J. Plasma Fusion Res. SERIES, Vol.4 (2001) 335-339

lon Acceleration in Laser Wakefield
ITO Hiroaki*, BAKHTIARI Mohammad, IMAI Masashi, YUGAMI Noboru and NISHIDA Yasushi
Energy and Environmental Science, Graduate School of Engineering,
Utsunomiya U niversity, U tsunomiya 32 1 -85 85' Japan(Received: 5 December 2000 / Accepted: 16 August 2001)

Abstract
A proton and/or heavy ion accelerator utilizing the transverse electric field of the laser wakefield isproposed. We have performed the simulation in the proton acceleration employing the transverse laser
wakefield. The results show that the energy gain per one stage is not large enough but the acceleration
gradient is several hundred times larger than the conventional proton acceleration scheme. The proton
acceleration by the transverse wakefield is more effective in lower proton energy. It will be possible to
make the compact proton accelerator with this method.

Keywords:
compact proton/ion accelerator, plasma based accelerator, high power laser, laser driven wakefield,
plasma wave

the plasma wave have been observed t4-61, but plasma
based electron accelerators are too premature to be used
as a real linear collider.

1. Introduction
There has been currently great interest in theapplication of the highly energetic electrons generated
from the interaction of an intense ultra-short laser pulse
with a plasma. Acceleration of electrons by an electron
plasma wave has been of considerable attention because
it has potentiality to exceed the acceleration gradientmuch larger than that of a conventional radio frequency(rfl linear accelerator. Several methods have been
proposed for high energy particle accelerators withultrahigh acceleration gradients with the help of theplasma wave generated by an intense microwave orlaser, such as the plasma beat wave accelerator, laser
wakefield accelerator (LWA) [1] in 1979, Ve x B
accelerator [2] and self-modulated laser wakefield
accelerator [3]. Present day high power laser systems
with the chirped pulse amplification technique canproduce an ultra short pulse with an intensity well above
1018 Wcm2 and enable us to perform proof-of-principle

On the other hand, the study of acceleration ofprotons and/or ions has a longer history than that ofelectron acceleration. More recently the "electron ring
accelerator" had been studied until early 1970's in
USSR, USA, Germany and Japan [7]. The studies haveterminated without remarkable successes. The
investigation on the proton/ion accelerators has not beenso active for several decades in spite of a high demandfor ion accelerators. Such developments of lasersystems, however, have promoted an interest in compact

ion accelerators with various applications for highenergy physics and medical field. The above mentioned

plasma based acceleration schemes which havesuccessfully accelerated electrons, cannot be employed

for the acceleration ofprotons and ions with energy lessthan 1 GeV, since the phase velocity of the plasma wave
is much faster than the particle's velocity because of
their heavier mass than electrons. Several ideas forexperiments of laser driven plasma accelerators.
Recently it has been reported that electrons accelerated
up to the energy of 300 MeV by the laser wakefield and02001 by The Japan Society of Plasma
Science and Nuclear Fusion Research335

lIo H. et al., Ion Acceleration in Laser Wakefield

accelerating proton/ion based on the plasma wave haveLaser

got an attention including the backward Ramman
scattering [8] and Alfv6n wave [9] which slow waves

Laser

for wakefield\for plasma production

are to trap the accelerated particles.

vt--\sAn acceleration method for accelerating proton
beam using lasers and plasmas is an acceleration method

using a transverse components of the laser wakefield
excited by the interaction of the high intense ultra shortlaser pulse with the plasma. This acceleration method-has been already proposed and reported in thegtrttruttl
rntttdtrntn

NL

Ylllltt+:r, =\^(9lonsimulations that protons are accelerated by transverse
laser wakefield [10]. The simulations in Ref. [10] havebeen performed for the one-dimensional motion ofIon

protons, i.e. the transverse direction. In this paper, we
perform the simulations extended to two-dimensions andtan?=wo/ \:4discuss in detail the behavior of protons in the laser/c (q :Ion velocity)

Fig. 1 Schematic diagram for the proton acceleration by
the laser driven wakefield.

driven wakefield and the phase matching between theproton beam and the transverse wakefield.

