Laser plasma accelerators.pdf

Laser plasma acceleratorsV. Malka Citation: Phys. Plasmas 19, 055501 (2012); doi: 10.1063/1.3695389 View online: http://dx.doi.org/10.1063/1.3695389 View Table of Contents: http://pop.aip.org/resource/1/PHPAEN/v19/i5 Published by the American Institute of Physics. Related ArticlesStudy on the effects of ion motion on laser-induced plasma wakes Phys. Plasmas 19, 093101 (2012) Target normal sheath acceleration sheath fields for arbitrary electron energy distribution Phys. Plasmas 19, 083115 (2012) Highly efficient generation of ultraintense high-energy ion beams using laser-induced cavity pressureacceleration Appl. Phys. Lett. 101, 084102 (2012) Efficient proton beam generation from a foam-carbon foil target using an intense circularly polarized laser Phys. Plasmas 19, 083107 (2012) Enhancing extreme ultraviolet photons emission in laser produced plasmas for advanced lithography Phys. Plasmas 19, 083102 (2012) Additional information on Phys. PlasmasJournal Homepage: http://pop.aip.org/ Journal Information: http://pop.aip.org/about/about_the_journal Top downloads: http://pop.aip.org/features/most_downloaded Information for Authors: http://pop.aip.org/authors

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Laser plasma acceleratorsa)

V. Malkab)

Laboratoire d’Optique Appliquee, ENSTA-ParisTech, CNRS, Ecole Polytechnique,UMR 7639, 91761 Palaiseau, France

(Received 16 December 2011; accepted 1 March 2012; published online 5 April 2012)

This review article highlights the tremendous evolution of the research on laser plasma accelerators

which has, in record time, led to the production of high quality electron beams at the GeV level, using

compact laser systems. I will describe the path we followed to explore different injection schemes and

I will present the most significant breakthrough which allowed us to generate stable, high peak current

and high quality electron beams, with control of the charge, of the relative energy spread and of the

electron energy. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3695389]

I. INTRODUCTION

The discovery of supra conductivity at a 4 K temperature

in mercury cooled with liquid helium, made by Onnes in

1911, opened a very active field of research. After decades

of effort, researchers have been able to produce new super-

conductors working at “high” temperature. Even if there

remain open fundamental questions, mastering superconduc-

tivity has allowed the discovery of tremendous applications

in magnetic resonance imaging (MRI) for medicine, in trans-

portation (magnetic suspension trains), and in modern accel-

erators (superconducting cavities). In parallel, since the first

1.26 MeV Hg ion beam made by Lawrence, accelerators

have gained in efficiency and in performance. With a market

of more than 3 Billions dollars per year, accelerators are

used today in many fields such as cancer therapy, ion im-

plantation, electron cutting and melting, and non-destructive

inspection. The most energetic machines, that deliver parti-

cle beams with energies greater than 1 GeV, represent only

1% of the total number of accelerators. They were developed

for fundamental research, for example for producing intense

x- ray beams in the free electron laser scheme. Such a source

has many applications in the study of ultra fast phenomena,

for example, in biology to follow the DNA structure evolu-

tion or in material science to follow evolution of molecules

or of crystal structures. Higher energy accelerators are cru-

cial to answer important questions regarding the origins of

the universe, of the dark energy, of the number of space

dimension, etc. The largest available one, the Large Hadron

Collider, is expected, for instance, to reveal very soon the

properties of the Higgs boson.

Since the accelerating field in superconducting radio-

frequencies cavities is limited to about 100 MV/m, the length

of accelerators has to increase in order to achieve higher

energy gain. To overcome this gigantism issue, Dawson1,2

proposed to use a plasma, which, as a ionized medium, can

sustain extreme electric fields. The pioneer theoretical work

performed in 1979 by Tajima and Dawson3 showed how an

intense laser pulse can excite a wake of plasma oscillation

through the non linear ponderomotive force associated to the

laser pulse. In their proposed scheme, relativistic electrons

were injected externally and were accelerated through the

very high electric field sustained by relativistic plasma waves

driven by lasers. In this early article,3 the authors proposed

two schemes: the laser beat wave and the laser wakefield.

