j. m. kindel et al- two-dimensional beat wave acceleration scheme

8/3/2019 J. M. Kindel et al- Two-Dimensional Beat Wave Acceleration Scheme

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TITLE: TWO-DIMENSIONAL BEAT WAVE ACCELERATION SIMULATION

AUTHOR(S): J. M. Kindel and D. W. ForslundLas Alamos National LaboratoryW. B. Mori, C. Joshi and J. M. DawsonUniversity of California at Los Angeles

LA-UR--35-233DEU5 005961

Society forSUBMITTEDTO: Optical Quantum ElectronicsMcLean, Virginia 22101

Proceeding+ of Internatlonnl Conference on Lasers 84,San Francisco, California, Novemt,er 1984

l==ombkammosAlamosNationalLaboratoryLosAlamos,NewMexico 87545


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TWO-DIMENSIONALBEAT HAVE ACCELERATION SIMULATION*by

J. M. Kindel and D. W. ?orslundLoe Alamo8 National Laboratory, P.O. Box 1663, Los AlamoB, RM 87545W. B. Mori, C. Joehi, and J. H. DaweonUniversity of California at LOB Angelee, Los Angelee, CA 90024

ABSTRACTFinite lacer beam particle eimulationa of beat wave acceleration chow that acoherent plaema wave excited by two-colinear laser beams at a difference frequencyequal to the plasma frequency can produce maximum electron energies ae predictedby Oimple one-dimensional theory. The time to maturation and the 8aturationamplitude of the plaama wave electric field agreee with the Roaenbluth-Liu theory.

Stimula ted Raman scat ter ing does not appear to degrade the electron accelerationprocess. Eventually eelf-focueaing and filamentation limit tne lifetime of thecoherent plasma wave to teno of picoeeconde for an Intense C02 lamer bean.

Beat wave acceleration ie the optical mixirg of two lacer beEimBsuch that their dif-ference frequency can drive up a long wavelength plaema wave propagating in the direction ofthe incident light.1 This large amplitude plasma wave, with phaee velocity elightly lessthan c, i.e., c(I - W2e/w2)lZ traps and accelerates electrone.z~ One-dimensional 8imula-tiona have confirme# the existence of the beat wave acceleration procetae. z-n An importantquention ie whether the proceea la altered by turbuenoe effeotm7 or more specifically bytwo-dimen~ional effects which could degrade the plasma wave and the acceleration process.Some of the new phenomena are: Raman sideacatter, melf-generated uagnetic fielde, wholebeam eelf-focueeing and filamentation. Although theBe come into play in two dimenaion~, wefind a regime can he identified which effectively reproduces the one-dimensionalacceleration.Befo:e showing the detaile of the aimulationa, we Indioate a fluid remult which ite con-firmed in both one- cnd two-dimensionalaimulationa. Firot we find that for laeele with afinite ri~e time, the time for the plasma beat wave to reack saturation can be described bya etraightforw~rd modification of the fllid treatment of Ro~enbluth and Liu.s The time toeaturatiun can be found in a eeparate publication,n where a (t) m Vb /c, which ie theC?lOCtrOnquiver VOIOOlty and where fOr heurietic purpoeee we qs Ume a l%~r rice time T furthe two laeere leading to the time of oaturatioil ta:t s 3.68 (MP y)4/7 (0 ,max~max)-2 7p s

end al(t; I aimAx. The amplitude of the plasma wave electric field at euturatlon II!eExcm = 4015 (aec pe 1 max %max) 97

(1)

(2)

Ae repreeentativa of the two-dimensional elootromagnetio, fully relativietio oimulationewith the WAVE oode, we dennribe a oaoe with q finiio laagr beam incident onto a uniformplasma with parametore as given in Fig. 1. The computational eyetem ie Cartesian whereeelf-coneietent motion 10 calculated in the x-y ?lane. FiCure 1 oontaine the lacer qlectricfield I at three different times illumtrcting i o evolution from q coherent finite beam toa nelf-focuoeed beam. Figure la ohowa eontoura of th e inoidont laeern E eldotric field qttime T - 150 u-l , whioh 10 one half of the lamer rise time. The full wid!h of tho inoidentbeam 10 20 c/8 or approximately 160 urn for q C02 lacer, qnd it 10 incident onto q uniformplnuma at 4$ ofp!ritical deneity,Figure 2 ehove the evolution of the plaema beat wnvo from T s 150 m-l to T - 300 u-l.The top columne (Figo, ?n, o, qnd e) ohow tho qlaotrio pot~ntlal oontot?o in x-y npa,while the bottom oolumne (Fign, ?b, d, qnd f) show tho qlootrio field E qt tho oentor ofthe beam ae q function of x, Figure 2n ahowe the potsntinl contoure of thd plaema wavo q replanar qt thio early time. The qesoaintod eloetrio field in Fig. 2b r~aohos q maximum ofc I 0.55 near tho lefthand boundary of the box qnd most importantly lo fairly coherent up to