2. Theory
An electron plasma wave (EPW) is excited by theponderomotive force of the EM wave exciting a density
oscillation with the plasma frequency in an underdense
plasma. The EPW with large amplitude driven by thewltn

laser pulse has both transverse and longitudinal

where 1.u* is the maximum laser intensity, u is the pulse

components. The transverse component is induced bothby the temporal and radial profiles of the laser pulse andduration at FWHM, w6 is the spot radius of the EM/. .\A=rtr a^r exo[ -%' | -!t-'" '\412€om"ca2

the longitudinal component corresponds to thewave at focus, a4 is the plasma frequency, m" is the rest
mass of the electron, and eo is the dielectric constant inlongitudinal motion induced by the temporal profile ofvacuum.

the pulse. The plasma electrons are described by cold
fluid equations with the ponderomotive potential term
induced by the spatial and temporal profiles of the laser
pulse. Assuming the linear approximation, in which theelectron density perturbation is small compared with theThe ratio of the two components of the density
perturbation on the laser axis is given by 6n,/5n"= (Lolnws)2, wherc Ip = 2nclap is the wavelength of theexcited plasma wave. Thus, the electron density
perturbation can be treated as longitudinal when $\piftws )) ),0 and radial when 7tw0 11 X.o [13,14J. In theconventional LWA, the transverse field is stronger thanthe longitudinal electric field, since EPW excitation
takes place mainly in the radial region. We proposed theequilibrium electron density and that ions are fixed, theequations can be solved. The longitudinal component of
the density perturbation 6n, corresponds to longitudinal

electron oscillations. The electric field E, deduced by
the Poisson equation is also longitudinal. The transverse

ion acceleration by employing the transverse wakefield,i.e. the ion beam is injected into the wakefield from theradial direction. Depending on its relative phase q c6r=- ftoz with respect to the wakefield, an injected ion iscontribution 6n. corresponds to cylindrical electron
oscillations associated with the radial electric field E.
Each component of a linear EPW excited by the intenselaser with Gaussian radial profile and a Gaussianaccelerated or decelerated by E. and focussed ordefocused by E,. Thus, as shown in Fig. I which
represents the ion motion in the frame of the wakefield,
the most effective acceleration occurs when the ionalways stays in the acceleration phase during thewakefield. The laser driven wakefield useful for thecharged particle acceleration is limited within the spot
size, since it decreases exponentially in the radial

temporal distribution, can be expressed [11,12] as

E,= Akpcos(aror-koef expl-:' rl.
\ w'o I/\lr.t\(l)u,= offisin (aror - roz)exp

( #)

(2)

336

ItoH. et al., Ion Acceleration in Laser Wakefield

direction as seen in Eqs. (1) and (2). The condition forthe most effective acceleration, which require phasematching between the transverse wakefield and the ion'and charge state. For the simplest discussion, let us

beam, is given by viT, = 2wo, where v1 is the ion velocity

performed two-dimensional time dependent simulations

across the area where the wakefield is excited and Zo =2n/rt, is the period of wakefield. This condition can bebased on the momentum equation in order to study theconsider the energy gain for the proton acceleration

utilizing the laser-driven transverse wakefield. We have

behavior of protons in the laser wakefield in detail. Eachsmall displacement of proton for the time step iscalculated by the Time center Leap Frog method [15].
The final proton energy is obtained by repeating theprocedure until the proton passes through the wakefield.

satisfied by adjusting the plasma density, since aro
depends on the plasma density, car= (n"lel2lqm)tt2.The

plasma density required for the appropriate ion
acceleration is rewritten asn.1"rn-t| =6x l0r7t' IMeV I
uw'^Iltml'

The simulation has been performed in the casewhere the laser for the excitation of EPW has the(3)parameters of wavelength 1, = 800 nm, and maximum

power P = I TW focused into the spot size 2wo - l0pm, corresponding to a Ti-Sapphire laser system.

