The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

BEAM DYNAMICS AND INSTABILITY IN FINAL BEAM BUNCHINGFOR HEAVY ION INERTIAL FUSION
T. Kikuchi*, T. Katayama, CNS, University of Tokyo, Saitama, 351-0198, Japan
M. Nakajima, K. Horioka, Tokyo Institute of Technology, Kanagawa, 226-8502, Japan
Abstract
Emittance growth and beam dynamics are investigatedby a particle simulation for longitudinal bunch
compression in an accelerator system of heavy ion inertial
fusion. Rapid bunch compression in final stage of thedriver system causes the emittance growth. Particlesimulations are carried out at various initial particle
distributions, and the emittance growths during the final
beam bunching are considered.

INTRODUCTION
Studies on space-charge-dominated beam are crucial
issue in inertial confinement fusion (ICF) [1] by using an
intense-heavy-ion beam, i.e. heavy ion inertial fusion(HIF) [2,3]. In the ICF, energy of several MJ must be
injected for a short time to a fuel pellet. The target pellet
irradiated by the energy driver is rapidly imploded. The
implosion can cause high energy density state at thecenter of the pellet, and a lot of thermonuclear reactions
are expected by the high temperature and dense plasma of
the fuel. The intense heavy-ion beam is one of theinfluential candidates as the energy driver for ICF system.
However, the required parameters of heavy ion beam
are several GeV particle energy, 100 kA total current, andaround 10 ns short pulse duration, so that the beam
parameters are far from those of conventional particle
accelerator. To this end, the beam dynamics and control
are important research issue. In the final stage of HIF
driver system, the beam pulse must be longitudinallycompressed from 100 to 10 ns. For this purpose, induction
voltage modulators, which have precise waveform
controllability, are useful device [4]. For the effectivepellet implosion, we should transport and compress thebunch of heavy ion beam without emittance growth aspossible. A final focus and beam irradiation are crucial [5],but large emittance interferes the focusing to the small
fuel pellet. For this reason, the final beam bunching is key
technology in the HIF driver system.
There is beam instability caused by space chargeoscillation [6-8]. The instability has threshold on strengthof the space charge effect. When the tune depression islower than 0.4, the beam transport may be unstable due tothe instability induced by the space charge effect. In theregion of the final beam bunching, the intense heavy-ion
beam just becomes the space-charge-dominated beam,and passes through the threshold.
In this study, we investigate the beam dynamics during
the longitudinal bunch compression in the final beambunching. Numerical simulation using particle-in-cell(PIC) method is carried out for the consideration ofparticle behaviour. The emittance growth is calculated andis compared with various types of initial particle
distribution.

TRANSVERSE PARTICLE BEHAVIOUR
In this study, the beam dynamics simulation requires
fully three-dimensional numerical scheme. From theviewpoint of the computational cost, such fullcalculations are difficult. While the longitudinal bunch
length is of the order of meter, the scale of the transverse
cross section is only a few cm in the regime of final beambunching [9]. As a result, the small-scale phenomena will
be dominated by the transverse beam dynamics. We deal
with the particle dynamics in the transverse cross sectionof the beam by multi-particle simulation, and the effect oflongitudinal compression is introduced as the beam
current increase [10].
The PIC method is used for descriptions of theFigure 1: Normalized charge density in initial KV beam on real (top) and phase (bottom) spaces, (a) at initialcondition, (b) at 87 l.p., (c) at 96 l.p., (d) at 108 l.p., and (e) at last (150 l.p.), respectively.
_________________________________________*tkikuchi@cns.s.u-tokyo.ac.jp

