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Suitability of Tunneling Ionization Produced Plasmas orthe PlasmaBeat Wave AcceleratorW. P. Leemans, C. E. Clayton, K. A. Marsh, A. Dyson, and C. JoshiDepartment of Electrical EngineeringUniversity of California at Los Angeles

56- 125B Engineering IVLos Angeles, CA 90024Tunneling ionization can be thought of as the highlimit of multi-photon ionizationExtremely uniform plasmas were produced by theat Rutherford lab for beat wave excitationPlasmas with 100%zation were produced with densities exceeding 1017 cmm3.a C02 laser (Imax = 5 X 1014 W/cm2)allows the formation of plasmas via the tunnelingour experiments we need plasmas with densitiese range of 5 to 10 x lOI6 cms3. Using Thomson

ture egime of tunneling ionization produced plasmas.that plasmas with densities up to lOI cmw3 canand that theseplasmasare hot. Beyond thisOUTprogram will be discussed.

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in our 10 pm CO2 laser system allowed us to reach intensitieswhere we could produce plasmasby tunneling ionization.

In plasmaacceleratorschemes uch as aser beat wave, laserfield, and electron wakefield acce lerators, t is desirable olong regions of homogeneous plasma at fairly high(lOI - lOI* cm-3). Such plasmas arewith aion, we were forced to abandon discharge-because the minimum discharge currentto produce a suitable electron density also produced aetic field large enough to prevent our 1.5 MeV electroneam from being trapped in the accelerating potentialthe plasma beat wave. But experiments with an intense0.5 pm laser have shown that plasmas with the desiredroperties could be produced by MPI? Later, improvements

Coulomb field

Figure 1 : Dep iction how an intense external electric field can leadto an electron tunnelling out of the confining potential of an ion.This work is supported by DOE contract number DE-AS03-83-ER40120.

In tunneling ionization,3 an external electric field lowers(on one side) the Coulomb potential which binds an electronto the nucleus, as shown in Fig. 1, thereby narrowing thebarrier to the outside world. If the field is high enough, theelectron has a high probability of tunneling through the barrierwhere it is free of the nucleus. Its subsequentmotion wilI becomposedof the usual quiver motion in the laser field plus aDC drift velocity needed to balance canonical momentumbefore and after the time of ionization. A landmark experimentby Corkum et al. showed that when ionizing atoms in thesingle particle regime, one can predict the exact electrondistribution functions (that is, the distribution of DC driftvelocities) given the laser polarization and pulse shape. Fromthe simple I-D theory, we expect to produce fully ionizedplasmas n the desired density range. For linear polarization,the calculated transverse (longitudinal) electron distributionfunction resembles a maxwellian with a width of about 50(cl) eV while for circular polarization the distribution functionshould be a squashed doughnut with a major radius(transverse to ho) of 2.5 KeV and a minor radius of 1 KeVwith a longitudinal thickness of only 4 eV (h, is thewavevector of the incident CO2 laser).This paper reports on our experiments designed o establishthe ionization mechanism and explore the characteristics ofthis plasma.

THE EXIWUMENTIn the experiment, a C02laser beam (up to 100 J, 350psec EWHM) is focused nto a vacuum chamber containing 0 -2 Torr of Hz, A r, or He gas. The peak laser intensity invacuum is around 5 x 1014 W/cm2. The plasma is producedover the Raleigh length of roughly 2 cm and is diagnosed by:(a) viewing the laser harmonic emission in the forwarddirection: (b) X-ray emission from the plasma; (c) collectiveThomson scattering of a frequency-doubled Y AG probe beam,looking at 2b density fluctuations; and (d) by viewing laserlight scatteredoutside the original cone angle of the beam.

