfAVEMMIlERc....·,

SF. PRESSURE (Torr)

Fig. 4. Multiline operation of a C02 oscil lator (a ) and fine struc

ture of the R(16)lO.27 and P(20)9.6 bands (b).

as N2 or Ar in an arc. Fig. 5 shows th e density evolution as a functionof time of a 4 Torr, 5 eV Ar plasma produced by a pulsed capacitive arc.

The axial density profi le measured interferometrically showed that , withinthe l imits of measurement accuracy th e condition ~ = w can be achievedpover th e depth of focus of th e f/7.5 lens.

The laser beam (75 ns FWHM) containing roughly equal powers in the

9.6 and 10.27 l ines was focused to an intensity of 1010 Wcm-2 by an

f/7.5 lens to a 300 spot on the plasma axis. The transmitted l ightplus any forward scattered l ight was collected by an f/2 lens, analyzed

by a double grating infrared spectrometer and detected by a very sensitiveHg:Ge photoconductor. The evidence for optical mixing was obtained by

the observation of a new l ine in the forward scattered l ight around 11 which is produced by Thomson scattering of the 10.27 l ine from the EPWgenerated by the beat wave. Moreover, this radiation was only generated

when wp = ~ as shown in Fig. 5. Although the FWHM of the input laserpulse was 75 ns th e 11 l ine was only about 25 ns wide. Another unusual

and at f i r s t rather puzzling effect was observed. Whenever ~ - wp ' very

strong refraction of th e beam occurred outside· the cone angle of the inc i dent beam. (Fig. 6) This phenomenon has been called resonant self-focusingdue to the ponderomotive force of th e EPW.14

The ponderomotive force FNL(plasmon) can be much larger than FNL(light).

The amplification factor A is given by

FNL(plasmon)

(7)FNL

(light)A = =

Ep is the electr ic f ield of the EPW. Poisson's equation gives Ep = 4 ~ e n l / k p and since Vo = eEo/mwo and vp = c we obtain the amplification factor

-201



rt l

w =6wp

o 5 10 15 20 25 30 to

PULSE DELAY (p,sec)

Fig. 5. Time evolution of the arc density and scattered power infrequency w2 = (10.27 ~ - wp •

Fig. 6. Forward refracted l ight in the 10.27 l ine vs. w p / ~ w with

density measured by ruby interferometry (0) and by Stark

broadening of a seed gas Ha l ine. The shaded areas indicateth e spread of difference frequencies in the incident beam.

0.' 0.' t.O t. t 1.2 t. I

Wp&I

Using the value of nl/n = 0.4% estimated from the absolute levels ofoThomson scattered l ight from the EPW and 10 = 1010 W cm-2 we obtain A > 20.

Since the wavelength of the EPW is about the same as the diameter of the

focal spot, the longitudinal and transverse gradients of the electr icfields are comparable and a density depression i s created on axis which

causes deflection of th e beam by refraction. I t i s not clear whether the

amplitude of the EPW in this experiment was limited by re la t iv is t ic effectsor ion dynamics, however, the time duration of the EPW was almost certainly

limited by the io n motion. The wave potential corresponding to nlln o - 0.4%

was about 2.5 kV, i . e . « mc2 and since T was only 5 eV no hot electronsedue to trapping were expected. However, this experiment did demonstratethat a short kp EPW can be generated resonantly via the opt ical mixing pro

cess. More experiments are needed to check out the predictions of th eoptical mixing theory at low laser powers, perhaps with shorter laserpulses.

The role of RFS ins tabi l i ty in hot electron generation was invest i gated in another experiment. 15 130 R thick, self-supported carbon foi lswere irradiated at normal incidence by intense; volc 0.3, 700 ps FWHM,

C02-laser pulses. 1-5% of the incident energy was backscattered androughly 50% of the incident energy was transmitted by the plasma. Thus i t

1000:IJJ

0 10

°Ew:t..0:_w1 - 0~ u::>( / )0

0:Wed:>

- 'W0:

to '

0-JC

ffi to·-E 2

()

0

-III

>- ffi.... to 'u;z g w0 II I

6

i t O '4

2

V nl )2 (n l /no)2A=-E.- = (8 )( v n v /c •000



can be assumed that th e foi l plasma becomes underdense around the peak of

the laser pulse. The electron temperature of th e bulk distribution wasdeduced from the slope of the ion spectra recorded absolutely using

