acceleration of injected electrons by the plasma beat wave ......the major attraction of the pbwa is...

Acceleration of Injected Electrons by the

Plasma Beat Wave Accelerator

C. Joshi, C.E. Clayton, K. A. Marsh, A. Dyson,

M. Everett, A. Lal, W.P. Leemans (a), R. Williams (b),

T. Katsouleas (c), and W. B. Mori

Electrical Engineering Department, UCLA, Los Angeles, CA 90024 (a) Lawrence Berkeley Laboratory, Berkeley, CA 94720 (b) Florida A & M University, Tallahassee, FL 32307

(c) University of Southern California, Los Angeles, CA 90089

Abst rac t

In this paper we describe the recent work at UCLA on the acceleration of externally injected electrons by a relativistic plasma wave. A two frequency laser was used to excite a plasma wave over a narrow range of static gas pressures close to resonance. Electrons with energies up to our detection limit of 9.1 MeV were observed when 2.1 MeV electrons were injected in the plasma wave. No accelerated electrons above the detection threshold were observed when the laser was operated on a single frequency or when no electrons were injected. Experi- mental results are compared with theoretical predictions, and future prospects for the plasma beat wave accelerator are discussed.

�9 1993 American Institute of Physics 379

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380 The Plasma Beat Wave Accelerator

I. In troduct ion

In the Plasma Beat Wave Accelerator 1 (PBWA), two co-propagating laser beams with frequencies and wavenumbers (~al, kl) and (w2, k2) resonantly drive a plasma wave with frequency wp = w2 - Wl and wavenumber k.p = k2 - kl. The amplitude modulated electromagnetic wave envelope of the laser pulse exerts a periodic nonlinear force, the ponderomotive force, on the plasma electrons, causing them to bunch. The resulting space-charge wave has a phase velocity vr = wp/k~ that is nearly equal to the speed of light c if wl ~ w2 >> ~p. If an electron bunch is now injected with a velocity close to this, it can be trapped and accelerated much in the same way as a surfer riding an ocean wave.

The major attraction of the PBWA is that extremely large acceleration gra- dients can be produced in the plasma wave. The longitudinal electric field associated with such a wave is given by E = 0.96r V/cm, where r is the density modulation (nl/no) and no is the plasma electron density in cm -3. Thus, for e = 0.1 and 1015 < n0(cm -3) < 101T, accelerating fields of "~ 0.3 < E(GeV/m) < 3 are possible. It is the purpose of our current experimental program to demonstrate such ultra-high gradient acceleration over a reasonable distance. This paper is organized as follows:

I. II. III. IV. V. VI. VII. VIII.

Introduction Experimental Parameters Numerical Modeling of the Experiments 3-D Particle Trajectory Simulations Experimental Set-Up Results Plasma Beat Wave Accelerator in the 100 MeV - 500 MeV Range Conclusions

II. Exper imenta l Parameters

Our experiment consists of four major components: the C02 laser driver to act as the electromagnetic energy source; the plasma to convert the transverse oscillating field of the laser into the longitudinal oscillating field of a plasma wave to accelerate particles; a pre-accelerated bunch of electrons for injection into the plasma wave; and diagnostics to detect the accelerated electrons, plasma wave and plasma characteristics. In Table 1 we give experimental parameters for the laser, the plasma, and the electron beam (injector). These parameters will be used throughout the rest of the paper unless otherwise noted.


C. Joshi et al. 381

1. Laser Wavelengths Energy per Line Electron Quiver Velocities/c Spot radius Rayleigh range 2zo Risetime FWHM

2. Plasma Density Plasma Frequency up Plasma wave wavelength Lorentz Factor %h Gradient for a 10% Wave Source

10.59 #m, 10.29 #m 60 J, 15 J 0.17, 0.07 150 #m 1.3 cm 150 ps 300 ps

8.6 x 10 ~s cm -3, Hydrogen 5.2 x 1012 s -1 360 #m 34 1 GeV/m Tunnel ionization

3. In jec tor Energy 2.1 MeV (7 = 5.2) Emittance 6~r mm-mrad Micropulse Frequency 9.3 GHz Electrons pe r micropulse 1.7 • 107 Spot Radius 125 #m

Table 1

III. Numer ica l Model ing of the Expe r imen t

Before we describe the experimental set-up and the results, we present the results from a simple one-dimensional model that includes plasma formation and the beat wave growth and saturation via relativistic detuning 2. The plasma is assumed to be formed via tunnel ionization 3 of the neutral gas which in our model is atomic hydrogen. In this model the plasma density increases as

dn(t) _ w(E, t)[no - n(t)] (1) dt

where n(t) is the time dependent electron plasma density, no is the initial equiva- lent monoatomic neutral gas density and w(E, t) is the laser dependent Keldysh tunneling ionization rate given by 4



Here EH and Ei are the ionization energies (potential) of hydrogen and the atom in question, ~ = E , / E ( t ) where E , = m2eS/h 4 "~ 5.21 • 1011 V/m is the atomic unit of electric field, and E(t) is the amplitude of the applied electric field. We also assume that only a small fraction of the total number of electrons leave the ionized volume and that the resultant space charge is sufficient to confine the remaining electrons.

Figure 1 shows the calculated evolution of the plasma density (normalized to neutral gas density) as a function of time assuming atomic hydrogen gas. The laser pulse had a 150 ps (linear) risetime, a full width of 300 ps, and a peak intensity of 1.2 x 1014 W/cm 2. Figure 1 (a) shows the growth of the laser intensity, in terms of its normalized electric field, vosc/c = e E / m w c . As shown in Fig. 1 (b), ionization begins at "~ 13 ps and a fully ionized plasma is formed within 10 ps after this. The peak density of the fully ionized gas in this example is 2% less than the exact resonant density. Here resonant density is that density at which the plasma frequency wp = (47rnoe2/m) 1/2 is equal to the difference frequency Aw ---- w2 - wl. Once the density is such that the beat frequency is within the bandwidth of this harmonically driven oscillator the plasma wave grows rapidly. The amplitude of the plasma wave is given by solving the equation 5

d d~ caAk -~( 'y -~) + w ~ = a la2 T sin ( A w t - Ak~) . (3)

