Interaction of ultrahigh laser fields with beams and plasmas.pdf

7/30/2019 Interaction of ultrahigh laser fields with beams and plasmas.pdf

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Interaction of ultrahigh laser fields with beams and plasmas*Phillip Spranglet and Eric EsareyBeam Physics Branch, Plasma Physics Division, Naval Research Laboratory,Washington, D. C. 203 7S-So00(Received 18 December 1991; accepted 5 February 1992)The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas s richin a wide variety of new phenomena.Advances in laser sciencehave made possiblecompact terawatt lasers capable of generating subpicosecondpulses at ultrahigh powers (2 1TW) and intensities () lo* W/cm). These ultrahigh intensities result in highlyrelativistic nonlinear electron dynamics. This paper briefly addresses number of phenomenaincluding (i) laser excitation of large-amplitude plasma waves (wake fields), (ii)relativistic optical guiding of laser pulses n plasmas, (iii) optical guiding by preformedplasma channels, (iv) laser frequency amplification by ionization fronts and plasma waves, (v)relativistic harmonic generation, (vi) stimulated backscattering from plasmas andelectron beams, (vii) nonlinear Thomson scattering from plasmas and electron beams, and(viii) cooling of electron beamsby intense asers. Potential applications of theseeffects are also discussed.

I. INTRODUCTIONAdvances n laser technology have made possiblecom-pact terawatt laser systems with high intensities ( 2 lo*W/cm2), modest energies 5 100J), and short pulses ( 5 1psec) ls2 This new class of lasers is referred to as T3(tabletop-terawatt) lasers.The availability of T3 lasers hasmade possibleexperiments n a new ultrahigh intensity re-gime. Previous laser interaction studies have been imited,for the most part, to relatively modest intensities. At ul-trahigh intensities, the laser-electron interaction becomeshighly nonlinear and relativistic, thus, resulting in a widevariety of new and interesting phenomena.3-8 hese phe-

nomena include: (i) laser excitation of large-amplitudeplasma waves (wake fields),3-5 (ii) relativistic opticalguiding of laser pulses by plasmas,5-7 iii) optical guidingby preformed plasma channels,* (iv) laser frequency am-plification by ionization fronts or plasma waves,5p9-3v)relativistic harmonic generation,14 (vi) stimulated back-scattering from plasmas and electron beams, (vii) non-linear Thomson scattering from plasmas and electronbeams, and (viii) the cooling of electron beams by in-tense lasers.* These phenomenamay have important ap-plications ranging from advancedultrahigh gradient accel-erators to advanced sources of ultrashort wavelengthcoherent radiation. This paper briefly discusses omeof thesalient features of these phenomena.An important parameter in the discussion of ultrain-tense aser nteractions is the unitless aser strength param-eter ae, where a,,=eAdm0c2 is the normalized (unitless)peak amplitude of the laser vector potential A,. The l aserstrength parameter s related to the power POof a linearlypolarized laser by

Pe[GW] ~21.5(uord;10)2, (1)*Paper 4IG2, Bull. Am. Phys. Sot. 36, 2373 (1991).+Invited speaker.

where r. is the spot size of the Gaussian profile, Lo is thelaser wavelength, and the power is in units of GW. Phys-ically, ao)l implies that the electron quiver motion in thelaser field is highly relativistic and nonlinear. This may beseen from conservation of canonical transverse momen-tum. In the one-dimensional 1-D) limit, uo=/pl, where yis the relativistic factor and /?I=v,/c is the electron quivervelocity. Hence, a,) 1 implies y) 1. The peak laser electricfield amplitude E. is related to the laser parameter a0 byEo[MeV/m]~3~106ac//20[~m]. (2)

