A Review Study on Amplification of X-Ray Free Electron Laser Pulse in Plasma

doi:10.4236/jmp.2012.312250

Paper Menu >>

Journal Menu >>

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

Email: [email protected]

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.

15 2

26 2

10 W/cm

17 2

W/cm

10 -

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

4π

eee



e

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

0 asec

0.5nm



can

be accessed only at NIF facility and there is no plan to

merge the NIF facility with LCLS to practise the ampli-

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

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

[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





 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

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,















1123

,icAA

 (1)

2 2















2 213

,icAA



 (2)















where

3312

,icAA



 (3)

iiei

eE mc



 is the electric field amplitude,

pump (i = 1

E of th) and the seed (i = 2) pulse nor-

lized by

ma ei

mce



, e

m is the electron mass, i



the pulse freqc the speed of light, i

v ithe

group velocity of the ght (plasmon) scaled by, i

uency, iss

li c



the inverse bremsstrahlung rate, 22

ipei



, an i

is the wave number of the pulse

s; 3ee

nen is th

Langmuir wave amplitude, 3



is the pcay rate,

and



lasmon de

2ccq



, where 2

34π

eee



 and

q is ave numerva-

tion in BRA reads 12

the Langmuir wber. The energy cons





 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-

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



in the range of

14 - 20 and the normalised laser f



ield



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

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

regime.







cm



Wcm

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.

REFERENCES

[1] W. Ackerman Free-Electron La-n, et al., “Operation of a

ser from the Extreme Ultraviolet to the Water Window,”

Natur e Photonics, Vol. 1, No. 6, 2007, pp. 336-342.

doi:10.1038/nphoton.2007.76

[2] P. Emma, et al., “First Lasing and Operation of an Ang-

strom-Wavelength Free-Electron Laser,” Nature Photon-

ics, Vol. 4, No. 9, 2010, pp. 641-647.

doi:10.1038/nphoton.2010.176

[3] T. Ishikawa, et al., “A Compact X-Ray F

Emitting in the Sub-Ångström R

ree-Electron Laser

egion,” Nature Photonics,

Vol. 6, No. 11, 2012, pp. 540-544.

doi:10.1038/nphoton.2012.141

[4] L. Young, et al., “Femtosecond E

Atoms to Ultra-Intense X-Rays

11018

110

lectronic Response of

,” Nature, Vol. 466, No.

7302, 2010, pp. 56-61. doi:10.1038/nature09177

[5] G. Doumy, et al., “Nonlinear Atomic Response to Intense

11020

110

11022

110

11024

110

0.1

0.01 Ultrashort X-Rays,” Physical Review Letters, Vol. 106, No.

8, 2011, Article ID: 083002.

A. SHARMA

2002

doi:10.1103/PhysRevLett.106.083002

[6] M. Hoener, et al., “Ultraintense X-Ra

tion, Dissociation, and Frustrated Abso

y Induced Ioniza-

rption in Molecu-

lar Nitrogen,” Physical Review Letters, Vol. 104, No. 25,

2010, Article ID: 253002.

doi:10.1103/PhysRevLett.104.253002

[7] J. P. Cryan, et al., “Auger Electron Angular Distribution

of Double Core-Hole States in the Mo

lecular Reference

Frame,” Physical Review Letters, Vol. 105, No. 8, 2010,

Article ID: 083004.

doi:10.1103/PhysRevLett.105.083004

[8] L. Fang, et al., “Double Core-Hole Productio

Beating the Auger Clock,” Physical Ren in N2

view Letters, Vol.

105, No. 8, 2010, Article ID: 083005.

doi:10.1103/PhysRevLett.105.083005

[9] S. M. Vinko, et al., “Creation and Di

Density Plasma with an X-Ray Free-El

agnosis of a Solid-

ectron Laser,” Na-

ture, Vol. 482, No. 7383, 2012, pp. 59-62.

doi:10.1038/nature10746

[10] Reiche, et al., “Start-to-End Simulation

X-Ray FEL,” Nuclear Insfor the LCLS

truments and Methods A, Vol.

483, No. 1, 2002, pp. 70-74.

doi:10.1016/S0168-9002(02)00288-7

[11] P. Emma, et al., “Femtosecond and

Ray Pulses from a Self-Amplified Spo

Subfemtosecond X-

ntaneous-Emission

Based Free-Electron Laser,” Physical Review Letters, Vol.

92, No. 7, 2004, Article ID: 074801.

doi:10.1103/PhysRevLett.92.074801

[12] E. L. Saldin, et al., “Scheme for Attop

at a X-Ray SASE FEL,” Optics and Cohysics Experiments

mmunications

, Vol.

212, No. 4, 2002, pp. 377-390.

doi:10.1016/S0030-4018(02)02008-4

[13] A. Jarre, et al., “Two-Dimensional Hard X-Ray

Compression by Combined Focusing a

Beam

nd Waveguide Op-

Lenses,” Applied Physics Letters

tics,” Physical Review Letters, Vol. 94, No. 7, 2005, Arti-

cle ID: 074801.

[14] C. G. Schroer, et al., “Hard X-Ray Nanoprobe Based on

Refractive X-Ray, Vol.

87, No. 12, 2005, Article ID: 124103.

doi:10.1063/1.2053350

[15] W. Liu, et al., “Short Focal Length

Mirrors for a Hard X-R

Kirkpatrick-Baez

ay Nanoprobe,” Review of Scien-

tific Instruments, Vol. 76, No. 11, 2005, Article ID: 113701.

doi:10.1063/1.2125730

[16] C. Bergemann, et al., “Focusing X-Ray Beams to Nano-

meter Dimensions,” Physical Review Letters, Vol. 91, No.