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th ie t ime. When the actual lace-rrise times are ue.ed,Eq. (1) predicts electric field Eeaturates at c = 0.7 at t = 150 w 1. One rex!on for thie discrepancybetween the observe~and predicted value of !, is thep!act that the J (c) in Eq. (6) of Ref. 8 was approximated.80unity. The electric field E aleo decaya aft?r Baturatlon in both our one-dirnenaional e.imulatione as pr~dicted in Ref. 8. and two-Further the time to maturation Ocalesinvereielyvith lacer intensity aa seen in Eq. (2). This manifeatO iteelf in the eplittingetructure o f the potential contour plot of Fig. 2C becauee of the com2 y tranverse intensityprofile. The rather good agreement between the Oaturatlon amplitude observed :n thie 2DSimulation and that predicted by the fluid theory leads ue to believe relatiTisticeffectsare the domi.~antmaturation mechaniema i n coll is ion le es plasmas. It ehould ]e emphasizedthat becauae our Eiimulationeare aperiodic the appropriate comparison ie made for a givenOpatial pooition.The electron phase space at T = 210 u-l (Fig. 3a) shows coherent accelerat ion of theelectronB similar to that eeen in the one-d?#enLional accelerat ion . 3-6 Figure 3b Ehows con-tinued acceleration at T = 300 u-]. The maximum energyl is predicted to be 4C w2/u2 mn C2 -16 NeV for c - 0.5, where c ia t~~ plasma wave amplitude. AB we aee from the elect~onph~eeepace, this 10 in excellent agreement with the aimulation~.A8 we have already noted, the incident laser beam as ohown in Fige lb and c, exhibitsvery eitrong.aelf-focuseing due both to relativiflticeffecteg aa seen in Fig. lb, and pon-deromotive force effecte ae seen in Fig. lc. The ion deneity profile hae not moved at thetime o f the eelf-focussing ae shown in Fig. lb and a correapo~.dingfixed ion eimulntion atthie time exhibits the same ~egree of self-focueelng. At thie time (210 W-l) the Eelectric field as seen in Fig. 2d la reasonably coherer?t. Coneietentwith thie c%%erence w~observe along the laser beam continued electron acceleration ae ehown in Figa. 3b and 3c.In fact, the plot in Fig. 3C of p VB y e-howea definite epike o f electron accelerationalong the laser axle. By the time ~= 300 up: the ponderomotive force hae begun to move thelone and the background density ie &ltered.A more qualitative ueaaure of the electron heating is obtained from the electron dis-tribution of particlee etr iking the r i%ht-hand bounda ry as ehown in Fig. 3d. Clearly, wehave a near thermal distribution of e~.ergetic electrons with a cutoff energy o f ap-proximately 4 c u2/u2 s 16 MeV. The amount of energy in thio tail in a few percent of theincident lacer energy.p The meet energetic particles, ae we note prev+,ouely,are acceleratedalong the beam axis. Thie c~llimatlon :,emaintained by the pinching of the acceleratedelectrons in their belf-magnetic field ae exhibited by the magnetic field contour plot inFig. 4a. The field indicatee evidence of a current pattern prouuced by the hot electronemoving down the axle and a relatively colder electron current at the outeide of the lacerbeam. The localized magnetic field peake are due to localized currents from trappedelectrons bunched in x moving along the lacer beam. The corresponding plasma wnve electricfield which produces the acceleration ie shown in Fige. F!eand 2f--which indicntes that theaccelerating fielde are becoming nonainuaoidal. If the laaer inteneity ie lowered eo thatthe maturated electric field value ie insufficientto trap background electronel the plasmawave still loses co:,erencethrough scattering off ion fluctuat!ono ~t wavelength peakingaround one half the plasma wBvelongth.The whole acceleration prooeee diminiehee!eubatantially when plaema hae he.? evacuatedfrom where the-laOer beame reeide. Figure 4h shows an ion x-y ~article plot at a very latetime, T = 480 w 1. Not only hae the acceleration become incoherent, but it ie highly inef-ficient beoaua~eae wa Bee in Fig. 4b, Oelf-focuseing of the laeere produce locally largeelectric fielde whoea ponJeromotive f o r c e evacuatea plaema from the interacting region. Theparticle plot in Fig. 4b olearly ahowe thie effect.Lnstly, q word about absorption and related miaulationa. At times when the plaema wavelb very efficiently accelerating electrone, the overall absorption can be ae high a~ 15$over the computational hex. At lmte times when the ncoeleration IS relatively Inefficient,the absorption dropo to a few percent.In addition, to the finite beam oimulatlone dincueaed here, we have also carried out afew uniform lacer Learnmimulationa. We obnerve Weibel instability beca$laeof the anieotropjomuoed by elccrone preferrnntinlly txcited in x, qnd the reeultant degradation of theeleotron acceleration. For the caee of an initialized DC magnetic field, at high laet,rpower, thero io B limitation of the number of trapped eleotrons. Becauee trapped electronoundergo ~ m ~ mot ion in the etat io magnet io field, they produce localized epikee intrenevorae current which alter thu background field and tend to limit the accel~rationprooeoeoAoknovledgmantu

W@ wioh to thank Prof. F. F. Chen and Dra. T. C, Kataouleau, D. Bnoh, F. Felher,P. Ooldatone qnd 8. Singer for many ntimulatlng dieicuneione.bTh im work wso eupported qt Lou Alamoa National Lnbormtory by the U.S. DOE and at UCLA bytho NSF .