For Lo= 1 pm and uo> 1, the laser electric field exceeds heCoulomb field associatedwith the hydrogen atom. In termsof the laser intensity, Io=2Pdr& the quantity a0 s givenbyuo~0.85~10-9ilo[~m]I~2[W/cm2], (3)

where /z. is in units of pm and IO is in units of W/cm2.Highly relativistic electron motion ( uo> 1) requires laserintensities greater than lOI* W/cm2 for wavelengths ofLo- 1 pm. Such intensities are now available from com-pact, T3 laser systems.Compact teruwutt hers. The T3 laser system is basedon the technique of chirped-pulse amplification (CPA),first applied to solid-state lasers n 1985. The CPA tech-nique allows for ultrashort (rL< 1 psec) pulses to be effi-ciently amplified in solid-state media, such as Nd:glass,Ti:sapphire, and alexandrite.lv2 n the T3 laser, a low-energy pulse from an ultrashort pulse, mode-locked oscil-lator is passed hrough an optical fiber to produce a linearfrequency chirp. The linear frequency chirp allows thepulse to be temporally stretched by a pair of gratings. Thestretched pulse is amplified to moderate energies n thesolid-state regenerativeand single-pass mplifiers. The am-plified pulse is now compressedby a second matched pairof gratings. Compression of the chirped, l ong-durationpulse is accomplished after it has been amplified, thus,avoiding undesirablehigh-field effects, e.g., self-focusing n

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1 PS1 J LASER WAKEFIELD ACCELERATOR

1 ns1 J

1 PS1 nJ

Oscillator Stretcher Amplifier Compressor

FIG. 1. Schematic of the chirped-pulse amplification (CPA) methodused in T3 laser systems.

the solid-statemed ium. The CPA method s schematicallyshown n F ig. 1. This methodhasbeen ppl ied o compactsystems T3 lasers) to produ cepicoseco nd ulses n thel-10 TW range.ls2 fforts are also under way o apply theCPA method o large-scale ystemswith the goal of pro-ducing aser pulsesof extremely high energies > 1 00J)and powers ( > 100 TW).19 In an alternative echnology,large-scale rF excimer asersystems an directly amp lifya singleshort pulse o terawatt power evels.20II. INTENSE LASER INTERACTION PHENOMENAA. Laser wake-field excitation

As an intense aser pulse propaga teshrough an un-derdense plasma, fw;4, wherecop= 4re2ndmo)12 ap= 2n-c/copis the plasma requ encyand no s theambientelectron density, the ponderomoti veorce associ-ated with the laser pulse envelope, ,-Vu2, expelselec-trons from the regionof the laserpulse. f the pulse ength,crL, is approximately equal to the plasma wavelength,crL=jlp, the pond eromotive orce excites arge-amplitudeplasmawaves (wake fields) with phas e elocitiesequal othe laserpulsegrou p velocity,3-5 e eFig. 2. The maximumwake-fieldamp litude genera ted y a linearly polarized a-ser pulseof amp litude uo, n the 1-D limit &$, is&,,,,[GeV/m] -3.8X 10-8(no[cm-3])12 4( 1+u22)2 (4 )where he maximum gradient E,,,,, is in GeV/m and theplasma density no is in cmm3.Typically, E max s a fewordersof magn itude reater han the accelerating radientsin conventional inear accelerators. h e accelerating radi-ent associated ith the wake ield can accelerate trail ingelectronbeam, .e., such as n the laserwake-fieldacceler-ator (LWFA) shown n Fig. 2. In the abse nce f opticalguiding, the interaction distance,Lint, will be limited b y

PlasmaWaveWakefieldAcceleratedElectronBunches

IntenseLaserPulse

FIG. 2. Schematic of the laser wake-field accelerator (LWFA) . The ra-diation (ponderomotive ) force of an intense laser pulse drives plasmawaves (wake fields) with phase velocities --c, which trap and acceleratetrailing electron bunches.

diffraction. Diffraction limits the interaction distance oLint rZR, where ZR=m$ Ao is the vacu um Rayleighlength. The maximum energygain of the electronbeam na single stage s A WZE,,,~~L~~~,hich , in the limit &l,may be written asAW[MeV] =580(ile/,$,)Po[TW]. (5 )