Several experiments have been performed in the beginning

of the 1990 s following their idea, and electrons injected at

the few MeV level have indeed been accelerated in a plasma

medium by electric fields in the GV/m range using either the

beat wave or the laser wakefield scheme. Before the advent

of short and intense laser pulses, relativistic plasma waves

were driven by the beatwave of two long laser pulses of a

few tens of ps (i.e., with duration much greater than the

plasma period). In this case, the plasma frequency, xp has to

satisfy exactly the matching condition, xp ¼ x1 � x2, with

x1;x2 the frequencies of the two laser pulses. The first ob-

servation of relativistic plasma waves was performed using

Thomson scattering technique by the group of Joshi at

UCLA.4 Acceleration of 2 MeV injected electrons up to

9 MeV (Ref. 5) and later on, up to 30 MeV (Ref. 6) were

demonstrated by the same group using a CO2 laser of about

10 lm wavelength. At LULI, 3 MeV electrons were acceler-

ated up to 3.7 MeV in beat wave experiments with Nd:glass

lasers of about 1 lm wavelengths by a longitudinal electric

field of 0.6 GV/m (Ref. 7). Similar works were also per-

formed in Japan at University of Osaka,8 in U.K. at Ruther-

ford Appleton Laboratory9 or in Canada at Chalk River

Laboratory.10 Few years later, plasma waves driven in the

laser wakefield regime at LULI by a few J, 300 fs laser pulse

were used to accelerate 3 MeV injected electrons up to

4.6 MeV.11 In all these experiments, because of the duration

of the injected electron which was much longer than the

plasma period and even longer than the life time of the

plasma, only a very small fraction of injected electrons were

accelerated and the output beam had a very poor quality with

a Maxwellian-like energy distribution. Optical observation

of radial plasma oscillation was carried out at LOA (Refs. 12

and 13) and in Austin14 with a time resolution that was much

less than the plasma period, by using time-frequency domain

spectroscopy. More recently, at CUOS, using the same tech-

nique but with chirped probe laser pulses, a complete visual-

ization of relativistic plasma wave was performed in a single

shot. These results revealed very interesting features such as

a)Paper XR1 1, Bull. Am. Phys. Soc. 56, 358 (2011).b)Invited speaker.

1070-664X/2012/19(5)/055501/11/$30.00 VC 2012 American Institute of Physics19, 055501-1

PHYSICS OF PLASMAS 19, 055501 (2012)

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the relativistic lengthening of the laser plasma wavelength15

visible in Fig. 1.

These first experiments demonstrated the acceleration of

externally injected electrons. With the development of more

powerful lasers, much higher electric fields were achieved,

giving the possibility to accelerate efficiently electrons from

the plasma itself to higher energies. A major breakthrough

was obtained in 1994 at Rutherford Appleton Laboratory,

where relativistic wave breaking limit was reached, with

measured electric field of a few hundreds of GV/m.16 In this

limit, the amplitude of the plasma wave is so large, that copi-

ous number of electrons are trapped and accelerated in the

laser direction, producing an energetic electron beam. The

corresponding mechanism is called the self modulated laser

wake field (SMLWF),17–19 an extension of the forward

Raman instability20,21 to relativistic intensities. In those

experiments, the electron beam had a Maxwellian-like distri-

bution as it is expected from random injection processes in

relativistic plasma waves. This regime was also reached in

other laboratory, including CUOS (Ref. 22) and NRL

(Ref. 23) in the United States. Because of the heating of the

plasma by these relatively “long” pulses, the wave breaking

occurred well before reaching the cold wave breaking limit.

The maximum amplitude of the plasma wave was measured

to be in the range 20%–60%,24 using a Thomson scattering

diagnostic. Energetic electron beams were produced with a

compact laser system working at 10 Hz at MPQ (Ref. 25) in

the direct laser acceleration scheme (DLA) and at LOA in

the SMLWF.26 At LOA, the increase of the electron peak

energy when decreasing the electron plasma density nicely

demonstrated that the dominant acceleration mechanism was

related to relativistic plasma waves. In 2002, another break-

through was obtained in the forced laser wakefield where

low divergent electron beams with energies up to 200 MeV

were obtained with the 1 J “salle jaune” laser at LOA.27 In

this highly non linear regime, the quality of the electron

beam was improved by reducing noticeably the interaction

between the laser beam and the electron beam.

To improve fairly the electron beam quality, electron

injection has to be reduced to a very small volume of the

phase space. In general, this means that injected electrons

must have a duration much shorter that the plasma period,

i.e., much less than 10 fs which is difficult to achieve today

with current accelerator technology. I will show in this

review article how this crucial problem has been solved by

exploring different schemes like the bubble regime, the den-

sity gradient injection technique, the space limited ionization

approach, and the colliding laser pulses scheme. The filrouge of this article is the physic of electron injection. Fol-

lowing this fil rouge, I will show that the control of electron

injection in a limited space and time region led us to produc-

ing stable and very high quality electron beam with some

level of control over the charge, the energy spread, and the

electron beam energy.

II. CONTROLLING THE INJECTION

Controlled injection is mandatory to produce high qual-

ity electron beam. It is particularly challenging, in laser

plasma accelerator, because the length of the injected bunch

has to be a fraction of the plasma wavelength, with typical

values in the [10–100 lm] range. In this case, electrons wit-

ness the same accelerating field, leading to the acceleration

of a monoenergetic and high quality bunch. Electrons can be

injected if they are located at the appropriate phase of the

wake and/or if they have sufficient initial kinetic energy. Dif-

ferent schemes have been demonstrated and allow to control

the phase of injected electrons.

A. Bubble regime

In 2002, using 3D particle in cell (PIC) simulations,

Pukhov and Meyer-Ter-Vehn revealed the existence of a very

promising acceleration regime, called the bubble regime,28

that leads to the production of a quasi-monoenergetic electron

beam. At lower laser intensity, such electron distributions can

also be obtained in the blow-out regime.29 In both regimes,

the focused laser energy is concentrated in a very small sphere

of radius shorter than the plasma wavelength. The associated

ponderomotive force expels radially electrons from the

plasma, forming a positively charged cavity behind the laser,

surrounded by a dense region of electrons. As the radially

expelled electrons flow along the cavity boundary and collide

at the bubble base, transverse wave breaking occurs30 provid-

ing a well localized region of injection in the cavity.

