Journal of Modern Physics, 2012, 3, 1998-2003
http://dx.doi.org/10.4236/jmp.2012.312250 Published Online December 2012 (http://www.SciRP.org/journal/jmp)
A Review Study on Amplification of X-Ray Free Electron
Laser Pulse in Plasma
Ashutosh Sharma
Department of Education, University of Lucknow, Lucknow, India
Received September 29, 2012; revised November 1, 2012; accepted November 9, 2012
ABSTRACT
In view of X-ray Free Electron Laser (XFEL) intensity prospects, we reviewed the past and recent work in view of am-
plification of powerful XFEL laser pulse to achieve intensity in the regime of high field science. We report here some of
the relevant work investigated in this field and predicted further scalings and possibilities for XFEL pulse amplification.
Keywords: X-Ray Free Electron Laser; Raman Amplification; Laser-Plasma Interaction
1. Introduction
The recent advent and active operation of X-ray free
electron lasers (FEL) enabled this machine to capture the
image of atoms and molecules in motion. These ma-
chines are routinely running experimental programme to
study the properties of condensed matter, nanosystem,
molecular and atomic processes, biological systems and
chemistry. The first soft x-ray FEL facility, FLASH at
DESY, has been in operation for users since 2005 [1].
The first hard x-ray FEL facility, the Linac Coherent
Light Source at SLAC [2], became operational in 2009.
More recently, the SACLA at SPring-8 [3] started its
user program beginning in 2012. A series of experiments
conducted at the Linac Coherent Light Source (LCLS) [2]
have shown how ultraintense and ultrashort X-rays in-
teract with various systems: light atom (Ne) [4,5], mole-
cule (N2) [6-8], and solid (Al) [9]. In this soft and hard
X-ray wavelength range FELs are the only source that
can produce coherent photons, with very high peak and
average power and brightness higher by any orders of
magnitude than for any other X-ray source and a number
of photons per coherent volume of the order of or
larger. There are high-field science applications of the
X-ray FEL, taking advantage of not only the high energy
and coherency of photons, but also their extreme high
fields, which interact with matter in unique way. If the
amplification of XFEL laser pulse can be practised; there
will be great exposure of these intense X-rays to explore
the issues of fundamental physics. In the spectral regime
of optical wavelength high field science regime begins to
occur at intensities of , where some
new atomic physics phenomena have been observed. At
relativistic intensity , relativistic effects fully
enter into dynamics. The frequency of the XFEL pulse is
four orders of magnitude higher than that of an optical
laser, the corresponding intensities would be 1022 - 1023
W/cm2 and , respectively. However the an-
ticipated intensity at LCLS, is 10 which is
much less than the relativistic intensity at X-ray wave-
length.
9
10
15 2
10
2
m
26 2
10 W/cm
17 2
W/cm
14
10 -
18
10 W/c
W/cm
In view of XFEL intensity prospects as mentioned
above, we reviewed the past and recent work in view of
amplification of powerful XFEL laser pulse to achieve
intensity in the regime of high field science. We report
here some of the relevant work investigated in this field
and predicted further scalings and possibilities.
Several schemes [10-12] are proposed for significant
reduction of duration of powerful X-ray pulses to 0.3 - 1
fs. Available optical techniques [13-15] are capable of
X-ray focusing to sub 50 - 100 nm spot size. There are
proposals [16,17] on focusing of X-rays to few nm spot
size. However these focusing techniques can withstand
only low intensity X-ray pulse and might not directly
applicable to powerful LCLS X-ray pulse for which fo-
cusing appears to be more challenging. By means of
backward Raman amplification [18] in plasmas one may
compress the X-ray pulse to electron plasma wave period




02πe
t where

12
2
4π
eee
nm  e n
3
cm
and is
electron density in plasma. For electron density = 1026

, 010asect

. Longitudinal compression of 2 mJ
X-ray pulse to 1 would produce the power 200
TW. The intensity of such X-ray pulse focused to spot
diameter of would be of the order 1028 W/cm2.
Since the electron density of the order of 26 3 10
0 asec
0.5nm
cm

can
be accessed only at NIF facility and there is no plan to
merge the NIF facility with LCLS to practise the ampli-
C
opyright © 2012 SciRes. JMP

A. SHARMA 1999
fication of X-ray laser. Thats why it is not clear that the
BRA mechanism can be practised in the X-ray regime or
not. A simple scalings based on the BRA in optical re-
gime is not sufficient to predict the efficient BRA in
X-regime because competing effects (inverse bremsstrah-
lung of the pump, collision and Landau damping of
plasma wave, plasma heating etc.) might narrow or close
the parameter window for efficient BRA operation. To
realize the Raman amplification of X-ray laser pulses,
requires the high plasma density (near to solid state den-
sity 26 3
10 cm). Fodensities below 19 3 10 cmr plasma