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

Figure 2: Normalized charge density in initial WB beam on real (top) and phase (bottom) spaces, (a) at initialcondition, (b) at 87 l.p., (c) at 96 l.p., (d) at 108 l.p., and (e) at last (150 l.p.), respectively.
transverse behaviour with the longitudinal compression,
the effect of which was evaluated by assuming linear
increase of the beam current. The charge and mass of thesuper particles are increased and the ratio performs thereweighting of the super particle with the beamtransport [10].
The beam parameters were assumed as Ref. [3], and thefinal bunch compression ratio is 25. The FODO magnetic
quadrupole lattice is used for the beam transport. Fromthe estimation by the longitudinal envelope equation, thetotal induction buncher length is assumed as 450 m with
FODO unit of 3 m [9]. The transverse calculation regionis fixed at 10 cm x 10 cm, and the boundary condition isgiven as a conductor wall. The Kapchinskij-Vladimirskij(KV) [11], waterbag (WB) [12], Gaussian (GA) [12], andsemi-Gaussian (SG) [13] distributions are given as theinitial condition.
Figure 1 shows the charge density maps of the beamions in physical and phase spaces at each lattice period(l.p.) for initially KV distributed beam. In the real spacemaps, the horizontal and vertical scales correspond to thefull calculation region. The charge density is normalized
by the maximum value at each map. The beam radius isextended with the beam current increase due to thelongitudinal bunch compression. As shown in Fig. 1,localized charge distribution in real space and the dilutionof the beam particle in phase space are indicated during

the final beam bunching. Also, qualitatively similar
behaviours with KV beam are observed in WB
distribution as shown in Fig. 2. On the other hand, as
shown in Fig. 3, the localized charge density is notformed in the initial GA beam. Figure 4 shows thenormalized charge density with initial SG beam. In thecase of SG beam, the behaviours are almost the same asGA case.

EMITTANCE GROWTH
We define the average of unnormalized transverse rmsemittance as ε=(εx,rms+ εy,rms)/2. The initial emittance isassumed at εi=εx,rms=εy,rms=10 mm mrad. At each initial
distribution, the evolution of the emittance ratio ε/εi,
which indicates the ratio of the average emittance andinitial one at each lattice period, is shown in Fig. 5. As
shown in Fig. 5, the emittance abruptly increases after 80
l.p. in the case of initial KV beam. As similar to the resultof KV distribution, the emittance at initial WB beam is
steeply increased over 90 l.p. The initial GA and SG
beam cases cause the gradual increase of the emittancewithout abrupt growth. The final emittance ratios at 150
l.p. are around 1.23, 1.15, 1.12, and 1.08 in the initially
KV, WB, GA, and SG distributed beams, respectively.
The space-charge-dominated beam plays as nonneutral
plasma, and the collective behaviour causes theFigure 3: Normalized charge density in initial GA beam on real (top) and phase (bottom) spaces, (a) at initialcondition, (b) at 87 l.p., (c) at 96 l.p., (d) at 108 l.p., and (e) at last (150 l.p.), respectively.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

Figure 4: Normalized charge density in initial SG beam on real (top) and phase (bottom) spaces, (a) at initial condition,(b) at 87 l.p., (c) at 96 l.p., (d) at 108 l.p., and (e) at last (150 l.p.), respectively.
restructuring of the space charge distribution. The
localized particle distribution in the beam interior isobserved in Figs. 1 and 2, and the abrupt increase ofemittance is also confirmed as shown in Fig. 5. Unstablebeam transport caused by azimuthally symmetric fluteperturbation is known as one of instabilities due to thespace charge effect [7,8]. At each mode number of theflute perturbation, the dispersion relation in KV
distribution can give growth rate of the instability. These
analytical considerations suggested that the emittance
growths observed by the particle simulations in the caseof KV and WB beams are attributed to the instability due
to the collective behaviour of space-charge-dominatedbeam during the final beam bunching [14].

CONCLUSIONIn HIF driver system, the transverse beam dynamics
was investigated during the final beam bunching. The
transverse PIC simulation with the increase of the beam
current, as a model of the longitudinal bunch compression,
was carried out for the study of the beam transport.
As a result, the numerical simulations indicated that thebeam is bunched accompanied by the restructuring of
charge density distribution and emittance growth during

Figure 5: Emittance ratio at each initial particle
distribution as a function of lattice period.

the final beam bunching. The initially KV and WB
distributed beams caused abrupt emittance growth due tothe instability induced by the space charge effect. On theother hand, it is expected that initial GA and SG beams
may pass through the final beam-bunching region without
instability excited by space charge oscillation.

ACKNOWLEDGMENT
A part of these calculation results was derived by theuse of the Special Application Server B in RIKEN
Computer and Information Division.

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