Nonresonant beat-wave excitation of relativistic plasma waves with constant phase velocity
for charged-particle acceleration
C. V. Filip,
1,
* R. Narang,
1
S. Ya. Tochitsky,
1
C. E. Clayton,
1
P. Musumeci,
2
R. B. Yoder,
2
K. A. Marsh,
1
J. B. Rosenzweig,
2
C. Pellegrini,
2
and C. Joshi
1
1
Neptune Laboratory, Department of Electrical Engineering, UCLA, 405 Hilgard Avenue, Los Angeles, California 90095, USA
2
Department of Physics, UCLA, 405 Hilgard Avenue, Los Angeles, California 90095, USA
Received 26 June 2003; published 17 February 2004
The nonresonant beat-wave excitation of relativistic plasma waves is studied in two-dimensional simulations
and experiments. It is shown through simulations that, as opposed to the resonant case, the accelerating electric
fields associated with the nonresonant plasmons are always in phase with the beat-pattern of the laser pulse.
The excitation of such nonresonant relativistic plasma waves is shown to be possible for plasma densities as
high as 14 times the resonant density. The density fluctuations and the fields associated with these waves have
significant magnitudes, facts confirmed experimentally using collinear Thomson scattering and electron injec-
tion, respectively. The applicability of these results towards eventual phase-locked acceleration of prebunched
and externally injected electrons is discussed.
DOI: 10.1103/PhysRevE.69.026404 PACS numbers: 52.35.Mw, 41.75.Jv, 52.70.Kz, 52.38.Kd
I. INTRODUCTION
Electron plasma waves that propagate with a phase veloc-
ity close to c have been proposed as high-gradient accelerat-
ing structures for charged particles 1. Such relativistic
plasma waves RPW’s have been excited using laser and
charged particle beams 2. An intense, two-frequency laser
pulse (
1
and
2
) propagating through a plasma can excite
such a RPW in, what is known as, a plasma beat-wave ac-
celerator PBWA3. The excitation process is most effi-
cient at the resonant density n
res
, when the beat frequency
=
1
-
2
, is equal to the plasma frequency
p
. Fur-
thermore, electrons have been externally injected in these
resonantly excited RPW’s and shown to gain energy 4,5.
However, in these experiments, no attempt was made to
phase lock the electrons with the RPW and consequently, the
accelerated electrons had a broad and continuous energy
spectrum.
For many applications of high-energy particles one needs
a nearly monoenergetic beam. To obtain monoenergetic ac-
celeration, the externally injected relativistic electrons are
tightly less a tenth of a plasma wavelength prebunched
with the same periodicity as the laser beat pattern that is also
used to excite the RPW’s 6,7. In the ideal case, it is then
possible to maintain the phase synchronism between the in-
jected electrons and the accelerating structure. Successful ac-
celeration of phase-locked electrons, in which the RPW has
typically a submillimeter wavelength, will depend on four
factors: ability to prebunch, ability to load the prebunched
electrons within the acceptance of the RPW structure, control
of the experimental time ( 100 fs) and space ( 50 m)
jitter, and control of the phase jitter introduced by the RPW
itself. This last factor can be a serious problem in resonant
excitation of RPW’s using the laser beat-wave technique.
Transverse and longitudinal plasma inhomogeneities, relativ-
istic saturation of the plasma wave near resonant densities,
small deviations from the exact resonance condition in an
otherwise uniform plasma, and fluctuations in the laser inten-
sity and rise time, can all dephase the beat wave driver and
therefore the prebunched electrons with respect to the RPW.
We have therefore explored a possible solution to this issue
in which the RPW is nonresonantly excited at plasma densi-
ties much greater than the resonant density n n
res
.
Conceptually, it is well known that a harmonic oscillator
driven far away from its resonance remains synchronous
with the driving force albeit with a smaller amplitude of
oscillation than that at resonance. Using two-dimensional
2D particle-in-cell PIC computer simulations we find
that, as opposed to the resonant case, the nonresonantly ex-
cited plasmons are similarly always in phase with the beat
pattern of the laser pulse. Although the normalized amplitude
of the oscillation is smaller, the longitudinal electric field of
such a wave can still be substantial if the plasma density is
much higher than the resonant density. Experimentally, we
have shown that such high accelerating fields can be excited
in plasmas with densities up to 14n
res
. We have diagnosed
these fields through collinear Thomson scattering of a probe
laser beam and by measuring the energy gained by externally
injected relativistic electrons. These results indicate that non-
resonantly excited RPW’s may be suitable for phase-locked
injection in the second generation PBWA experiments, where
the goal is to demonstrate a high-gradient monoenergetic
electron acceleration 2.
II. SIMULATIONS
A. Resonant excitation
The excitation process of a RPW when =
p
was in-
vestigated by Rosenbluth and Liu 8. They showed that the
amplitude of the plasma wave = n / n is limited to 1 by
an amplitude dependent phase shift, which saturates the
plasma wave. Here, n / n is the normalized density pertur-
*Author to whom correspondence should be addressed; electronic
address: cfilip@ucla.edu
PHYSICAL REVIEW E 69, 026404 2004
1063-651X/2004/692/0264048/$22.50 ©2004 The American Physical Society 69 026404-1