The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Recent Progress and Perspectives of Laser-Plasma Accelerators
Kazuhisa NAKAJIMA and Atsushi OGATA
High Energy Accelerator Organization, Tsukuba, Ibaraki, 305, Japan

Abstract

Recent progress of laser-plasma accelerators has matured a concept of particle acceleration owing to plasma
waves excited by laser or electron beams as a possible
next generation particle accelerators promising ultrahighaccelerating gradients and a compact size. Four major
concepts of laser-plasma accelerators, the plasma beatwave accelerator, the laser wakefield accelerator, the selfmodulated laser wakefield accelerator and the plasma
wakefield accelerator are reviewed on accelerator physics
issues and experiments demonstrating basic mechanismsof their concepts. As a perspective to the future practical application, a design of 5TeV linear colliders basedon the laser wakefield accelerator is discussed.
1 Introduction

A proposal of Tajima and Dawson has initiated amodern history of the plasma acceleration[!]. Their paper proposed two laser-based schemes, which are now
called beat wave acceleration (BWA) and laser wakefield
acceleration (LWA). Because lasers to meet the requirements of the LWA were hardly available on 1980's, theexperimental studies of the BWA was started. Several
years later, Chen proposed a scheme which uses particle beams instead of lasers in order to excite plasma
waves[2]. This scheme is now called plasma wakefield
acceleration (PWA). It was soon noticed that the beamdriven and laser-driven methods have physics much incommon. It is this PWA which has first produced considerable amount of accelerated particles[3]. Following
this, quite a few good experiments on the BWA havebeen reported successively[5, 6, 7]. Meanwhile, invention of the chirped-pulse amplifier (CPA) [8] has enabled
us to use a high-power laser with pulse width aroundthe wavelength of high-density plasma wave. Sprangle
called attention to the LWA[9]. The first experimentof the LWA was made by KEK group, using the CPA
laser at ILE[lO]. Recently a wakefield of the order of
10 GeV /m in a plasma has been directly observed by
the use of a compact terawatt laser system so called T 3
lasers[22].
The self-modulated laser wakefield acceleration (smLWA) has its roots in old Raman scattering. Russiangroup and NRL group h;;tve pointed that the mechanism is positively useful for acceleration, if it utilizes
the recent high power lasers[ll, 12]. The experiment by
KEK demonstrated ultrahigh gradient electron acceleration of the order of 30 GeV /m, using a multiterawatt
short laser pulse[13]. Recently experimental demonstration ofthe sm-LWA has been reported by several groups[14, 15, 16]. Although the sm-LWA can generate the accelerating field exceeding 100 GeV /m, this mechanism
could be not applicable to a practical accelerator because of a short acceleration length limited by dephasingof accelerated electrons or depletion of pump pulses.

The first-generation studies on laser-plasma accelerators have succeeded in demonstrating the proof-ofprinciple experiments to prove ultrahigh field generation
in a plasma and electron acceleration by plasma waves.
It is of importance for practical applications to generatea high energy gain with a good beam quality as well as
high gradient acceleration. The second-generation study
has been started to aim at realization of high energy
laser-plasma accelerators in the world-wide community.
Their efforts are concentrated on overcoming two difficulties. The one is the development of optical guiding
methods in plasmas to extend the acceleration length
for laser-based schemes. The other is the developmentof spatial and temporal matching technologies of electron beams to be accelerated by plasma waves. The former issue is a topical subject on laser-plasma interaction
physics. The latter issue includes a very low emittance,-short-bunch electron source, such as a photocathode RF
gun [29] and a plasma cathode driven by intense ultrashort laser pulses[30], and a femtosecond synchronization technology.
Next two sections of this paper summarizes principles of plasma accelerators and hitherto experiments.
A perspective of high energy laser-plasma accelerators
is discussed about accelerator physics issues and linear
collider design based on LWA in Section 4.
2 Principles of Laser-Plasma Accelerators