Thomson parabolas, to be -20 keV for both front· and rear expansions. Theangular distribution of the electrons escaping the plasma was measured

using two absolutely calibrated electron spectrometers in the range 0.41.5 MeV.

o

Fig. 7 shows th e absolute electron spectra measured at e = 5 in theforward direction and e = 150 in the backward direction from the thin carbon

foi l plasmas. If a Maxwellian distribution is assumed then these distr ibut ions can be characterized by temperatures of 90-100 keV in the forward

direction and of 40-50 keV in the backward direction. Electrons with

energies up to 1.4 MeV were observed in th e forward direction. The highestenergy e l ~ c t r o n emission ( > 1 MeV) was strongly peaked in the directionof the laser. Electrons up to 400 keV were observed nearly isotropically,however, probably at tr ibutable to 2wp decay and Raman sidescattering.

Integrating over th e measured angular distribution, assuming azimuthal symmetry, -1011 electrons with energy greater than 400 keV were found to

escape the plasma. Although no direct measurements of the target potentialdue to this loss of electrons were made, we note that target potentials of

-200 keV have been measured under similar irradiance conditions. 16A simple estimate shows that RFS is important in our experiment. The

growth rate for the RFS process 17 is given by y = ~ ( v o / c ) w Z l w and the

f ini te length l imit on growth is y L / ( c v g ) ~ > 1, where vg = P3 ~ p v ~ / w p , andL is the interaction length. Assuming vo/c - 0.3, Te - 20 keV, wp/wo - 0.46,we obtain for L/A - 50, Y/w

o- 0.03 and we have nearly 27 e-folding growths

from the in i t ia l noise level . Fo r backscatter the growth rates are comparable to those for the forwardscatter but backscatter suffers much more

10 ....... - ~ . . . . , r - < l ~ .....-e-.,...-..,...----,

Fig. 7. Experimental electron energy distributions in the forward andbackward directions from thin C fo i l plasmas.



severe Landau damping due to the shorter wavelength and th e lower phase

velocity of the backward EPW. The assumption of a homogeneous plasma with

L/A 50 is reasonable, since we expect the instabi l i ty to occur in th e

density plateau region, separating the front and the rear expansions. This

region has a density scalelength somewhere in between th e focal spot diameter (150 ~ and th e ion acoustic speed times the FWHM pulse length (1000 ~ ) In any case the depth of focus of the laser beam was ~ 5 wavelengths.

Simulations were carried out on the ID relat iv is t ic electromagneticpart icle codel l with the periodic boundary conditions where similar wavesetups were .used as in reference 1. The plasma was in i t ia l ly thermal,

Te 20 keV and uniform, w Iwo 0.46. The propagating electromagnetic

pulse had a vole 0.3. The distr ibut ion function f(PI \) as well as theelectrostat ic wave spectra are displayed in Fig. 8. The temperature andthe maximum electron energy observed in the simulation distributions were

similar to the experimentally measured values. For instance, simulations

show electrons with (Emax)F = 1.3 MeV and (THOT)F - 100 keV in th e forwarddirection compared to experimental values (Emax)F- 1.4 MeV and (THOT)F - 90

100 keV. Similarly, simulations show (Emax)B - 0.9 MeV and (THOT)B - 60 keVin the backward direction compared to experimental values of (Emax)B 0.8 MeV and (THOT)B - 40-50 keV. In view of the possible influence of the

target potential on the experimentally measured electron distributions,this rather excellent agreement between the experiment and the simulationsmay be rather fortuitous, particularly for the maximum electron energy

unless the target potential was indeed much smaller than Emax. The elect rostat ic wave spectra (Fig. 8b) shows that the backscatter mode kb (whichgrows ini t ial ly) is swamped by other modes with a smaller wave number, the

most intense of which is the plasma wave associated with forwardscatter kp .In addition, there are some wavenumbers which are less than kp. Thus th eheated electron distributions obtained by the experiment and the simulations

agree well with most of th e electron heating due to th e RFS process (and/or

multiple RFS processes since repeated k matching is possible only for th e

RFS process), but is not so much due to the backward process.