20, 2003, Article ID: 204801.

doi:10.1103/PhysRevLett.91.204801

[17] C. G. Schroer, et al., “Focusing Har

meter Dimensions by Adiabatically F

d X Rays to Nano-

ocusing Lenses,”

Physical Review Letters, Vol. 94, No. 5, 2005, Article ID:

054802. doi:10.1103/PhysRevLett.94.054802

[18] V. M. Malkin, et al., “Compression of Powerful X-Ray

Pulses to Attosecond Durations by Stimulated Raman

Backscattering in Plasmas,” Physical Review E, Vol. 75,

No. 2, 2007, Article ID: 026404.

doi:10.1103/PhysRevE.75.026404

[19] P. J. Mardahl, et al., “Intense La

Using Raman Backscatter in Plasm

ser Pulse Amplific

a Channels,” Physics

ation

Letters A, Vol. 296, No. 2, 2002, pp. 109-116.

doi:10.1016/S0375-9601(02)00194-9

[20] D. S. Clark and N. J. Fisch, “Particle-in-Cell S

of Raman Laser Amplification in Pr

imulations

eformed Plasmas,”

Physics of Plasmas, Vol. 10, No. 12, 2003, pp. 4848-4855.

doi:10.1063/1.1625940

[21] D. S. Clark and N. J. Fisch, “Raman Laser Amplification

in Preformed and Ionizing Plasmas,” Laser and Particle

Beams, Vol. 23, No. 1, 2005, pp. 101-106.

doi:10.1017/S0263034605050172

[22] R. M. G. M. Trines, et al., “Simulations o

man Amplification into the Multip

f Efficient Ra-

etawatt Regime,” Na-

ture Physics, Vol. 7, No. 1, 2011, pp. 87-92.

doi:10.1038/nphys1793

[23] W. Cheng, et al., “Reaching the Nonlinear

Raman Amplification of

Regime of

Ultrashort Laser Pulses,” Physi-

cal Re vie w Le tter s, Vol. 94, No. 4, 2005, Article ID: 045003.

doi:10.1103/PhysRevLett.94.045003

[24] J. Ren, et al., “A Compact Double-Pass Raman Back-

scattering Amplifier/Compressor,” Physics of Plasmas,

Vol. 15, No. 5, 2008, Article ID: 056702.

doi:10.1063/1.2844352

[25] D. Strickland and G. Mourou, “Compres

fied Chirped Optical P

sion of Ampli-

ulses,” Optics and Communica-

tions, Vol. 56, No. 3, 1985, pp. 219-221.

doi:10.1016/0030-4018(85)90120-8

[26] N. J. Fisch and V. M. Malkin, “Generation

Intensity Laser Pulses,” Physics of P of Ultrahigh

lasmas, Vol. 10, No.

5, 2003, pp. 2056-2063. doi:10.1063/1.1567290

[27] J. R. Murray, et al., “Raman Pulse Compression of Exci-

mer Lasers for Application to Laser Fusion,” IEEE Jour-

nal of Quantum Electronics, Vol. 15, No. 5, 1979, pp.

342-368. doi:10.1109/JQE.1979.1070009

[28] C. J. McKinstrie and A. Simon, “Nonlinear Saturation of

the Absolute Stimulated Raman Scattering Instability in a

Finite Collisional Plasma,” Physics of Fluids, Vol. 29, No.

6, 1986, pp. 1959-1970. doi:10.1063/1.865623

[29] V. M. Malkin and N. J. Fisch, “Quasitransient Regimes of

Backward Raman Amplification of Intense X-Ray Pulses,”

Physical Review E, Vol. 80, No. 4, 2009, Article ID: 046409.

doi:10.1103/PhysRevE.80.046409

[30] V. M. Malkin and N. J. Fisch, “Quasitransient Backward

Raman Amplification of Powerful Laser Pulses in Dense

Plasmas with Multicharged Ions,” Physics of Plasmas,

Vol. 17, No. 7, 2010, Article ID: 073109.

doi:10.1063/1.3460347

[31] L. D. Landau and E. M. Lifshitz, “The Cl

of Fields,” 2nd Edition, Elsevi

asssical Theory

er, Oxford, 1975.

ion

[32] M. Tamburini, F. Pegoraro, A. Di Piazza, C. H. Keitel

and A. Macchi, “Radiation Reaction Effects on Radiat

Pressure Acceleration,” New Journal of Physics, Vol. 12,

No. 12, 2010, Article ID: 123005.

doi:10.1088/1367-2630/12/12/123005

[33] A. Zhidkov, J. Koga, A. Sasaki an

tion Damping Effects on the Interacti

d M. Uesaka, “Radia-

on of Ultraintense

Laser Pulses with an Overdense Plasma,” Physical Re-

view Letters, Vol. 88, No. 18, 2002, Article ID: 185002.

A. SHARMA

2003

doi:10.1103/PhysRevLett.88.185002

[34] N. H. Burnett and P. B. Corkum, “Cold-Plasma Produc-

tion for Recombination Extremeultraviolet Lasers by Op

tical-Field-Induced Ionization,” Journ -

al of Optical Soci-

ety of America B, Vol. 6, No. 6, 1989, pp. 1195-1199.

doi:10.1364/JOSAB.6.001195

[35] S. V. Kukhlevsky and L. Kozma, “Modal and Focusing

Properties of Plasma Based Waveguides for X-Ray Beams,”

Contributions to Plasma Physics, Vol. 38, No. 5, 1998,

pp. 583-597. doi:10.1002/ctpp.2150380503