The most promising characteristic of laser-plasma
accelerators is their ability to support extremely highaccelerating gradients. In conventional rf-driven accelerators, the accelerating gradients are limited to approximately 100 MV /m due to electrical breakdown onmaterial surfaces. In ionized plasmas, one can generate electron plasma waves with electric fields of the order of the nonrelativistic wavebreaking field given by
Eo= mewpcje or(1)where wp = [47rnpe 2 /me] 112 is the electron plasma frequency and np is the ambient electron plasma density. Itmeans that the plasma density of np = 10 18 cm- 3 gives
the acceleration gradient of 100 GeV jm.
To be used for acceleration, the phase velocity ofthe plasma wave should be nearly equal to the particle
velocity, which is the light velocity in light particles suchas electrons. We have at least four methods to generatesuch waves. They are depicted in Fig. 1. Let us assume
here that the test particles are electrons.
In the PWA, repulsion of plasma electrons against
beams triggers plasma oscillations. The maximum wakefield amplitude excited by the drive electron beam withdensity nb is given by

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J2)

The I 1th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

where ,\ is the laser wavelength and I is the laser intensity. In the LWA, the maximum wakefield amplitude isgiven by

(a)

(5)

PWA

In the BWA, the maximum electric field at the saturation of the plasma wave is given by

(b)

(6)
where a 1 and a 2 are the normalized vector potentials of
two lasers[18). The mechanism of the sm-LWA is more
complicated than the BWA and the standard LWA. It
uses laser pulses which satisfies two requirements; first,
the pulse width should be much longer than the plasma
wavelength, and second, its power should exceed the critical power of the relativistic self-focusing of the laser Pc,
where

BWA

(c)

(7)
with WL, the laser frequency.
This relativistic self-focusing is understood as following; The refraction index of the laser in a plasma isgiven by

LWA

(d)

(8)
In a strong laser field, the plasma frequency becomes
smaller;sm-LWA(9)
Fig. 1 Generation of plasma waves. Background intensity shows the plasma density, the balls
show particles and solid lines show laser amplitudes.
The PWA is in principle a transformer converting highcurrent low-energy beams to low-current high-energy
beams. Let us write the charge and energy of the primary and secondary beams as C 1 , E 1 , C2, E 2 . Becauseof the energy conservation, it is constrained by the relation C 1 E 1 > C 2 E 2 . Moreover, if the bunch lengths of thetwo beams are infinite small, there is another constrain
called transformer limit;.i.e.,(3)
It means that the energy gain of the secondary beam isless than twice of the energy of the primary beam.
In the BWA and LWA, the ponderomotive force oflasers triggers the oscillation. Difference between two
methods is in that the BWA uses two lasers, of which frequency difference is equal to the plasma frequency, while
the LWA uses a laser pulse with width nearly equal to theplasma wavelength. The fourth method, sm-LWA uses
a laser with high power and long pulsewidth. The laser
pulse excites the plasma wave, and is instead modulatedby the plasma frequency. A parameter useful in discussing the ponderomotive force is the normalized vector
potential defined as a = eA/mec 2 . Its peak amplitudeof a linearly polarized laser is given by

where Wpo is the ambient plasma frequency. Physically,
this is due to the fact the electrons make relativistic
oscillation transversely in the laser fields, which increases
their relativistic mass. The large a on the laser axis thus
gives small Wp there. The refraction index distribution
becomes such that the index is largest on the axis anddecreases as r increases. This distribution focuses thelaser.
In the linear regime, the plasma wave is a simple
sinusoidal oscillation as far as the density perturbationis small; i.e., fmpfnp ~ 1. In the nonlinear regime, theelectric field becomes a sawtooth form associated withwave steepening and peaked density oscillation as shownin Fig. 2[17]. The nonlinear wave in which Dnpfnp 2:: 1
can be excited in the PWA using drive beams in which
the electron density is higher than in the plasma;i.e.
nb > np. It is also possible in the LWA using a laser
with high intensity; rigorously, if its normalized vector
potential exceeds unity; ao > 1. The sm-LWA drives
nonlinear wakefields even if ao < 1.

