The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

GENERATION OF A HIGH QUALITY ELECTRON BEAM BY THE
COLLIDING TWO LASER PULSES
Hideyuki KOTAKI, Masaki KANDO, Shin-ichi MASUDA, Shuji KONDO,Shuhei KANAZAWA, Takayuki HOMMA, and Kazuhisa NAKAJIMA
Japan Atomic Energy Research Institute,Kizu, Kyoto, 619-0215, Japan
Abstract
We investigate generation of electron beams injectedby the interaction of two laser pulses. A single laser pulse
produces an electric field (wakefield). By using two laserpulses electrons can be injected from the plasma into thewakefield. We term the scheme "colliding pulse opticalacceleration". We perform theoretical analysis andnumerical simulation of the colliding pulse opticalacceleration by two laser pulses. The accelerated electron
beam has a small energy spread and ultrashort pulse
duration. Also, the electron beam has an emittance lower
than the best quality beam produced by conventional RF
accelerator technology. We find that a high quality
intense relativistic electron beam is generated.

INTRODUCTION
Electron beam injection triggered by an intense
ultrashort laser has been proposed as an injector ofultrashort electron beams referred to as "optical injection".
Presently there are three major schemes: nonlinear
wave-breaking injection[1], transverse optical injection[2],and colliding pulse optical injection[3][4][5]. Three laser
pulses consisting of a pump pulse for wakefield excitationand two injection pulses for trapping the electrons fromthe plasma make up the colliding pulse optical injector.
The colliding pulse optical injection is a high quality
optical injector. The optical injection, however, is themost difficult.
The counter-propagate laser pulses inject electrons
from the plasma into a wakefield excited by one of thelaser pulses. One of the laser pulses injects andaccelerates electrons. We call the mechanism "collidingpulse optical acceleration". The experiment of thecolliding pulse optical acceleration is easier than thecolliding pulse optical injection, and has the possibility tobecome a high quality electron injector similar tocolliding pulse optical injection. We present opticalinjection and acceleration schemes that utilize twocounter-propagating laser pulses.

COLLIDING 2 LASER PULSESTwo counter-propagating laser pulses each produce
plasma waves. The interaction of pulse 0 and pulse 1
generates a standing wave. We assume the electric field EisE = E0cos(k0z-ω0t)+E1cos(k0z+ω0t),
where ω0 and k0 are the frequency and the wave numberof the laser, and E0 and E1 are electric field of the laser
pulses. The momentum pinj of the injection is obtainedpinj = γinjmec = CE0E1[sin(2ω0t)-2ω0tcos(2k0z)],
where γinj is the normalized energy of injection and C ise2/2meω03. This equation shows that electrons in theplasma are accelerated from oscillations generated by thecolliding laser pulses. Electrons in the plasma are injected
into the wakefield, when the laser pulses collide and thelaser strength parameter is above the trapping threshold.
For the laser strength parameters a0 of 1.0 and a1 of 0.4,
the rms electron pulse duration τe(rms) is written byτe(rms) = 0.10 τL(FWHM),
where τL(FWHM) is the full width at half maximum pulse
width of the laser pulse. The electron bunch compression
effect is included in the pulse duration.

SIMULATION RESULTS OF THE
OPTICAL INJECTION
In order to estimate the quality of the generated
electron beam, we performed 1-D Particle-in-Cell (PIC)
simulations[6] for the colliding pulse optical accelerationin the linear regime. The length of the simulations is 1mm, and the colliding point of two laser pulses is at thecenter. A portion of the electrons in the plasma is trapped
and accelerated to high energy by the wakefield excitedby the pump pulse. The accelerated electron beam isclearly separated from electrons in the plasma.
The electron beam at ne=7×1017cm-3 for a0=1.0 and
a1=0.4 has a pulse duration of 7.4 fs (rms) and a charge of
31 pC corresponding to the peak current of 1.5 kA. It
would be difficult to generate such an ultrashort intenseelectron beam with conventional RF accelerators. Figure
1 shows the pulse duration of the injected and accelerated
electron beam. The dotted lines show the theoretical valueat λp[mm]=0.8τL(FWHM)[fs]. The simulation results are
consistent with the theoretical values. The electron bunch
injected into the wakefield excited by the pulse 0 is also
compressed and stretched in the field before becoming
relativistic. The pulse duration of the accelerated electron
beam changes after trapping into the wakefield whichworks as a compressor and a stretcher not only anaccelerator.
Figure 2 shows the accelerated electrons energy at
ne=7×1017cm-3 for a0=1 and a1=0.4. The accelerated
energies are consistent with linear theory and the energy
spread is very small. The energy and the energy spreadare 9.5 MeV and 1.42%, respectively.
For the quality of the electron beam, the emittance is
one important parameter. Figure 3 shows the distributionof the transverse normalized velocities βt of theaccelerated electrons at ne=7×1017cm-3 for a0=1.0 andThe 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