,
ioniz electron-ion collisions do not often occurs
during the pump-plasma interaction time to be of much
relevance. When we proceed to practice the Raman am-
plification of X-rays beam which needs plasma density
much higher than 19 3
10 cm then wt overlook
the effect of ionization and electron-ion collisions [18].
ation and
no
a
hd experiment
action process of
e can
rd Raman
9-22] an
ter
2. Overview on Backw
Amplification in Plasma
e review study of simulation [1T
la
[23,24] results has shown the possibility and potential to
focus and compress the intense laser pulses (optical and
X-ray regime) through Backward Raman amplification
(BRA) in plasmas. We report here the review study of
these results and similar scalings for efficient BRA to
compress and amplify the intense X-ray pulse. Before
explaining the review work we outline first the BRA
process in plasmas. BRA is based on the fact that a
plasma can withstand very high energy densities due to
its ionized nature. This has motivated research to realize
a plasma amplifier to further boost the power of an ex-
isting CPA system [25] or as an alternative technique that
will replace CPA itself [26]. The idea of the Raman ef-
fect in various media to amplify laser pulses extends
back to work carried out 40 years ago when researchers
used gases and liquids to amplify excimer laser pulses for
the purpose of laser-based nuclear fusion [27]. The idea
of using plasmas for this same purpose is however more
recent. Proof-of-principle experiments demonstrating BRA
in a plasma have been reported by several groups over
the last 10 years. These studies have focused primarily
on the amplification of ultrashort Ti:Sapphire laser pulses
with the goal of creating ultrahigh peak intensities by
significantly increasing the amount of energy contained
in a single femtosecond-scale pulse.
BRA in plasmas is a three wave in
ser light with a plasma of density lower than one quar-
ter of the critical density. Here critical density is that
density where the plasma frequency equals the laser fre-
quency. The three waves in BRA consist of a long low
intensity pump laser pulse, a short low intensity seed
laser pulse that is to be amplified, and an electron plasma
wave that is excited by the beating of the two laser pulses.
The pump and seed are both electromagnetic waves
while the electron plasma wave, or Langmuir wave, is an
electrostatic wave. The stimulating Raman scattering
(SRS) process is somewhat different from the BRA
process. The SRS instability occurs when a light wave
with a frequency 0

and wave vector 0 k enters a
plasma and Thomson scatters from noise density fluctua-
tions via a resonant interaction that picks a specific 1

and 1
k for the scattered light to conserve energy and
momtum at frequency 201 en

  and wave vector
201
kkk

. The scatterern beats with the
ht to create a ponderomotive force propor-
tional to the gradient of the product of their individual
amplitudes. This force will then reinforce the density
noise resulting in even larger perturbations inside the
plasma which become a plasma wave with 2
d light in tu
incident lig

and 2 k.
The plasma wave behaves like a density gring whh
causes further collective scattering of the incident light as
the instability cycle continues. The cycle is maintained as
long as phase-matching and conservation of total wave
action are satisfied. BRA relies upon the backward SRS
instability to amplify the short seed laser pulse. In this
direct backscatter geometry the pump laser is collided
with a counter-propagating injected short seed laser in-
side the plasma. The seed laser frequency is downshifted
from the pump laser frequency by the plasma frequency
in order to achieve the resonance that would have auto-
matically occurred in backward SRS from the plasma
noise. Because the injected seed laser in BRA is stronger
than the initially Thomson scattered light from backward
SRS, the ponderomotive force and the driven plasma
wave amplitude in BRA are larger which can induce a
greater amount of energy transfer from the pump to the
seed mediated by the plasma wave. The seed can cause
pump depletion, suppressing the SRS instability. The
slow moving plasma wave has a phase velocity in the
same direction as the pump, but its group velocity moves
with the short laser pulse being amplified. Since this
process is based on the backward SRS instability, the
seed gets amplified until the pump begins to be depleted.
As mentioned above, the attraction of this idea is due
at ic
to the fact that a plasma is capable of withstanding laser
pulses of very high intensities that normally would de-
stroy solid state optics such as diffraction gratings used
in a CPA system. However a plasma exhibits an abun-
dance of other complex nonlinear behavior not found in
ordinary media. For instance, a plasma is highly suscep-
tible to additional transverse and longitudinal instabilities
in the presence of a high intensity laser beam. The trans-
verse instabilities can adversely affect the laser spot
quality and the longitudinal instabilities can cause the
pulse shape to break apart. Both types of instabilities can
play a role in reducing the efficiency of the energy trans-

