N.A. Ebrahim, P. Lavigne and S. Aithal- Experiments on the Plasma Beat-Wave Accelerator

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IEEE Transactions on Nuclear Science, Vol. NS-32, No. 5, October 1985 3539EXPERIMENTS ON THE PLASMA BEAT-WAVE ACCELERATOR

N.A. Ebrahim* 1Applied Physics, Yale University, New Haven, Connecticut, U.S.A.andP. Lavigne and S. AithalINRS-Energie, Varennes, Quebec, Canada JflL 2PO

SummaryWe report an experimental study of the beat-waveexcitation of plasma waves using a short pulse, highintensity CO, laser with two colinearly propagatingbeams to excite the fast wave (v, 2 c) in a long-scale-length underdense plasma. Gximum plasma waveamplitudes nI/no = 0.19 with effective longitudinalelectric field gradients of = 6 GV/m over a distanceof 0.5 mm were achieved in these experiments.

IntroductionIn the past decade there have been numerousanalytical and numerical studies of the beat-wave

excitation of plasma waves because of a number ofpotentially important applications in the fields ofplasma physics, astrophysics, and particle acceleratorphysics. The theoretical work to date has been summf-rized in a recent review on this subject by Cohen .Over this period however, there have been very fewexoerimental studies of this prohlem. The firstIexperimental study of the beat-wave excitat$on ofplasma waves was reported by Stansfield et al. , whoused the optical mixing of two dye laser beams toexcite the plasma waves in a plasma jet and observedthese waves by Thomson scattering of a probe rubylaser beam. This experiment has recently beenrepeated using a long pulse, low intensity CO, laserwith two counter-propagating beams ins which a slowelectrostatic wave (vp < c) was excited .In this paper we report an experimental study ofthe heat-wave excitation of plasma waves using a shortpulse, high intensity, CO, laser with two colinearlypropagating beams to excite the fast wave (vin a long-scale-length underdense plasma. A xithat the potential troughs associated with the longi-tudinal plasma wave can trap sufficiently energeticelectrons from a plasma background and accelerate themto relativistic energies, when the appropriate densityresonance condition is satisfied.

ExperimentsThe schematic of the experimental arrangement isshown in Fig. 1. The experiments were performed witha Cf12 laser delivering about 50 Joules in a 1.2 ns

FWHM oulse4. For dual wavelength experiments, thelaser chain was used to amplify the 9P(ZO) line at1046.8 cm-l (x = 9.55 urn) and the lOP(16) line at947 i4 Cm- (x = 10.55 Ilmj. Since these iines havesimilar small signal gain, a good control of the rela-tive energy at each frequency could be maintained.The use of reflective focusing optics and parallelwindows all along the laser chain ensures a beamcolinearity of better than 0.15 prad as measured inthe far field. The P-polarized light beam was focusedat near normal incidence (< 8") by an f/2.8, 25 cm

*Present address: Atomic Energy of Canada LimitedChalk River Nuclear LaboratoriesChalk River, Ont., Canada KOJ 110

.- -_...Oscillator

,2!5ns

HighPressureAmplifier -

Foil

ElectronSpectrometer

10.6 micronProbe PulseElectronSpectrometer

w

Fig. 1 Schematic of experimental arrangement.focal length, diamond- turned parabola. At best focus,50% of the energy was contained within a 120 Mmdiameter focal spot. The displacement at the focus ofthe parabola was less than 20 pm between the two wave-lenqths. Only those shots for which the synchroni-zation between the pulses at each frequency was betterthan IOIl ps as measured on a 1 GHz oscilloscope. wereretained for analysis.

The underdense plasma was produced by exploding a;hi;Q,Earbonz foil (120 A) with a high intensity- * W/cm ) laser prepulse which preceded the mainpump pulse by 25 ns. The carbon foils were mounted onaluminum washers with a clear aperture of about 3 mm,and produce a parabolic density profile (Fig. 1).Transmission measurements on the 120 A foil show thatapproximately 35% of the energy in the prepulse istransmitted, so that the foil goes underdense shortlyafter the peak of the prepulse. As the plasmaexpands, the peak electron density decreases until itreaches the required resonant value for the two wave-lengths, during the main pulse.The plasma density was measured with a Mach-Zehnder interferometer using a 10.6 1~1 probe pulsewith a 1 ns time resolution, which observed the plasmain a direction perpendicular to the la-ser axis, sothat plasma on both sides of the original foil couldhe observed simultaneous ly. A typical density profileon the hackside of the foil taken at the beqinning ofthe main pulse is shown in Fig. 2. On the frontside,the plasma profile was very similar to that shown inFig. 2 . The peak electron density at the beginning ofthe main pulse is close to the quarter-criticaldensity for the 10.6 pm beam (ne = 2.5 x 1018 cms3),

with a density plateau around the resonant density of1o17 cm-3.OOIS-9499/85/1OCO-3539$01.000 1985 IEEE

