The 13th SympaYium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Laser-plasma ion acceleration
Alexei Zhidkov1*, Akira Sasaki2, Mitsuru Uesaka1
Nuclear Engineering Research Laboratory, Graduate School of Engineering, University ofTokyo 2-22 Shirane-shirakata, Tokai, Naka, lbaraki, 319-1188 Japan
12Advanced Photon Research Center, JAERI, 8-1 Umemi-dai, Kizu-cho, Soraku-gun, Kyoto,

619-0215 Japan
Abstract
Multiple-charged ion acceleration from a plasma slab
irradiated by an· intense, short laser pulse is studied via
the collisional particle-in-cell simulation including
various mechanisms of plasma ionization. The forward
ion acceleration by the shock wave produced by theExll force, the bluster-type ion acceleration, is found tobe very efficient. Effect of contamination on the forward
and backward ion acceleration is analyzed.

1 Introduction
Plasmas irradiated by a short pulse laser can be anefficient, compact, and flexible source of MeV protons
as well as highly charged MeV ions. Hot electrons
produced by the laser pulse irradiating a solid target
drive ion emission. Due to highly anisotropy distributionof the hot electrons, the emittance of a source ofenergetic ions is comparable to that of ion beams
produced via electrostatic acceleration.· This has been
demonstrated through numerical kinetic simulations [1]and recent experiments [2-4]. There are three· principal
mechanisms of ion acceleration from solids irradiated bya short laser pulse, see Fig. 1. The

first is the backward ion acceleration (BIA) driven by
the hot electrons from the front side of the target toward
the laser pulse. The second is the forward ionacceleration (FIAR) from the rear side of a slab target
dominated by hot electrons penetrating through the slab.
The third is the forward ion acceleration by the shock
wave produced by the relativistic acceleration force(ExH) from the front side of the target [5] (FIAF). ~eefficiency, maximal ion energy, and emittance of tonacceleration ·vary differently with the laser intensity,pulse duration, and plasma density for different
acceleration mechanisms.
Contamination may have a strong effect on the ion
acceleration. If no special measure made, thecontamination layer has usually 10 nm thickness. The
contamination consists of water absorbed from theatmosphere. Since the charge-to-mass ratio is the largest
for protons, these particles are mostly accelerated. by ?ot
electrons in either direction. To produce effective ton
acceleration, the surface cleaning should be performed.
In the present work, we investigate numericallyvarious mechanisms •of energetic ion emission from slab
targets irradiated by an obliquely incident picosecond
pulse laser, as well as very intense subpicosecond pulse
lasers and effect of contamination on these mechanisms.
We use the collisional PIC simulation employing theaverage ion model to include transient plasma ionization.
Effect of plasma induce4 field ionization on the FIAR isstudied. By applying the Langevin equation, we makethe method conformed to direct Fokker-Planck
simulation.

2 Ion acceleration mechanisms
protons. 8! •. :.:.aser pulse

proto~~···---IC:::It---_:) Hot electrons
10 runcontamination

Figure 1: Various mechanisms of ion acceleration*Corresponding author: E-mail:zhidkoy@tokai.t.u-tokvo.ac.jp: Fax: +81-29-287-8488

The BIA dominated by the electrostatic field generated
due to hot electrons produced via the resonanceabsorption is quite efficient for moderate laser intensity.
CalculationS show with total laser absorption efficiency
over 40%, , about 100/o of the laser energy ca.Il be
funneled into ion acceleration over 1 MeV, which.
corresponds to more than 1011 fa st tons
per pul se WI'th
10 TW, picosecond Ti-Saph laser. The emittance of such
beams can be about 1-2 1t rnm mead. With the laser
intensity I, the maxilnal ion energy increases as i 12 •However the plasma corona produced by the laser
prepulse can strongly affect on the emittance due to-304-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

