23P147-P
Effect of Radiation Process in Relativistic High Energy Electron Transfer
相対論的高エネルギー電子輸送における輻射過程の影響
Manabu Fujita, Tomoyuki Johzaki1, Hideo Nagatomo
藤田学,城﨑知至1,長友英夫,
Institute of Laser Engineering, Osaka University
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan
大阪大学 レーザーエネルギー学研究センター 〒565-0871 大阪府吹田市山田丘2-6
1Institute for Laser Technology
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan1(財) レーザー技術総合研究所 〒565-0871 大阪府吹田市山田丘2-6
In cone-guiding fast ignition, an Au-cone is used to introduce heating laser close to a compressed core. In
such a high Z material, not only collisions with bulk plasma particles, but radiation dumping will be
important for transport of relativistic fast electrons generated by irradiation of ultra-intense laser. We
analyse the effects of collision and radiation on the energy transport of fast electrons in a cone by assuming
various material on the basis of Particle-In-Cell simulations.

2100

Total
Collisional
Radiative

10Ratio
10.1
0.1

110
Energy [MeV]

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
100

Radiative / Totaltransport in the cone material especially for in thehigh Z material.
Mass Stopping Power [MeV cm /g]

1. Introduction
Fast Ignition Realization Experiment program(FIREX) [1] is advanced in Institute of Laser
Engineering , Osaka university. In this project, adense fuel core imploded by low-intensity and longpulse GEKKO XII laser is heated by aultra-high-intensity and short-pulse LFEX laser.
The aim of this project is demonstrate fast heatingof fusion fuel up to the ignition temperature (5keV).
Generally, low density plasma ablated byimplosion laser irradiation exists in the surroundingof a dense core. It prevents the heating laser fromreaching close to the core. Kodama et al. [2]proposed a cone-shell target that an Au cone ispickled in fuel shell to introduce the heating laser
near the core. Using the cone-shell target, 20%
heating efficiency was attained in the integrated
experiments.
On the other hand, in recent integrated
experiments using Au cone attached shell targets,it was observed that the grate amount of γ-ray isgenerated by irradiation of heating laser, and theγ-ray affects measuring instruments directly, as
well as measurement of fusion neutron yields via
the (γ,n) reactions in chamber structure materials.
Additionally, for transport of relativistic fastelectron in a high Z material such as Au, not only
collisions with bulk plasma particles but alsoradiation dumping can not be neglected. For
instance, in the room-temperature solid-density Au,
the contribution of radiation to the stopping power
for fast electron (shown in Fig.1) becomes larger
with increasing energy of fast electrons, e.g, thecontribution is 11% for 1-MeV electron and is
50% for 10-MeV electron. Hence, we should
consider the radiation dumping in the fast electron

Fig. 1 .Energy dependence of the stopping power
to the high energy electron in room-temperaturesolid-density Au.
In this work, we examine the effect of radiation
dumping on energy transport of fast electron invarious materials on the basis of theParticle-In-Cell (PIC) code including collision andradiation processes.
2. Simulation method
We use relativistic electromagnetic PIC code ofwhich the typical cycle in one time step is shown inFig.2. In the conventional PIC code, the equationsof charged particle motion and time development ofelectromagnetic field are simultaneously solved(Fig.2 blue line). Since the aim of this work isanalyze of energy transport in high density material,
we have to consider both collision and radiation
processes (Fig.2 red line).
Related to generated γ-ray, assuming its stopping

range is large enough to the cone and implosion
core size, so we don’t consider radiation transport
process. We assume that γ-ray freely escape fromthe cone and the core with keeping its direction andenergy at emission. For extract of fundamental
properties, one dimensional simulation is preferable
since the PIC simulations for the target with wide
density scale (from laser critical density to the solidone) are very expensive. So, we carried out
simulations in one dimensional real space andthree-dimensional velocity space in the view ofboth developing and computation execution.

changed. Once the scattering angle is determined,
we can get the change in momentum of the particle
in the collision P. Using both P and theconservation of the total momentum through thecollision process, we get the momenta for twoparticles after the collision.
𝑷′1 =𝑷1 + 𝛥𝑷
(4)𝑷′2 =𝑷2 − 𝛥𝑷
(5)Finally, the momenta in COM frame aretransformed to those in laboratory frame. These
calculations are done for all particles in every step.