Here Ak = k2 - kl, ~ is the Lagrangian displacement variable describing the wave oscillating quantity, ~ = (1 - (~/c)2) -1/2 is the relativistic Lorentz factor, and al,~ = eEi,2/mwl,~C are the normalized quiver velocities in the laser fields of amplitudes E1,2. As can be seen from Eq. (3) the plasma responds to the driving force as an anharmonic oscillator, the anharmonicity coming from the mass dependence of wp. As the amplitude of the plasma oscillation grows the natural frequency (wp) decreases due to the relativistic increase in the electron mass. Consequently, the driver and the plasma wave gradually shift in phase and saturation occurs when the two are ~r/2 out of phase with one another. In Fig. l(c) we see that for the conditions of Fig. 1 (a,b), the plasma wave begins to grow once the ionization is complete at 23 ps and saturates at 75 ps, well before the peak of the laser pulse. The saturated amplitude is e = n l / n o = 0.13. The accelerating electric field is related to the amplitude by eEo~ = emazp which in this case (see Table 1 for experimental parameters) is 1.2 GeV/m even though the plasma density was 2% less than the resonant density.

Figure 2 shows the saturated value of the plasma wave amplitude and the time to saturation versus density, normalized to resonant density. The time to saturation includes the time it takes to ionize the gas. It can be seen that the optimum plasma density is ~ 3% above the resonance value. In this case the plasma wave builds up to a peak amplitude of 37% in about 120 ps. In terms of ion plasma periods saturation occurs in < 2v~ 1. Thus any instabilities involving ions do not have a chance to grow significantly. Therefore, damping of the beat-driven plasma wave by mode coupling s to the ion-acoustic wave


C. Joshi et al. 383

(SBS) is probably not too severe, and neither self-focusing T nor the modulational instability s are very important. Thus, this simple 1-D model is very useful for narrowing the parameter space for the experiment. From Fig. 2 it can be seen that for our conditions a density mismatch of +4% is still allowable for ~ to be greater than 5% for our laser intensities. It should be noted that while exact density resonance is not critical, plasma homogeneity is. Spatially inhomogeneous plasmas will produce phase mixing and the acceleration process will be degraded.

IV. 3-D Par t ic le T ra j ec to ry Simulat ions

We have carried out computer simulations of trajectories of injected particles in a finite diameter electron plasma wave to see the expected number and energy spectra of the accelerated electrons in our experiment. The model has been extensively tested and documented in a previous publication 9. For our experimental conditions, it is reasonable to assume from Equation (2) that several Rayleigh ranges will be fully ionized by the laser. The laser intensity relative to the peak is assumed to vary as 1/(1 + z2/z~o), assuming gaussian optics. In this case, the axial envelope of the plasma wave amplitude just prior to saturation is given by

E (z) = 1 + , (4)

where E,~x = emcwp/e as before. The radial profile of the accelerating field is assumed to be gaussian and the radial field component Er(r_, z, t) has a form given in Ref (9), equation 19. The resonant density plasma is assumed to exist over a length +3zo where zo -- 8 mm. We inject 2.5 • 105 electrons with energy 7 -- 5 and an emittance of 6~r mm-mrad and collect electrons exiting from the plasma wave in a f/10 cone. In Fig. 3 we plot a histogram of the number of electrons accelerated versus energy (7) for a 15% wave. The spectrum peaks at the injected energy of 7 = 5 and exponentially decreases to an energy of approximately 7 = 16. The distribution then shows a long tail, with energies up to 7 = 25 possible for this condition. In addition to the accelerated electrons, electrons have also been decelerated by the plasma wave to energies of 7 = 3 or 4. Also note that in the simulations 2.5 • 105 electrons were injected as opposed to in the experiment where a microbunch contains up to 1.7 • 107 electrons. Thus, each electron in Fig. 3 represents 70 accelerated electrons in that energy bin in the experiment.

V. Expe r imen ta l Se t -Up

i) Laser System The experimental apparatus is shown schematically in Fig. 4. The CO2

laser system used in this experiment was specifically designed for the beat-wave



iii) Electron B e a m Transport S y s t e m and Acceptance Considera- t ions

Figure 6 shows the various components of the beam transport line and the calculated trajectory of the electron beam spatial envelope. The emittance of the beam at the final focus was estimated by measuring the beam spot size (Xo) and divergence (X~o). The emittance is given by e = ~rXoX'o, and was measured to be 67r mm-mrad. In our experiment the laser beam diameter (and therefore the plasma wave diameter) and the plasma wave wavelength have comparable dimensions. This means that the radial field Er(r, z) of the plasma wave is on the same order of magnitude as the longitudinal field. Our 3-D particle trajectory simulations (Section IV) discussed earlier have shown that these radial fields can cause a large net loss of injected electrons for finite emittance beams. To quantify the coupling efficiency, the well known concepts of accelerator acceptance and beam matching can be applied to our experiment 12. To minimize the electron loss, the beam emittance should be smaller than the PBWA acceptance. It can be shown that the electron transmission by the plasma wave can be expressed a s

~l"Gn8 (5)

for T < 1 where a is the acceptance given by

a = V no7 9 (6)

Here nl /no is the plasma wave amplitude, 7 is the injector energy and R is the spot size (radius) of the laser. Thus, for hi~no of 10% for example, a ~- 4.6~r mm mrad and T ___ 0.60.

Even if the beam emittance is small, the electron beam must be properly focused into the accelerator or some electrons will be lost. Therefore, in the experiment the electron beam is focused to a spot size (Xo) somewhat smaller than the radius of the plasma wave. The optimum beam divergence (X'o) is given by x' o = a/Xo. For our conditions the optimum value of X~o = 40 mrad. The final

' = 50 mrad. This condition focusing of the electron beam is f/10 which gives x o is close to the optimum but can vary with n , /no and errors in the calculated acceptance value.

iv) Electron Detec t ion As shown in Fig. 4, both the accelerated and the non-accelerated electrons

enter a variable-field imaging electron spectrometer. The non-accelerated electrons are dumped onto low density plastic. Lead shielding reduces the flux of background x-rays reaching the electron detectors thereby reducing the background or noise levels to a value negligibly small compared to the signal levels ultimately obtained. The accelerated electrons exit the vacuum through a 25 #m


C. Joshi et al. 385

thick Mylar window and are detected either electronically by one or more silicon surface barrier detectors (SBD) or photographically by the tracks they leave in a cloud chamber. The SBD has a 600 #m copper window which is "light tight" to soft x-rays but still "transparent" to energetic electrons with greater than 3 MeV energy. Along with a charge-sensitive preamplifier, the SBD produces about 20 mV per electron in the range 1-10 MeV. The preamplifier saturates at around 2.5 V thus limiting the number of detectable electrons to about 125 before saturation.