As an example,considera rL= 1 psec inearly polarizedlaser pulse with PO=10 TW, /2,= 1 pm and ro= 30 pm(uo=0.72). The requirement that crL=Ap implies aplasmadensityof no= 1.2~ lOI cmp3. The wake-fieldam-plitude (acceleratinggradien t) is E,,,=2.0 GeV/ m an dthe interaction length is Li,=O.9 cm. Hence a properlyphasedailing electronbunchwould gain an energyof A W= 18 MeV. The interaction length, and co nsequently heelectronenergygain, may be greatly ncreased y opticallyguiding5-* he laser pulse n the plasma.The self-consistent volution of the nonlinear plasmawave has beenstudied numericall y n the 1-D limit.5 Fig-ure 3 shows he plasmadensity variation Sn/no=n/no- 1and the correspond ing xial electric field E, for a laserpulseenvelopewith cr,=$ In this figure, crt=,$,=0.03cm, A= 10pm, and u,=2.0. The steepening f the electricfield an d the increase n the period of the wa ke field areapparent or the highly nonlinear ituation shown n F ig. 3.6. Relativistic optical guidi ng

For a laserpulse o propagaten a plasmabeyond helimits of vacuu mdiffraction, i.e., large distances omp are dto Za, some orm of optical guiding s necessar y. or suf-ficiently powerful, lo ng l aser pulses, diffraction can b eove rco me y relativistic effectsand the laser pulse can beoptically guided n the plasma.5-7 nonlinear analysisofintense aser pulse propagation n unde rden se lasmas n-dicates hat the index of refraction VR characterizing helaser pulseevolution s givenby5VR- I- (4@) (dyne>, (6)

2242 Phys. Fluids B, Vol. 4, No. 7, July 1992 P. Sprangle and E. Esarey 2242Downloaded 03 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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101

z 5552 0 II:.,lJ e--5-I10

IIII\\

\Laser envelope

-15' I I I I

3

2

1

0 -$

-1

-2

-3-0.10 -0.08 -0.06 -0.04 -0.02 0.00

DISTANCE E ( cm)

FIG. 3. Density variation &/no= n/n,- 1 and axial electric field E, inGeV/ m for a laser pulse with a,,=2 and c~~=,$,=O.03 cm.

where n is the perturbedelectron density. For a long p ulselaser (long ri se time), crL,Lp, it may be show n5 thatn/yncE(l+&2)- 12.A necessary equirement or opti-cal guiding is that the refractive ndex havea maximum onaxis, aqR/ar < 0. This is the case or a long laserpulsewithan intensity profile peake don axis, a&& < 0. Analysis ofthe waveequationwith the index of refraction givenby Rq.(6) indicates hat the main body of a long laser pulse willbe optically guided, provide d he laser PO xcee ds criticalthreshold PO Pcrit,where6P,,.JGW]E 17.4(/2d;1,,)2. (7 )

As an example, or a plasmaof density no= 5 x lOI cmm3(A,=20 pm) and laser wavelengthof &= 1 ,um, the crit-ical laser powe r is Pcrit= 1.36 TW. For sufficiently shortpulses, r, < l/c+, the pl asma has insufficient time to re-spond o the laser pulse.The modification of the refractiveindex occurs on the plasma frequency ime scale, not onthe laser requen cy ime scale.Therefore , f the laser pulseduration is comparable o or shorter than a plasmaperiod,i.e., rt- < l/up, relativistic optical guiding doe snot occur.C. Optical guiding by density channels

To optically guide short intense aser pulses n plas-mas, preformed plasma density channels can be used.8Conventionaloptical light pi pesconsist of fibers having a nindex of refraction that varies as the squ areof the radialposition. Optical light guides can be formed within aplasma by creating a hollow density channel. The plasmachannelcan be formed by propagatingeither a low-currentelectron bea m or a low-intensity laser pulse through theplasma. n either case, he plasma s expelledby the beam,leaving a density depressionhat can guide the laser pulse.The plasma channel modifies the ind ex of refraction,which, in the absen ce f relativistic effects, s given by

Optical Guiding in a PlasmaDensity Channel

Plasma Density/Laser, Profile

Transverse Position

FIG. 4. Pl asma channel profile ne cessar y for optical guiding in a pre-formed plasma channel.