Particle-in-Cell (PIC) simulation with Collisional Processes (Monte Carlo Models)

4. Radiation process
When the high energy electrons pass through thehigh density plasmas, the large angle scattering by
bulk ions occurs and the high energy photons areemitted via the bremsstrahlung process. The emitted
-ray has the energy from hundreds keV to several
tens MeV. The energy of emitted photons becomes
impossible to ignore in the kinetics in the large
angle scattering of high energy electrons.
The treatment of large angle scattering isbasically the same as that for the small angle binary
collision noted above except for the collisioncross-section. In addition, we calculate the radiation
emission due to the bremsstrahlung. The radiation
probability of bremsstrahlung is calculated byquantum electrodynamics [6]. The energy andmomentum losses of fast electrons are also
calculated to keep the energy and the momentum
balances between electrons and photons.

•Relativistic Coulomb collision•Bremsstrahlung•(Ionization)
 Equations for Particle motiondPiPi q i (E i  Bi )dt
mi c i

dx i
P
 i
dt
mi  i Interpolation of fields to particles

 Interpolation of particles tocharge and current on a Gridt(E, B) j  (E, B) i

(x, v ) i  (ρ, j) j

 Maxwell’s equation (solved on grids)

1 E4 B Jc tc
1 B   Ec tFig. 2. Typical cycle in one time step in relativistic
electromagnetic particle simulation consideringcollision and radiation processes.
3. Relativistic Binary Collision
We briefly present the relativistic binary collisionmodel. The collisional model is based on Ref. [4](basic concept) and Ref.[5] (relativistic binary
collision between different weighted particles).
After choosing two particles, the calculation ofcollision is done in center of mass (COM) flame.
The coordinate system of momentum space isrotated to the system in which the pz-axis is alignedwith the momentum vector p1 of the first particle.
This transformation is represented by𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜑( −𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜑𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜑𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜑−𝑠𝑖𝑛𝜃 𝑝𝑥00 ) (𝑝𝑦 ) = (0)𝑝𝑧𝑝𝑐𝑜𝑠𝜃(1)

The relativistic collisional frequency is given by𝜈12 =4𝜋(𝑒1 𝑒2 )2 𝑛𝐿 𝛬𝑝𝑟𝑒𝑙 2 𝑣𝑟𝑒𝑙

(2)

where,  is the Coulomb logarithm, nL is the lower
density among the first particle density n1 and thesecond one n2, 𝑝𝑟𝑒𝑙 and 𝑣𝑟𝑒𝑙 are the relative
momentum and velocity between two particles. The
scattering angle  is chosen randomly from
distribution of  that has the zero mean value andthe variance of〈tan2(𝛩/2)〉 = 𝜈12 𝛥𝑡(3)where 𝛥𝑡 is time step duration of simulation. Themagnitude of the momentum p is unchanged in thebinary collision process, but only the direction is

5. Concluding Remarks
We simulated the transport of fast electrons indense plasmas by assuming various materials forplasma with PIC code including collision andradiation process. We will discuss the contributionof radiation emission to energy loss of fastelectrons.
References[1] H. Azechi and the FIREX Project, Plasma Phys.
Controlled Fusion 48, B267 (2006).
[2] R. Kodama, et al., Nature 418, 933 (2002).
[3] ICRU Report 37, ICRU, Bethesda, MD, USA,Oct. (1984).
[4] T. Takizuka and H. Abe, J. Comp. phys. 25,205 (1997)[5] Y. Sentoku, et al. J. Comp. Phys. 227, 6846
(2008)[6] W. Heitler, The Quantum Theory of Radiation.
(Clarendon, Oxford 1954)