The electron track detector is a diffusion cloud chamber 13 which uses su- persaturated methanol vapor in 1 atm of air to form visible tracks as electrons ionize the molecules along their path. The lead-shielded chamber has a 6 #m thick Mylar window over a 3 mm entrance hole located about 5 cm from the vacuum window. Electron scattering in the two windows and the intervening air is calculated to be less than 1 ~ for 5 MeV electrons. The tracks are recorded with a CCD camera. A uniform, 260 G magnetic field can be applied to the active region of the cloud chamber from coils located outside the lead shielding. The cloud chamber has a much wider dynamic range than the SBD. At low electron fluxes, one can count individual electron tracks while at high fluxes, the brightness of the cloud chamber image was calibrated (with the 2.1 MeV linac beam) to be roughly proportional to the flux of electrons, at least up to 400 electrons/mm 2.

v) Optical Diagnostics The plasma wave was probed with three optical diagnostics as well as with

an electron beam. The density fluctuations associated with the beatwave were probed directly with near-forward scattering of the CO2 laser itself into the Stokes sideband 14. This light is collected in a forward annulus with a half-angle range of f/10 and sent to a spectrograph/pyroelectric array combination for time- integrated spectral measurements. The other two optical diagnostics, Thomson scattering and backscatter, do not probe the beatwave directly, but rather its mode-coupled daughter wave 6 at around ks - 2kl due to the presence of an ion acoustic wave at 2kl from stimulated Brillouin scattering (kl is the wavevector of the stronger 10.591 #m pump). In Thomson scattering, a frequency-doubled YAG probe beam of 5 nsec duration is focused to a 50 #m diameter spot within the 10 mm core of the plasma mentioned earlier. The geometry has been chosen to k-match to waves with k = (2.0 + 0.5) kl. Thus, in addition to mode coupled waves, the diagnostic will pick up scattered light from stimulated Compton 15 and Brillouin 16 driven density fluctuations. The scattered light is sent to a spectrograph/streak camera combination with 0.5 A and 25 psec resolution. The third optical diagnostic is the time-integrated spectrum of the backscattered CO2 light captured on a frame-grabbed pyroelectric camera.



VI. Results

i) P lasma Formation As discussed previously, one of the most crucial requirements for the beat

wave acceleration experiment is the formation of a homogeneous, magnetic field free plasma of the required density (8.6 x 1015 cm -3) that is at least 1 cm long. Such plasmas were produced by tunnel ionization of a static gas in the interaction chamber. That the plasmas were indeed produced by tunnel ionization and the physical properties of such plasmas are documented in various publications 3,1z. Here we show evidence of plasma size, density and temperature. The visible emission from the plasma was imaged onto a CCD camera on every data shot. One such image is shown in Fig. 7(a). This shows the overall plasma size to be more than 20 mm long in the axial direction with a core region of the plasma emitting uniform intensity visible radiation that is about 10 mm long. We point out that while this visible image is not a conclusive measure of either plasma density or homogeneity (being dependent on both density and temperature), it is reasonable to assume that in this core region (that is less than 2Zo long) both are fairly constant. Thus we will take the interaction length to be 10 mm.

The density and temperature of the plasma were estimated from the Comp- ton scattered spectrum part of the Thomson scattering diagnostic 1T. One example is shown in Fig. 7(b). The fitting of the observed scattered light spectrum to the theoretical spectrum is only possible at early times and gives in this case a density of ne = 6 + 1 x 1015 cm -3 and a parallel (or longitudinal) temperature of 7il = 75 + 10 eV. Therefore, k~d ~-- 1.0 in this case. The measured density is in reasonable agreement with the fill pressure of the hydrogen gas (100 mT in this case). Clearly in this strongly damped regime IT the scattering diagnostic cannot be expected to give the plasma density with any accuracy greater than this. We also found that strong refraction of the laser beam due to plasma lensing effects takes place for fill pressures corresponding to fully ionized densities of "~ 2 x 1016 cm -3. Thus we assume that fully ionized plasmas with densities less than 1016 cm -3 can be produced simply by varying the static pressure of the fill gas in the chamber, with plasma densities between 6.6 x 1015 cm -a and 1.3 x 101~ cm -3 corresponding to pressures in the range 100-200 mT.

ii) Electron Acceleration Since the object of this experiment was the demonstration of acceleration

of externally injected electrons by the beat-excited relativistic plasma wave, we carried out several important control experiments to ensure that what we were expecting to observe was a real PBWA effect. We carefully calibrated the SBDs for distribution of noise signals from background x-rays as shown in Fig. 8(a). Here the SBD was set to observe 3.5 MeV electrons. At higher energy settings of the electron spectrometer magnet the noise level spectrum shifts to lower mean values of the signals than shown in Fig. 8(a). Figure 8(b) shows the


C. Joshi et al. 387

cloud chamber image when the injected electrons are dumped into the beam dump plastic but the cloud chamber is set to look at 5.2 MeV electrons. In this picture only low energy electrons produced by photoionization by x-ray noise photons can be seen. No energetic electrons were observed on either detector when none were injected into plasmas produced by either single or dual frequency beams. This implies that in our experiments there is no contribution to the observed signal due to self-trapping of the background plasma electrons TM. This is in contrast to recent Osaka experiments 19 where high energy electrons were reportedly observed with single and dual frequency laser-plasma interac- tions. In addition, for single frequency illumination no acceleration of electrons was observed even with injection of 2.1 MeV electrons. This implies that with dual frequency illumination and injection, accelerating fields associated with waves generated by Raman forward scattering have a negligible contribution to the observed signal 2~ Finally, no signal was detected when the laser and the electron beam were simultaneously fired into an evacuated chamber (no plasma) as expected.