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Fig. 2 Electron density profile on the backside ofthe foil. Profile on the frontside is verysimilar to this.

The high energy electron emission was observedwith two absolutelv calibrated. 180' focusina spec-trometers, one in ihe forward direction (laser- propa-gation direction) and the other in the backwarddirection making an angle of 27' with respect to theincident laser beam. The enersv ranae covered by thespectrometers was 200 keV to 3 hileV for the forwardspectrograph and 200 keV to 2 MeV for the backwardspectrograph.When two travelling electromagnetic waves (wo,kl) at 10.6 vrn are injec tedunderdense plasma of resonant densitythe beat of the two waves qives rise to a

non-linea; pondermotive force V which excitesplasma oscillations at the frequency wp and wave-number k P where"P = w. - w1 and t =P To -7tp (1)

This process may also be regarded as opticalmixing or forward Raman scattering.the phase velocity vo is given by Since w. >> "p,23 = 0 1VP = kp F-7 = vg = c "Pi il/2

l-7 -=c (2)6is the group velocity of the electro-

Figure 3(a) shows typical high energy electronemission in the forward direction with dual wavelengthirradiation of a 120 A carbon foil target. In the twowavelength case, the intensity in the two wavelengthswas approximately equal (= 3 x 1Ol3 W/cm '). In theforward direction electrons with energies up to 3 YeVwere observed, the electron emission being peaked inthe direction of the laser beams. In the backwardsdirection (Fig. 3(b)) the electron emission was abouttwo orders of magni tude lower than in the forwarddirection, was nearly isotropic and the maximum energyof electrons observed was under 2 YeV. When the sameunderdense plasma was irradiated with a single wave-length heam (10.6 lfm)intensity (7 x 10 at approximately the sameW/cm') the backward emission

remained unchanged. However the forward spectrum wasreduced by about two orders of magnitude and the maxi-mum energy electrons observed were now only under2 MeV, so that the forward spectrum was now verysimilar to the backward spectrum. Integrating underthe curve for the forward emission (under dual wave-;length illumination) we find that there are 3 x 10electrons/Sr accelerated in the forward direction withenergies between l-3 MeV. The electrons in the back-ward direction and in the forward direction withsingle wavelength illumination are emitted when thefoil is first irradiated by the prepulse (as was con-firmed by numerous experimental observations) and areprobably due to a combina tion of resonance absorption,two plasmon decay and stimulated Raman 'back-scattering. The larqe number of electrons with thehighest energies are- only observed in the forwarddirection with two wavelength illumination. Further-more, there appears to be a resonant density at whichenergetic electrons are observed in the forwarddirection. With the same level of prepulse, the samedelay between the prepulse and main oulse. and withthe same energy in 'each wavelength as'in F;g. 3, themost energetic electrons were only observed with afoil thickness between 120-160 A.

; 1041I I

Fig. 3 (a)

Fig. 3 (b)

Electron Energy (MeV)

Accelerated electron distribution in theforward direction with two wavelengthlaser irradiation.Accelerated electron distribution in theforward direction with single wavelengthlaser irradiation. In the backwarddirection the distribution was verysimilar to this under single or dualwavelength irradiation.