3 Acceleration Experiments
The hitherto obtained main experimental results are
summarized in Table 1. The table gives only the firstand best results of each method. A more comprehensive
table is found in a review by Esarey[18).
Among the four schemes, the sm-LWA results in extremely large acceleration gradients. Figure 3 shows the
RAL results. The laser with the power of 25TW wasused. No electron was injected, so the results show
plasma electrons trapped and accelerated by the laser
field. The number of electrons accelerated was 108 and-37-

The II th Symposium on Accelerator Science and Technology, Harima Science Garden City, I997

Table 1. Experimental results of laser-plasma electron acceleration.
energy gain/ acceleration length no. of particles
institution, year, ref.
200keV /40mm
ANL 89[3]20MeV /1m,...., 10 9
KEK 92[4]10MeV/3-7mm< 103
ILE 92[5]28MeV /10mm< 104
UCLA 93[6]12MeV /10mm,...., 10 2
KEK 93[13)300MeV /20mm,...., 10 2
KEK/JAERI/Tokyo 96[19]18MeV /0.6mm,...., 110 2
KEK/ILE 93[13]44MeV/0.3mm,...., 10 10 /MeV /sr
RAL 95[14]

PWA
BWA
LWA
sm-LWA

2

1.0

lal

1011

""en
..._

0.5

0

0

>Q) 1010 •
•
~

•

Q)

0.

0
w"

!<..

.i

ID
0.

•
•

-2

-o.1o

-o.oe -0.04

~o.oa

-o.02

1QB

-1.0

o.oo

15 . - - - - - - - - - - - - - , 3,w...,

I

10

rl
II
I

II
I

'

~
g
w"

/

I

' ' .... _
\

--

I

'

/

\
\

0

,_

!

-10
.~5

~

-0.08

.0.06

-0.04

DISTANCE

20

30

40

50

point. If we loose the focus, the acceleration length canbe lengthened, but the acceleration gradient becomes
weak so that the energy gain cannot be increased. A
parameter which expresses this length is the Rayleighlengthwhere rrr is the rmfiWarsF(izre- ~tft\re, laser.
(10)
The second is the dephasing length. It is the distanceaccelerated electrons outstrip the laser wakefield, given
by
(11)

-6

-0.10

detector limit

Fig. 3 The electron energy spectrum measured for alaser power of ,...., 25 TW in the RAL experiments.

2

I
I
I
I
I I

I

I
I I
I I
I

•

•

4
(a)n0 .!1.Sx10 19--(b) n0 = 1.5x 10 19
0 (c) n0 = 1.Sx 1019•(d) n0 =1.0x10 19• (e) n0 = o.sa x 10 19

Energy (MeV)

(a)

II

........

1---_..!!...--

8 910

e

DISTANCE

0

•

-0.02

0.00

e

(b)

Fig. 2 Linear( a) and nonlinear(b) plasma wave andtheir fields. a= 0.5 in (a) and a= 2 in (b).

This limit is caused because the group velocity of a laser
in a plasma is given by v 9 = c[1- (wp/wL) 2]11 2, whichis smaller than the light velocity.
The third is the pump-depletion length in which thelaser loses its power and cannot pump wakefields any
more. One expression of this length given by Bulanov,
et a1.[20] is