In our experiments, injected electrons were seen to gain energy only when a two frequency laser beam was fired in a static gas over a narrow range of pressures. Fig. 9(a) and (b) show tracks from two laser shots for which the plasma density was nearly resonant (143 mT fill pressure), with the laser op- erating on both wavelengths, and with external electrons injected at 2.1 MeV. For these shots the electron spectrometer was set to direct 5.2 MeV -4- 0.5 MeV electrons into the cloud chamber and 5.9 MeV electrons into the SBD. In Fig. 9(a), the magnetic field of the cloud chamber is turned off and the image shows hundreds of accelerated electrons entering the cloud chamber. On this shot, the SBD signal was saturated. In order to estimate the number of electrons in this particul.ar image, we calibrated the brightness of the image against other images produced by using the 2.1 MeV injector as the source. This was done in the following way: First the electron linac current was measured vs. the filament current (cathode temperature). Then the electron spectrometer magnet current was adjusted to send the linac electrons directly into the cloud chamber (Fig. 9(c,d)), and the cathode temperature of the linac's gun was varied to obtain cloud chamber images in the brightness range of those measured (as in Fig. 9(a)). The image in Fig. 9(c) shows an electron flux of 60 electrons/mm 2, while Fig. 9(d) corresponds to a flux of 480 electrons/mm 2. Using this method we estimate that the image shown in Fig. 9(a) is produced by 150 electrons/mm 2 flux at 5.2 MeV with an error bar of ~30%. From knowledge of the dispersion and vertical imaging of the electron spectrometer, we estimate that this flux corresponds to 2 x 104 electrons in the 5.2 + 0.25 MeV energy bin.

In Fig. 9(b), we show at this same energy setting of the electron spectrometer the effect of applying a 260 G external magnetic field to the cloud chamber. The magnetic field of the cloud chamber is used to bend these electrons inside the cloud chamber. The solid line superimposed on this figure is the calculated



trajectory of a 5.2 MeV electron using the relativistic gyroradius formula

re = (~2_ 1) '/2 m e / e B . (7)

It can be seen that the trajectories of the central particles match closely with the calculated trajectory and therefore confirms that these electrons have indeed gained energy from the beat wave - plasma interaction. The other trajectories have the same radius of curvature but are due to electrons entering the cloud chamber at various angles due to the imaging property of the dipole magnet of the electron spectrometer and the finite emittance of the beam. The SBD signal on this shot was 360 mV or about 18 electrons (assuming a SBD sensitivity of -~ 20 mV/electron). This agrees closely with the number of tracks seen in approximately the same solid angle in the cloud chamber image, confirming that the SBDs are indeed "seeing" electrons. This diagnostic, we believe, gives irrefutable proof that the externally injected electrons have gained substantial energy in our experiment.

The experiment was repeated over a range of fill pressures with the electron spectrometer set to observe various energies. Fig. 10(a) shows a summary of the signals obtained on the SBDs at various acceleration energies. After each shot with a high electron signal, a noise spectrum such as the one shown in this figure was taken by firing up to 80 linac shots. The noise spectrum in Fig. 10(a) was taken at a spectrometer setting of 3.5 MeV. As mentioned earlier, at higher energy settings the noise level shifts to even lower values. The measured electron signals are clearly many standard deviations larger than the noise, and seven shots saturated the detector. Fig. 10(b) shows the signal levels on the SBD's at various energies versus the fill pressure. As stated previously, at these laser intensities, fully ionized plasmas are formed up to a plasma density of n~ < 2 • 1016 cm -3. Therefore we assume that the desired density up to this limit can be obtained by changing the measured gas pressure. From Fig. 2(b) the calculated pressure range over which a 5% amplitude or greater plasma wave is expected is 128 - 137 mT, with the exact resonance being at 131.5 mT and the optimum pressure (for compensating the relativistic detuning) at 136 roT. Figure 10(b) shows that the signals are essentially in the noise below 131 mT, rising rapidly around 140 mT. However, there are not enough shots above 148 mT to confirm the exact location of the peak of the electron signal. The data points bracketed with an arrow indicated that on these shots the SBD signals were saturated. Thus these data points areindicative of the lower bound of the electron signal. However, the experiment appears to work best with about 5-10 mT higher pressure than the expected optimum. This may be a result of hydrodynamic expansion of the hydrogen plasma which could lower the density by 5 - 10% during the 70-100 ps growth time of the plasma wave. The maximum magnetic field of the electron spectrometer limited the highest observable electron energy to 9.1 MeV. Even at this energy, we were still able to saturate the SBD. Thus many electrons gained at least 7 MeV in traversing


C. Joshi et al. 389

long plasma wave, implying an accelerating gradient of more than 0.7 CeV/m which corresponds to a wave amplitude of at least 8%.

iii) Estimate of Number of Accelerated Electrons In our experiment the injected electron microbunch is not deterministically

synchronized to any particular point in the plasma wave with an accuracy (jit- ter) better than • ps. As a result, the numbers of accelerated electrons can vary greatly from one laser shot to the next. However, by taking a large number of shots one can estimate the maximum number of electrons observed in a particular energy bin and thereby crudely calculate the number of accelerated electrons in a particular energy interval. From the cloud chamber data, we found 2 • 104 electrons at 5.2 MeV within a 0.5 MeV energy bin. The saturated signal at 9.1 MeV indicates that we had at least 125 electrons (2.5 electrons/mm 2 on the SBD) at that energy. Assuming that the accelerated electron spectrum between 5.2 MeV and 9.1 MeV is exponentially decreasing from 2 • 104 to 125, and using the known dispersion of the spectrometer, we estimate that the total number of electrons in this part of the accelerated spectrum is 4 • 2 • 104. Our micropulse contained about 4.25 • 106 electrons in both accelerating and focusing phases of the buckets of the plasma wave. Thus approximately 1% of the available electrons were observed to be accelerated. A better estimate based on the single shot measurement of the complete spectrum of the accelerated electrons is currently under way.