where n(r) is the electron density profile. Optical guidingcan occur when the pl asma density is minimum on axis.Analysis of the wave equation or a fixed parabolic plasmadensity channel ndicates hat optical guiding of a Ga uss -ian laser pulse occurs when the channel density depth isgiven by*An = l/n-r&, (9 )

where An =n(ro) -n( O) and r,=e2/m& is the classicaelectron radius ( seeFig. 4). For example, he density de-pressionnecessaryo guide an optical bea m having a spotsize of ro=30 pm is An z 10 cme3. Fully nonlinear sim-ulations of pulse propagation, which include the self-consistent evolution of the density channel, ndicate thatthis mecha nism s cap able of overcoming diffraction forshort pulse engths and high intensities.*The self-consistent, wo-dimensional (2-D) axisym-metric propagation of intense aser pulses n plasma sha sbeen ecently analyzed heoretically and numerically.8Fig-ures 5 a) and 5 b) show the normalized aser ntensity a2as a function of c=z-ct and r. These igures show s heintensity initially, at z=O, and after propagati on en Ray-leigh lengths n a preformed plasma channel. Figure 6(a)show s he l aser spot size after ten Rayleigh lengths. Thefront of the laserpulse s optically guided while the body ofthe pulse s focused.Figure 6(b) shows he evolution of thespot size as a function of propagatio n distance. The spotsize oscillatesabout its initial value during the full prop a-gation distance. n addition, as he pulsepropagates ithinthe plasma channel, it genera tes large-amplitude wakefield. The acceleratinggradient remained at a relativelyconstant value of Em,,=3 GeV/m.D. Laser frequency amplifications

A laser pulse that copropagates ith an electron den-sity wave, i.e., a traveling density gradient, can continu-33AR Phvc FIIkic R Vnl A Nn 7 .I~flv 1003 P Cnrsnnln cl,-4 E CccJr..sr OOAQDownloaded 03 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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10 r 1.01

(b)FIG. 5. The self-consistent propag ation of an intense laser pulse, witha,=0.9, A,,=1 pm, and crL=r0=AP=0.03 cm, in a density channel withn(r=O) = 1.2~ lOi cmW3. (a) The initial intensity profile a. (b) The a*profile after propagating lOZa, where Za=28.3 cm.

ously chan ge ts frequency. t9-2 he traveling electron den-sity gradient can b e a large-amplitude wake field9F0 r arelativistic ionization front.5V1P2onsider a laser pulse co-propagating with a traveling density gradien t which maybe locally approximated by drz/dc= -tzo/d, where c=z-ct, d is the length of the density gradient, and d > crL isassumed s shown n Fig. 7(a). The local phasevelocity isgiven approximately byvp({)/c- I+ (;1~2/2;)n(S)/no. (10)

Hence he phasevelocity near he front of the pulse will beless than the phasevelocity at the back of the pulse, pro-vided the density is less at the front of the pulse. Thisallows the individual phasepeaks n the laser field to movecloser ogether.This results n a decreasen the wavelengthand an increase n the frequency. Analysis of the waveequati on with an electron density gradient of the formdn/dc= -ndd, shows hat the laser requencyevolvesac-cording to5Y9-12(11)

o.ot, L,, ,I-2.5 -2.0 -1.5 -1.0 -0.5 0.0

(a) C/h,

0.6 t i

o.ot : I I , ,0 2 4 6 a 10

(b) CT/&?FIG. 6. The self-consistent propagation of an intense laser pulse in aplasma channel with the same parameters as for Fig. 5. (a) The laserpulse spot size after lOZa, where Za=28.3 cm. (b) The behavior of thespot size at the pulse center as a function of propagati on distance.