Since the injection is well localized, at the back of the

cavity, all the injected electrons have similar initial proper-

ties in the phase space. The trapping stops automatically

when the charge contained in the cavity compensates for the

ionic charge, leading to the generation of a quasi-

monoenergetic electron beam, as experimentally observed in

2004.31–33 The spectral width of the electron beam is also

reduced by the rotation in the phase-space.34 Compared to

other acceleration mechanisms, the fact that electrons are

trapped behind the laser, where they no more interact with

the laser field, contributes also to improve the quality of the

electron beam. The scheme of principle of the bubble/blow-

out regime is illustrated in Fig. 2.

Several laboratories have obtained quasi monoenergetic

electron beams in the bubble/blow-out regime: in France33

with a laser pulse shorter than the plasma period, but also

FIG. 1. The laser pulse, that propagates from left to right, drives a strong

wake with relativistic curved front. Reprinted with permission from Ref. 15.

055501-2 V. Malka Phys. Plasmas 19, 055501 (2012)

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with pulses slightly longer than the plasma period, in Eng-

land,31 in the United States,32 then in Japan,35 in Tawain,36

in Germany,37,38 and in Sweden.39 Electrons at the GeV

level were observed in this regime using in a uniform

plasma40,41 or in a plasma discharge, i.e., a plasma with a

parabolic density profile42 that allows the intense laser beam

to propagate over a longer distance of a few centimeters. In

all these experiments, the laser beam parameters did not fully

satisfy all the bubble/blowout regime criteria. Nevertheless

thanks to the self focusing and self shortening43 effects, the

non linear evolution of the laser pulse allowed such trans-

verse injection. Besides, some of these experiments were in

a regime between the forced laser wakefield and the bubble/

blowout regime. Figure 3 illustrates in a single experiment

the transition between the self modulated laser wakefield, the

forced laser wakefield, and the bubble/blowout regime. The

experiment was performed at Laboratoire d’Optique Appli-

quee with a 10 Hz, 30 TW Ti:sapphire laser system operating

at a wavelength of 0:82 lm.44 The laser pulse had a duration

of s ¼ 30 fs full width at half maximum (FWHM). It was

focused using a 1 m focal length off axis parabolic mirror,

onto a focal spot of 18 lm FWHM producing a laser intensity

of 3:2� 1018 W=cm2. The corresponding normalized vector

potential was a0 ¼ 1:3. At this intensity, the homogeneous he-

lium gas45,46 jet is fully ionized early in the interaction. Since

the electron density is relatively small, ionization induced

refraction did not play an important role. The focal position

with respect to the sharp gas jet gradient was measured and

varied in order to optimize the electron beam parameters.

The optimum position for the laser focus was found to be on

the edge of the plateau of the gas jet. At high electron plasma

densities, for densities greater than 2� 1019 cm�3, the elec-

tron beam had a Maxwellian like distribution with a corre-

sponding temperature that increased as plasma density

increased. In this range of density, the self modulated regime

is the dominant acceleration mechanism. At lower densities,

for densities comprised between 7:5� 1018 cm�3 and

2� 1019 cm�3, the forced laser wakefield regime dominates

and a plateau appears in the electron beam distribution. The

bubble/blowout regime appears only in the very low density

range, below 6� 1018 cm�3 with a quasi-monoenergetic elec-

tron distribution.

In all the experiments performed so far, the laser plasma

parameters were not sufficient to fully enter the bubble/

blowout regimes. Yet, with the increase of laser system

power, this regime will be reached, and significant improve-

ment of the reproducibility of the electron beam is expected.

Nevertheless, since self-injection occurs through transverse

wave breaking, it is hardly appropriate for a fine tuning and

control of the injected electron bunch.

B. Injection in a density gradient

One solution to control electron injection with current

laser technology was proposed by Bulanov et al.47 It

involves a downward density ramp with a density gradient

scale length Lgrad greater than the plasma wavelength kp.

Injection in a downward density ramp relies on the slowing

down of the plasma wave velocity at the density ramp. This

decrease of the plasma wave phase velocity lowers the

threshold for trapping plasma background electrons and

causes wave breaking of the wakefield in the density ramp.

This method can therefore trigger wave breaking in a local-

ized spatial region of the plasma. Geddes et al.48 showed the

injection and acceleration of high charge (> 300 pC) and sta-

ble quality beams of ’ 0:4 MeV in the downward density

ramp at the exit of a gas jet (Lgrad ’ 100 lm� kp). These

results, although very promising, have the disadvantage that

the low energy beam blows up very quickly out of the

plasma due to space charge effect. To circumvent this issue,

one should use a density gradient located early enough along

the laser pulse propagation so that electrons can be acceler-

ated to relativistic energies.49 This can be achieved by using,

for instance, a secondary laser pulse to generate a plasma

channel transversely to the main pulse propagation axis.50 In

this case, the electron beam energy could be tuned by chang-

ing the position of the density gradient. In this pioneering

experiment, the electron beam had a large divergence and a

Maxwellian energy distribution because of a too low laser

energy. However, 2D PIC simulations showed that this

FIG. 2. The laser pulse that propagates from left to right, expels electrons

on his path, forming a positively charged cavity. The radially expelled elec-

trons flow along the cavity boundary and collide at the bubble base, before

being accelerated behind the laser pulse.