iv) Correlation with Optical Diagnostics: Thomson and Raman Scatter

The measured electron signals were correlated with optical diagnostics to further confirm that the acceleration observed was associated with the relativistic plasma waves. The time resolved Thomson scattered spectrum is shown in Fig. 11(a). It shows a broad band of scattered frequencies between 0 < (Wo - ws)/Aw < 1.5 which are due to SCS 21 or SRS. Here, Wo and ws are the scattered and incident frequencies of the Thomson probe respectively, and Aw = w2 - wl is the beat frequency. There is in addition a narrower but much more intense feature at a frequency shift corresponding to/kw. This feature gen- erally shows two temporal bursts. The first has a typical growth time of 50-70 ps and is thought to be due to the mode coupling of the relativistic plasma wave 6 from the still growing ion acoustic wave. As expected, the strongest electron signals were observed on shots when the first burst at Wo - w~ = Aw was intense while SCS was still occurring. This is shown in Fig. ll(c). Not all laser shots with a strong burst a t /kw produced electron signals because of the 60% prob- ability of the synchronization of the electrons and the plasma wave mentioned earlier. The second peak, which persists after SCS is over, is thought to arise from counter-propagating optical mixing which excites a slow phase velocity plasma wave. Such a wave cannot accelerate relativistic electrons significantly.



The backscatter spectrum, Fig. 11 (b), typically shows two distinct peaks on two frequency laser shots. The first peak is shifted from the laser frequency by ~ 0.8Aw (10.80-10.86 #m), and is present on all two frequency shots. Its location varies 5-10% from shot to shot, and its origin is still being studied. The second peak is shifted from the laser frequency by ~ Aw (10.9 #m). It appears only on shots in which a plasma beat wave is excited. As with the Thomson scattering diagnostic, the strongest electron signals were observed when the feature at ~ 10.9 #m was relatively intense (see Fig. 1 l(c)). The correlation of the electron signal with strong scattering signals in the Thomson and the backscatter spectra further supports the notion that the electrons are accelerated by the relativistic plasma wave excited by collinear optical mixing.

v) Correlation with Forward Scatter Beat wave excitation of a relativistic plasma wave is a four wave process. In

addition to the pump waves wl and w2 coupling to Stokes sideband at wl-wp and anti-Stokes sideband at w2 + wp must be considered la. For small plasma wave amplitudes the generation of Stokes and anti-Stokes sidebands can be considered as Bragg scattering of the incident pump waves from the plasma wave, which acts as a moving phase grating. Thus, the observation of the Stokes and anti-Stokes sidebands in the same direction as the pump waves is diagnostically important because not only does it confirm that the relativistic plasmon has been excited but it also can give an independent estimate of the amplitude length product, (nl/no. L), of this wave. This same quantity is also responsible for the energy gain of electrons since nl/no (x E,~. In our experiments we monitored the Stokes sideband at Wl - wp. However, because of the choice of the particular wavelengths and the high laser intensities, we found that rotational Raman scattering in the 100 meters of air (between the laser output window and the vacuum chamber) produced Stokes signals that were comparable to the Stokes radiation generated by the plasma.

To try to separate the rotational Raman light from the Stokes light generated from the plasma wave, we blocked a central f/14 cone in the forward scattered light and collected radiation in an annulus out to f/10.5. Since the Stokes radiation should originate in a smaller spot size than the incident radiation, it should therefore be diverging at a larger angle. The resulting Stokes shifted signal had a similar correlation with electrons to that observed with the backscatter and Thomson scatter (Fig. 11 (c)), suggesting that the Stokes radiation did originate from the plasma, but more work is needed to conclusively resolve this issue. At any rate, large Stokes signals always accompanied any electron signals indicat- ing at least that we have a two frequency laser pulse where both frequencies are temporally overlapped with one another.


C. Joshi et al. 391

vi) Est imate of P l a s m a Wave A m p l i t u d e F rom T h o m s o n Sca t t e r ing M e a s u r e m e n t s

As seen in a previous section, the electron energy gain measurements imply that plasma waves of amplitude nl/no greater than 8% were excited over a 10 mm length in this experiment. Since the maximum energies observed were detection system limited, this is likely to be an underestimate. Estimates of the relativistic plasma wave amplitude, however, can also be made from three features of the Thomson scattered spectra: harmonic components, the mode coupling feature at Aa;; and sub harmonic components. We shall briefly discuss each of these.

When the relativistic plasma wave becomes large it can steepen. Its steep- ened waveform can be decomposed into Fourier harmonics of the plasma frequency as 22

n e - n o = ~ ( n l ~ " m TM no ,,~=1 \n-~o] 2m-lm! (8)

where nl/no is the amplitude of the fundamental component. Thus

n2/nl ~- nl/no n~ - no - - , (9) no

n2/r~o --~ ( h i / n o ) 2 . (10)

In other words, the ratio of the second harmonic to the fundamental gives a measure of the absolute density pertubation of the fundamental.

In the experiment, the Thomson scatter does not measure the Fourier components of the relativistic plasma wave directly but its coupling to the ion acoustic wave due to stimulated Brillouin scattering. However, if the relativistic wave contains harmonics (nwp, n ~ = nAk), then since nAk


where E is the wave electric field normalized to the cold plasma wave-breaking amplitude E~o~d = mcwp/e; :no is the depth of the periodic ion pertubation, k~ is the ion ripple way:number, and ~ = 3kT~/m~. If we assume that the maximum amplitude of the plasma wave is much less than that due to relativistic detuning we can neglect relativistic effects and obtain the saturated amplitude of the relativistic plasma wave E(g/o) and its coupled mode E(g/1) as

and

E,~,t (g/o) = a,a2f(p)/e

E~,t (g/,) = otl(~2/e,

where f(.) =. + (: + :) + :)-',2 -_

for ~ >> I and p = (3/:) (kiAo) 2. Thus

(12)

(13)

(14)

Es,~t (g/o) = 2pEs,, (g/:). (15)

Taking e = 0.2% - 0.4%, T = 180 eV, n~ = 8.5 • 1015 cm -3 and E~,t (g/l) = 3 x 10 -4 we obtain E,,t (g/i) or (nl/no)~,t = 22-44%. Clearly, this model is only valid for nl/no smaller than 37% which is the relativistically limited maximum amplitude. However, the point is that the amplitude one obtains using this method is comparable to the harmonic ratio method and is greater than 10%.