where CT s the laser propagationdistance. t may also beshown that the laser pulse length increasesaccording toT~(T)/T~(O) =w(7)/oo. Furthermore , when the densitygradient is due to a large-amplitudewake field, the laserstrength parameter decreases s a,( ~)/a~(0) =w( 7)/w@This implies that the laser pulse gains energy from thewake field as it propagates.However, when the densitygradient is due to an externally generate d ionizationfront, the amplitude of the laser electric field decreases,E,(T)/E,(O) =wdw(~). This implies that the laser pulseloses energy to the ionization front. Experimentally, suchfrequency blue shifts havebeenobservedby laser pulsespropagating hrough gaseswhile producing self-generatedionization fronts.* As an example, a 0.1 psec KrF laserpulse (ito=0.25 pm) ionizing hydrogen gas at 1 atm(/2,-4.5 pm) will double ts frequencyafter propagatingadistance of CT= 3.0 cm, according to Eq. ( 11) assumingd=m,(O) =30pm. Figure 7(b) shows he laser pulse pro-file after propagati nga distancec7L= 3dwi/o$ in the pres-ence of a n ionization front, as obtained from numerically2244 Phys. Fluids 6, Vol. 4, No. 7, July 1992 P. Sprangle and E. Esarey 2244Downloaded 03 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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rz: P1as111aDrnsitJ /c t,it

t (wd(8)

G 0.57k 0.0.t?2irl -0.5

-1.0~-- ,I. I... .-.,I -Ll-40 -30 -20 -10 '.- 0t L4

(b)FIG. 7. The initial laser pulse and ionization density are shown in (a) asa function of 6=2--c?. (b) The laser pulse after propagating the distancerequired for frequency doubling, as obtained from numerical ly solving the1-D wave equation.

solving the 1-D wave equation. Notice that n(r) &/2,&(r) -&(0)/2, and ~~(7) --2~~(0), as predicted by the-ory. Alternatively, frequency amplification may be obtainedby reflecting the laser pulse off a counterpropagating, rel-ativistic ionization front.13 In this case, the frequency ofthe reflected radiation will be relativistically Dop-pler upshifted by w= ( 1+p,)2$ oo, where fif= u/c,y/= (1 -p;, -12, and uf is the velocity of the ionizationfront. Furthermore, the length of the reflected pulse will becontracted, crL~crL(0)/( 1+flf)yP However, the poorreflectivity of this relativistic pseudomirror places imi-tations on the applicability of this method.

E. Relativistic harmonic generationThe nonlinearities associatedwith the relativistic elec-tron quiver motion in a linearly polarized laser field canlead to the production of harmonic radiation at odd mul-tiples of the incident laser frequency, i.e., with wavelengths/2,v=UN, where N= 1, 3, 5,... . Coherent relativistic har-monic radiation5V4will be generated n the forward direc-tion (propagating parallel to the incident laser pulse) as aresult of the relativistic plasma currents induced by theincident laser pulse. Initially, the amplitude of the har-monic radiation grows linearly with the laser pulse propa-gation distance. Saturation of the relativistic harmonics oc-curs by phasedetuning.14The nonlinear dispersion relation

for a laser pulse that is long compared to the plasma wavlength, crL&, is given by02=c2k2+w~( 1+ag2)-2, (12

where w is the frequency, k is the wave number, and linearly polarized laser pulse has been assumed n the 1-limit. Equation (12) valid for the incident laseb,k) = (cwW, as well as for the harmonic(w,k) = (wN,kN), where a,,,= Nwo. The detuning distanLd, defined to be the distance over which the relative phabetween the harmonic radiation and the incident laser equal to rr, is given by Ld(AkNI =P, wheAkN=kN(cuN/kN -wo/ko). The detuning distance, in thlimit @A;( 1+a22) 12( 1, is given by

(13At saturation, the ratio of power in the Nth harmonic tthe incident laser power is given by

c!2LcN(~)2~N-1~( l+$)-3cN-1)2, (14where C, are constants that decrease apidly with increaing harmonic number, C3=4.9X 10m3 nd C,=2.4~ lo-.Furthermore, dr iven relativistic harmonic generation is nonresonant nteraction; hence, the process s not sensitito thermal plasma effects.As an example, consider an incident laser with PO= 1TW, ilo= 1 ,um and spot size ro= 10 pm (ao=2.2), inteacting with a plasma of density no=102 cmA3 (/2,=3.4pm). For the third (and fifth) harmonicP,/Po=2.2X 10V5 (4.6X10-) and L,=S.O ,um (4.pm). Hence, 22 MW (0.46 kW) should be observed at wavelength of ;1= 3300 A (2000 A). Clearly, the limitations due to phase detuning are restrictive. If a scheme ophase matching could be conceived, the interaction ditance, and thus the harmonic power PN-L2, could be increased.Furthermore, a fully ionized plasma has been asumed in which atomic and ionization effects have beneglected. Atomic and ionization16 effects may substatially enhance he amount of forward harmonic generatioThis has been the case in low-intensity laser interactioexperiments with neutral gases n which coherent radiatiowell beyond the 61st harmonic has been observed.15