where q is the initial ion energy and M is the ratio of theion mass to the proton mass. In the ideal case in which

the above condition is satisfied and the effect ofAssuming that the proton is injected in the +r direction,
we need to take into account the dependence of theelectric field E, on the relative phase E for obtaining

longitudinal wakefield is negligibly small, the maximum
energy gain is obtained as

rc=2,[n*oE,dr =2A(l -er)(ev).

more efficient acceleration of the proton by the laser
wakefield. Thus, in the simulations the proton is injected
into the wakefield when its phase is e = x. Figve 2
represents the typical simulation result for the protonwith an initial energy e, = 1 MeV, where the plasma
density is n. = 1016 cm-3 satisfing viT, = 3wo. In this(4)The coefficient A is a function of the product a4r and ismaximum when a)o? = i7. Fo. the proton energy q - I

MeV, for examples, the maximum energy gain is
expected when the plasma density is n" = 16to cm-3 andsimulation, the laser pulse duration is assumed to be r =250 fsec, since the wakefield amplitude is maximum at
aor = "Ji as above-mentioned. The solid and dashedlines represent respectively the proton energy and theelectric field of the wakefield acting on the proton while

the laser pulse duration is z = 250 fsec.

3. Simulation Results
The acceleration mechanism of heavy ion is thesame as that of proton in principle in spite of thedifference between the proton and heavy ion, i.e. mass(a)ocllJ SO

20

c25\Er,,lI

III\IItl

Ic'o->\ 100gfrom Fig. 2 that the proton continuously feels the30

200I 150

the proton travels through the wakefield. It is evidentII

200 a 15IIII-2 -1.5 -1 4.5 0 0.5 1 1.5 2(b)2.51\fi.sIIo,,15p ,q10e10ir.9d58]uotr-5r)-(,E, /^\1.5,c)']l-/l/lt l\tl\-:./ tl\IEilEc)

0.5 Eo)----2 -1.5 -1 4.5 0 0.5 1 1.5 20lU
4.5

Radius (in wo units)

Radius (in wo units)

Fig. 2 Variation of the proton energy and the electric field of wakefield accelerating proton as the proton travels. (a) and(b) represent the radial and axial component of the proton's motion. Solid and dashed lines are the proton energy
gain and the electric field of the wakefield, respectively.
337

ItoH. et al., Ion Acceleration in Laser Wakefield

is not also easy to excite the wakefield with large
amplitude in high density region. Figure 4 shows theenergy gain as a function of the plasma density. Theacceleration force in the wakefield and is accelerated
with the energy gain of about 175 keV. Considering thatthe acceleration length is 3wo =lJ pm, the acceleration
gradient is estimated to be 12 GeV/m, which is much

most effective acceleration occurs at the plasma density
which satisfies the matching condition Eq. (3). The
proton traverses the deceleration phase of wakefield,

larger than the conventional rf accelerator. On the otherhand, it is obvious from Fig. 2 that the longitudinal
electric field is ten times smaller than the transverse one
and that the proton is accelerated little in the axial

since the oscillation period of plasma wave becomeslarge with increase of the plasma density. It turns out
from Fig. 4 that the matching condition can be satisfied
by adjusting the plasma density.
Finally, we propose the compact proton accelerator

direction.
Neglecting the nonlinear effect, we can expect thatthe proton is accelerated to high energy in proportion to
the laser power, because E. is directly proportional tothe amplitude of the laser wakefield and so the incident
laser power. If the laser with power l0 TW is used forthe excitation of the wakefield, the proton with the same

1000

injection energy can be accelerated with the energy gainof about 1.7 MeV.
The amplitude of the wakefield depends on theinitial proton energy, since the mean plasma density_F5o roo.c(Eneed to be adjusted to satisfy the phase matchingcondition between the laser wakefield and the proton. Itis important to perform the simulation of thedependence of the energy gain on the initial injectionenergy. The simulation result is shown in Fig. 3, where,/o6c\,/
10LU

the laser pulse duration is 100 fsec and other parameters
are the same as the above simulation. It is seen that this1acceleration method employing the transverse wakefield

0.01

is not suitable for the high energy proton acceleration. It0.1

1100

Initial Energy (MeV)

is readily shown from Eq. (2) that the wakefield
amplitude decreases exponentially beyond the maximum.r:-.

