Growth and Saturation of Large Amplitude Self-Modulated Wakefield in 60 TW Laser Plasma and Possible Electron Acceleration Yoneyoshi Kitagawa*, Michiaki Mori1^ Hisaoki Asatsu**, Shin Akamatsu*, Ryosuke Kodama*, Kazuo A. Tanaka*, Hidetsugu Yoshida*, Takayoshi Norimatsu*, Takahisa Jitsuno*, Shuji Sakabe*, Yasukazu Izawa*, Kunioki Mima*, Tatsuhiko Yamanaka* and Yasuhiko Sentoku* ""Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871, Japan ^TARA Center, Tsukuba University, Tennodai 1-1-1, Tsukuba 305-8577, Japan **Osaka Gas Company, Ltd., Hiranocho 4-1-2, Osaka, Osaka 565, Japan ^General Atomics, P.O.Box 85608, San Diego, California 92121-1194, USA Abstract. A 25 J -1.053 jUm pulse in 0.45 ps (a0= 2.2) was injected into a gas jet. This excited a large amplitude self-modulated wakefield. By increasing the pulse length from 0.45 to to 1.2 ps, the wakefield grew close to the wave-breaking limit, which sustained a 350 ±150 GV/m acceleration field over a 1 mm dephasing distance along the laser axis in a plasma with density 2 x 1019 cm~3. This resulted in electrons accelerated to 300 MeV. The amplitude saturation of the wakefield is explained by a pump depletion effect to the large amplitude forward Raman instability. The Petawatt Laser is completed, which will be used to accelerate electrons above one GeV. INTRODUCTION The laser-plasma accelerator concept was first presented in 1979 by Tajima and Dawson[l]. 10 years later, two frequency CO2 lasers demonstrated the concept[2, 3] in the laboratory. The laser pulses, however, were as long as nanoseconds and the intensities were low, resulting in excited plasma wave amplitude of only a few % , corresponding to acceleration fields of no more than a few GV/m. The electron gain was 20 to 30 MeV. A few years later, short-pulse ultra-intense lasers brought significant progress to laser- plasma accelerator studies, especially to the laser wakefield approach[l, 4, 5]. If the laser intensity becomes so high that the quivering velocity is larger than the light velocity, the excited wakefield affects the amplitude modulation on the pump laser at the plasma period[6], which results in extremely high wakefield generation [7]. In 1995, injecting a 3 TW, 1 ps laser into a helium gas, the ILE group at Osaka University and the KEK group had obtained an acceleration field of 30 GV/m and accelerated 1 MeV/c electrons to 18 MeV/c[8]. In this experiment the seed electrons were generated from an aluminum target illuminated with a 200 ps laser. Also in 1995, the Rutherford Appleton Laboratory and the UCLA group had injected a 25 TW, 0.8 ps pulse into a gas jet and had observed forward electrons with energies near 100 MeV [9]. they reported a field of about 150 GV/m. In 2000, we obtained the field of 160 GV/m, using a 60 TW, 1.053jum, 0.4 ps laser in a hydrogen plasma of 1 x 1019/cm3[10]. Thus, CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli © 2002 American Institute of Physics 0-7354-0102-0/02/$19.00 634 an ultra-intense laser was shown to easily excite an accelerating field on order of one hundred GV/m via the self-modulated wakefield. However, since the self-modulated wakefield is an instability (that is the forward Raman scattering), it needs a finite time to overcome any damping mechanism and grow to a saturation level. It is reported that the wakefield decays into ion acoustic waves in a few ps [11]. Nevertheless, we have no information about the growth and saturation of the wakefield at early times. It would be interesting to know what the optimum pulse length for the wakefield growth under a given plasma density is, or whether it is possible to attain a field larger than the wave breaking limit. The wave-breaking-limited field is classically given by E O (W O ) = mQ)pC/e = 30(ft0/1017)2 [GV/m], where nQ is the electron density in cm~3. The ultra-intense