F. Stimulated backscattered harmonic generationStimulated backscattering17 f intense aser pulsesmaoccur from a stationary plasma or from a counterstreaminelectron beam, i.e., a laser-pumped free-electron las(FEL).21 Low-intensity lasers used in previous experments resulted in the observation of only the fundamentbackscattered field. At ultrahigh intensities, higher hamonic backscattered adiation will be generated. 7 The frequency of the stimulated backscattered harmonic (SBHradiation is given by w=NMowo, where N= 1,3&j,..., s thharmonic number and MO s the Doppler shift factor give

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Electron Beam

Intense Pump Laser, c&lo

Backscattered Harmonics, a0 = Nld,f.~,

FIG. 8. Schematic of an intense laser of frequency oe producing stimu-lated backscattered harmonic radiation f rom a plasma or a counter-streaming electron beam. The frequency of the backscattered radiation iso=NMcoc, where Ma is the frequency Doppler shift factor, and N=135t ,..., is the harmonic number.

I1, plasma,Mo= & 1+&)2/( 1+a22), e beam, (15)whereyo= ( 1 &) -2, PO ve/c, an d u. is the initial ve -locity of the counterstreamingelectron beam. This isshownschematically n Fig. 8. Th e backscatteredadiationgrowsexponen tially rom the front of the laserpulse o theback until saturation is reac hed.The exponentialgrowthrate I of the Nth harmonic s found to be

r=fJi

Pow;@dMoFN 13)oyo(l+wJ2 (16)where N=b(J(,-I)/,-J(N+,)/2) 2 is the har monic cou-pling function, J=J(b) are Bessel functions,b=N(a24)/( 1+a22) and po= (1 +aQ2)-12 for aplasma, and po= 1 for an electron beam. For a low-intensity incident l aser interacting with a plasma, ai4 1,

Eq. ( 16) reduc es o the stan dardexpressionor the growthrate of the fundamentalRa man backscatter nstability inthe strong-p ump (or strongly coupled) regime.22 or alow-intensity incident laser interacting with an el ectronbeam,Eq. ( 16) gives he growth rate of the fundamental(N= 1) radiation of a laser-pumped EL in the strong-pump (or high-gain Compton) regime.21P23he growthrates or the higher N harmonicsbec ome ignificant onlywhen a,) 1. This is shown n Fig. 9, in which Fy - r isplotted as a function of (a$4)/( 1+afj/2).Growth of the SBH radiation continuesuntil th e radi-ation am plitude s sufficiently large o caus e article trap-ping. At saturation, h e ratio of the harmoni cpower o thatof the incident laser s found to beipN-=PO (17)

Sincestimulatedbackscatterings a resonantprocess,t issensitive o electron hermal effects, .e., the axial elec trondistribution must be sufficiently cold before exponentialgrowth of the radiation is achieved.Specifically, he ther-ma l velocity must satisfy17&h( poo;t 1+Mo) 3 F{3w&f; (18)

00 0.1 0.2 0.3 0.4 0.5

(09/4)/(1 + a6/2)FIG. 9. The function F k, proportional to the growth rate of the SBHradiation, versus the parameters (&4)/( I+ ~$2).