To compare with theory, we use the optical mixingtheory of Rosenbluth and Liu' to calculate the ampli-tude of the plasma wave. According to this theory,the amplitude of the plasma wave grows linearly intime until it saturates as a result of the relativ-istic frequency shift.given by The saturated amplitude is

1= 16 l/30 (-3 49) z 6 ,y 10-q 1j30


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where Y = eEi/mnc = vOi/c is the oscillatoryvelocitv of an electron in the laser beam. and In isthe intensity in each line assuming that the pumplines are of equal strength. However in our finitegeometry, the plasma wave energy can also be lost byconvection either axially or radially. Calculationsof this effect show that convection could limit thewave amplitude to a value given by

where L is the interaction length. For an interactionlength equal to the depth of focus (= 500 Pm), con-vectiy5 limif! is important below an incident intensityof lo- W/cm for our experimental conditions.The maximum energy Emax of 6an electron acceler-ated by a plasma wave is given by

E = 2y2,,,2($ = 1.022 ($($4 (5)max

where y = (1 - v~*/c~)-~/*= wo/"p = (n,/nc)'/*.

For equal intensities 10 = 3 x lOI W/cm*,Eq. (3) gives nl/no = 0.19 and the maximum electronenergy Emax 5: 20 MeV. However the accelerationdistance for the electron to acquire this ener;;"a I Emax/eEL = (2c/op)(nc/no) 2 3.3 mm.our experiments , the interaction length is limited bythe depth of focus which is approximately 500 Pm, sothat the maximum electron energy expected is approxi-mately 3 MeV in good aqreement with experimentalohservations of electrons with energies of 3-3.5 MeV(Fig. 3(a)).

An important point in these experiments is themanner in which the electrons are trapped by the highphase velocity wave. An electron with a velocity v'and kinetic enerqy (T'-l)moc' in the wave fr+ame 'Strapped in the wave of potential lfe9' > (u'-l)moc*. llsing the Lorentz transformationthis-condition can he expressed in terms of thelahoratory frame quantities as

(6)where y = (l-3')-'/',

yp = (l-$*)-'/2,BP = vp/c, and

B = v/c,v being the particle velocity in the laboratoryframe. Normaliz ing the above inequality by thetrapping condition at wavebreaking in a cold plasma ltcan be shown, that particles will be trapped if

For vp = c and nl/nc = 0.19, B = 0.7 and themin imum energy of particles in the laboratory framewhich can be trapped is 150-200 keV. Thus with anestimated hackground temperature of between 500 eV and1 keV, electrons are not accelerated from the thermalbackqround distribution . Instead, the enerqetic back-ground electrons are generated by the stimula ted Ramanbackscattering instability excited by the main laserpulse, at the quarter critical density. For a density

scalelength of approximately 500 ?yrn the2 thresholdintensity for this process is = 10 W/cm , which isexceeded by the main las'er pulse. The phase velocityof the Raman-genera ted plasmons at the quarter criti-cal density vp = c/43, so that electrons with maxi-mum energy E = 2mvB

* = 340 keV are generated. Theseelectrons are trap ed by the beat-wave excited plasmawaves and accelerated to approximately 3.5 MeV.Conclusions

We have experimentally demonstra ted the beat-waveexcitation of plasma waves using a short pulse, highintensity CO2 laser. Electrons with initial energiesabove 150 keV, generated by Raman backscatteringinstability, were trapped by the plasma waves andaccelerated to maximum enerqies of 3.5 MeV, corre-sponding to a wave amplitude nl/no = 0.19. Theeffective electric field aradient achieved in theseexperiments was approximp$ ely 6 GV/m for a modestlaser intensity of 3 x-10 W/cm2 at each wavelength,over an acceleration distance which was typically0.5 mll.Acknowledgments

This work was performed under the auspices of theNatural Sciences and Engineering Research Council ofCanada, Le Ministere de 1'EducationOuebec and the U.S. Oepartmentcontract DE-ASO&84OP40194.of the province ofof Energy under

References1. R.I. Cohen, Com ments PlasmaFusion, 8, 197 (1984). Phys. Controlled

2. R. Stansfield, R. Nodwell and J. Meyer, Phys.Rev. Lett., z, 149 (1971).3. 4. Amini and F.F. Chen, Phys. Rev. Lett., 53, 1441(1984).4. P. Lavigne, T.W. Johnston, 0. Pascale, H. Pepin,M. Piche and F. Martin, Phys. Fluids, E, 409(1984).5. M.N. Rosenbluth and C.S. Liu, Phys. Rev. Lett.,29, 701 (1972).6. T. Tajima and J.M. Oawson, Phys. Rev. Lett., 43,267 (1979).

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N.A. Ebrahim, P. Lavigne and S. Aithal- Experiments on the Plasma Beat-Wave Accelerator