laser, of which the ratio of the quivering velocity to the light velocity, a0 = vosc/c = (I/(1.23 x 1018W/cm2))! > 1 enhances the field to (1) where nl is the perturbed electron density associated with the wave. If a0 > 1.3 and H-^/HQ = 1, Emax becomes above E O (W O ). This paper will discuss first the optimum growth and saturation of the self-modulated wakefield within a strong laser pulse, where a0 reached 2.2. A 60 TW laser was injected into a hydrogen, helium or argon gas jet and excited a large amplitude self-modulated wakefield. By increasing the pulse length from 0.45 to to 1.2 ps, the amplitude increased close to the wave-breaking limit value. 2 x 1019 cm~3 gas plasmas sustained a 350 ± 150 GV/m acceleration field over 1 mm distance along the laser axis. Either the dephasing or diffraction length seems to determine the distance. Temporal change of the amplitude of the wakefield was consistent with the idea that the large amplitude forward Raman scattering rises from a thermal noise and saturates due to a pump depletion effect[12]. The pump depletion length Lp is given by the length over which the laser energy is transferred to the plasma wave. The world biggest Petawatt laser (PW laser) was completed [13]. The beam size was 50 cm to extract 1 PW or 500 J in 0.5 ps. The PW Laser will excite the self-modulated wakefield of 200 GV/m or provide the electron acceleration of 2 GV at 5 mm length. SELF-MODULATED WAKEFIED EXCITATION USING GAS PUFF PLASMA The GEKKO-MII CPA laser, used here, produced 25 J at 1.053 jum with 0.45 (60 TW) or with 1.2 ps pulse length [15, 16]. The laser beam was focused into a gasjet by an off axial parabola mirror of f/3.7. 68% of the beam energy was measured to the spot size of 25 jum in diameter. The intensity on target was 3 x 1018 W/cm2. The prepulse level was 10~3. Figure 1 shows the experimental setup. The gas jet was formed by a puff, electro-magnetically switched at 10 kV. At 2 mm above the puff nozzle of 6 mm aperture, we obtained a gas molecular density of 1019/cm3 over 4 mm long, as shown 635 CCD D Sidescattrer 800~1000nm from Compressor 1053 nm 25 J in 0.4 ~ 1.2 ps FRS Transmission to Spectrometers ^^900-1600 410 640 nm FIGURE 1. Experimental setup for laser acceleration. 10' 10 n 10 n - 2 0 2 Radial position from center R (mm) FIGURE 2. mm. Radial distribution of molecular density at 2 mm above gaspuff nozzle. The aperture is 6 in Fig. 2. The figure provides the density scalelength to be 1.5 mm. Twice the Rayleigh length 2ZR = 2nr^/^ for a given spot radius r0 was also 1 ~ 1.4 mm, which permitted the wakefield to accelerate electrons over 1 mm. The time in which the gas reaches its maximum density, is 100 ms for a reservoir pressure of 3000 Torr. The laser was focused 1.75 mm apart from the nozzle center. The intensity was 2.1 x 1018 W/cm2. The spacial image of the plasma wave was taken by a CCD camera through a bandpass filter from 800 nm to 1000 nm at!20° backward the laser axis and in the direction of the laser polarization. The sideview image lengths were 1.1 ~ 1.7 mm either for hydrogen, helium, or argon gas, close to 2ZR and the plasma scale length. The anti-Stokes line shift gave the electron density to be 1.1 x 1019/cm3. The wakefield, or excited plasma wave, becomes a moving grating, scattering the pump laser to Stokes and anti-Stokes satellites. 636 105 (a) 10 4 o o 100 10 1000 1200 1600 1400 Wavelength (nm) 400 450 500 550 600 650 700 Wavelength (nm) 400 450 500 550 600 650 700 Wavelength (nm) FIGURE 3. (a) Stokes and anti-Stokes spectrum (shot#13860) at COQ and (b) at 2coQ at for pulse width 1.1 ps and aQ = 1.5. (c)Spectrum at 2o)0 for pulse width 0.4 ps and aQ = 2.2. nQ = 1.1 x 1019/cm3. 