Finally, we have observed sub-harmonic components (Aw/2, ~Aw) in the Thomson scattered spectrum (Fig. 12(b)). We have previously shown in a theoretical paper that a large amplitude relativistic plasma wave can develop such subharmonic components in the presence of an ion ripple 2a. Although we do not infer the plasma wave amplitude from these components we can assume that their observation implies a large amplitude plasma wave.

VII . P l a s m a Bea t Wave Acce le ra tor in the 100 M e V - 500 M e V R a n g e

In this section we would like to propose the next phase of experimental program on the Plasma Beat Wave Accelerator. The main goals of such a program are:

1) The demonstration of substantial energy gain for the injected electrons. The design goal is a 100 MeV to 500 MeV accelerator.

2) Acceleration of a substantial number of electrons, perhaps greater than l0 s .

3) Demonstrate that the injected electrons are deeply trapped; consequently the mierobunches that are formed have a small energy spread.

Our proposal uses a ~ 1 #m laser as a driver. In order to keep the plasma length small, we employ a higher plasma density than has been hitherto em- ployed in 1 #m beat wave experiments at the Rutherford Laboratory (U.K.) 24 and at Ecole Polytechnique (France) 25. This avoids the need for employing any


C. Joshi et al. 393

laser beam guiding techniques to keep the laser beam focused over a length much greater than that in vacuum. The parameters of the laser beam and the plasma as well as those of the plasma wave are summarized in Table 2.

1. Laser

Wavelengths Wavelength difference Energy per line Pulse duration (FWHM) Peak intensity per line Electron Quiver Veloeities/e Spot radius Rayleigh range zo

2. P l a s m a

Plasma wave wavelength Density Source

1.053 #m, 1.086 #m 285 cm-t: Vibrational Raman 10 J 4 ps 1016 W/cm 2

0.1 90 #m 2.4 cm

35 #m 9 x 1017 cm -a, Hydrogen multi-photon ionization

3. P l a s m a Wave Final Energy > 500 MeV 7ph 33 hi~no 0.25 Accelerating gradient 22.8 CeV/m Acceleration length ~ 2.4 cm

Table 2

The two laser lines needed to resonantly drive the plasma wave are generated by Raman shifting the driver (1.053 #m) wavelength on a vibrational transition of 285 cm -1. The oscillator for this laser will probably be a Ti-sapphire oscillator working on 1.053 #m wavelength. Such an oscillator has been shown to generate sub 100 fs pulses 26. The oscillator pulses are stretched on a grating to a few hundred picosecond long injection pulse. Such a pulse can then be amplified in a series of Nd:phosphate amplifiers to give an output energy of up to 30 J. This amplified pulse can then be Raman shifted using an oscillator-amplifier Raman downshifting technique 27. Conversion efficiency of up to 30% into the first Stokes sideband seems possible. If the laser output at 1.053 #In is not of the desired spatial quality, it may be necessary to use the first and the second Stokes to do the beat wave excitation 2T. These frequency shifted lines should be focusable to a nearly diffraction limited spot size.



Fig.13(a) shows the amplitude (nl/n0) of the excited beat wave versus the laser pulse width for a constant laser energy of 10 J per line and a plasma density of 9 x 10 IT cm -3. The laser pulse is assumed to be triangular with a risetime equal to the full-width at half-maximum. It can be seen that for a 4 ps pulse the saturated plasma wave amplitude is in excess of 0.25, limited by relativistic detuning at the exact resonance. If one precompensates for the relativistic detuning by introducing an initial density mismatch (as shown in Fig.13(b)) one can obtain plasma wave amplitudes in excess of 30%. Assuming a plasma wave of 25%, the accelerating field is 22.8 GeV/m, which implies that an energy gain of greater than 500 MeV can be obtained over an acceleration length in a uniform field of only ~ 2.2 cm. As can be seen from Table 2, for a laser spot diameter of 180 #m, the Rayleigh range is 2.4 cm. Thus for a peak intensity of 1016 W/cm 2 at the beam focus we expect a fully ionized plasma over

two Rayleigh lengths due to multi-photon ionization. A deterministically synchronized short pulse, high current electron injector

is necessary for this experiment. The ideal injector is a photoinjector driven RF gun giving an output bunch containing 1 nc or greater in a < 4 ps long pulse. Recently such an injector has been developed at UCLA 2s and is available for the experiment. Preliminary measurements show that up to 1.5 nC of charge with energy of ~ 4 MeV can be extracted in an approximately 10 ps long bunch from a gun that is only about 10 cm long.

We are currently studying all the relevant design issues associated with car- rying out such an experiment.

VIII. Conclusions

In summary, high-gradient acceleration of externally injected electrons by a relativistic plasma wave excited by a two frequency laser beam has been demon- strated. No accelerated electrons were observed when none were injected or when the laser was operated on a single frequency. However, electrons up to our detection limit of 9.1 MeV were observed when 2.1 MeV electrons were injected in a plasma wave excited (over a narrow range of static gas pressures close to the resonance) by a dual frequency laser beam. The accelerated electron signal was found to be correlated with indirect measurements of the amplitude of the plasma wave using Thomson scattering, Raman backscatter, and Raman forward scatter. The energy gain of the electrons suggests plasma wave amplitudes of at least 8% over a 10 mm interaction length. Thomson scattering measurements indicate plasma wave amplitudes up to 15-30%, offering the possibility of measuring even greater energy gains in future experiments.