the normalized emittance was calculated as 51TJ.lm forelectrons with energy around 30MeV. Recent report saysthat a new detector has found electrons with energy up
to 100MeV.
The laser wakefield electron acceleration has been
carried out by KEK/JAERI/U. Tokyo group[19], using(12)
a 2 TW, 90 fs laser pulse synchronized with 17 MeV
RF linac electron beam injector at the repetition rate of
10 Hz. They observed high energy electrons accelerated
The standard LWA is limited by diffraction, while theover 100 MeV up to 300 MeV by the wakefield of,...., 15 sm-LWA is often limited either by the dephasing or by
Ge V /m excited over a few em long. underdense plasma the pump depletion.
as shown in Fig. 4.
The dephasing length and the pump-depletion
One drawback of laser accelerators is their short ac- length are long enough as far as we use plasmas withceleration length. Acceleration length is limited by the moderate density, so our effort has been paied to exshortest among the three below. First is the diffrac- . ceed the limit of the diffraction. One way is to go into
tion length or the depth of focus of the laser. It means
the regime in which the relativistic focusing is possible.
that the acceleration is possible only around the focal
However, another way in the nonrelativistic regime has-38-

The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

.0.25

.-..

--d

~
0)

u

e

~
~

0""'
"'o:s
0)

c:

.0.40
0.8

0.9

1.0

1.1

1.2

1.3

.1.4

Time (ps)Fig. 5 Measurement of the plasma density oscillation
excited by a 1 TW pump power in a He gasof 2 Torr. The solid curve shows a fit of theplasma wave with oscillation period of 360 fs.

already been adopted in industry. It is the principle ofan optical fiber, in which lasers can propagate without
diffraction. Refraction index of an optical fiber has atransverse distribution, in which the index is maximum
at the core center, and low at the clad. If we could
produce similar index distribution in a plasma along thelaser axis, the laser would propagate without diffraction.
The refraction index in a plasma has already been given
in eq.(8). A plasma density distribution minimum at thelaser axis will realize the index distribution suitable forlaser propagation. Such an optical channel has been successfully produced by Durfee and Milchberg[21]. They
used another laser to produce the channel. This laser
pulse, focused by an axicon optics, prepared a shockdriven axially extended radial profile in plasma density
distribution. The main laser, injected at the proper timing, was guided by the preformed channel for 24 timesof the Rayleigh length.
The plasma wave excited by the LWA has been
recently observed independently by two groups(22].
They measured the plasma electron density oscillation
with the frequency domain interferometry technique.
KEK/JAERI/U. Tokyo group also measured the plasma
wave oscillation with the frequency domain interferometer to make confirmation of wakefield excitation by an
ultrashort laser pulse in an underdense plasma[19]. Figure 5 shows the electron plasma wave measured at 2
Torr for the pump peak power of 1 TW. The measured
density perturbation was (6n/ne) "' 15% corresponding
to the longitudinal wakefield of"' 2 GeV jm. This measured amplitude is in good agreement with the accelerating wakefield of 2.2 GeV jm theoretically expected for
1 TW.
Although the PWA has ever attained smaller acceleration gradient than the laser drivers, it is limited neither diffraction nor dephasing. In order to obtain highenergy gain in the PWA, it is essential to overcome thetransformer limit. Three methods are proposed; The
first is the use of driving beams consisting of multiple
bunches(23]. Experiments by this method are plannedat INP[24]. The second is the use of a sirigle properly

shaped driving beam. A triangular-shaped beam which
has a linear rise over a length Lb = NAp followed bya rapid termination gives the transformer ratio 1r N [25].
This experiment is planned at SLAC(26]. The third is. to
go to non-linear regime. If the beam density nb exceeds
the plasma density np, the beam blow out all the plasma
electrons and a nonlinear wave with large amplitude iscaused[27]. The experiments are planned at ANL[28].
High-current high-density beams are essential as drive
beams in these experiments. The three experiments will
use such good beams in order to attain 0.1-1GeV /macceleration gradient.
4 Perspectives of Laser-Plasma Accelerators