637 According to the Bragg scattering theory, we estimated the wakefield amplitudes from the intensity ratio of the Stokes to pump wave intensities [14]. The second harmonics of the pump laser is also scattered from the same plasma wave. For the pump power P0, the scattered m-th Stokes harmonic powers Pm are given as nnmn0Lz]2\sin(MIz) where nm is the m-th harmonic density perturbation and Lz is the distance over which the plasma wave is excited. A& shows a phase mismatch of three wave mixing. The momentum conservation between the electromagnetic and electrostatic wave requires: 0 s p ~ 2 c nc' Now A&= 3 mm"1 for nG = 1019/cm3. In the case of Lz ~ mm, it is difficult to fix the last bracket value in the right hand term in Eq. 2. Thus this term can reduce the data reliability. The line ratio between the first and second Stokes harmonics was then used to cross check the absolute amplitude[17]. The line ratio between Stokes harmonics provided an absolute amplitude without any assumption on the three wave phase mismatch between the pump, scattered and plasma waves. In addition, the second harmonic of a large amplitude plasma wave is given by [18]: n2/nQ ~ [nl/n()] . Combining this result with Eq. 2, we obtain a relation between the second Stokes scattering P2 and the density fluctuation due to the plasma wave as follows: P •*• 1 1 P IP •*• 1I '/ •*• f\ U in /n \j'}I2 V\ 'M 1'/ **f\ (n In \j }'2I \\ ''1 I' / f*(\ (4) Thus by measuring the Stokes harmonics, we obtain the wakefield amplitude as a function of the electron density. The electron density is obtained from the Stokes shift from the pump frequency. Figure 3 (a) shows the first Stokes Pl and the second Stokes P2 spectrum around the co0 pump PQ for the pulse length of 1.2 ps and at a0 = 1.5(Shot # 13860). The Stokes shift k(Pi) — A(P0) = 16 nm gives an electron density of nQ = 2 x 1019/cm3. Equation 4 predicts the density fluctuation nl/n^ to be 44 %, and Eq. 1 predicts Emax to be 230 GV/m. Since the indium-gallium-arsenide (InGaAs) array limits the detection range from 900 nm to 1600 nm, no anti-Stokes line was detected. Figure 3(b) is the same shot as (a), but the Stokes satellites Pl and P2 can be observed around the second harmonic pump PQ. For this case, n^jn^ is 77 % and Esat is 490 GV/m. In this case, the antiStokes peak /*_! can clearly be seen. We found that the 2co light is also scattered by excited plasma wave. Consequently, we can get the density and its fluctuation both from co Satellites and from 2co satellites. Figure 3(c) shows the Stokes satellites Pl,P2,P_l,P_2 around the second pump for a 0.45 ps pulse width. Although the density is nearly the same as for the above cases (1.1 x 1019 /cm3 and a0 even increases to 2.2) nl/nQ decreases to 20 % and Esat drops to 126 GV/m. Figures 3 (b) and (c) suggest that the wave grows with increasing pulse width from 0.45 to 1.2ps. 638 [ps] Pla sm a De ns ity ne e [cm ] -3 ] /m] de [GV Amplitu Pul se w idth τ 1.5 FIGURE FIGURE 4. 4. Acceleration Acceleration field field of of self-modulated self-modulated wakefield E Emax max is plotted for pulse length in x axis and and electron electron density density in in yy axis. axis. SELF-MODULATED WAKEFIELD GROWTH ESTIMATION OF SELF-MODULATED AND SATURATION Since the wakefield is forward Raman scattering, scattering, the wave must grow with time. The Since initial density fluctuation nn1l/n initial /nQ0 may arise from a thermal noise nth /nQ0 as the Raman th/n instability grows. However, since since the simple exponential growth model is too sharp instability explain the experimentally measured growth between 0.4 and 1.2 1.2 ps, we introduce to explain characteristic damping terms, such such as pump depletion, dephasing, and Rayleigh lengths. characteristic The dephasing dephasing length length is aa phase slip slip distance between the laser and the wakefield as well The as aa slip slip distance distance between the wakefield and the electrons. Assuming that the damping as is in in the