These experiments have shed light on what is important in future experiments. First, that tunnel or multi-photon ionized plasmas are homogeneous enough for coherent, macroscopic acceleration. Second, the laser pulse should be short to reduce the ion effects (typically r < 3v~ ) and the modulational instability. Third, the peak laser intensity should be such that IA 2 .-~ 2 x 1016


C. Joshi et al. 395

W/cm 2. #m: in order to get substantial beat wave amplitudes. These consid- erations will play an important role in the designs of a 100 MeV and a 1 GeV plasma beat wave accelerator experiment. The present experiment has the potential to show energy gains of 15-20 MeV. The maximum energy gain in this experiment will be limited by the length of the plasma available for acceleration due to the laser intensity profile. By going to a 1 #m laser and a two orders of magnitude higher plasma density, it may be possible to reach hundreds of MeV energy gain.

Acknowledgments The authors would like to acknowledge useful discussions with Drs. W. B.

Mori and P. Mora, and Professors J. M. Dawson and T. Katsouleas and thank M. T. Shu and D. Gordon for their technical assistance. This work is supported by the U. S. Department of Energy under grant no. De-FG03-92ER40727.



References

1. T. Tajima and J.M. Dawson, Phys.Rev.Lett. 43, 267 (1979).

2. The 1-D simulation is a Fortran code that integrates the differential equation (3) by the Runge-Kutta method. It includes tunnel ionization and relativistic saturation effects.

3. W.P. Leemans et al., Phys.Rev.Lett. 68,321 (1992).

4. L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Pergamon Press), 1978.

5. M.N. Rosenbluth and C.S. Liu, Phys.Rev.Lett. 29, 701 (1972).

6. C. Darrow et al., Phys.Rev.Lett. 56, 2629 (1985).

7. C.E. Max et al., Phys.Rev.Lett 33, 209 (1974).

8. D. Pesme et al., Laser and Particle Beams 6, 199 (1988).

9. R.L. Williams et al., Lasers and Particle Beams 8, 427 (1990).

10. E. Yablonovitch and J. Goldhar, App.Phys.Lett 25, 580 (1974).

11. C. Clayton and K. Marsh, Rev.Sci.Inst., to be published, March 1993.

12. K. Marsh, UCLA PPC-1469, 1992.

13. A. Langsdorf, Jr., Rev.Sci.Inst. 10, 91 (1939).

14. B. Cohen et al., Phys.Rev.Lett 29, 581 (1972).

15. W.P. Leemans et al., Phys.Rev.Lett 67, 1434 (1991).

16. C.E. Clayton et al., Phys.Rev.Lett. 51, 1656 (1981).

17. W. P. Leemans, Ph.D Thesis, UCLA, 1992.

18. D. W. Forslund et al., Phys.Rev.Lett 54, 558 (1985).

19. Y. Kitagawa et al, Phys.Rev.Lett 68, 48 (1992).

20. C. Joshi et al., Phys.Rev.Lett 47, 1285 (1981).

21. W.P. Leemans et al.,Phys.Rev.A (1992).

22. D. Umstadter et al., Phys.Rev.Lett 59, 292 (1987).

23. H. Figueroa and C. Joshi, Phys.Fluids 30, 2294 (1987).


C. Joshi et al. 397

24. A.E. Dangor et al., Phys.Scrip. T30, 107 (1990).

25. F. Amironov et al., Phys.Rev.Lett 68, 3710 (1992).

26. J. Kafka et al., IEEE J.Quant.Elec 28, 2151 (1992).

27. Y.R. Shen, The Principles of Nonlinear Optics (John Wiley and Sons), 1984.

28. S. Park et al, same proceedings.


r r oo

*O

o

Fig.

1.

Sim

ulat

ion

of i

oniz

atio

n an

d pl

asm

a w

ave

grow

th,

a) T

he i

nten

sity

of

one

lase

r (v

o/c

= 0.

1) v

ersu

s ti

me.

b)

P

lasm

a de

nsit

y du

e to

tun

nel

ioni

zati

on b

y th

e el

ectr

ic f

ield

of

the

lase

r.

The

den

sity

sat

urat

es a

t 23

ps

due

to 1

00%

io

niza

tion

of

the

neut

rals

, c)

Gro

wth

and

sat

urat

ion

of t

he r

elat

ivis

tic

plas

ma

wav

e.

In t

his

exam

ple

the

full

y io

nize

d pl

asm

a ha

s a

dens

ity

2% b

elow

the

res

onan

t va

lue

whe

re A

ca =

~ap

.


C. Jo sh i et al. 399

v

(D "O .__= E}. E

q}

"o

t~ or)

4 0

3 5

3 0

2 5

2 0

15

1 0

5

0

S a t u r a t e d W a v e A m p l i t u d e

- - - T i m e to S a t u r a t i o n (ps )

............ ~ ............. ~ ............. T . . . . . . . . . . . . . . i i ............. i ............

............ ! i ............. i i ............. i # - / i ILi ~~~~ .......... i ............. i i ...........

........... i ............. i.~ -.-.< ..~---~------. l ~, -! ............. i ............

........... i....~.....~ ........... ~ ............ -: .......... ~ ........... ~ ............ i i i ! , , i

i i i (a ) i i o 0 . 9 4 0 . 9 6 0 . 9 8 1 .00 1 .02 .04 1 .06 1 . 0 8

R e l a t i v e D e n s i t y

1 2 0

90

60

30

-4 3

o

v

- - - 4O

a~ 3 5

3O El. E 2 5

<

m 2 0 t~ ~ 15

~ 10 ~ 5

1 26 128 130 132 134 136 138 140

P r e s s u r e ( m T o r r )

Fig. 2. Saturated value of the plasma wave ampli tude es~t = (nl/no) and the time in psec to reach saturat ion versus plasma density relative to the exact resonant density. The conditions axe the same as in Figure 1.



(n

c 0 L_

0

(D

L .

0 0 <

N,--

o

(D . m

E Z

10 6

10 5

10 4

10 3

10 2

10 1

10 0

10 " I ~ ~ ~ 0 ~ ~ ~ 0 ~ ~

Electron Energy (Gamma)

Fig. 3. Results of the 3D particle trajectory simulations which include longitudinal and radial fields of the plasma wave and finite emittance of the injected electron beam. Histogram showing number of particles in an energy bin with A7 = 1 versus 7 for a n~/no = 0.15.