A. SHARMA 2000
fer process. Therefore the physical restrictions on energy
transfer efficiency may place limitations on the amount
of seed amplification and the final intensity the seed
pulse can reach.
BRA in plasma is a three wave interaction process and
can be numerically modeled by fluid model [28]. The
interactions among the pump pulse, seed pulse and Lang-
muir wave are modeled through the Maxwell equations
and the electrom momentum and continuity equations.
The three wave interaction in plasma can be expressed
as,
11
vA
tx







1123
,icAA  (1)
2 2
vA
tx







2 213
,icAA

 (2)
33
vA
tx







where
3312
,icAA

 (3)
iiei
A
eE mc

 is the electric field amplitude,
pump (i = 1
i
E of th) and the seed (i = 2) pulse nor-
lized by
e
ma ei
mce

, e m is the electron mass, i

is
the pulse freqc the speed of light, i
v ithe
group velocity of the ght (plasmon) scaled by, i
uency, iss
li c

is
the inverse bremsstrahlung rate, 22
ipei
c

 , an i k
is the wave number of the pulse
d
s; 3ee
A
nen is th
Langmuir wave amplitude, 3

is the pcay rate,
and

lasmon de
2
33
2ccq

, where 2
34π
p
eee
nm   and
q is ave numerva-
tion in BRA reads 12
the Langmuir wber. The energy cons
p
e

  and the momentum
conservation reads q12 k k.
3. Recent Work and Scalings on BRA
the ap-Past work on BRA in optical regime has shown
plicability of this novel process in future laser system as
a plasma amplifier and compressor. The findings of BRA
in optical regime has motivated the several group to im-
plement the BRA process in X-ray regime. We focus
here on reviewing the results based on focusing and
compression of intense X-ray laser pulse in plasmas via
the BRA process. Compression of powerful X-ray pulses
to attosecond durations by stimulating Raman backscat-
tering in plasmas has been reported by Malkin et al. [18].
They estimated the theoretical short wavelength limit for
intense X-ray pulse compression and focusing through
BRA in plasma medium. They reported the 1 nm shortest
wavelength mJ X-ray pulse that can be compressed and
focussed to intensities sufficient for vacuum breakdwon
intensity 29 2
10Wcm. To attain these high intensites,
however onlinear suppression of Landay
damping of the Langmuir waves mediating the energy
transfer from the pump to the seed pulse. Malkin and
Fisch [29] further classified the quasitransient regime of
backward Raman amplification of intense X-ray laser
pulses. Quasitransient regime are of the most critical
importance for X-rays BRA because the X-ray BRA
needs plasma densites as large as those of condensed
matter in order to provide enough coupling between the
pump and seed laser pulse. High density plasma causes
strong damping of the Langmur wave that mediatee en-
ergy transfer from pump to seed pulse. Such strong
damping could reduce the coupling efficiency and BRA
will be hard to detect. Since the assumption that the lin-
ear BRA is transient (i.e. that the Langmuir wave damp-
ing can be neglected within the pumped pulse duration)
could be justified only for a small enough Langmuir
wave damping, while the stronger damping would make
BRA harder to observe. In summary the efficient QBRA
is capable of tolerating the mediating Langmuir wave
damping exceeding the linear Raman growth rate up to
20 times for strong seed pulse, and up to 10 times for
moderate seed pulses. Malkin and Fisch [30] investigated
further the plasma parametric regime, where the efficient
QBRA of powerful X-ray laser pulse is possible in dense
plasma with multicharged ions. Their theoretical calcula-
tion is applicable to infrared, ultraviolet, soft X-ray and
X-ray laser pulse. They demonstrated the electron tem-
perature-concentration regime for effecient QBRA of X-
ray at 10 nm
needs the n