Fig. 3 Proton energy gain as a function of the initialenergy. The laser parameters are ).= 800 nm, P=
1 TW. and u = 100 fsec.

point Copt = !2. Thus. the wakefield acceleration forprotons is not adequate for the high energy particles. It

1.15

Initial Energy: 1 MeV

o10fre:1.0 x 1016 /cml
1.5 x l016 /cm:

11I. ICD

0.8 x 1016 /cml

ogLU

co 1.05

2.0x1016 /cmz

IL

Radius (in wo units)
Fig. 4 Dependence of proton energy on plasma density.

338

ItoH. et al.. Ion Acceleration in Laser Wakefield
employing the above-mentioned acceleration method. InAcknowledgement

order to realize this accelerator, the multistage

This work is supported in part by the Grant-in-Aidfor Scientific Research from the Ministry of Education,

acceleration has to be used, since the energy gain per
one stage is small. We expect that this method can beScience, Sports and Culture, Japan.

realized by precisely arranging the position and theinterval of mirrors.

tllReferencesT. Tajima and J.M. Dawson, Phys. Rev. Lett.43,267 (1979).

4. Summary
We have proposed a proton acceleration method

l2l Y. Nishida, M. Yoshizumi and R. Sugihara, Phys.

and the design of the accelerator employed this method

Lett. 105A, 300 (1984), Y. Nishida, M. Yoshizumi
and R. Sugihara, Phys. Fluids. 2E,1574 (1985).
t3l N.E. Andreev, L.M. Gorbunov et al., JETP Lett.

mentioned in this paper. Possibility of the proton
acceleration due to the laser driven wakefield has been

confirmed from the simulations. Thus, it has been

ss,571 (1992).
t4l H. Dewa et a/., Nucl. Inst. and Meth. A410, 357(l998).

demonstrated that this acceleration method can be used
for the heavy ion. The energy gain per one stage is notlarge, the acceleration gradient, however, is several
hundred times larger than a conventional rf acceleration
scheme. We expect that the compact proton accelerator
employing this scheme can be realized by using thepresent apparatuses. The increase of laser power canlead to increased gain in proton energy per stage at thecost of the accelerator's compactness. Such a proton

t5l D. Bernard er a/., Nucl. Inst. and Meth. L432,227(1999).

[6] J.R. Marqu6s et al., Phys. Rev. Lett. 76, 3566(1996), C.W. Siders et al., Phys. Rev. Lett. 76,3570 (1996).

t7l M. Reiser, Seminar on New Trends in Particle

as a compact accelerator. Similar to the electron
accelerator which the longitudinal component ofAcceleration Techniques, Capri (1982).
t8l A. Ogata and T. Katsouleas, Proc. 1998 Workshop
on Advanced Accelerator Concepts, AIP Conf. 472,551 (1999).

wakefield traveling with the incident laser is used, there

t9l B. Rau and T. Tajima, Phys. Plasmas 5, 3575

accelerator using a huge laser system cannot be regarded

are some limitations in the accelerator with thisfl998).

ll0l M. Bakhtiari, H. lto et al., Jpn. J. Appl. Phys. 39,

acceleration scheme. 1) The radius of accelerated beamcannot be larger than the laser spot size.2) The lengthof the beam will be smaller than the pulse of laser.

L1097 (2000).

Il] E. Esarey, P. Sprangle et al.,IEEE Trans. Plasma

However, we consider that these problems may beSci. 24, 252 (1996).

ll2l F. Amiranoff et a/., Phys. Rev. Lett. 81, 995

solved by using some parallel lasers. There seems to besome room for making improvements including new
acceleration schemes. More detailed discussions are
required for further improvement of the acceleration(1998).

t13l J.R. Marquds et al.,Phys. Plasmas 5,1162 (1998).
[14] F. Dorchies, F. Amiranoff et a/., Phys. Plasmas 6,2903 (1999\.

efficiency.

t15l C.K. Birdsall and A.B. Langdon, Plasma Physics
via Computer Simulation (McGraw-Hill, NY 1985).

339