The reason why the backscattering is suppressed is the following: Whenthe backscattering EPW is excited, heavy Landau damping or electron trapping

(0 )

1S(k)

-2 o I 2

(b )

PII/IT'C-

Fig. 8. Simulation (under th e same conditions as in Fig. 7) ofelectron energies (a) at t • 250 w ~ as well as (b) theelectrostat ic mode spectra at t = 00 wj;l.



~ N UJ

::E

I - ,....

Fig.

1023

, , , I

+EXPERIMENT

I • SIMULATION21

10,;:;-

'E(. )-> (/ ) 21

101-

ZwCl + ~ <{

wa..

1020,0

4000A CARBON

NINe Iw 3w

123

TIME (ns)

9. (a ) A typical streak record of Raman backscattered l ight from a 4000 th ick carbon fo i l

plasma and,(b) comparison between experimentally obtained maximum plasma densi ty an d 2D LASNEX pre-

dict ion. Times 1 ns and 2 ns correspond to peaks of th e 1 ~ prepu1se and 0.35 ~ mainpu1se respectively.



by this EPW saturates i t at a low level thus l imiting the backscattering

to a small value. The phase velocity of the backscattering EPW vp = wp/kpwhich for this case is -1.6 ve' Thus this wave i s heavily Landau dampedto begin with and as i t grows in amplitude t more and more particles will be

trapped by i t and the damping will grpw. The trapping width is given

approximately by ~ V = ( 2 e E E P l ~ p / m w p ) ~ t where EEPW is the electr ic fieldfor th e plasma wave. The condition that a l a ~ g e number of electrons aretrapped is given9 by v

p- ~ V $ 2ve = 2(T

e/m) . The maximum electrostat ic

wave intensity is obtained for a cold plasma by set t ing ve = O. This gives

for the saturation amplitude EEPW for the longitudinal wave as (eEEPw/mw p)= vp /2. For our case, the phase velocity is O(ve) and we expect l i t t l e

growth; in any case, the saturation intensity for a cold plasma i s lessthan 6% of the l ight waves. In addition th e two plasmon decay instabi l i tywould also saturate at a low level even i f Wo were choseri to be 2wp because

strong Landau damping sets in much earl ier for 2wp decay than i t does for

th e forward Raman process. The RFS process appears to be the las t parame

tric process to saturate in this hot underdense plasma.

RecentlYt we have been exploring the possibi l i ty of producing ultra-

high electr ic f ields on th e order of half-TeV per meter by using a short

wavelength ultra-violet laser to drive the RFS instabi l i ty in a high density

underdense plasma. The maximum energy gain by a trapped particle is simplya function of the plasma density to the cri t ical density rat io (!max 2y 2mc2 - 2(wolwp)2 mc 2 - 2nc /n mcZ). This i s because although the electr icf ield is higher at a shorter wavelength, the wavelength of the electronplasma wave i s shorter and the f ! ·d! is a constant. Thus by going to ashorter wavelength the main gain i s in obtaining the same energy in a muchshorter distance c o m p a r ~ d to when a long wavelength laser i s used. For

example, i f we use a 0.35 laser , (third harmonic. of 1 glass laser)then for a density rat io nc/n of 103 we may expect to achieve 1 GeVelectrons over an incredibly short distance of only 3.5 rom instead of

-10 cm for a 10.6 COZ laser . At shorter wavelengths we might also expect

a much higher beam luminosity since the plasma density is higher.

In exploratory experiments, carried out at the National Laser Users'

Facil i ty of the University of Rochester 4000 i thick carbon foi l targetswere irradiated by a low intensity (101i W/cmZ) 1 prepulse to produce apreformed underdense plasma. The 0.35 mainpulse, 1015 W / ~ m Z t was t ightlyfocused at the center of the preformed plasma by an f/12 lens to excite theRFS ins tabi l i ty . The mainpulse and the prepulse were delayed by 1 nsec to

allow the preformed plasma to expand and establish a reasonable densityscalelength. The plasma temperature was -700 eV and length was -150 laserwavelengths. Raman backscattering instabi l i ty was excited during the r ise-

time of the 3w laser pulse as evidence by the time resolved Raman back

scat ter spectrum shown in Fig. 9(a). The shi f t of the long wavelength cutoff. of the Raman backscatter spectrum to the blue i s due to the plasma densi ty decreasing as a function of time because of the frequency matching