electric fields after the laser pulse as well as the magnetic
field. The FIAR process appears in slab targets with thethickness that is less than the hot electron free path. Inthat case, the hot electrons penetrating the target andmaxwellizing at the rear side of the target drive theforward ion emission. Due to the very directed velocity
distribution of those electrons, the emittance of ions isbetter than that of BIA. The efficiency of the FAIR
depends on the laser intensity and target thickness. If thefree path of an electron with the energy - T~t, thetemperature of hot electrons, is less than the target
thickness, the efficiency ofFIAR is comparable with thatof BIA. The- maximal ion energy increases as i'2 withthe laser intensity as well. In contrast to FIAR and BIA,
the FIAF strongly depends on plasma density. Under
action of the laser pulse, the positively charged layerwith the thickness d-liN. is formed at the front surfaceof the target. The maximal energy of forwardly
accelerated ions equals to the potential difference at thislayer t:P-Neef-IIN.. In solid density plasmas, themaximal energy of FIAF is comparably small. The
efficiency is much smaller than that ofBIA. Since FIAF'ions have to pass through the target, their emittance ismuch worse than the emittance of BIA and FIAR. The
typical velocity distribution of ions emitted from a foil
irradiated by subpicosecond laser pulse is shown inFig. I. One can see that the maximal ion energy of FIAR
is much higher than those of FIAF and BIA. In the caseof BIA, the hot electrons, which dominate ionacceleration~ are decelerated by ExH force suppressing
the ion acceleration. The small maximal energy of ionsfrom FIAF is a result of the steep density gradient at thefront size of the target.
Nevertheless, the FIAF mechanism can become
important if the plasma corona with low density isformed at the target surface due to the laser prepulse. Inthat case, the potential difference gets very large and theenergy

10"1c:.o~ 1C12·c:
1nintensity and plasma density. When the backgroundplasma becomes underdense, the overdense solitons (ionbunch) can be further accelerated by the ExH force toenergy considerably higher than the maximal energy of
the FIAR. The spatial distribution of density and velocity
in the ion bunch are shown in Fig. 2 and Fig. 3 forseveral time points. The acceleration by the Ex/! isclearly seen. After 3 ps, the AI ions acquire 50 MeV
energy. Since the Ex/! force is very directed, the ionbunch must have a very low emittance.
2.5

cr0§

"'0"X~

1=5><101W/cm2
2.0 r-3 ps duration
2.5ps

1.5 r-~~c:Cl)

1.0 r-'iii

11

1

3ps

2ps

-c:

0.5---0.2•

jl. Jll#lot.la...l

0.0
OE+O

2E-3

1E·3.II

3E·3

4E-3

Position [em]Figure 2: The ion density distribution in an C plasma
irradiated by 3 ps laser pulse with intensity ofSxl0 18 W/cm2, A.=0.8 mm

ICIJ

1:Ol2

•

1E-3

2E-3

3E-3

4E-3

Position [em]•Figure 3: The temporal evolution of the velocity
distribution in the ion bunch in the C plasma.

i:5c:
..92

46Energy(MeV]
Figure 2: The typical velocity distribution of accelerated
ions from a foil irradiated 100 fs laser pulse of 10 19
W/cm2acquired by ions can be comparable or even higher thanthat of FIAR ions. The shock wave produced by ExH
force has complicate structure. After passing through thedensity maximum, the shock wave divides into several
solitons. The number of solitons depends on the laser

In long pulse (>100 ps) laser-produced plasmas,electron inelastic collisions are the main cause ofionization. However, if the duration of a laser pulse isshort (<I ps), although the plasma is heated rapidly,highly charged states inside the bulk plasma cannot be
produced because the collisional ionization time112.
as IzT•
mcreases. I and. . . potentta, where Iz t he 10ruzat10nT. the electron temperature. Moreover, since the rate ofcollisional ionization is proportional to the density, theionization occurs only in the high density plasma bulk. Inthe plasma corona the rate becomes negligibly small.
In the presence of an intense laser pulse the opticalfield ionization (OFI) becomes important on the plasma-305-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

surface. The ionization in the backward expanding
plasma corona is sustained as long as the laser field ispresent. The maximal charge of ions created by OFI may
be estimated from the field ionization probability,v
EI )= 4m ( --'LARy