the form of aa phase velocity divided by the characteristic length, then is n1 nth 11 11 1I —- = = -^ exp exp γ − c( + + ) τ . (5) n0 n0 L p Ld ZR √ 2 2 /2] is the pure growth rate of the Here γ7 = =ω co^/(\/8a) <z0 /[1 + aa^/2] the forward forward Raman Raman Here 0 /[l + p /( 8ω00)) ·•a 0 scattering (FRS) (FRS) [19], [19], L pp = = (a (a0Q/3 /3n)(ric/n^)k scattering π )(nc /n0 )pλ p is the damping rate due to to pump pump depletion depletion of the the laser laser and and Ldd = = 6a0QL pp is the damping due to dephasing [12]. dephasing[12]. of The thermal noise nnthth/n /nQ0 could be on the order of vv^/c, The th /c, since the equation of continuity can can be be written written as as − —con + kvfhthnnQ0 = continuity ω nthth + = 0 and the FRS phase velocity velocity co/k ω /k ~ ∼ c, where cc is is the the light velocity. The The electron electron temperature of of 11keV keV provides nnthth/n /nQ0 = = 0.04. where If we we assume assume that the density fluctuation nn1l/n If /nQ0 in Eq. 11 obeys the above-mentioned growth, we can simply simply substitute substitute Eq. 5 into Eq. 1, 1, which which leads leads to to the the saturated saturated field field growth, £maxThe E E . The temporal behavior of E is plotted in Fig. 4. One horizontal axis is the max max max plasma density nw00.. 639 FRS Field [GV/m] 1000 800 3x1019 /cm3 3x1019/cm 2x1019 600 1.3x1019 400 1x1019 200 1x1019 0.2 0.4 0.6 O.S 1 Pulse width τ [ps] 1.2 1.4 Pulse width t [ps] FIGURE 5. Emax as a function of the pulse length. FIGURE 5. Emax as a function of the pulse length. Figure 4 shows that the amplitude saturates between 0.5 ps and 1ps for the densities on 19 /cm 3 . Since shows that the amplitude 0.5 ps and the Ipssaturation for the densities on the Figure order of4 10 L p Ldsaturates ∼ ZR forbetween these parameters, is mainly 19 3 the order of 10 /cm . Since The Lp<^L for these parameters, the saturation d~ ZR pulse ps at ne =is2mainly × 1019 due to the pump depletion. optimum length is τ ∼ 1.2 19 −3to due the pump depletion. The3 optimum pulse ~ 1.2 ne = 2 xof10the cm . Both the data from Fig. (b) and (c) are length plottedisinx Fig. 5 ps as aatfunction 3 3 . The of cm~ width. . BothLines the data Fig.from 3 (b)Fig. and4(c) plotted Fig. 519asW/cm a function the pulse are from replotted for are n0 = 1, 1.3,in 2, 3×10 results 19 3 pulse width. Lines are replotted from Fig. 4 for n = 1,1.3,2,3 x 10 W/cm . The results seem to show that the amplitude saturates due toQ the pump depletion and 1.2 ps is close to show that thewidth amplitude due to the pump andis 1.2 ps is close toseem the optimum pulse in thesaturates present system. The best depletion fitted curve at the electron 19 −3 to the optimum pulse width in the present system. The best fitted curve is at the electron density n0 = 1.3 × 10 19cm 3. density nQ = 1.3 x 10 density cm~ . for hydrogen, helium and argon gas is shown in Fig. Emax versus plasma 18 2 . Data £max versus plasma density hydrogen, helium andW/cm argon gas ispoints shownfrom in Fig. ??, where the laser intensity wasfortaken to be 2.5 ×1018 2ω0 2 ??, where the laser intensity was taken to be 2.5 x 10 W/cm . Data points from 2coof 0 Stokes seem to be 1 ∼ 2× higher than the ω0 Stokes. Since the P2 spectral width Stokes seem to be 1 ~ 2x higher than the co Stokes. Since the P spectral width of 0 2 ω0 Stokes is twice the P1 width in Fig. ??(a), if we compare not the peak ratio but co0 integrated Stokes is twice the ratio, Pl width in Fig. ??