a1=0.4. We can obtain an emittance of the electron beamfrom βt = 0.0029. The normalized emittance εnx of theelectron beam is approximately,εnx = ρeγββt,where re is the electron beam radius, γ is the normalizedenergy, and β is the longitudinal normalized velocity ofthe electron. For the electron energy of 9.5 MeV, γ and β
are approximately equal to 18.6 and 1, respectively.
Assuming the electron beam radius, re=15mm, thenormalized emittance of the accelerated electrons is 0.3 πmm mrad (rms). This emittance is smaller than the best
quality beam produced by conventional RF accelerator
technology such as a photocathode RF-gun[7][8].
These results show that the colliding pulse opticalacceleration by two laser pulses has a possibility of smallenergy spread and low emittance electron injection.

Fig. 1 The pulse duration of the electron beam
for a0=1.0 and a1=0.4CONCLUSIONS
We have explored the generation of a high quality
electron bunch by using colliding pulse opticalacceleration by two counter-propagating laser pulses thatare a realistic method for experiments of high quality
electron generation. The mechanism is a new one forelectron injection and acceleration. We have made anumerical simulation of the optical injection scheme andcompared it to the calculation of the optical acceleration.
In particular, we have studied the pulse duration of theinjected and accelerated electron bunches. The wakefieldcompressed the electron bunch and the space charge
stretched the electron bunch. The colliding pulse
acceleration scheme investigated has the ability to
produce relativistic electron bunches with low energy
spread; low normalized transverse emittance, and shortbunch length.

Fig. 2 The energy spectrum of accelerated
electrons at ne=7×1017cm-3 for a0=1 and
a1=0.4

REFERENCES[1] S. Bulanov, N. Naumova, F. Pegoraro, and J. Sakai,Phys. Rev. E 58, R5257, 1998
[2] D. Umstadter, J. K. Kim, and E. Dodd, Phy. Rev.
Lett. 76, 2073, 1996
[3] E. Esarey, R. F. Hubbard, W. P. Leemans, A. Ting,and P. Sprangle, Phy. Rev. Lett. 79, 2682, 1997
[4] C. B. Schroeder, P. B. Lee, J. S. Wurtela, E. Esarey,and W. P. Leemans, Phy. Rev. E 59, 6037, 1999
[5] E. Esarey, C. B. Schroeder, W. P. Leemans, and B.
Hafizi, Phys. Plasmas 6, 2262, 1999
[6] S. Masuda, T. Katsouleas, and A. Ogata, Nucl. Inst.
and Meth. A 455, 172, 2000
[7] K. Nakajima, Nucl. Instr. and Meth. in Phys. Res. A455, 140, 2000
[8] X. J. Wang, M. Babzien, K. Batchelor, I. Ben-Zvi, R.
Malone, I. Pogorelsky, X. Qui, J. Sheehan, J.
Sharitka, and T. Srinivasan-Rao, Nucl. Instr. andMeth. A 375, 82, 1996; X. J. Wang, X. Qiu, and I.
Ben-Zvi, Phys. Rev. E 54, 3121, 1999.

Fig. 3 The distribution of the transverse
normalized velocity βt of theaccelerated electrons for a0=1.0 anda1=0.4 at ne=7×1017cm-3 and a laser
pulse width of 50 fs.