High-Energy Electron Beam Generation by a
Laser Pulse Propagating in a Plasma
H. Suk% C. Kirn*, G.H. Kim% J.U. Kirn*, HJ. Lee* and W.B. Morf
* Center for Advanced Accelerators, KERI, Changwon 641-120, Korea
^ Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095
Abstract. The previous study [1] showed that background plasma electrons would be trapped and
accelerated to a relativistic high energy when a high-energy electron beam passes through a plasma
with a sharp downward density transition. A similar trapping effect is expected if an intense laser
beam is used instead of an electron beam. Although there are some subtle differences between the
two cases, particle-in-cell simulations show that plasma electrons can be trapped and accelerated to
a relativistic high energy with a laser pulse. In this paper, detailed 2-dimensional simulation results
and the planned experiment at KERI (Korea Electrotechnology Research Institute) are presented.
INTRODUCTION
In plasma-based advanced accelerators [2-4], beam injection is an import issue. So far,
various injection methods have been studied, but they can be classified as a few major
groups. They include an external injection with an injection accelerator, optical injection
with lasers [5, 6], and self-injection [7-9]. In the self-injection scheme, plasma electrons
are injected into the acceleration phase of a wakefield and they are accelerated to a
high energy. Compared to other injection methods, the self-injection is very simple,
i.e. it does not need any other accelerator or lasers for injection. Furthermore, the
self-injection method can abolish difficult timing problems that are common in other
injection methods. Hence, it has some advantages over other injection methods.
Recently one of the self-injection methods was proposed by Suk et al. [1]. According
to this method, plasma electrons are self-injected and trapped by a plasma wakefield
when an electron beam passes through an underdense plasma with a sharp downward
density transition. We expect a similar phenomenon would happen if the electron beam
is replaced by an intense laser pulse. Nowadays compact T 3 (Table-Top Terawatt) lasers
are common and laser beams can be adjusted flexibly in pulse duration, radius, intensity,
beam shape, etc. Furthermore, if a laser beam is used, it will be possible to employ a
higher plasma density that will give a higher acceleration gradient. In these points of
view, therefore, the laser-based method would be better if a similar trapping effect can
be achieved with a laser beam.
In this paper, we investigate the possibility of using a laser beam instead of an electron
beam pulse. Detailed 2-D PIC simulation results and the planned experiment with a T 3
laser at KERI are presented.
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
710
(c)
FIGURE 1. Phase space plot (r,z) of the plasma electrons, in which the black dots represent electrons
in the plasma. Note that some plasma electrons are injected and focused after the laser wake wave passes
the density transition.
2-D SIMULATION RESULTS
In order to investigate the trapping phenomenon with a laser beam, we performed 2-D
PIC simulations with the OSIRIS code [10]. In the simulations, the plasma has a density
of HQ — 5 x 1018 cm~3 and n^/n^ is varied between 0 and 1. To study the effect of the
density scale length Ls, it is also changed in the range of 0 < Ls < A7/.
Figure 1 shows an illustration of the trapping process, in which a laser pulse of
duration tiaser = A7/c is propagating to the right direction. Here, c is the velocity of light.
In this simulation, the plasma has a density transition of n1^ = 5 x 1018, n^ = 0.75/10,
and LS=Q. Figure l(a) shows that a laser wake wave is generated behind a laser pulse
and some plasma electrons are injected after passing the downward density transition
(in the figure the density transition is observed as a vertical line). As time goes on, the
trapped electrons are focused by the background ions of the plasma (see Fig. l(b)). If the
trapped plasma electron beam gains a higher energy, its space charge effect is reduced
and this leads to a further decrease in transverse beam size (see Fig. l(c)). However, this
situation changes suddenly if the beam moves out of the plasma. In free space a strong
focusing force due to the so-called plasma lens effect [11] does not exist anymore, so the
711
FIGURE 2. Phase space plot (pz, z) of the plasma electrons in Fig. 1 (c). The trapped electrons are shown
to have a relativistic energy and to be well concentrated in a rather small phase space area.
beam expands rapidly. This expansion in beam size leads to rapid emittance growth. If a
slowly decreasing plasma density is used in the plasma-vacuum boundary, an adiabatic
expansion process happens and as a result the rapid emittance grouth can be reduced.
This effect was confirmed in the simulations.
For the case of Fig. l(c), the phase space plot (pz,z) is shown in Fig. 2. The figure
indicates that the trapped electrons are clearly separated from other background particles
and gained energies up to 15 MeV or so. This result implies that an intense laser pulse
can replace an electron beam pulse to trap and accelerate plasma electrons in a density
transition, although there are some clear differences between the two methods. In the
simulations, it was shown that the energy of the tapped electrons can increase further,
but it is eventually saturated. One of the dominant factors in limiting the energy gain
is the diffraction effect of a laser pulse as a laser beam size increases by a factor of
\/2 after propagating the Rayleigh range of ZR = ;FW0/A0. Here, w0 is the laser beam
radius and A0 is the laser wavelength. Roughly speaking, therefore, the energy gain E of
the trapped electrons reaches a maximum over an acceleration distance of 2zR. Another
important factor limiting the energy gain is the dephasing effect. If the electrons have
a relativistic high energy, the velocity exceeds the phase velocity of a laser wake wave
that is given by the laser group velocity vg = cJ\ — (cop/Co^)2. Here, cop and COQ are
plasma and laser frequencies, respectively. This phenomenon is observed in simulations
(see Fig. 1). Hence, the accelerated electrons move faster than the laser wake wave in
phase and this leads to the phase slippage, which eventually prevents a further energy
gain.
712
bo
O
b
-»>
-»•
co
-»•
OD
ro
b
M
ro
§
Trapped Charge Q (pC)
(PBJLU-UULU
> . » s.$ g E \ .