(a), if we compare not the peak 1.5 ratiotimes, but the intensity the data from ω0 Stokes will increase at least the integrated ratio, from Between co0 Stokesthewill increase at leastis 1.5 times, Stokes. gas species, there not a clear which is closer intensity to the data fromthe 2ωdata 0 which is closer to the data from the gas thereisisfrom not aFig. clear4, 0 Stokes. Between difference of either density or its2co perturbation amplitude. Thespecies, solid curve difference of either density or its perturbation amplitude. The solid curve is from Fig. 4, which is larger than the classical wave breaking limit E0 (n0 ), as shown by a dashed line, which is larger than the19classical wave breaking limit E (/Z ), as shown by a dashed line, O O −3 19 −3 between n0 = 1.4 × 10 19cm−33 and 3.2 × 1019 19 cm 3. At 2.4 × 10 19 cm 3 , the predicted between nG =800 1.4GV/m, x 10 cm~ x 10some cm~experimental . At 2.4 x 10points cm~seem , the to predicted field reaches 1.8 × and E0 (n3.2 ) and exceed 0 ) and some experimental points seem to field reaches 800 GV/m, 1.8 x £ (ft 0 the wave breaking limit. The data0 points are averaged to be 350 ± 150 GV/m exceed around The data points are averaged to be 350 ±150 GV/m around 19 W/cm3limit. nthe =wave 2 × 10breaking . ft0 0 = 2x!019W/cm3. W/cm3 , but it is smaller for 1019 W/cm3 or more. If Ld is larger than 2ZR for n0 1019 Ld is larger than 2ZR for rc0 < 1019W/cm3, but it is smaller for 1019W/cm3 or more. If we take the acceleration distance to be Lz = min[Ld , ZR ], the energy gain Wa = Emax · Lz , we take the acceleration distance to beL z = mintL^Z^], the energy 3gain Wa = Em3X-Lz, W/cm , L is estimated to which is plotted in Fig. 6 as dotted curve. At n0 = 2 × 1019 which is plotted in Fig. 6 as dotted curve. At nQ = 2 x 1019W/cm3, Lzz is estimated to be 0.5 mm, giving Wa = 300 MeV. If the acceleration distance is the full plasma column be 0.5 mm, giving W = 300 MeV. If the acceleration distance is the full plasma column length ∼ 2 mm and Eamax = 350 GV/m, then Wa is 700 MeV. The electron spectrometer length ~ 2 mm and E = 350 GV/m, then Wa is 700 MeV. The electron spectrometer points up to 22 MeV, max although there are no more data points, suggests that the slope points up to 22 MeV, although there are no more data points, suggests that the slope temperature of the accelerated electrons is 35 MeV and the maximum maximumenergy energyisisover over100 100 temperature of the accelerated electrons is 35 MeV and the MeV, as shown in Fig. 7. The self focusing of the laser beam in plasma will suppress the MeV, as shown in Fig. 7. The self focusing of the laser beam in plasma will suppress the 640 10 3 10 3 103 103 Cal.Field Cal.Field g limit reakin I 10 22 10 2 102 10 Energy gain [MeV] FRS Field [GV/m] ave b I Cal.gain H- 1 He-1 Ar-1 H- 2 He-2 Ar-2 10 1 10 1 0.6 0.6 19 0.8 10 10 0.8 2 10 19 3 10 19 cm -33]] nn [[cm0 2 18 W/cm2 . Solid circle is from ω Stokes and open FIGURE versus electron density at 2.5 ×1018 FIGURE6.6. EEmax max versus electron density at 2.5 x 10 W/cm . Solid circle is from (O0 0Stokes and open circle from 2 ω Stokes. Solid line is from Eq. 1 and dashed line the classical classical wave-breaking wave-breaking limit. limit. circle from 2o)00 Stokes. Solid line is from Eq. 1 and dashed line is is the =35MeV €>.,. Noise level 10 20 40 60 80 100 Energy (MeV) 19 ◦ direction. FIGURE7.7. Electron Electron spectrum spectrum to to 43 43° direction. Solid point:Laser 1.2 × x 1019 W/cm FIGURE W/cm22 and and 1^=1.3 ne =1.3x× 19 −3 3 18 2 18 3 19 18 2 18 −3 10 cm, Open point: 5.1 x 10 W/cm and 3.0 x 10 cm. 10 cm , Open point: 5.1 × 10 W/cm and 3.0 × 10 cm diffraction and and make make 2Z 2ZRR longer[20]. longer[20]. However, However, Ldd will not become longer, diffraction longer, unless unless we we useaatapered taperedplasma plasma duct, duct, thus thus compensating compensating the phase shift[21]. shift[21]. use PETAWATT LASER LASER COMPLETION PETAWATT Theworld world biggest biggest Petawatt Petawatt laser laser (PW (PW laser) laser) was was completed completed [13]. [13]. The The The beam beam size size was was 50 cm to extract 1 PW or 500 J in 0.5 ps. The design parameters of the PW Laser 50 cm to extract 1 