condition. Fig. 9(b)shows

the comparison of the e x p e r ~ e n t a l l y measured

peak density and the results of a 2D hydrodynamic simulation of our exper

iment using the code LASNEX. The cr i t i ca l density for 0.35 laser l ightis 9xl02l cm-3 • I t can be seen that a plasma with nc/n - 102 was produc

ed at the peak of the 0.35 laser pulse. Unfortunately, the laser intensi ty was not sufficient , or the plasma density scalelength long enoughto excite the fast wave (vp - c) characterist ic of the RFS instabi l i ty.We observed high energy electrons with energies out to 350 keV but theirangular distribution and polarization dependence suggested 2wp decay as thegeneration mechanism. We are continuing experiments along these l ines to

exploit the potential of short-wavelength lasers for producing ultra-highelectr ic f ields .



FUTURE EXPERIMENTS

The two experiments described infuis paper have demonstrated th efollowing:

(a) Using a multiline COZ laser of only 1010Wcm-Z, electron density

fluctuations can be reasonantly excited for up to 25 ns.

(b) When an intense COZ laser pulse is incident on a hot, tenuous

plasma, re la t iv is t ic energy electrons can be produced in th e direction ofth e laser beam. The energy distribution of these hot electrons is not monoenergetic but is rather Maxwellian.

In addition, we have been looking at the use of short wavelength lasers

for producing ultra-high electr ic f ields propagating close to the speed of

l ight . This is just the beginning. Crucial experiments need to be donewhich combine the phenomena of opt ical mixing and RES to check how th e

maximum electron energy scales with vole, wn/wo and the depth of the focus

of the laser beam. Computer simulations described in the paper by Tajima19

would suggest rather a weak dependence on the laser intensity provided the

RFS threshold is exceeded. On the other hand the maximum energy in simula

t ion scales as (wolwp)Z, i . e . , inversely proportional to the plasma density.Similarly the Thomson scattering diagnostic described in this paper needs

to be exploited to obtain the complete electrostat ic wave spectrum S(k, w)

generated in the two beam case and compare i t to the simulation spectrum.

I t is also of some importance to investigate to what extent two dimensional

effects such as sidescattering and bubble formation are important. Another

crucial question that may be more conveniently addressed to in simulationsis 'how important is the background temperature of the plasma in determining

th e relat ive importance of Landau damping and particle trapping?' Experi

ments designed to answer these questions should form the next stage of

research on the plasma beat wave accelerator. I f the results look promising

and very large longitudinal electr ic f ields ca n indeed by produced using

existing 1 or 10 laser faci l i t ies , then i t would be of enormous interestto see i f an externally injected, nearly monoenergetic beam of electrons or

protons can be accelerated to GeV(s) while keeping i t relat ively monoenergetic.

ACKNOWLEW EM ENTS

I wish to acknowledge th e contribution my colleagues; C. Clayton, Dr.

F. F. Chen, Dr. N. A. Ebrahim, Dr. H. A. Ba1dis, H. F.lgueroa and Dr. K.

Estabrook, gave in successfully carrying out the work described ~ this paper.Stimulating discussions with T. Tajima and D. Sullivan are acknowledged

with pleasure.

This work was supported by DOE contracts: DE-AS08-81DP40163, DE-AS0881DP40l35, DE-AS08-81DP40166 and NSF grant ECS-80-03558.

REFERENCES

1. T. Tajima and J . M. Dawson. Phys. Rev. Lett . 43. 267 (1974).

2. B. T. Cohen, A. N. Kaufman, and K. M. Watson. Phys. Rev. Lett . 29. 581(1972) .

3. N. A. Ebrahim. C. Joshi and H. A. Baldis, Phys. Rev. A 25 , No.4 (1982).4. N. Krall, A. Ron and N. Rostoker. Phys. Rev. Lett . 13, 83 (1964),

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10. This formula is nonre1ativistic but is i l lustrative for th e present

purpose.

11. A. T. Lin, J . M. Dawson and H. Okuda, Phys. Fluids 1I, 1995 (1974).

12. M. Ashour-Abda11a, J. N. Laboeuf, T. Tajima, J . M. Dawson and C. F.Kennel, Phys. Rev. A23, 1406 (1981).

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published in Laser Interaction and Related Plasma Phenomena, \bl . 6.Ed. G. Miley and H. Hora, Plenum Press.

19. T. Tajima-Proceedings of this conference.

C. Joshi- The Plasma Beat Wave Accelerator- Experiments

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