8/3/2019 D. J. Sullivan- Simulation of Preaccelerated Particles in the Plasma Beatwave Accelerator

1/3

IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983SIMULATION OF PREACCELERATED PARTICLES IN THE PLASMA BEATWAVE ACCELERATOR

3159

D. J. SullivanMission Research CorporationAlbuquerque, New Mexico 87106

One-dimensional relativistic and electromagne ticsimulations show the Plasma Beatwave Accelerator to bea viable approach to obtaining large acceleratingfields. The plasma wave excited. by Raman ForwardScattering has a longitudinal electric field on theorder of 100 MeV/cm to 10 GeV/cm based on plasma den-sities of 1016 cm-3 to IOzo cm-3. The use of opticalmixing to grow a plasma wave of the proper frequencyabove the noise level greatly reduces the laser in ten-sity needed to drive the Raman instability. TeV ener-gies for plasma electrons or preaccelerated chargedparticles in short distances appear feasible. Resultswhere an injected electron beam is accelerated coher-ently from 1 MeV to 20 MeV in one millime ter are pre-sented. Two- and three-dimensional effects mus t stillbe resolved.

in the y direction appeared uniform because of period-icity. Each of these macrocells initially contained24 particles. The risetime of the laser pulses wastypically 25 up-l. The ions were taken to be aninfinitely massive neutralizing background except inone run. Different simulations were made in which the

Abstract

IntroductionIntense laser beams are capable of producingtrgnsvfl;se electromagnetic fieids high10 -10 Volts/cm . The Plasma Beatwite Acceleri:tar'** is one 'of a number of particle acceleratorconcepts uti lizing the high fields inherent in intenselaser beams. In this case, EM waves interact nonlin-early with an underdense plasma through optical mixingor Raman Forward Scattering (RFS) to excite large amp-litude$plasma waves. The plasma self-fields providethe acceleration. Thus, the concept is a collectiveeffect accelerator. The longitudinal electrostaticfield of the plasma depends on the plasma density andis typically on the order of mcwp/e, where m is theelectron rest mass, e is the electron charge, c is thespeed of light and wp is the electron plasma fre-

quency. For a lo* cm-3 plasma this expression isequal to 1 GeV/cm. It explains the very high acceler-ating fields obtainable with this mechanism.Because previous papers,3-6 cover the theory indetail, we will immediate ly discuss the simulations.Our results address optical mixing, Raman ForwardScattering, wave synchronism, streaming instabilitiesand frequency match ing. Only the wave-wave processeswill be reviewed here. A simulation which coinjectsan electron beam with the laser pulse will be des-cribed in detail.

SimulationsSimulations were carried out using a two-dimen-

sional, fully relativistic and electromagnetic par-ticle-in-cell code. The code can solve self-consis-tently for the time dependent trajectories of tens ofthousand of plasma particles over thousands of plasmaperiods. All variables are expressed in dimensionlessterms. Therefore, length is in units of c/up; timeis measured in units of up-l; and particle velocityis given by vi = sir (i = 1, 2, 3), where wp iSthe initial electron plasma frequency.In simulations on the Beatwave Accelerator twoplane-polarized electromagnetic waves are launchedinto a Cartesian geometry. Periodic boundary condi-tions in the transverse (y) direction make configura-tion space effectively one-dimens ional. In general,the simulation has 1250 cells in the longitudinal (2)direction modelling a length of 100 C/W,. The cells

values of otJup I wlbp, Eo and electron tem-perature, T,, were varied where wo and W, are thetwo 1 aser frequencies. *Usually, a vacuum region of 10k C/W, long wasleft between the left hand boundary and the plasma inorder to accurately determine the dynamics of laserinjection into the plasma. When the laser pulseencounters the plasma, the nonlinear ponderbmotiveforce resulting from the intensity gradient causes theelectrons to snowplow. This continues until the forcearising from charge separation is greater than theponderomotive force, and the electrons attempt torestore the charge imbalance by moving in the negativez direction. This motion initiates a train of largeamplitude plasma waves.The one drawback evident in the single wavepacketscheme's5 was the short pulse (r < 2~ up-'). Thisimplied an instantaneous risetime to very high inten-sities. It is obviously unattainable. The beatwaveapproach, on the other hand, is a practical means ofobtaining the required intensity gradient necessaryfor the nonlinear ponderomotive force to establishlarge amplitude plasma waves. The beatwave resultsfrom two parallel coherent EM sources w. and w1where w. - w1 = w . This can be accomplished byutilizing two separa ! e colinear lasers or exciting twoappropriate bands of the same laser.3