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References;:3.4.5.6.7.8.9.

10.

T. Tajima and J. M. Daweon, Phys. Rev. Lett. 43, 267 (1979).B. I. Cohen, A. N. Kaufman and K. M. Watson, ~ya. Rev. Lctt. @ 581 (1972).W. Mori, Masters Thesis, UCLA PPG Report (1984).W. Mori, C. Joehi, and J. M. Daweon, IEEE Trana., NS-30, 4, 3244 (1983) and referencestherein.J. M. Dawson, Bull. of APE ?&, 8, 1029 (1983); J. M. Kindel, I?.W. Forslund, and w.Mori, op cit. p. 1192.D. J. Sullivan and B. B. Godfrey, AIP Conference Proceedings, APS. Edited by P. J.Channel, 1, 43 (1982).?--ajiua an W. Horton, Proc. of Lacers 84 [1984).M. N. Roaenbluth and C. S. Liu, Phye. Rev. Lett., 2Q, 701 (1972).D. W. Forslund, J. M. Kindel, W. B. Mori, C. Joahi, and J. M. Dawson, Two DimensionalSimulation of Single Frequency and Bent Wave Laser Plaema Heating, eubmitted to PRL(1984).C. E. Max, J. Arons, and A. B. Langdon, Phye. Rev. Lett., ~, 209 (1974).

T=150wp&l T=300fdw-1 T=480wp&l

x ( c / q J a )

\1 to 63x(c/wp,)

the Ez electric field in the x-y plane where Ez, ise/mempeo where uDe ie the plasma frequency. Two inci-

Fig, 1. Contcur plots ofgiven in units ofdent la sers of equal-RMS ampli%ufle eEo/mewpe = 0.4 at frequencies,1 E 4 Wpe and W2 = 5 Wpe are launohed from the left boundary with a O-100$ rise time of 300 w~~. The beam width ie a coezy function with zeroamplitude at 20 and 40 CIU 11)y. Note that the eyetem iIY60 C/IIJpeby60 C/Wpe in x and y. Oti%r sit,uLatiGnparametore with eitandnrddefini-tion are as followe: Ta/Ti = 1, Mi/me m 183C and Te = 0 . 0 0 5 m c2 , (a)theEz field nt T = 150 w~~ exhibits the inittal beam width and beat wavemodulation in x; (b) At T r 300 u~~, Ez uhous clear ~slf-focueeing: (c)At T E 480 u~~ we ~ee eelf-focussing ov>r an even enorta r dietanoe andeubeIequentexpannim of the beam.


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. .

t

- 4 -

T=150Wpe-I T2104upa-1 T=300@Pe-t

Y(

Y=30(C/tdpe) Y30(c/wpe) Y=30(c@pe)

Fig.

6 LoEx

o c

-6 0 -LoX ( C/ t A / p e x ( c h p ~ ) 6 0 0 X( c l f d p l ) ) 6 0

2 . FOY the above simulation we plot at T = 150 u~~ (a) the contours ofpotential showing the planar plaema wave (b) the associated Ex electricfield at Y = 30 CIU ] as a function of x; at T = 210 ~-l; (c) the

repotential contour8; (d, the Ex field; and at T = 300 u~~; (e)p~he Poten-tial contours, and; (f) the Ex field. Note the irregularity in the beatplaema wave at the lqtter time.


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T=210wP-12s0 ELECTRON PHASE SPMEI (o) I I ! ..-2:Ba(mo W o x(ckpel) m

F i -1

-25.0 I I 10 x(c/fAlp@~

ELEC7RONPHAsE SPACEi ,. .,,

It$ ELECTRWS -

D

(d)FE

K?o Ss.oENERGY (m~c%Fig. 3. For the above Simulation (8) the electron uomentum

Px(me c) as q function of x at T = 210 tij~ ; (b) attime T s 300 mj~: qnd, (o) the electron uomentumPx/mec as a function of y at T = 300 u~~. %otepinohing due to eelf-genarated magnetic fieldo; (d)the aleotrun distribution Fe qt th e right boundary qtT - 300 ti;i; hot electrons otriking this boundnry arereplaoed by ould once.

a

MIN.~-,07e MAXP0070I I 1(0) I1

i

M ION MTICLE

Fig. 4. For the abovo 8imu18tion (a) Contours of the Bz mag-netio field qt T s 300 a~&. This plot qhous oloarevidenoe of fielde produood by both the aooeleratedeleotrone moving down the qxim snd return ourrentelectrons outnids the oenter qxinl (b) An X-Y ionpmrtiolo plot qt T - 480 u;; qhowin~ tho qffeotm ofnelf-focumeing by plaama qvaoumtion.

j. m. kindel et al- two-dimensional beat wave acceleration scheme

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