FIG. 3. Electron beam distribution for different plasma densities showing the

transition from the self modulated laser wakefield and the forced laser wake-

field to the bubble/blow-out regime. From top to bottom, the plasma density

values are 6� 1018cm�3; 1� 1019cm�3; 2� 1019cm�3, and 5� 1019cm�3.

055501-3 V. Malka Phys. Plasmas 19, 055501 (2012)

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method can result in high quality quasi monoenergetic elec-

tron beams.51 At LOA, a density gradient across a laser cre-

ated plasma channel was used to stabilize the injection.52

The experiment was performed at an electron density close

to the resonant density for the laser wakefield (cs � kp) to

guaranty a post acceleration that deliver high quality electron

beams with narrow divergences (4 mrad) and quasi monoe-

nergetic electron distributions with 50 to 100 pC charge and

10% relative energy spread. The use of density gradients at

the edges of a plasma channel showed an improvement of

the beam quality and of the reproducibility with respect to

those produced in the bubble/blowout regime with the same

laser system and with similar laser parameters. However, the

electron energy distribution was still found to fluctuate from

shot to shot. The performances of the experiment could be

further improved and could potentially lead to more stable

and controllable high quality electron beams. In particular,

sharper gradients with Lgrad ’ kp coupled with a long plasma

can lead to better beam quality.53

For example, at LBNL as shown in Fig. 4, electrons at

30 MeV were produced in a density ramp and accelerated up

to 400 MeV in a second stage 4 cm parabolic plasma chan-

nel, formed with a plasma discharge.54 Here also, the density

gradient injection led to an improvement of the stability and

of the electron beam quality. The electron energy, diver-

gence, charge, and relative energy spread were found to be,

respectively, 400 MeV, 2 mrad, 10 pC, and 11%. It was

shown that steeper density transitions, with Lgrad � kp, can

also cause trapping.55 Such injection was successfully dem-

onstrated experimentally, using the shock-front created by a

knife-edge inserted in a gas jet.56,57 Figure 5 illustrates the

improvement of injection in a sharp density gradient, with a

characteristic length on the order of the plasma wavelength

and a peak electron density of about 5� 1019 cm�3. The

experiment was performed at Max-Planck-Institut fur Quan-

tenoptik using a multi-TW sub-10-fs laser system that deliv-

ers for this experiment pulses with 65 mJ energy on target

and a duration of 8 fs FWHM. The laser pulse was focused

down to a spot diameter of 12 lm FWHM into the gas target

yielding a peak intensity of 2:5� 1018W=cm2. The compari-

son between the self injection and density transition injection

shows a reduction of the relative energy spread and of the

charge of a about a factor of 2.

C. Injection with colliding laser pulses

In 2006, stable and tunable quasimonoenergetic electron

beams were measured by using two counterpropagating laser

beams in the colliding scheme. The use of two laser beams

instead of one offers more flexibility and enables one to sep-

arate the injection from the acceleration process.58 The first

laser pulse, the pump pulse, is used to excite the wakefield

while the second pulse, the injection pulse, is used to heat

electrons during its collision with the pump pulse. After the

collision has occurred, electrons are trapped and further

accelerated in the wakefield, as shown in Fig. 6.

To trap electrons in a regime where self-trapping does

not occur, one has either to inject electrons with energies

greater that the trapping energy or dephase electrons with

FIG. 4. Top: The target schematic representation with embedded supersonic

gas jet into a capillary that is filled with hydrogen gas, Bottom: the charge

(squares), energy (circles), and energy spread (triangles) as a function of the

peak jet density. Reprinted with permission from Ref. 54.

FIG. 5. A few shots representative for those 10% of all the shots with lowest

energy spread for self-injection (top) and injection at a density transition

(bottom). The horizontal axis in each image corresponds to the transverse

electron beam size; the vertical axis shows electron energy. Reprinted with

permission from Schmid et al., Phys. Rev. ST Accel. Beams 13, 091301

(2010). Copyright VC 2010 by the American Physical Society.

055501-4 V. Malka Phys. Plasmas 19, 055501 (2012)

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respect to the plasma wave. As mentioned earlier, electrons