Nonlinear Wave-Wave ProcessesAn alternative method of depicting the beatwaveacceleration is in terms of two nonlinear wave-waveinteractions. At low intensities where E. (0,l)

8/3/2019 D. J. Sullivan- Simulation of Preaccelerated Particles in the Plasma Beatwave Accelerator

2/3

3160(0,1)/c s eEo(O,l)/mcw(O,l) = .04 and .05 was con-ducted. The plasma was cold at WIT = 0. The lineargrowth of the'plasma wave is depicfed in Figure 1. Atthis time (up? = 150) the density fluctuations are10% of the initial density. The analytical equation'indicates saturation should occur at a fluctuationlevel of 5%. Indeed, 'time histories of the laserfields indicate a cascade to lower frequencies insteps of wp indicative of an RFS instability. By

@PT = 300 the plasma field amplitude has saturatedat .2 mcwp/e, the density variations are as high ds.75 of the initial value, and the RFS instability isfully developed. However, as expected, these fieldlevels are not sufficient to trap plasma electrons atrest.:::10 -11.00, I Iz 0.6032 0.0-N L-,-0.60,-1.00 1 / I L I0.0 31 ;:I, 112 160

+Fig. 1. ,Time history inside the plasma of thelongitudinal electric field. Simulation para-meters are 'ao=5.0 UP, wi=4.00p and E,(0,1)=0.2mcwp/e.The importance of this result must be stressed.It indicates that large amplitude plasma waves can begrown from relatively low intensity laser sources, dueto RFS excitation by optical mixing. Consider thecold plasma simulation just discussed. If wo is2.36~10'~ set-l (X7;:;1ym),t$en A1 is 8 urn and theplasma density is cm- . The equivalent laserintensity is only 1.3~10'~ W/cm *, yet the plasma waveaccelerating field is 166 &V/cm .

This lower intensity makes the Plasma BeatwaveAccelerator an extremely attractive candidate forapplication to high energy physics accelerators. Thelower intensity implies the focal spot size may belarger, thus lessening diffraction of the laser pulsein the plasma. The fact tha t plasma electrons are nottrapped is advantageous for injection of preacceler-ated bunched particles. As has been shown in otherwork , large numbers of trapped particles lead to wavedamping and loss of synchronism.At higher intensities the RFS instability growsexponentially to a saturation level. Figure 2 depictsthe plasma wave amplitude and spectrun for the case ofvosc (0,1)/c - 0.5. Note the presence of spectralcomponentsatw=wo+W1 aswellasti=wo-w =wp and higher harmonics. Graphic evidence of thisinstability is also given in Figure 3 , which is thetime history and power spectra of the laser waves in-side the plasma.This downward cascade of energy intomultiples of up is a clear signature of Raman insta-bility. The upward cascade is the result of multiplefour-wave interactions in which each wave is coupledto all other waves in a multiwave parametric proc-ess.ll The sidebands are often referred to as Stokes(downshifted) and Anti-Stokes (upshifted) lines.This simulation is particularly interestlny,because the parameters model a CO, laser emitting inthe 9.6 pm and 10.6 urn bands at a combined intensityof 1.3~10'~ W/cm*. The laser pulse is incident on ahot 1Ol7 cmq3 plasma. Excitation of these CO, linesat this intensity and production of such a plasma isnot beyond current technology. The higher saturation

level of the electrostatic field is only a factor of

kBds3d3a

-10.0 , , I I0.0 26.0 60.0 14.6 99.9

103101

10-l-3'10 -6nl 0.0 9.8 19.6 29.6 39.3w/wpFig. 2. Time history and the power spectrum in-side the plasma of the longitudinal electricfield. Simulat ion parameters are wp=10.6 wp,~1=9.6 up and Eo(0,1)=5.0 mcwp/e.

T. 0.60es 0.00

7-I~-0.60 ' "' 'II'-1.00' "i 10.0 26.0 60.0 74.9 99.9

n,* 10 IB't IO6f*sOI IO3za 101

0.0 9.8 19.6 29.6 39.3w/w P

Fig. 3. Time history and the power spectrum in-side the plasma of the two Plane polarizedlaser wave electric fields. Parameters arewo=10.6 wp, ol=9.6wp and Eo(0,1)=5.0 mcwp/e.three larger in this simulation than in the run whereoptical mixing was important. This implies a field of188 #V/cm based on the lower plasma dens ity. Thecombined laser intensities here, however, are equival-ently 100 times larger. Nevertheless, there are someadvantages to this higher intensity.

