23P152-P
Fast Electron Beam Guiding for Efficient Core Heating
高効率加熱のための高速電子ビームガイディング
T. Johzaki, A. Sunahara, H. Nagatomo1, S. Fujioka1, H. Sakagami2, K, Mima1
城﨑知至, 砂原淳，長友英夫1, 藤岡慎介1，坂上仁志2, 三間圀興1
Institute for Laser Technology
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan(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
1Institute of Laser Engineering, Osaka University
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan1
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
2
Fundamental Physics Simulation Research Division, National Institute for Fusion Science322-6, Oroshi-cho, Toki, Gifu 509-5292, Japan
2核融合科学研究所基礎物理シミュレーション研究系 〒509-5292 岐阜県土岐市下石町322-6
In cone-guiding fast ignition, the guiding of fast electron beam with significantly large beam divergence is
one of the most important issues for achieving efficient core heating. We proposed two guiding schemes,
one is the “Tongari” tip guiding by resistive magnetic field and the other is the guiding by externally
applying axial magnetic field. The guiding performances for these two schemes are demonstrated byParticle-In-Cell and Fokker-Planck simulations.

1. Introduction
In cone-guiding fast ignition [1], fast electrons
generated inside the cone propagate the distanceof 50m ~ 100m to the imploded dense core,
and then heat the core up to ignition temperature.
Thus, the fast electron beam control (e.g.,enhancement of energy coupling of heating laser
to fast electrons, optimization of fast electronenergy spectrum, reduction of beam divergenceand beam guiding to core) is one of the most
crucial issues to achieve the ignition and highgain in fast ignition.
According to the previous work [2], the fastelectron beam has large beam divergence (fullangle of ~100 degree), which could be one of themain factors for lowering the core heatingefficiency. To improve the heating efficiency,
there are some ideas on beam guiding using
self-generated magnetic fields [2, 3]. The otherone is the guiding by external magnetic fieldalong to the beam propagation direction [4].
In the present paper, we propose the beam
guiding schemes by the self-generated resistive
magnetic fields and external magnetic fields, andevaluate the fundamental performances.
2. Resistive Guiding
The magnetic field growth in collisional plasmas isderived from Faraday’s law and Ohm’s law,
together with the assumptionof quasi
neutrality for
beam and return currents ( j fe   jbe );B  (  j fe )    j fe ,twhere is the resistivity. The first and second terms
are the sources by the radial gradient of fastelectron current and by the gradient of resistivity.
Here, we use the magnetic field caused by thesecond term, which works to confine the fastelectrons in the higher-resistivity region [5]. To
guide the fast electron beam, we propose “Tongari”
cone tip (“Tongari” is Japanese word, means“pointed”). If we use higher-Z material for the tip
compared with the surrounding imploded plasma,Fig. 1 Spatial profiles of (a) inital density ofstandard Au flat top tip and (b) DLC Tongari tipand (c) resistive magnetic field at 500fs. The
yellow lines in (a) and (b) show the beam
injection points.

Table I summary of guiding performance of Tongari tip.
Tip material
Bmax [T]Econe*
Ecore*
Te0*
Au
1250
1.90.81.0Cu1020
1.8
1.0
1.4
Al977
1.3
1.3
1.8
DLC723
1.4
1.3
1.9*The values of deposited energies in cone tip Econe and incore Ecore, and electron temperature enhancement at corecenter Te0 due to heating are normalized by the values
for the standard Au flat cone tip (5m thickness) case.

3. External Field Guiding
Under the sufficiently-strong axial magnetic
fields, the generated fast electrons twist around themagnetic field lines and are expected to be guided
into the core. In addition to the guiding effects, thefast electron stopping rage becomes effectively
shorter due to the gyro-motion. The preliminary
evaluation of guiding performance was done by 2D
PIC simulations (collisionless), where we assumed
that an Au plane target (50ncr, Z=40) with 1mscale pre-plasma is irradiated by an intense laser
pulse with 1m wavelength, 1019W/cm2 intensity,
200fs flat top (30fs rising) duration and 5m spot
diameter. The external magnetic fields with strengthof Bx,ext = 0 ~ 10kT are uniformly applied along tothe beam propagation direction. In Fig.4, the beam

Beam Divergence angle  div [deg.]

the confinement field will be generated at thematerial contact surface. Though ahigh-Z material,
such as Au, is preferable for generating the strong
magnetic field, the energy loss and scattering of fastelectrons become large in the high-Z material. So,
we estimate the guiding performance for different
cone materials (Au, Cu, Al, DLC) by Fokker-Planck
simulations where we used the fast electron beamprofiles obtained from a 2D PIC simulation [2] for a30-degree cone with 1019W/cm2 heating pulse, anda spherically compressed CD core (Gaussiandensity profile with peak density of 200g/cm2, R =0.12g/cm2 and uniform temperature of 300eV) wasassumed (Fig. 1 (a)-(b)). The spatial profile ofmagnetic field for the case of DLC Tongari tip at t =500fs is shown in Fig. 1 (c). It is found that thestrength of magnetic field is ~ 0.7kT at this moment.
The simulation results are summarized in Table I.
The strength of confinement magnetic fields
generated at the cone-plasma interface is about 1kTand it increases with material-Z. The collisional
effects are also large in the high-Z material. As theresults, the core heating rate for the Au and Cu
Tongari tip cases is smaller than that for thestandard Au cone. The core heating rate is enhanced
for the Al and DLC tip cases, which means thelow-Z material such as Al and DLC is preferable.

6050403020
1000.1

1Bx,ext [kT]

10Fig. 2 Beam divergence angle div as a function of
external magnetic field strength Bx,ext.
divergencediv is plotted as a function of Bx,ext. It isfound that t div starts to decrease at Bx,ext = 0.1kT
and reaches div = 0o at Bx,ext = 3kT. These results
indicate that the effective guiding can be achieved
with Bx,ext > a few kT. Such a high field could beachieved by implosion [6] of spherical shell target
with external magnetic field [7].
4. Concluding Remarks
On the basis of PIC and Fokker-Planck
simulations, we showed the guiding performances
for two types of guiding concepts, i.e., one is theresistive guiding by Tongari tip and the other is theguiding by externally applied axial magnetic fields.
We propose the guiding scheme by combination oftwo guiding concepts and plan to introduce it into
FIREX-I integrated experiments.
Acknowledgments
This work is partially supported by JSPS
Grant-in-Aid for Scientific Research(C) (22540511).
The authors are grateful for the support of thecomputer room of ILE and the cyber-media centerat Osaka University.
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