23P165-B
Numerical Analysis of Beam Dynamics for Final Pulse Compression Simulatedby Compact Electron Beam Device for Heavy Ion Inertial Fusion
小型電子ビーム装置を用いた重イオン慣性核融合の最終段パルス圧縮を模擬した
ビーム動力学数値解析	 
Takashi Kikuchi1), Kazuhiko Horioka2), Toru Sasaki1), and Nob. Harada1)
菊池崇志, 堀岡一彦，佐々木徹，原田信弘
1)

Department of Electrical Engineering, Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, 940-2188,
Japan
長岡技術科学大学・電気系	  〒940-2188	  新潟県長岡市上富岡町1603-1
2)

Department of Energy Sciences, Tokyo Institute of Technology, 4259, Nagatsuta, Yokohama, 226-8502, Japan
東京工業大学・創造エネルギー専攻	  〒226-8502	  神奈川県横浜市長津田4259
In a final stage of an accelerator system for heavy ion inertial fusion (HIF), pulse shaping and beam current
increase by bunch compression are required for effective pellet implosion. A compact simulator with anelectron beam was constructed to understand the beam dynamics. In this study, we investigate theoreticallyand numerically the beam dynamics for the extreme bunch compression in the final stage of HIF
accelerator complex. The results indicate that high current-low temperature condition in comparisons withcurrent status of experimental compact simulator is necessary to create the space charge dominated beam.

2. Theoretical Estimation to Create Space
Charge Dominated Beam Condition
Using a longitudinal beam envelope equation,
the ratio between the repulsion forces due to thespace charge and the emittance of the beam bunch
are estimated. The envelope equation is written
by [3]

zm'' + kz zm !

2
K L ! zz'!
=0zm2 zm3

(1)

where zm is the half bunch length, K L is thelongitudinal perveance, kz is the longitudinalfocusing force, εzz' is the longitudinal emittance,
respectively. From Eq.(1), the condition of thespace charge dominated beam is obtained by
K L zm3egI b0" b0=!1(2)2! zz'
40# ! 0 zm kBTL

where e is the elementary charge, g is the geometry
factor, Ib0 is the initial beam current, τb0 is the initial
pulse duration, ε0 is the permittivity in vacuum,kBTL is the longitudinal temperature, respectively.
The estimation result normalized by the initialbunch length zm0 is shown in Fig.1. The initial beam
current Ib0 is 100 µA and the initial pulse duration
τb0 is 100 ns. As a result, it is predicted that thecompression ratio of 57.8 is required to demonstrate
the space charge dominated beams in the apparatus
for kBTL=1 eV.
1000
Space Charge / Emittance Ratio KLzm / εzz’

1. Introduction
A compact simulator with an electron beam
was constructed to understand beam dynamics
during final pulse compression for inertial
confinement fusion (ICF) driven by heavy ion
beams [1]. It is important to clear the beam
dynamics for the precise control of high-current
charged particle beams due to effective fuel pellet
implosion of ICF.
To investigate the limitation of longitudinalpulse compression, we study the space-charge
dominated beam dynamics with theoretical andnumerical simulation approaches [2].

100

TL=0.1eV

10TL=1eV1
TL=10eV

0.1
0.01
0.001

110100Compression Ratio zm/zm01000

Fig.1. Ratio of longitudinal repulsion force due to spacecharge and emittance as a function of compression ratio

Ez = !

g d#
4! " 0 dz

me" mT !t%e2e $$+'L '&# 2eV02! V0(4)where me is the electron mass, V0 is the extraction
voltage of the electron beam at the electron gun, Tis the pulse duration of the applied voltage, L is thebeam transport distance with solenoid magnetic
field, respectively. In this study, V0=2.8 kV, T=100ns, L=2 m are assumed in comparison with theexperimental condition. By the applied voltage as
given by Eq.(4), the head of the beam bunch isdecelerated, while the tail of the beam bunch is notmodulated. As a result, the beam pulse iscompressed during the transport.
It is assumed that the extracted electrons arethermalized at the electron gun as

vth =kBTLme*+$,-./!/0-.1$2$34#*+5$,-./!/0-.1$2$34#!"##*+$,-./!/0-.1$2$34#6#%(3)

where λ is the line-charge density. The electronbunch is extracted from an electron gun assisted bythermal emission. The electron bunch is modulatedby the applied electric field in the gap. The voltage
pulses produced at each module are overlapped at
the gap using induction modulator technology [1].
The overlapped voltage pulse Vg at the gap is given
byVg (t) =$#78$+$978#9

3. Numerical Simulation during BunchCompressionwithSolenoid
Transverse
Confinement
Numerical simulations based on particle-in-cell(PIC) code [4] are carried out. The model is a
one-dimensional electrostatic PIC code with thelong wave approximation for the longitudinal
space charge calculation [3]. The longitudinal
self-electric field Ez is calculated by(5)

where vth is the initial thermal velocity.
Figure 2 shows the calculation results of the ratioof the beam current to the initial one, i.e., the pulse
compression ratio. As shown in Fig.2, the applied
voltage for the pulse compression is good enoughfor the operation for the case without the spacecharge effect and in quite low temperature
condition. However the space charge effect and theinitial temperature of electron bunch interfere theextreme pulse compression. In this experimental
condition, it is found that the initial temperature ofelectron bunch is main issue of interference for theextreme pulse compression.

$%&'$%&($%&)

$%&"

$%&&

30:-$;<=>
Fig.2. Pulse compression ratio during beam transport.
The red curve indicates the result with space charge
effect and kBTL=0, the green line shows the resultwithout space charge effect and kBTL=0, and the blue
curve shows the result with space charge effect andkBTL=0.01 eV, respectively.

4. Conclusions
To understand the beam dynamics during final
beam compression for inertial fusion energy driven
by heavy ion beams, the compact simulator withelectron beam was constructed. We studied thebeam dynamics with theoretical and numericalsimulation approaches to investigate the limitationof longitudinal pulse compression.
Using longitudinal beam envelope equation, theratio between the repulsion forces due to the spacecharge and the emittance of the beam bunch wereestimated. Also numerical simulations are carriedout. These theoretical and numerical approaches
suggested that in the compact simulator the strong
pulse compression and/or higher beam current areneeded to observe the beam dynamics around thestagnation point at the unneutralized bunch
compression.
References[1] K. Horioka, et al.: 18th International Symposium on
Heavy Ion Inertial Fusion (HIF2010), Darmstadt,
August-September 2010, TUS-0404.
[2] A. Namprom, T. Wiboonphon, T. Sasaki, and T.
Kikuchi, Nob. Harada: 3rd Euro-Asian Pulsed Power
Conference / 18th International Conference on
High-Power Particle Beams EAPPC-BEAMS 2010,Jeju, Korea, October 10-14, 2010, MoB3-5, p.108.
[3] M. Reiser: Theory and Design of Charged Particle
Beams (Wiley, New York, 1994).
[4] R. W. Hockney and J. W. Eastwood: Computer
Simulation using Particles (IOP publishing, Bristoland Philadelphia, 1988).