RESLJLTSAND DISCUSSIONHarmonicsThe frequency spectrum of the transmitted or forwardscattered aser light was found to contain discrete lines atharmonicsof the laser frequency. The relative power in theselines are shown in Fig. 2(a) vs harmonic number. The oddharmonics are predicted from the tunneling picture ofionization.5 As the laser electric field oscillates at wo,

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ionization will occur twice per cycle when the electric fieldreaches its positive or negative extreme. Thus the electrondensity II increases step-wise in time at 20, (and in spaceat2k,). This second harmonic density modulation ft(2wo,2ko)times the quiver motion v(w,,~) due to the laser generatescurrents J(lw,&) = -evA, 1 = 3, 5, 7,... which radiate theharmonic spectrum. In circular polarized light, the laserelectric fie ld does not oscillate in magnitude but only indirection. Thus the density should not be modulated in timeand the odd harmonics should go away. This indeed occurs asl

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Figure 2: (a) Normalized power measured in the various laserharmonics. (b) Dependence f the level of the secondand thirdharmonicson the polarization of the laser, changing from linearpolarization to circular polarization.shown in Fig. 2(b) which plots the amplitude of the thirdharmonic as a function of the ellipticity of the beam. We alsoobserved second harmonic generation and find it to beinsensitive to polarization. This harmonic is not predictedfrom tunneling ionization theory. We believe it is due to thepresenceof laser light bending through a density gradient andhence a signature of refraction of the laser light. Thisrefraction has serious consequences s will be discussed ater.Temperature

Apart from harmonics, the other crucial prediction oftunneling ionization theory is that the temperature can becontrolled through the polarization of the ionizing laser light.Fig. 3 shows the integrated X-ray flux falling on a siliconsurfacebarrier detector filtered to detect about 800 eV photonsand above. The three sets of data points are for circularpolarization, linear with the detector looking along the electricfield, and linear looking transverse to the electric field. Asignificant difference in the X-ray flux is indeed seen when

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60 10 ,w 120Laser Energy (J)Figure 3: IntegratedX-ray flux on a 800+ eV detectorVS aserenergy for three situations: for circular polarization e), linearpolarization with detector viewing perpendicular to the laserelectric field (o ), and linear polarization with detector viewing

along to the laser electric field (*).changing the polarization from linear to circular. What issurprising is the presence of any high energy photons in thelinear polarization case as we expected a temperature of < 50eV. We suspect the existence of an anomalous laser heatingmechanismand have seensuch evidence n other experiment&as well.Density

Our main density diagnostic is based on the detection ofelectron plasma waves excited by the C@ laser beam. Thesewaves have a frequency Wgc = wp(1 + 3 kp2 IDe2) wherewp = (4nnoe2/m)*/2 is the plasma frequency, no is theelectron density, kp = 2kc, is the wavenumber for the plasmawaves, and XD, = (Tet1/4xnoe2)1/2 is the electron Debyelength with Tel\ the electron temperature parallel to kc,. Thisexpression is approximately true for kp hi, c 0.5 or so whichshould be true for most of our cases. In these cases,WBG iswell defined and a spectrum of the electron plasma waves at k= 2k, should show an isolated peak at Wgc. Figure 4 showsa typical spectrum of electron plasma waves obtained bycollective Thomson scattering of a visible probe beam fromthe plasma. The spectrum is time resolved with 10 psecresolution with a streakcamera. Instead of the expectednarrowfeature at a density corresponding to the fully ionized fill gas,we consistently saw a broad spectrum with a maximumfrequency shift corresponding to a fairly low density of 1 - 2 x1016cmS3. The broadband spectra ndicate that kp ADe s not< 0.5 but much higher indicating some 2-D heatingmechanism unanticipated in the 1-D model of tunnelingionization. More importantly, we found that the maximumfrequency shift is proportional to the fill pressure of thevacuum chamber only up to densities around 2 x 1016 cme3and is clamped to approximately that value for all higher fillpressures. To verify that the low density measurement iscorrect, we attempted beatwave excitation of plasma wavesusing two-frequency illumination. When the beat frequencywas chosen to correspond to a density of 8 x 1015 cm3, wealways saw a response in the streaked spectrum. Thesebeatwave satellites can be seen n Fig. 4 at about 8 A f shift.These exist because the plasma can always respond if the

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0 200 400 600Time(psec)Figure 4: Time-resolved frequency spectrum of 2k, electron

density fluctuations. Frequency increases upwards and timeincreases to the right. The feature near zero shift is from ionwaves and is not important here. The electron plasma wavefeatures range from 0 - 20 A shift. The feature at around 8 A is abeat wave response of the plasma.density is higher than the beat frequency. However, if wechoose a beat frequency corresponding to lOI cme3 (thedesired density), then thesesatellites were never seen ndicatingthat the density was indeed clamped below lOl7 cme3.Refraction