C. Joshi et al. 401

To Forward Scatter

Diagnostics

Pole piece for imaging electron spectrometer

T Surface barrier detector Cloud

Chamber

CCD camera

Probe beam

/ Vacuum chamber

2.1 MeV trajectory

Aperture

I • ] • Lead ~ Plastic

D Magnet

Thomson ----- scattered

light Collinear pump beams -b- and electron probe beam

T! Backscatter Diagnostics

Fig. 4. Schematic arrangement of the electron acceleration experiment.



150

:~ 100

C 50 c

0 1.9

I

2.0 2.1 2.2 , 2.3 Energy (MeV)

Fig. 5. a) Schematic of the micropulses (20ps wide), separated by 108 ps, and ~he plasma beat wave; b) the energy spectrum of the injected electrons.


C. Joshi et al. 403

KEY: l = Helmholt~ coils $ = Insertable profile monitor ~ = Solenoid lens

0 = Current monitor I~ = Beam position monitor

Linac

Mylar foi l ml~rSe~ cusing Final focu S

(a)

N

E

.10

.c_

. J

I

I

I

l

I \ 1 / i \ ! / I. \ I I I I I I

0.0 Position along beamline (m)

/ 2.8

Radius (mm) bl xl b2 x2 b3

Theory 2.2 0.20 2.8 1.0 8.9

Measured 2.5 0.22 3.0 0.60 6.5

x3

0.16

0.12

(b)

Fig. 6. a) The beam transport line and diagnostics, b) The measured and LheoreticaJ beam envelope size.



Fig. 7. a) The image of the visible radiation emitted by the plasma b) Line outs from Thomson scattering (single frequency) at 2kl from electron fluctuations due to stimulated Compton scattering and a theoretical fit to this measured spectrum. The theoretical fit gives the plasma density no = 6 x 1015 and plasma longitudinal temperature 7111 = 75 eV.


C. Joshi et al. 405

Fig. 8. a) The surface barrier detector signal levels due to statistical noise from x-rays, b) Cloud chamber image showing only signal produced by low energy electrons produced in the cloud chamber by photoionization by x-ray photons.


o r~

t~

N

t~

Q

i-, 1

Fig.

9.

a) A

ccel

erat

ed e

lect

rons

tra

ject

orie

s at

5.2

MeV

in

the

clou

d ch

ambe

r w

ith

no a

ppli

ed c

loud

cha

mbe

r m

agne

tic

fiel

d ;

b) C

urve

d ac

cele

rate

d el

ectr

ons

traj

ecto

ries

at

5.2

MeV

whe

n a

260

G f

ield

is

appl

ied

to t

he c

loud

cha

mbe

r.

In

this

im

age,

the

len

gth

is 7

.25c

m a

nd t

he h

eigh

t is

3.4

cm.

c) T

he t

raje

ctor

ies

of t

he i

njec

ted

2.1

MeV

ele

ctro

ns i

n th

e cl

oud

cham

ber

(no

B f

ield

), w

ith

a fl

ux o

f 60

ele

ctro

ns/m

m 2,

and

d)

480

elec

tron

s/ra

m 2.


C. Joshi et al. 407

Fig. 10. a) Surface barrier detector signal levels (raw data) and noise histogram (shown in hatched bar). b) Surface barrier detector signal levels versus fill pressure of neutral gas.



150

v 7 5

c

O3 0

10.7 10.8 10.9 11.0

Wavelength (gin)

1000 s

C. Joshi et al. 409

8000

6000

4000 C

2000

0

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . :

. . . . . . . . . . T ............ i . . . . . . . . . . . . . . . . . . . . . . : '

-" .0 0.0

! 2A(o

..... i ........... ! ..........

1.0 2.0 Frequency Shift / & co

2500

2000

~" 1500

g ~ooo

500

I

: (b)

........... i ............. i ............ i ............ " ................................... i ..........

-1 .0 0.0 1.0 2.0 Frequency Shift / &m

Fig. 12. a) A scan through a Thomson scas spectrum at ks -~ 2kl showing a large scattered peak at Ace and a smaller but distinct peak at 2AaJ. b) Subharmonic components at Aa;/2 and 3/2 Aa; in a Thomson scattered spectrum at ks -~ 2ki.


410 The P l a s m a Beat Wave Accelera tor

"m

E <

0 . 4 0

0 . 3 5

0 . 3 0

0 . 2 5

- - A m p l i t u d e

' ' I . . . . ! . . . . : !

................. ~ .......................................... i . .~ .............. ~ ...................

i i / / i i

....... .................... i . . . . . . . . . . . . . . . . . . i .................... i ...................

(a) i 1 1 L I t i i I i i I , l a

- - - S a t u r a t i o n T i m e ( p s )

1 0 . 0

O0

7 . 5

o

5 . 0 =

3

2 . 5 "o (D

0 . 2 0 0 . 0

0 2 4 6 8 1 0 P u l s e W i d t h ( p s )

(D

__=

Q..

E <

- - A m p l i t u d e

0 . 3 5 . . . . . . . . . . . n . . . . i . . . . . . . . . . . .

0 . 3 0 ............ ~ ............... ? .............. ~ . . . . . . l .............. i .............

0 . 2 5 ............ :..= ............. ~ . . . . . . . . . . . . ~ .......... ~ .............

0.20 ............ J . . . . . . . . . . . . . . . . . . . . . . i .............

o . 1 5 ............ i ....... ~ - - - - i . . . . . . . . . . . . .

o . l o . . . . . . . . . . . .

o . o s .- ......................................................... ~ .............. ; .................. i b i -

o . o o . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . 2 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04

- - - S a t u r a t i o n T i m e

9

8

7

6

5

4

3

D e n s i t y M i s m a t c h

U)

t - -

6 --1

(D

Fig. 13. a) The amplitude nl/no of the plasma beat wave versus laser pulse width for a laser energy of 10J per line, a density no = 9 x 1017 cm -3, and wavelengths )h = 1.053#m and A2 = 1.086#m. b) The plasma wave amplitude versus density mismatch, for a laser energy of 10J, pulse width of 4 ps, and a density no = 9 x 1017 cm -3.


acceleration of injected electrons by the plasma beat wave ......the major attraction of the pbwa is...

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