need to be injected in a very short time (< kp=c) in order to

produce a monoenergetic beam. This can be achieved using

additional ultrashort laser pulses whose only purpose is to trig-

ger electron injection. Umstadter et al.22 first proposed to use

a second laser pulse propagating perpendicular to the pump

laser pulse. The idea was to use the radial ponderomotive kick

of the second pulse to inject electrons. Esarey et al.59 pro-

posed a counter-propagating geometry based on the use of

three laser pulses. This idea was further developed by consid-

ering the use of two laser pulses.60 In this scheme, a main

pulse (pump pulse) creates a high amplitude plasma wave and

collides with a secondary pulse of lower intensity. The inter-

ference of the two beams creates a beatwave pattern, with a

zero phase velocity, that heats some electrons from the plasma

background. The force associated with this ponderomotive

beatwave is proportional to the laser frequency. It is therefore

many times greater than the ponderomotive force associated

with the pump laser that is inversely proportional to the pulse

duration at resonance. As a result, the mechanism is still effi-

cient even for modest laser intensities. Upon interacting with

this field pattern, some background electrons gain enough mo-

mentum to be trapped in the main plasma wave and then

accelerated to high energies. As the overlapping of the lasers

is short in time, the electrons are injected in a very short dis-

tance and can be accelerated to an almost monoenergetic

beam. This concept was validated in an experiment,58 using

two counter-propagating pulses. Each pulse had a duration of

30 fs FWHM, with a0 ¼ 1:3 and a1 ¼ 0:4. They were propa-

gated in a plasma with electron density ne ¼ 7� 1018cm�3

corresponding to cp ¼ k0=kp ¼ 15. It was shown that the col-

lision of the two lasers could lead to the generation of stable

quasi-monoenergetic electron beams. The beam energy could

be tuned by changing the collision position in the plasma as

shown in Fig. 7.65

PIC simulations in 1D have been used to model electron

injection in the plasma wave at the collision of the two lasers

and their subsequent acceleration. In particular, the PIC sim-

ulations were compared to existing fluid models59 with pre-

scribed electric field. They showed significant differences,

such as changes in the behavior of plasma fields and in the

amount of injected charge. The fluid approach fails to

describe qualitatively and quantitatively many of the physi-

cal mechanisms that occur during and after the laser beams

collision.61 In this approach, the electron beam charge was

found to be one order of magnitude greater than in PIC simu-

lations. For a correct description of injection, one has to

describe properly (i) the heating process, e.g., kinetic effects

and their consequences on the dynamics of the plasma wave

during the beating of the two laser pulses and (ii) the laser

pulse evolution which governs the dynamics of the relativis-

tic plasma waves.62 Unexpectedly, it was shown that effi-

cient stochastic heating can be achieved when the two laser

pulses are crossed polarized. The stochastic heating can be

explained by the fact that for high laser intensities, the elec-

tron motion becomes relativistic which introduces a longitu-

dinal component through the v� B force. This relativistic

coupling makes it possible to heat electrons even in the case

of crossed polarized laser pulses.63 Thus, the two perpendic-

ular laser fields couple through the relativistic longitudinal

motion of electrons. The heating level is modified by tuning

the intensity of the injection laser beam or by changing the

relative polarization of the two laser pulses.64 This conse-

quently changes the volume in the phase space of the

injected electrons and therefore the charge and the energy

spread of the electron beam. Figure 8 shows at a given time

(42 fs) the longitudinal electric field, during and after colli-

sion for parallel and crossed polarization. The solid line cor-

responds to PIC simulation results, whereas the dotted line

corresponds to fluid calculations. The laser fields are repre-

sented by the thin dotted line. When the pulses have the

same polarization, electrons are trapped spatially in the beat-

wave and cannot sustain the collective plasma oscillation,

inducing a strong inhibition of the plasma wave which per-

sists after the collision. When the polarizations are crossed,

the electron motion is only slightly disturbed compared to

their fluid motion, and the plasma wave is almost unaffected

during the collision, which tends to facilitate trapping.

Importantly, it was shown that the colliding pulse

approach allows to control the electron beam energy which

is done simply by changing the delay between the two laser

pulses.58 The robustness of this scheme permitted also to

carry out very accurate studies of the dynamics of the

FIG. 6. Scheme of principle of the injection with colliding laser pulses: (a)

the two laser pulses propagate in opposite direction, (b) during the collision,

some electrons get enough longitudinal momentum to be trapped by the rela-

tivistic plasma wave driven by the pump beam, and (c) trapped electrons are

then accelerated in the wake of the pump laser pulse.

055501-5 V. Malka Phys. Plasmas 19, 055501 (2012)

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electric field in the presence of a high current electron beam.

Indeed, in addition to the wakefield produced by the laser

pulse, a high current electron beam can also drive its own

wakefield as shown in Fig. 9.

This beam loading effect was used to reduce the relative

energy spread of the electron beam. It was demonstrated that

there is an optimal load which flattened the electric field,

leading to the acceleration of all the electrons with the same

value of the field and producing consequently an electron

beam with a very small, 1%, relative energy spread.66

Thanks to the beam loading effect, the most energetic elec-

trons can be slightly slowed down and accelerated to the

same energy as the slowest one. In case of low charge beam,

this effect does not play any role and the energy spread

depends mainly on the heated volume. For very high current,

the load is too high and the most energetic electrons slow

down so much that they eventually get energies smaller than

the slowest electrons,66 increasing the relative energy spread.

The existence of an optimal load was observed experimen-

tally and supported by full 3D PIC simulations, and it corre-

sponds to a peak current in the 20–40 kA range. The

decelerating electric field due to the electron beam was

found to be in the GV/m/pC range.

FIG. 8. Longitudinal electric field computed at t¼ 43 fs in 1D PIC simula-

tion (solid red line), and in fluid simulations (dotted blue line). The trans-

verse electric field is also represented (thin dotted line). The laser pulse

duration is 30 fs FWHM, the wavelength is 0.8 lm, a0 ¼ 2, and a1 ¼ 0:4.