For a plasma, he thermal energ y s hEth= moc2 2. Foran electronbeamwith yo>1, he normalizedenergy preadis givenby Ayth/yo= yzoth. Note that, for th e fundame ntal(N= 1) in the limit yoyo )and az(l, the thermal require-ment s Ahy,h/3/o


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Laser Pulsee-Beam

SynchrotronRadiation

Final InitialDistribution

;JEnergy

FIG. 10. Schemati c of an intense laser interacting with a counterst ream-ing electron beam producing incoherent Thomson scattered radiationwhich leads to radiative cool ing of the electron beam.

the third-harmonic power to the pump laser power isP,/p,=l.l X 10e9, i.e., PN= 17 kW. The electronic effi-ciency at saturation is ve=0 .87%.This example llustrates the difficulty of generati ng o-herent SBH radiation, given the present state of electronbea m e chnology. n particular, the limitations on the elec-tron bea m energ y sprea d for realistic current densitiespresent a serious difficulty. If the ele ctron distribution isnot sufficiently cold, h owever , harmoni c radiation can begenerated ia nonlinear Thomson scattering rom individ-ual electrons.G. Nonlinear Thomson scattering

Nonlinear T homs on scattering of intense aser radia-tion may be achieved using either a dense plasma or acounterstreaming lectron beam.* For example,nonlinearThomson scattering of an intense laser from a counter-streamingelectronbeamproduces ynchrotron adiation inmuch the samemanner as a static undulator magnet n astorage ing generates ynchrotron radiation (seeFig. 10).An advantage n using an intense aser pulse over a staticundulator is that the waveleng thof the laser pulse s sev-eral orders of mag nitude shorter, - 105, han that of theundulator. Hence, or a given electronbeamenergy,a laserpulse can produce significantly shorter wavelength syn-chrotron radiation than an undulator. In the following,some mportant aspectsof nonlinear Thomson scatteringfrom a stationary plasmawill be discussed. cattering roman electron beam may be describedby preforming the ap-propriate relativistic transformations on the plasma scat-tering results.

For low-intensity lasers (ai< 1 , the freq uencyof thescattered radiation2 from a denseplasma (w,, I/rL) isgiven by o =wc. Since the interaction for a& 1 is highlynonlinear, the scattered adiation containsa continuum ofharmonic radiation out to the harmonic numberN,,,. Theradiation will contain appreciable requen cy compon entsup to a maximu m (critical) frequency, given bywma xNmaxwO= gc/p, wherep is the electrons nstanta-neou s adius of curvature and y is the electrons elativisticfactor.26For a& 1, analysis of the electron orbits in thelaser field shows that the maxi mum har monic number isgiven by*

N,,,,, = jai, (19 )wher e a circularly polarized incident laser field has beenassumed.Furthermo re, for a dense plasma in the limita&= 1, the scattered adiation is predominantly perpend icular to the incident laser, 0,=7~/2.The total pow er n the scattered adiation may be cal-culated rom the relativistic form of Larmo rs formula. Theratio of scatteredpowe r to incident laser powe r for a cir-cularly polarized laser pulse nteracting with a pl asma ofdensity no s given by*

P/Po=(8d3)no&~~. l+a;), (20)where , is the classicalelectron radius. As an example, ora circularly polarized aserwith ilo= 1pm, TV= 1 psec,anduo=2, interacting with a plasmaof density no= 1019 mm3the total scatteredpower s givenby P/PO 1 OX 10m6. hemaximum harmonic number is N,,,-24, which corre-sponds o a minimum wavelengthof A=-420 A. The pulselength of the scattered adiation is determinedby the laser-plasma nteraction time.

Furthermore, ex tremely short-wave length radiationmay be generated y scatteringan intense aser pulse off acounterstreaming lectron beam. The frequencyof the ra-diation scattered off an e lectron beam will be relativisti-tally Doppler shifted by MO,given by Eq. ( 15)) n additionto the harmon ic factor. The scattere d adiation is also wellcollimated within a narrow cone of angle 8,-l/y in thedirection of the electron beam.

H. Laser cooling of electron beamsAn electron bea m nteracting with a counterstreaminlaser pulseemits incoherent adiation via nonlinear Tho m-son scattering,as s show n n Fig. 10. As the electronbeamradiates, t is subseque ntly cooled, i.e., the normalizedemittance and energy spread of the electron beam aredamped . T his is the result of the radiation reaction orce,which an electron experienceswhile emitting radiation.The normalizedelectronbeamemittanceE, will be damp edaccording o the relation*E,=E,o/( l+z/L&?), (21)

where E,~ s the initial normalized emittance, andL,[prn] =3.4X 106/2~[~rn]/~+& (22)