From the tunneling ionization theory, the only way thatthe density cannot be equal to the fill pressure is if theintensity does not increase beyond 5 x lOI W/cm m2 theionization threshold) for the 20 to 30 psec equired to reach fullionization. This would be the case f the laser beam refracts asit begins to ionize at 5 x 10 3 W/em-2, blowing up the spotsize and preventing further ionization. This ionization-inducedrefraction must occur for gaussian beams where the intensityprofile and hence the ionization profile peaks on axis. Theplasma then looks like a negative lens to subsequent laserlight.To see whether this refraction is important for ourparameters, we measured the amount of light exiting theplasma outside the original cone angle of the beam as afunction o f fill gas pressure. The result is shown in Fig. 5 forH2 and Ar gas. In Ar, as we raised the fill pressure from

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Figure 5: Variation of the energy refracted out of the originaligure 5: Variation of the energy refracted out of the originalcone angle of the laser beam vs fill pressure. Note the suddenone angle of the laser beam vs fill pressure. Note the suddenonset of refraction in Ar gas beyond about 200 mT.nset of refraction in Ar gas beyond about 200 mT.

vacuum we saw a suddenonset of refraction at around 200 mT.This corresponds to a density of around 0.7 x 1016 cmm3.When we repeated the experiment in H2, we noticed that therefraction is a more gradual function of pressure. Thedifference is due to the different ion masses.On the laser pulsetime scale the Ar ions are relatively immobile and theionization profile is frozen in whereas the H2 ions can moveand relax the density gradients in the plasma and thus reducethe defocusing. It therefore seems hat refraction is indeed themechanism imiting our density to < 1 - 2 x 1Ol6 cm3.

CONCLUSIONSAlthough multiphoton ionization with 0.5 pm laser light wasshown to produce large, uniform plasmas at a density of lOI7cmT3, tunneling ionization with 10 pm laser light is limitedto densities below about 1 - 2 x lOl6 cmm3. In the 10 pmcase, he density limit is 0.1 - 0.2% of the critical density overabout 1 cm of length. The refraction angle should scale asIn,(x) dx along the axis of the plasma. Thus, if we canreduce the length of plasma by a factor of 10 we can possiblyraise the density a factor of 10. This is the motivation for thenext experiment where we have already installed a 1.5 mmdiam, Mach 8 gas et for a target rather than a static Ii11of gas.It seems likely that the laser intensity will reach a highenough intensity on both s ides of the gas jet to achieve fullionization across he jet.1.

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REFERENCESC. Joshi, C. E. Clayton, W. P. Leemans, K. A. Marsh, M. T.Shu, and R. L. Williams, Beatwave acceleration experimentsat UCL.A, in hoc. IEEE Particle Accelerator Cog.., Chicago,Il. March 1989, pp. 726-730.A. E. Dangor, A. K. L. Dymoke-Bradshaw. A. Dyson, T.Garvey, 1. Mitchell, A. J. Cole, C. N. Danson. C. B. Edwards,and R. G. Evans, Generation of uniform plasmas for beatwave experiments, IEEE Trans. Plasma Sci.. vol. PS-15 , pp.161-166. April 1987.L. V. Keldysh, Ionization in the field of a strongelectromagnetic wave, Sov. Phys. JETP. vol. 20, pp. 1307-14, May 1965.P. B. Corkum. N. H. Burnett and F. Brunel, Above-thresholdionization in the long-wavelength limit. Phys. Rev. Lett.,vol. 62, pp. 1259-62, March 1989.F. Brunel Harmonic generation due to plasma effects in a gasundergoing multiphoton ionization in the high-intensitylimit, I. Opt. Sot. Am. B, vol. 7, pp. 521-26, April 1990.W. P. Leemans, C. E. Clayton, K. A. Marsh, and C. Joshi,Stimulated compton scattering from pre-formed underdenseplasmas, submitted to Phys. Rev. Lett..

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