The high value of v osc/c and its associatedrelativistic effects lead to particle trapping andacceleration of a small number of electrons. Thisalso occurs if Te = 0 for the same parameters . Thetrapped particles originate at wavelength intervalswhere Byy is a max imum and are not associated withany overall temperature. These results are importan tif the plasma is to be the source of accelerated par-ticles. In addition, the particle bunching at higherintensity is more pronounced and coherent. Ps a ref-erence, assume the focal spot size for the laser pulsedescribed above is 10m4 cm*.tion results, Then, based on simula-a particle pulse occurs every .18 psec,contains 5x10" electrons, carries a peak current of96 kA at a current density of 960 Rgamps/cm*. Themain reason for belaboring this point is to indicatethe potential the plasma has for confining and accel-erating high density bunches of preaccelerated ions.

8/3/2019 D. J. Sullivan- Simulation of Preaccelerated Particles in the Plasma Beatwave Accelerator

3/3

3161_ 1.00T

7 15.0\3ii 0.00 9;i 0.0

74p3 2-1.00 -16.00.0 25.0 50.0 0.0 25.0 60.0Plasma Plasma

Beam Beam

%(C/WJ1 AC/W p)Fig. 4. Plots of a) plasma wave electric field, b) laser electric field, c) plasma electron longitudinal, d) plasma

electron transverse, e ) beam longitudinal, and f) beam transverse momentum phase spaces at WIT = 74.0. Simula-tion parameters are ~~-10.6 tip, wl=9.6 op, E,(O,l) = 5.0 mcwp/e and Te = 0 kev.A 1 t&V electron beam with a density of 1Ol4 cm-3was coihjected with a 1016 W/cm CO, laser emitting at10.6 pm and 9.6 urn. Thus, the beam to plasma densityratio was -001. The plasma was cold. As before, asmall number of plasma electrons are trapped andaccelerated resulting in a monotonically decreasingdistribution. Because the electron beam was notbunched at injection, its accelerated emittance is

large. Notably, the beam particles bunch at a phasein the wave which is different from the plasma elec-tron bunches. Yet no streaming instability results.Plots of various quantities of interest are given inFigure 4. The total longitudinal distance is 0.8 mmfor the given plasma density. A more conclusive testusing prebunched, monoenergetic ions at a laser inten-sity which does not allow plasma trapping is needed.If this indicates a problem, we will lower the ratioof beam to plasma densities to determine at what pointthe growth is negligible. These studies will alsoaddress emittance growth. Both issues will helpestablish the expected beam luminosity as it exits theaccelerator.

AcknowledgementThis work was supported by the Air Force kaponsLaboratory. The author is pleased to acknowledge manyuseful discussions with Drs. B. Godfrey, C. Joshi, A.Sessler, T. Tajima and W. Willis.

References1. T. Tajima and J. M. Dawson, Phys. Rev. Lett. 5,267 (1979).2. T. Tajima and J. M. Dawson, IEEE Trans. NuC.Sci. NS-28, 3416 (1981).

4.

5.

6.

7.

8.

9.

10.11.

T. Tajima and J. M. Dawson, in Laser Accelerationof Particles, edited by P. J Ch 11 (AConference Proceedings, No. 91,' Newa?iFk, '1982fyp. 69.D. J. Sullivan and B. B. Godfrey, IEEE Trans.Nut. Sci. NS-28. 3395 (1981).D. J. Sullivan and B. B. Godfrey, in LaserAcceleration of Particles, edited by P. J.nannell (AIP Conference Proceedings, No. 91,New York: 1982), p. 43.B. I. Cohen, A. N. Kaufman, and K. M. Watson,Phys. Rev. Lett. 29-, 581 (1972).M. N. Rosenbluth and C. S. Liu, Phys. Rev. Lett.29, 701 (1972).-C. Joshi, T. Tajima , J. M. Oawson, H. A. Baldis,and N. A. Ebrahim, Phys. Rev. Lett. 3, 1285(1981).K. Estabrook, W. L. Kruer, and 8. F. Lasinski,Phys. Rev. Lett. 45-, 1399 (1980).D. Eimerl, R. S. Hat-grove, and J. A. Pasiner,Phys. Rev. Lett. 46, 651 (1981).

3. C. Joshi, in Laser Acceleration of Particles,edited by P. J Ch 11 (AI ConferenceProceedings, No. 9i, Nei"!zrk: 1982)', p. 28.