S194 CHINESE OPTICS LETTERS / Vol. 5, Supplement / May 31, 2007
Electron acceleration by a propagating laser pulse in
low-density plasma
Fengchao Wang (
þþþ
), Baifei Shen (
ÞÞÞ
ììì
), Xiaomei Zhang (
),
Xuemei Li (
), and Zhangying Jin (
)
State K ey Laboratory of High Field Laser Physics, Shanghai I nstitute of Optics and Fine Mechanics,
Chinese Academy of Sciences, Shanghai 201800
Electron acceleration by a propagating short ultra-intense laser pulse in a low-density plasma has been
investigated. Electrons have the maximum energy when meeting the peak of the laser pulse. If a propagat-
ing laser pulse is abruptly stopped by a solid target, the highly energetic electrons will continue to move
forward inertially and escape from the laser field. The envelope of the laser pulse is taken into account
and there is an optimal position between the electron and the solid target. The electron maximum energy
depends on the laser intensity and initial electron energy, and has nothing to do with the polarization
of the pulse, but a linearly polarized laser pulse is more effective to accelerate electron than circularly
polarized one under the same laser energy. The influence of the reflected light has been taken into account
which makes our model more perfect and the results give good agreement with particle in cell simulations.
OCIS co des: 140.7090, 350.5400, 350.5720, 260.2160.
Based on the chirped-pulse amplification technique, ul-
trahigh and ultrashort laser has been rapidly developed.
This has stimulated many new research areas about laser-
plasma interaction, such as laser-driven nuclear
[1]
,parti-
cle acceleration. Among these, laser acceleration of elec-
trons has received great attention in recent years
[2−7]
be-
cause of the large variety of applications of high energy
electrons, such as fast ignition of fusion reaction
[8,9]
,and
X-ray generation
[10−12]
.
Two prominent approaches to laser driven electron ac-
celeration are direct laser acceleration
[13,14]
and accel-
eration by laser driven plasma wave
[15,16]
.Thefor-
mer depends on self-generated strong azimuthal mag-
netic field, and the latter involves beat wave mechanism
and wake field mechanism. For sufficiently short and in-
tense laser pulse, direct electron acceleration in the pulse
dominates
[17]
. It is known that electrons can be more
efficiently accelerated by a propagating laser pulse than
by a standing wave. The electron energy, scaling as the
laser intensity I at the peak of the propagating pulse, can
be much higher than that (scaling as
√
I) from a stand-
ing wave pulse
[18]
. How to extract the energetic electrons
from the laser pulse is a very important issue. It is well
known that a planar-wave cannot be used for electron ac-
celeration, since the pondermotive force pushes an elec-
tron forward in the ascending front and pulls an electron
backward in the descending part of the laser pulse when a
wave overtakes the electron. So electrons have the maxi-
mum energy when they meet the peak of the laser pulse.
If the propagating laser pulse is abruptly stopped by a
solid target, the highly energetic electrons will continue
to move forward inertially and escape from the laser field
as well as the target without much energy loss if their
stopping distance is much larger than the laser skin depth
and the target thickness, respectively. Yu et al.
[19]
have
researched this proposed acceleration and extraction pro-
cesses by particle in cell (PIC) simulations, and given out
the electron maximum energy by using well-known ana-
lytic solution for relativistic electron motion in a plane
electromagnetic wave propagating in vacuum. An ana-
lytical model has been presented in Ref. [20], the author
adopted the constant amplitude laser pulse and discussed
the relationship of the maximum energy and the phase
of the laser wave.
In this paper, the envelope of laser pulse is taken into
account, so it is difficult to ascertain the optimal position
of the solid target where the electron gains the maximum
energy. This problem is solved very well in our model,
we adopt a Gaussian laser pulse and introduce the po-
sition of the target z
1
in the expression of the reflected
wave, so we can easily find the optimal position of the
target by changing z
1
. In this scheme a very low density
preplasma is produced at the front of the solid target
to supply electrons to be accelerated. It is known that
if the density of the preplasman is low relatively to the
critical density n
c
, n/n
c
< 0.02, the instability of plasma
can be neglected, and the light propagation as well as
theelectrondynamicsinthelow density preplasma are
approximated by that in a vacuum.
We consider the propagation of a laser pulse with vec-
tor potentials,
A = A
0
exp{−[t − (z − z
0
)/c]
2
/τ
2
}
×[ˆx cos(ωt − kz)+β ˆy sin(ωt − kz)], (1)
where A
0
is the maximum amplitude of laser pulse, z
0
is
the initial position of pulse peak, z
1
is the position of the
target, ω is the frequency of laser, k is wave vector, τ is
the pulse duration, c is the light velocity in vacuum, and
β =1andβ = 0 correspond to circularly and linearly
polarized laser pulse, respectively. Based on the ideal
conductor model, the reflected wave can be expressed as
A
= A
0
exp{−[t +[z − (2z
1
− z
0
)]/c]
2
/τ
2
}
×[−ˆx cos(ωt + k(z − 2z
1
))
−β ˆy sin(ωt + k(z − 2z
1
))]. (2)
The electromagnetic fields related to the vector poten-
tial of the laser pulse are
E = −
∂
A
∂t
and
B = ×
A. (3)
The equations governing electron momentum and energy
1671-7694/2007/S1S194-04
c
2007 Chinese Optics Letters
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