and 1 nm. At this wavelength regime
the reqtron plasma concentration needed are
comparable to the compressed condensed matter. In this
wavelength regime, the large ion charge can no longer be
tolerated.
The work
uired elec
by R. Trines et al. [22] at Rutherford Ap-
pl
g laser
produce
eton Laboratory identified the parametric regime for
the BRA in which a 4 TW, 700 μm full-width at half-
maximum (FWHM), 25 ps lonwith 800 nm wave-
length can be amplified to 2 PW peak intensity with 35
efficiency. In addition they shown that the same process
can be scaled appropriately to compress a 250 fs long,
0.2 μm wide soft X-ray pulse (10 nm wavelength),as
d by facilities like FLASH or LCLS, to subfem-
tosecond duration and 500 TW peak power, that is,
21 2
10Wcm. They argued that seed pulses having very
izes may be affected by various transverse
effects such as self-focusing and filamentation. They
emphasized the importance of finding the right combina-
tion of plasma density, pump intensity, and propagation
distance for the purpose of maintaining the focusability
of the wide seed and keeping a very low level of fila-
mentation so high peak intensities can be reached. The
optimal regime for efficient Raman amplification (as
shown by Trines et al.) is estimated by incorporating the
effect of the plasma density and the pump intensity on
energy-transfer efficiency (determined by the pump Ra-
man backscattering growth rate) and instabilities (deter-
mined by the growth rates of pump Raman forward scat-
small spot s

A. SHARMA 2001
terin and probe filamentation).
We followed the optimal reg
influ of electromagnetic field emitted by each elec-
ime for efficient BRA as
obtained by Trines et al. [22] to realize the BRA in X-ray
regime while keeping the ratio 0
p


in the range of
14 - 20 and the normalised laser f

ield

92
0.85 10W/cmμmaI 

 in th
0e range of 0.01
- 0.03. We have shown below the w
parameters (i.e. laser intensity and
pl
pump FW
ractise the BRA in X-regime we also need to mod-
ify
able 1. Summary of parameters for efficient BRA in X-ray
Electron density Pump FWHM intensity
indow of plasma den-
sity and pump laser intensity corresponding to pump la-
ser wavelngth. We may expect the efficient BRA in
X-ray regime for the given optimal value of laser-plasma
parameters and can be tested via the PIC simulation but
needs high accuracy on account of time and efficinet
computing facility.
Scanning of the
asma density as mentioned in Table 1) reflects the fact
that amplification of 1 angstrom X-ray laser pulse needs
the plasma density 26 3 10 cm (available at NIF facility)
and corresponding HM intensity should be
order of 222
10 W/cm for efficient BRA. The parametric
regime needed for efficient BRA is still looking far away
for practical realization of XFEL pulse amplification.
Since the efficient operation of the process needs the
joint facility of NIF and LCLS. Hence due to unavail-
ability of practical tools, we may test the efficient BRA
X-regime via the simulation codes. However we need to
modify our existing Particle-In-Cell (PIC) simulation
codes to test BRA in x-regime where we expect to have
very high plasma density and very intense pump FWHM
field. Since most of PIC codes are considering the colli-
sionless plasma but in high density plasma, we can not
ignore the role of electron-ion collisions and we need to
implement the collisional process (including absorption
of laser energy and Landau damping [18]) in simulation
code.
To p
PIC code at high laser intensity by modifying the ex-
act force experienced by the particles in plasma medium.
Since the laser-plasma interaction at extremely high laser
intensities, elctrons can become ultrarelativistic within a
fraction of wave period experiencing superstrong accel-
erations and therefore emitting relativily large amount of
electromagnetic radiation. Radiation Reaction (RR) is the
T
regime.

nm 

3
cm

2
Wcm
10
ence
tron on the motion of electron itself [31] and may be-
come essential under extreme conditions mentioned
above. Recently it is found [32] that at intensities ex-
ceeding 22 2
10 W/cm

the RR force strongly affects the
dynamics for a linearly polarized laser pulse. There is
need to test the BRA operation of X-ray laser pulse in
PIC simulations with RR effects included either using an
approach similar to the Landau-Lifshitz (LL) equation
[31] or using a different RR modeling [33].
4. Possibility of Focusing X-Ray Beam Using
Th a parabolic profile of the
Plasma Waveguide
e plasma channel having
electron density with a density minimum along the axis
acts as an optical waveguide. The optical guiding in
plasma may be of practical interest to focus [34] the
x-ray beams. Kukhlevsky and Kozma [35] investigated
the modal and focusing properties of the plasma based
waveguide having a parabolic profile of the electron
density. They pointed out that the focusing properties of
plasma waveguide structure depend on waveguide length
and wavelength. To focus the parallel soft X-ray beam


40 nm   in 1-cm-long plasma guide they calculated
the plasma density gradient 23 5 10 cm. However their
model to focus the x-ray beam is based on paraxial-
envelope equations that only considers the central portion
of the beam (portion of the beam near to axis), not the
whole beam. We may further extend this model con-
sidering the non-paraxial approach where one may include
the on axis and off axis portion of the beam in the model
calculations. The non-paraxial model of plasma wave-
guide may predict more accurate results in favor of X-ray
beam focusing through plasma wave-guide.
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