Beam loading is understood as the reverse processof the PWA[31]. In PWA, a bunch of particles leaves
a plasma wave behind. The amplitude of the wakefieldis given by Ez = eN/( f.o7rr5), where r0 is the radius of
the field. This equation gives N = f.o7rrfiEzfe. Supposethat a test bunch with these N particle is injected into
this wakefield Ez. The test bunch consumes all the energy of the wave and leave a quiet plasma behind. The
N then gives the estimate of the maximum number ofaccelerated particles with 100% energy spread.
It should be noted that this number N is not verylarge if we assume the use of typical T 3 lasers. The standard LWA will attain Ez = 1GeV /m and ro = 50JLm,
which gives eN =70pC or N = lOs, at 100% energy
width. The pulse power of a laser is given by laser energy
divided by pulse duration. Such a laser has certainly
large puise power, but the TW output was attained by
reducing the denominator down to lOOfs range. Highenergy is necessary to obtain large current..
An inconspicuous feature of the plasma accelerators,
compared with the high acceleration gradient, is its highbunch frequency and short bunch length. Specifically,
the bunch frequency becomes equal to the plasma frequency, which is in the 10 12 - 1015 Hz range if plasmas
in the density range of 10 15 - 1020 cm- 3 are used. Suchfeatures may be useful in radiation generation. Plasma
waves have a property bunching continuous beams, just

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The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

as the rf waves have.
Emittance of the plasma accelerators is decided bytheir injectors. The rf laser cathode is regarded as thebest injector at the present, because it gives not only
good emittance but also high current and short bunch
length. In addition, the laser cathode makes the synchronization easy between test beams and laser beams todrive the plasma waves. An rf laser cathode developedby BNL/SLAC/UCLA collaboration has a normalized
emittance around......, brJ.tm[29].
The most serious problem oflaser-based accelerators
is the poor efficiency of lasers. The efficiency from wallplug power to microwaves of conventionallinacs is about
25%; i.e., the efficiency of a klystron power supply has......, 80%, that of a klystron itself is . . . , 50%, that of awaveguide is ......, 90%, and the structure efficiency is . . . ,70%. To the contrary, the efficiency from the wall-plug
power to the laser power is below ......, 0.1% in present T 3
lasers. It is expected that the use of laser diode arrays
will improve this value up to the order of . . . , 10%. The
efficiency from laser power to the plasma wakefield isbelow . . . , 25% in linear scheme. It could exceed ......, 50% if
we go to nonlinear regime. The efficiency from wall-plug
power to plasma waves is thus below......, 2.5% in the linear
regime using the diode laser pumping to be developed,
which is 1/10 of that of conventional rf linacs.
Table 2. Linear collider design based on LWA.
Collider parameters
Energy5TeV (2.5TeVx 2.5TeV)
Luminosity
1035 cm- 2 sec- 1
Bunch length""'1pm(= (3*)
Emittance
1pm (round beam)
No. of electrons per bunch 10 7
Bunch frequency
40kHz
Disruption parameter25
Beamstrahlung percentage 30%,8B = 0.3
103
Upsilon parameter
Luminosity enhancement
3
Average beam power
0.25MW
LWA parameters
Plasma density
1017 cm- 3
Acceleration length
1mEnergy gain per stage
10GeV
Number of stages
500
Laser power per stage
40kW
Laser energy per stagelJ
Average laser power
20MW
As an example of applications to high energy accelerators, a 5 Te V linear collider design based on the standard LWA is described in Table 2[32]. First assumed
were wall-plug power, luminosity and the percentage ofbeamstrahlung. Because of the poor efficiency of thelaser, the number of particles per bunch must be small.
Their solution is small emittance, small final-focus beam
size and short bunch length, all of which are on the orderof pm. Each accelerator of the colliders has a laser-rf injector, a linac for pre-acceleration and 250 stages of laser
wakefield accelerators. Each stage is 1m long, and has
10 GeV energy gain. The length is approximately equal

to the dephasing and pump-depletion lengths. Two laser
beams are fed to each stage, one of which create an optical channel, and the other is guided in the channel.
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