The laser pulses propagate in a plasma with electron density

ne ¼ 7� 1018cm�3. In (a), the case of parallel polarization and in (b) the

case of crossed polarization.

FIG. 9. Normalized longitudinal electric field (continuous line). (a) The laser

(dotted line) wakefield. (b) The electron bunch (dashed line) wakefield. (c)

Field resulting from the superposition of the laser and electron beam wake-

fields. The normalized vector potential is a0 ¼ 1, the laser pulse duration is 30

fs, ne ¼ 7� 1018 cm�3; nbeam ¼ 0:11� ne, the bunch duration is 10 fs and its

diameter is 4 lm. Reprinted with permission from Rechatin, Ph.D. thesis.

FIG. 7. (a) Evolution of the electron beam peak energy and its energy spread

as a function of the collision position zinj for two parallel polarized laser

beams. The electron beam peak energy is shown in red, and the energy spread

in blue. Each point is an average over 35 shots and the error bars correspond

to the standard deviation. The position zinj ¼ 0 corresponds to injection at the

middle of the gas jet, whereas zinj ¼ 500 lm corresponds to early injection

close to the entrance of the gas jet. Reprinted with permission from Ref. 58.

(b) Evolution of charge (red solid line with squares), DE at FWHM (blue dot-

ted line with circles) with the angle between the polarizations of injection and

pump lasers (0�, parallel polarizations; 90�, crossed polarizations). Parameters

are a0 ¼ 1:5; a1 ¼ 0:4, 3 mm gas jet, ne ¼ 5:7� 1018cm�3; zcoll ¼ �450 lm.

(c) Deconvolved spectra with a high resolution spectrometer

measurement. Physical parameters: a0 ¼ 1:2; a1 ¼ 0:35, 3 mm gas jet,

ne ¼ 7:1� 1018cm�3; zcoll ¼ �300 lm. Reprinted with permission from

Rechatin et al., Phys. Rev. Lett. 102, 164801 (2009). Copyright VC 2009 by the

American Physical Society.

055501-6 V. Malka Phys. Plasmas 19, 055501 (2012)

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D. Injection triggered by ionization

Another scheme was proposed recently to control the

injection by using a high Z gas and/or a high Z-low Z gas

mixture. Thanks to the large differences in ionization poten-

tials between successive ionization states of the atoms, a sin-

gle laser pulse can ionize the low energy level electrons in

its leading edge, drive relativistic plasma waves, and inject

in the wakefield the inner level electrons which are ionized

when the laser intensity is close to its maximum. Such ioni-

zation trapping mechanism was first demonstrated in elec-

tron beam driven plasma wave experiments on the Stanford

linear collider (SLAC).67 Electron trapping from ionization

of high Z ions from capillary walls was also inferred in

experiments on laser wakefield acceleration.68 In the case of

self guided laser driven wakefield, a mixture of helium and

trace amounts of different gases was used.69,70 In one of

these experiments, electrons from the K shell of nitrogen

were tunnel ionized near the peak of the laser pulse and were

injected into and trapped by the wake created by electrons

from majority helium atoms and the L shell of nitrogen.

Because of the relativistic self focusing effect, the laser is

propagating over a long distance with peak intensity varia-

tions that can trigger the injection over a long distance and in

an inhomogeneous way which leads to the production of a

high relative energy spread electron beam. Importantly, the

energy required to trap electrons is reduced, making this

approach of great interest to produce electron beams with a

large charge at moderate laser energy. To reduce the distance

over which electrons are injected, experiments using two gas

cells were performed at LLNL (Ref. 71), as shown in

Fig. 10. By restricting electron injection to a small region, in

a first short cell filled with a gas mixture (the injector stage),

energetic electron beams (of the order of 100 MeV) with a

relatively large energy spread were generated. Some of these

electrons were then further accelerated in a second, larger ac-

celerator stage, consisting of a long cell filled with low-Z

gas, which increases their energy up to 0.5 GeV while reduc-

ing the relative energy spread to < 5% FWHM.