3
o c n o o i o o i o o i o c n o
,. i.... i.... i.... i.... i.... i.... i.... i.... i..
ro
ro
ro
b>
O
p
bo
j*.
Trapped Charge Q (pC)
«'
k>
b
O
a, >~ a>o
(O
Q
JO
p
p
b
O
O
The trapped charge Q will change if the density ratio changes. To study this issue, the
density ratio n0/ftQ7 is varied for a fixed density with n1^ — 5 x 1018 cm~3. The simulation
result for this case is shown in Fig. 3, which leads to a rough relation Q <* (n^/n1^/2.
This result implies that Q increases as the density ratio increases. Fig. 3 also indicates
that the normalized emittance £n is approximately proportional to n^/n1^. For a given
ratio of n0/«Q7, the trapped charge is expected to increase if lower densities are used. A
simple model results inQ^ \/ Jn1^ for a given density ratio. Hence, the trapped charge
is expected to scale up to tens of pC if an experiment employs a low density plasma in
the range of n0 = 1016 cm~3.
So far, a step function for density transition, i.e. Ls = 0, was used in the simulations.
However, it should be noted that Q will be reduced if the density scale length is not
0. In order to investigate this effect, simulations were performed for 0 < Ls < A77, and
the result is shown in Fig. 4. The result indicates that the trapped charge is reduced by
about 50 % if Ls is increased to the plasma wavelength A77. This is better than what
was anticipated before, and it implies that the requirement for sharp density change is
mitigated significantly.
PLANNED EXPERIMENT AT KERI
The simulations in the previous section showed that the suggested trapping and acceleration would occur with a laser beam, but it needs to be verified experimentally for
confirmation. We have an experimental plan to do that at KERI. In the simulations in
this paper, high density plasmas (in the range of nQ ~ 1018 cm~3) were used, but using
the high density was just to reduce the simulation time. In experiments, the plasma density will be significantly reduced down to the order of 1016 cm~3. In the case of using
a rather low density plasma, one of major advantages is to mitigate the requirement for
the density scale length as Ls ^ \j\fn^.
The experiment will use a T3 Ti:sapphire/Nd:glass hybrid laser system shown in Fig.
5, which consists of a mode-locked Nd:glass oscillator (T ~ 200 fs, f=76 MHz, average
power^ 150 mW), Ti:sapphire regenerative amplifier (f=480 Hz, E ~ 0.5 mJ/pulse),
gratings for pulse stretching, Nd:glass amplifier, and pulse compression gratings. After
compression the laser beam of A0 = 1.053 jUm is expected to have an energy of more
than 1 J/pulse and a pulse duration of about 500 fs, which gives about 2 TW in power.
In the laser-plasma interaction chamber, the laser beam will be focused to 20 jUm
~ 30 jUm in radius, which leads to an intensity on the order of 1017 W/cm2-s. For
these laser parameters, the plasma densities are chosen to be «Q = 1.7 x 1016 cm~3
and «Q7 ~ 0.75n07. These experimental parameters will give an acceleration gradient of
several GeV/m. In this design, A77 is quite large (340 jum) so that the density scale
length Ls needs to be less than 340 jum for efficient trapping. In order to have such
a short density transition, several different approaches are tried now at KERI. If high
energy electron beams are produced from the plasma, beam parameters, such as energy,
charge, emittance, size, etc., will be diagnosed by several tools.
714
Ti:Sapphire Regenerative Amplifier
& Puke Stretcher
FIGURE 5. Layout for the Ti:sapphire/Nd:glass hybrid laser system
CONCLUSIONS
Two-dimensional PIC simulations showed that a significant amount of relativistic high
energy electron beams could be generated when an intense laser pulse passes through
a sharp downward plasma density transition. The generated high-energy beams seem to
have fairly good quality in terms of energy spread and transverse emittance. Hence,
the laser-based self-injection method may be a good candidate for a compact highenergy electron accelerator in the future. Although there are some challenging technical
questions, we believe that they are solvable. Hence, the self-injection scheme will be
eventually verified experimentally with a T3 laser system at KERI and the experimental
result will be reported later.
ACKNOWLEDGMENTS
One of the authors (H. S.) would like to thank Prof. J.B. Rosenzweig at UCLA and Dr.
E. Esarey at LBNL for useful discussions on some issues.
715
REFERENCES
1. H. Suk, N. Barov, J.B. Rosenzweig, andE. Esarey, Phys. Rev. Lett. 86,1011 (2001).
2. T. Tajima and J. M. Dawson, Phys. Rev. Lett. 43,267 (1979).
3. E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE Trans. Plasma Sci. 24,252 (1996).
4. D. Umstadter, Phys. Plasmas 8,1774 (2001).
5. D. Umstadter, J. Kirn, E. Dodd, Phys. Rev. Lett. 76,2073 (1996).
6. E. Esarey et al., phys. Rev. Lett. 79 (1997) 2682; E. Esarey et al., Phys. Plasmas 6, 2262 (1999).
7. S. Bulanov, N. Naumova, F. Pegoraro, and J. Sakai, Phys. Rev. E 58, R5257 (1998).
8. K. Nakajima et al., Phys. Rev. Lett. 74,4428 (1995).
9. C. Joshi, T. Tajima, J.M. Dawson, H.A. Baldis, andN.A. Ebrahim, Phys. Rev. Lett. 47, 1285 (1981).
10. R. G. Hemker, K. C. Tzeng, W. B. Mori, C. E. Clayton, and T. Katsouleas, Phys. Rev. E 57, 5920
(1998).
11. P. Chen, Part. Accel. 20,171 (1985).
716