2247 Phys. Fluids B, Vol. 4, No. 7, July 1992 P. Sprangle and E. Esarey 2247Downloaded 03 May 2006 to 210.212.158.131. Redistribution subject to AIP license or copyright, see http://pop.aip.org/pop/copyright.jsp


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is the characteristic damping distance, where y. is the ini-tial energy of the electron beam and a circularly polarizedlaser has been assumed. The mean energy, 7, of the elec-tron beam also decreasesj= rc/( 1+z/LR) . Furthermore,it can be shown that the fractional beam energy spreaddecreases,Ay/;ji= ( Ayc/yo)/( 1 -z/L,), where Aye is theinitial beam energy spread.This radiative cool ing effect canbe significant. As an example, consider a ,Io= 1 pm laserwith uo= 10 nteracting with an electron beam of yo=200.The damping length for these parameters s LRe 170 pm.The energy ost by the electron beam appears n the formof synchrotron radiation.III. CONCLUSlON

An attempt has been made to briefly discuss some ofthe research areas that may be impacted by the develop-ment of compact ultraintense lasers. An important mea-sure that characterizes ultraintense laser interaction phys-ics is the laser strength parameter uo, which is proportionalto the square root of the laser intensity. When this param-eter is significantly greater than unity, the electron dynam-ics becomes ighly relativistic and nonlinear, thus resultingin a wide variety of new phenomena.This high laser fieldregime has not been fully analyzed. Potential applicationsof thesephenomena nclude advancedaccelerators,such asthe laser wake-field accelerator, advanced radiationsources, such as nonlinear Thomson synchrotron sourcesand laser-pumpedFELs, as well as a laser cooling conceptfor electron beams. Although a number of distinct intenselaser nteraction phenomenahave been discussed, t shouldbe emphasized hat this is only a partial list of phenomenain a researcharea that is rapidly growing.ACKNOWLEDGMENTS

The authors acknowledge useful discussions with J.Krall, G. Joyce, A. Ting, W. Mori, D. Umstadter, and G.Mourou.This work was supported by the U. S. Department ofEnergy and Office of Naval Research.D. Strickland and G. Mourou, Opt. Commun. 56, 216 (1985); P.Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J.Quantum Electron. QE-24, 398 (1988); M. Pessot, J. A. Squier, G. A.Mourou, and D. J. Harter, Opt. Lett. 14, 797 (1989); M. Ferray, L. A.Lompre, 0. Gobert, A. LHuillier, G. Mainfray, C. Manus, and A.Sanchez, Opt. Commun. 75, 278 (1990); C. Sauteret, D. Husson, G.Thiell, S. Seznec, S. Gary, A. Migus , and G. Mourou, Opt. Lett. 16, 238(1991); J . Squier, F. Salin, G. Mourou, and D. Harter, Opt. Lett. 16,324 (1991).2M. D. Perry, F. G. Patterson, and J. Weston, Opt. Lett. 15, 1400(1990); F. G. Patterson, R. Gonzales, and M. Perry, Opt . Lett. 16, 1107(1991); F. G. Patterson and M. Perry, J. Opt. Sot. Am. B 8, 2384(1991).3T. Tajima and J. M. Dawson, Phys. Rev. Lett. 43, 267 (1979); L. M.Gorbunov and V. I. Kirsanov, Zh. Eksp. Teor. Fiz. 93, 509 (1987) [Sov.Phys. JETP 66, 290 ( 1987)]; V. N. Tsytovich, U. DeAngelis, and R.Bingham, Comments Plasma Phys. Controlled Fusion 12, 249 ( 1989);V. I. Berezhiani and I. G. Murusidze, Phys. Lett. A 148, 338 ( 1990); T.C. Katsouleas, W. B. Mori, J. M. Dawson, and S. Wilks, in SPZEConference Proceeding 1229, edited by E. M. Campell (SPIE, Belling-ham, WA, 1990), p. 98.4P. Sprangle, E. Esarey, A. Ting, and G. Joyce, Appl. Phys. Lett. 53,2146 (1988); E. Esarey, A. Ting, P. Sprangle, and G. Joyce, Comments

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