III. FUTURE OF THE LASER PLASMAACCELERATORS

The work achieved this last decade on the development

of laser plasma accelerator has been paved by many success-

ful (and unsuccessful) experiments. These pioneering works

and the outstanding results achieved recently have demon-

strated the huge potential of this acceleration scheme. Now,

the time has come where technological issues have to be

addressed in order to build a reliable machine that could oper-

ate in a robust way. To interpret the experimental results, to

predict beam parameters for designing experiments, or to

check new concepts or ideas, reliable simulations are manda-

tory. Depending on the required degree of accuracy, different

kind of codes can be employed. A full description of all the

physical processes taking part in the acceleration of energetic

electrons are very challenging and will required tremendous

computational resources. Faster codes, such as Wake72 or

QuickPIC (Ref. 73) codes are particularly useful for studying

very long propagation paths, for which full 3D PIC simula-

tions are out of reach. These codes do not resolve the laser fre-

quency, but use the quasistatic approximation, i.e., they

assume that the laser pulse does not change during the time a

plasma electron takes to pass the pulse. The main drawbacks

of these codes are that they cannot describe self-injection or

electron trapping in regions of significant laser field, and that

they fail when non linear effects (large spectral changes, pulse

distortion, self compression,74 etc.) break the quasi static

approximation. Two dimensional PIC codes are also inten-

sively used because they can describe, with more or less accu-

racy number of physical processes. Nevertheless since laser

plasma interaction is intrinsically three-dimensional, 2D PIC

codes fail when describing properly and quantitatively phe-

nomena such as self-focusing or beam loading effects. Thus

any attempt to give a realistic description requires the use of a

three-dimensional, fully kinetic approach. The particle-in-cell

technique is a well established method to solve Vlasov equa-

tion for the different plasma species coupled with Maxwell

equations. Fully electromagnetic relativistic particle-in-cell

codes provide accurate information on laser plasma accelera-

tors related physics, and they constitute nowadays the most

powerful method to perform this research. Several 3D PIC

codes have been applied to the study of laser plasma accelera-

tion, as for example, OSIRIS (Ref. 75), VLPL (Ref. 76),

CALDER (Ref. 77), and Vorpal (Ref. 78). However, they

require extreme computer resources. Indeed, resolving the

high frequency laser fields requires to work with small time

steps and cell sizes, and therefore, large number of simulations

cycles and large grids. In this context, alternative schemes

have been implemented in 3D PIC codes. By carrying out the

simulations in an optimal Lorentz frame79 (different from the

laboratory frame) that minimizes the time and space scales to

be numerically resolved, important computational gain was

FIG. 10. (a) Schematic of the experimental setup showing the laser beam,

the two-stages gas cell, on left the injector part and on right the accelerator

part. (b) Magnetically dispersed electron beam images from a 4 mm

injector-only gas cell (top) and the 8 mm two-stages cell (bottom). Reprinted

with permission from Pollock et al., Phys. Rev. Lett. 107, 045001 (2011).

Copyright VC 2011 by the American Physical Society.

055501-7 V. Malka Phys. Plasmas 19, 055501 (2012)

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achieved. Such a new scheme was used in simulating electron

energy gain in the 50 GeV (Ref. 80) and 1 TeV range.81

Another approach that takes benefit of the symmetry of laser

plasma interaction in underdense plasma is the use of a

Fourier decomposition in a PIC scheme.82 This scheme allows

to reduce the computational load to roughly that of a

bi-dimensional simulation, while preserving the three-

dimensional nature of the interaction and obtaining a good

quantitative agreement with full 3D simulations.

The recent diagnostics that have been developed and/or

adapted to measure the laser, plasma, and electron beam pa-

rameters have played a major role in understanding relativis-

tic laser plasma interaction. These accurate measurements

are crucial for performing numerical simulations with input

parameters as close as possible to the experimental ones. In

some cases, one to one 3D PIC simulations allow to repro-

duce the measured electron beam parameters, without adjust-

ing any parameter.62

New ideas regarding injection control, such as the cold

injection scheme or assisted magnetic field scheme, are

always welcome for future possible electron beam quality

improvements. In the cold injection scheme,83 two laser

pulses with circular polarization collide in the plasma and

produce a standing wave that freeze electrons at the collision

point, as shown in Fig. 11. After the collision, these electrons

are accelerate in the plasma wakefield driven by the pump

beam. In this case, no heating is needed and electrons cross

the separatrix because they keep a constant longitudinal mo-

mentum. The use of an external magnetic field was recently

proposed84 to control off-axis injection bursts in laser driven

plasma waves. It was shown theoretically that this magnetic

field can relax the injection threshold and can be used to con-

trol the main output beam features such as charge, energy,

and transverse dynamics in the ion channel associated with

the plasma blowout.

In the near future, the development of compact free elec-

tron lasers could open the way to the production of intense x

ray beams, in a compact way, by coupling the electron beam

with undulators. Thanks to the very high peak current of a

few kA,85 comparable to the current used at LCLS, the use

of laser plasma accelerators for free electron laser, the so-

called fifth generation light source, is clearly identified by

the scientific community as a major development. For this

application, the relative energy spread has to be reduced, and

solutions have to be found to keep the electron beam proper-

ties, during its transport from the electron accelerator to the

undulator. Because of the large divergence of the electron

beam, that is proper to laser plasma accelerators, one has to

use, for example, ultra high magnetic gradient quadrupoles

to reduce the temporal stretching of electrons which is due to

off axis electrons having longer path than on axis electrons.

Undulators86 and synchrotron87 radiations were recently

obtained by coupling an undulator with an electron beam

from a laser plasma accelerator. Alternative schemes to pro-

duce ultra short x ray beams, such as Compton, betatron, or

Bremsstralhung x rays sources, have also been considered.