512

E exp( - -2 ( --'LI )_L
EL

3 Ry312

JE_L
EL

fully ionized, while ions emitted from the rear surface
are not. However, the plasma induced field ionization
increases considerably ion charges so that carbon
nuclei and H-like ions are maJnly presented. Thecalculation performed for carbon slab target with I 0 nm
contamination layers in either side shows no ion
acceleration; only energetic protons are observed.

and t the pulse duration satisfYing the condition

ni12 )t=1, where 12 is the ionization potential for ion
2 s 4
4 3
with charge z, EA=m e /h the atomic field, OJA=me /h
2 42Electron Density

the atomic frequency, Ry=m e 12h , EL the laser electricfield. By solving this equation we find the maximal
potential / 2 which is approximatelyE[ (23+ln(dl00fs)+l n(EL I EA))
12 =RyE:
1921lon Densi]m2

As the laser intensity rises from 10 to 10 W/cm, thepotential increases from 1 keV to 5 keV for the 100 fs
pulse duration. For example, this potential corresponds++to ionization potentials 21 and 38 ions of Zr (Z=40)
respectively. The collisional ionization time (>I ps) forsuch ions is much greater than the laser pulse durationeven in the plasma bulk. Furthermore, the electric fieldof the laser exists only within the thin skin layer near thetarget surface. Within the conventional theory, it isunable to have fully ionized ions at the rear side of thefoil. However, the field ionization can occur at the rearside of the thin foil [6]. In the present study, the typicalfoil thickness is d-(0.1-1 )/, which is less than theexcursion length of hot electrons and greater than theskin depth. Hot electrons accelerated into the bulk bythe ponderomotive force give rise to electrostatic fields
on the foil surfaces. Under this condition, theelectrostatic field at the rear side of the target can, inone dimension, be estimated via Poisson's equation,

0~_.--~~--~~~~--._~0481216Position [c/ro]

20Figure 5: The spatial charge distribution in a carbon foilof 200 nm thickness irradiated by 1=4xl0A.=800 nm, t=SO fs pulse laser at t=lOO fs.

192W/cmConclusion
We have studied efficiency of various mechanisms ofion acceleration from plasmas irradiated by an intense,
short laser pulse in overdense plasmas by the collisional
particle-in-cell simulation including plasma ionizationand contamination effects. The bluster like ionacceleration, is found to be efficient and to have a lowemittance. We believe that effects of contamination andionization delay can be reduced for this mechanism ofion acceleration.

Referenceswhere Nh=1]N0V/VT is the density of hot electron, TJ theabsorption efficiency, N0 the critical density, v0 theelectron quiver velocity, vT the thermal velocity ofplasma electrons. Under condition discussed, the hot
electron density approximately equals to the criticaldensity and the electric field eErear/mc(l)-axi/c is of thesame order as the laser field. The spatial distribution of
the electric fields in the case of a Ti foil is shown in Fig.2
for t=SO fs. The strength of the calculated electrostatic is
close to the estimation. Thus, at the rear side of the foil,
the plasma induced field ionization (PFI) becomessignificant and as efficient as OFL The maximal
ionization potential is up to 600-800 eV for the laser
intensity over 1019 W/cm2. Since ions leaving the plasma
bulk are further ionized by this field, they acquire grater
charges and energies.
Typical charge distribution of ions emitted from thefoil irradiated by a short laser pulse is given in Fig. 5
Due to OFI, the ions emitted from the front surface are[1] A. Zhidkov, S. Sasaki, and T. Tajima, Phys. Rev.
E61, R2224 (2000)[2] A Zhidkov, A. Sasaki, T. Tajima, T. Auguste eta/.,Phys. Rev. E60, 3273 (1999)(3] S. P. Hatchett, C.G. Brown, T.E. Cowan et a/.,Phys. Plasmas 7, 2076 (2000)[4] E.L. Clark, K. Krushelnick, M. Zepf et al., Phys.
Rev. Lett. 85, 1654 (2000)[5] A.Maksimchuk, S.Gu, K. Flippo et al., Phys. Rev.
Lett. 84, 4108 (2000)[6] A. Zhidkov, S. Sasaki, Phys. Plasmas 7, 1357
(2000)-306-