J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)376–378
000–000

Effects of Plasma Foil Target Geometry on Achievable Energy ofFast Ions Generated by an Intense Ultra-Short Laser Pulse
OKADA Toshio, KITADA Tsuneyuki, OKUBO Kouta, SUGIE Michio and ANDREEV Alexander A.1
Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan
1
Institute for Laser Physics, St. Petersburg 199034, Russia(Received: 9 December 2003 / Accepted: 17 May 2004)

Abstract
Particle-in-cell (PIC) simulations of fast particles produced by a short laser pulse of duration of 40 fs and intensityof 1020 W/cm2 interacting with a foil target are performed. Dependence of the generated fast ion energy on the target
geometry is examined. The absorbed laser energy is transferred to fast electron, which interact with the foil and arepartially ejected from the foil surfaces. These electrons produce an electric field that causes an ion beam to be emitted
from the foil rear surface. Mechanism of fast (multi-MeV) ion acceleration in the foil plasma and the influence of thefront density gradient and other laser and plasma parameters on ion acceleration are analyzed.
Keywords:
intense ultra-short laser pulse, fast electron generation, fast ion generation

1. Introduction

2. PIC simulation

Fast particles generated by laser-plasma interactions canbe used in many applications, from manufacturing tomedicine and even for the initiation of tabletop nuclear
reactions. Fast ion generation by the interaction of an ultrashort high intensity laser pulse with a plasma has been
demonstrated in recent theoretical [1] and experimental [2]papers, with maximum ion energies of up to 0.5 GeV having
been observed. Different methods of fast ion generation havebeen proposed for both gas [3] and solid [4] targets. It has
been shown that the energy of a laser pulse can be efficiently
converted into fast ion energy using foil targets. Simulation[5] has shown that the mechanisms for generating ion
acceleration are the ambipolar field and the Coulomb
explosion. It has also been shown that fast electrons ejectedfrom the foil by the laser field create a strong ambipolar field,
which is the main source of acceleration of ions ejected fromthe back of the foil. Thus a collimated ion beam can beproduced by focusing an intense laser onto the surface of asolid film [4]. Fast ions are accelerated normally to the foil
surface [6]. Most experimental high power lasers produce a
pre-pulse, which generates a plasma layer with a smoothdensity gradient on the surface of the foil. In this paper, we
attempt to develop a simulation model to analyze themechanism of ion acceleration in plasma layers with smoothdensity gradients. We select a very short (40 fs) laser pulse
and thin foil (2 µm).

In solid target experiments with focused intensities
exceeding 1020 W/cm2, high-energy electron generation andenergetic protons have been observed on the backside of thetarget [7]. We apply a PIC method to simulate the interactionof a plasma layer with an intense ultra-short laser pulse. The
method is based on the electromagnetic PIC and is appropriate
for analysis of the dynamics of over dense plasmas createdby arbitrarily polarized, obliquely incident laser pulses. The
two dimensional (using a Cartesian coordinate system)
relativistic, electromagnetic code [6] is used to calculate theinteraction of an intense laser pulse with an over-dense
plasma. Calculations with ion mobility allowed were carriedout for a plasma with the initial density profile shown in Fig.
1. Simulations were performed for laser wave length of 1 µm

Fig. 1 Target density profile.

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: okada@cc.tuat.ac.jp1376

Okada T. et al., Effects of Plasma Foil Target Geometry on Achievable Energy of Fast Ions Generated by an Intense Ultra-Short Laser Pulse

and laser intensity of 1020 W/cm2. The time step is chosen tobe 0.03c/ω where ω is the laser frequency, and the mesh size
is chosen to be 0.03c/ω, where c is the velocity of light. The
number of x-axis grid points is 104 and the maximum electron

0.9µm

0.9µm

density is 4nc, where nc is the critical density. The plasma
density gradient varied 155 ≤ ω x/c ≤ 183 and the constant
plasma density was at 183 ≤ ω x/c ≤ 239 (see Fig. 1). We havedemonstrated fast ion production and focusing from the rearsurface of the foil. We consider three kinds of target here,
which are slab target, target with triangle cavity and target
with circle cavity. Figure 2 shows the geometry of the targets
with the triangle and circle cavities.

3µm

3. Fast ion production from the rearsurface of the foil
The absorbed laser energy is transferred to fast electrons,
which interact with the foil and are partially ejected from thefoil surfaces. These electrons produce an ambipolar field thatcauses an ion beam to be emitted from the foil rear surface.
Fast ions accelerate normally to the foil surface because thisis the direction of the ambipolar field. We note that ions areejected from both sides of the target: but fewer fast electrons,
and hence fewer ions, are ejected from the front side. Thus,
we only consider the rear side of the target. In Figs. 3, 4 and5, spatial distributions of ion density at different times areshown for the slab target, the target with triangle cavity and3µmFig. 2

Geometry of a target containing a cavity withgeometrical sizes.

Fig. 3

Spatial distribution of ion density from the slab targetat (a) ωt = 0, (b) ωt = 400 and (c) ωt = 800. The density
scales are limited to (a) 4ne , (b) 2ne and (c) 2ne .

Fig. 42377

Spatial distribution of ion density from the target withtriangle cavity at (a) ωt = 0, (b) ωt = 400 and (c) ωt = 800.
The density scales are limited to (a) 4ne , (b) 2ne and (c)2ne .

Okada T. et al., Effects of Plasma Foil Target Geometry on Achievable Energy of Fast Ions Generated by an Intense Ultra-Short Laser Pulse(a)2101100n / nc

1010-1

10-210-310-4
10-50102030
ion energy (MeV)

40

50

40

50

4050(b)210101n / nc

100
10-1
10-2
10-3
10-4
10-50

102030ion energy (MeV)(c)
210101Fig. 5n / nc100

Spatial distribution of ion density from the target withcircle cavity at (a) ωt = 0, (b) ωt = 400 and (c) ωt = 800.
The density scales are limited to (a) 4ne , (b) 2ne and (c)
2ne .

10-1
10-2
10-3
10-4
10

the target with circle cavity, respectively. In Fig. 6, ion energy
distributions at ωy/c = 250 for ω t = 800 are shown in thethree cases of the target. It is clear that these ions could befocused by a target with circle cavity in a small volume.

Fig. 6-50102030
ion energy (MeV)

Ion energy distributions at ωy/c = 250 for ωt = 800 with(a) the slab target, (b) the target with triangle cavity and(c) the target with circle cavity.

4. ConclusionWe have shown numerically that a laser pulse of intensity
1020 W/cm2 and a duration of 40 fs will generate an intense
ion bunch that propagates directly from the rear surface ofthe foil. Finally, we get a maximum ion energy of 32.4 MeV
at ω t = 800 from the target with circle cavity, a maximum
ion energy of 29.8 MeV at ω t = 800 from the target withtriangle cavity and a maximum ion energy of 28.6 MeV atω t = 800 from the slab target. We can conclude that the target
with circle cavity is the most useful target to generate anintense ion bunch in these different targets.

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References[1] C. Wilks, Phys. Fluids B5, 2603 (1993).

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