Tremendous progresses have been made regarding the study

of betatron radiation in a laser plasma accelerators. Since its

first observation in 2004 (Ref. 88) and the first monitoring of

electron betatronic motion in 2008 (Ref. 89), number of

articles have reported in more details on this new source,

including measures of a sub ps duration90 and of a transverse

size in the micrometer range.91 The betatron radiation was

used recently to perform high spatial resolution, of about

10 lm, x ray contrast phase images in a single shot mode

operation.92,93 It was also used to get very subtle information

on electron injection in capillaries94 and electron accelera-

tion dynamics that cannot be obtained with other diagnos-

tic.95 Measuring the angular and the energy spectra of this

radiation gives an alternative method for estimating the

transverse electron beam emittance and for confirming previ-

ous measurements using the pepper pot technique. The typi-

cal value of the normalized transverse emittance was found

to be in the few p mm mrad for tens MeV electrons,96–98 and

to increase when the electron energy decreases.96,99,100 This

approach for measuring the emittance is particularly perti-

nent when the pepper pot technique stops to be relevant,

for example, for higher electron energies. Regarding

FIG. 11. (a) Principle of the injection by colliding laser pulses: in the “hot”

injection scheme, injection is achieved thanks to momentum (red/continuous

arrow) gained by electrons from the plasma wave (green/dashed curve) dur-

ing the collision, which allows them to cross the separatrix (blue/continuous

curve). Injection principle in the cold injection scheme: electrons are

injected by being dephased from the front of the main pulse to its back with-

out momentum gain (balck/dashed arrow). After dephasing, electrons are

efficiently injected over the separatrix. (b) Principle of electron dephasing in

a standing wave (dotted line) generated by the collision between two coun-

ter-propagating circular laser pulses. Reprinted with permission from

Davoine et al., New J. Phys. 12, 095010 (2010). Copyright VC 2010 IOP

Publishing Ltd and Deutsche Physikalische Gesellschaft.

055501-8 V. Malka Phys. Plasmas 19, 055501 (2012)

Downloaded 06 Sep 2012 to 134.99.164.81. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions

longitudinal beam emittance, coherent transition radiation

diagnostics were used to measure electron bunch duration as

short as 1.5 fs RMS. Time resolved magnetic field measure-

ments confirmed the shortness of the electron bunch pro-

duced in laser plasma accelerators101 and have revealed

interesting features of laser plasma accelerating and focusing

fields.101,102 Optical transition radiation diagnostics were

also very useful in identifying the existence of one or two,103

or even more electron bunches, produced in different arches

of the plasma wakefield, and the possible interaction between

the electron bunch and the laser field.103 The evolution of

short-pulse laser technology, a field in rapid progress, will

likely contribute to the improvement of laser plasma acceler-

ation and help to the development of societal applications, in

material science for example for high resolution gamma radi-

ography,104,105 in medicine for cancer treatment,106,107 in

chemistry,108,109 and in radiobiology.110–112

For longer term future, the ultimate goal is to develop

accelerators for high energy physics. That will require very

high luminosity electron and positron beams of TeV energies.

Reaching these features with laser plasma accelerators might

take at least 5 decades and significant works to develop this

technology are required. The tremendous recent improvement

in the energy and beam quality of laser based plasma accelera-

tors seems promising for high energy physics purposes. But

electron energy is not the only important parameter. It is also

necessary to consider the extremely high luminosity value

required for this objective. For TeV electrons, the luminosity

should actually be must greater than 1034 cm2 s�1. Reaching

this value will require to produce electron bunches at least at a

kHz repetition rates, with 1 TeV in energy and 1 nC per

bunch. The corresponding average power of the electron

beam will be of about 1 MW. Assuming a coupling of 10%

from the laser to the electron beam, which is today the best

coupling for a 10% relative energy spread electron beam, at

least 10 MW of photons have to be produced. For a 1% rela-

tive energy spread, this efficiency drops to 1%, and the

required laser power rises to 100 MW. Since the laser wall-

plug efficiency is below 1%, one needs at least in the most

favorable case 10 GW of electrical power to reach this goal.

The laser efficiency conversion could be increased up to 50%

by using diode pumped systems, thus reducing the needed

power to 0.2 GW. These considerations were done neglecting

several other issues such as the propagation of electron beams

into a plasma medium, laser plasma coupling problems, laser

depletion, emittance requirements, and others.113

Nevertheless, before reaching a more accurate conclu-

sion on the relevance of the laser plasma approach for high

energy physics, it will be necessary to design a prototype

machine (including several modules) in coordination with

accelerator physicists. An estimation of the cost and an iden-

tification of all the technical problems that have to be solved

will permit an estimate of the risk with respect to other

approaches (particle beam interaction in plasma medium, hot

or cold technology, or others). In conclusion, while a signifi-

cant amount of work remains to be done to deliver beams of

interest for high energy physics, the control of the electron

beam parameters is now achieved and many of the promised

applications have become a reality.

ACKNOWLEDGMENTS

I acknowledge warmly my former Ph.D. students X.

Davoine, J. Faure, S. Fritzler, Y. Glinec, C. Rechatin, and

former post-docs J. Lim, A. Lifschitz, O. Lundh, and B.

Prithviraj, my co-worker I. Ben-Ismail, S. Corde, E. Lefeb-

vre, A. Rousse, A. Specka, K. Ta Phuoc, and C. Thaury, who

have largely contributed during this last decade to the pro-

gress done in laser plasma accelerators research at LOA. I

acknowledge the different teams from APRI, CUOS, IC,

JAEA, LLNL, LLC, LBNL, MPQ, RAL, UCLA, and others

that have in a competitive and fair atmosphere made signifi-

cant progresses sharing with passion this wonderful adven-

ture. I also acknowledge the support of the European

Research Council for funding the PARIS ERC project (Con-

tract No. 226424).

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