PW or 500 J in 0.5 ps. The design parameters of the PW Laser are are 641 TABLE 1. PW Laser Design Parameters Front out Amp. out Comp. out Spectrum Pulse length Beam diam. Inner diam. Energy 6nm 3ns 10mm 10 ml 32cm 13 cm 800 J 3.0 nm 500 fs 50cm 20.3 cm 500 J On target 14/un(2/A) > 1019W/cm2 listed in Table 1. Figure 8 shows a diagram of its configuration. The front end includes a Ndiglass oscillator, a stretcher, and an optically parametric chirped pulse amplifier (OPCP Amplifier), which provides 20 ml with a 6 nm bandwidth. The main amplifier consists of eight glass disks in Cassegrain geometry. Since the spectral width of the amplifier output limits the pulse width of the compressed beam, we made the preamplifier gain low and the main one high, which results in getting the spectral width larger than 3 nm for a 1 kJ output. As a result, we obtained a pulse shorter than 1 ps. The output beam is transported to the Target I room, where a deformable mirror compensates for phase distortions on the wave front. A pair of 1-m diffraction gratings, grooved at 1485 lines per mm and set in double path configuration, compresses the pulse length to 500 fs in vacuum. Though the amplifier provides output up to 1.1 kJ, the damage threshold of the grating limits the current output to below 500 J. The compression chamber, shown in Fig. 9 is placed on iron frames at the heigh of 7.16 m from the floor. The focusing system consists of two plain mirrors and a 21-degree offaxial parabola mirror of 3.8 m focal length (f-number is 7.6). The chamber is connected through a gate valve to the horizontal port of the target chamber. The pointing accuracy is about 10 juradian at the focusing point. A 1-ns/l-nm chirped light, partially sliced from the front end, directly drives the GEKKO XII laser system. Therefore the PW laser beam can illuminate the imploded core plasma within ± 10 ps accuracy. The PW Laser can excite the self-modulated wakefield of 200 GV/m or provide the electron acceleration of 2 GV at 5 mm length, which is plotted on the progress curve of the acceleration field, as shown in Fig. 10. CONCLUSION A 60 TW Laser has excited a self-modulated wake field via forward Raman scattering in 1019 cm~3 plasma column. The laser intensity is 3 x 1018 W/cm2, one order higher than the self focusing threshold. The self-modulated wakefield grows from thermal noise and saturates due to pump depletion. The optimum pulse length is 1.2 ps at nQ = 1.3 x 1019 cm~3. The plasma wave (self-modulated wakefield) amplitude is > 70%, corresponding to an accelerating field of 350 ± 150 GV/m. The field can exceed the wave breaking limit. Plasma waves were likely excited over the Rayleigh length (1~ 2 mm axial length) which can accelerate electrons to energies > 300 MeV. The PW Laser will excite the self-modulated wakefield of 200 GV/m or provide the electron acceleration of 2 GV at 5 mm length. 642 OSCILLATOR ROOM GEKKO XII COMPRESSOR FIGURE 8. Diagram of the PW Laser configuration. ACKNOWLEDGMENTS The authors would like to thank the GMII laser operation member for their technical supports and all the PEII members for their encouragements. The authors also thank the Petawatt Laser construction project member. S. Wilks, LLNL, C. Joshi and C. Clayton, UCLA, are acknowledged for their kind and useful discussions. This work was partially supported by the Ministry of Education, Science, Sports and Culture, the Grant-in Aid for Scientific Research (B) 09480092. REFERENCES 1. 2. 3. 4. 5. T. Tajima and J. M. Dawson, Phys. Rev. Lett.56, 267(1979). Y. Kitagawa, T. Matsumoto, T. Minamihata, et al, Phys. Rev. Lett.68, 20(1992). C. E Clayton, K. A. Marsh, A. Dysonet al., Phys. Rev. Lett.70, 37(1993). L. M. Gorbunov and V. I. Kirsanov, Sov. Phys. JETP66, 290(1987). P. Sprangle^ al., Appl. Phys. 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