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

BEAM DYNAMICS AND INSTABILITY IN FINAL BEAM BUNCHING
FOR HEAVY ION INERTIAL FUSION
T . K i k u c h i * , T . K a t a y a m a , C N S ，U n i v e r s i t y o f T o k y o , S a it a m a , 3 5 1 - 0 1 9 8 , J a p a n
M . N a k a j i m a ，K . H o r i o k a , T o k y o I n s t it u t e o f T e c h n o l o g y , K a n a g a w a , 2 2 6 - 8 5 0 2 , J a p a n

A b stra c t
Emittance growth and beam dynamics are investigatedby a particle simulation for longitudinal bunch
compression in an accelerator system o f heavy ion inertial
fusion. Rapid bunch compression in final stage o f thedriver system causes the emittance growth. Particle
simulations are carried out at various initial particle
distributions, and the emittance growths during the final
beam bunching are considered.
IN T R O D U C T IO N

Studies on space-charge-dominated beam are crucial
issue in inertial confinement fusion (IC F )[ 1 ] by using anintense-heavy-ion beam, i.e. heavy ion inertial fusion(HIF) [2,3]. In the ICF, energy o f 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 o f the pellet, and a lot o f thermonuclear reactions
are expected by the high temperature and dense plasma o fthe fuel. The intense heavy-ion beam is one o f theinfluential candidates as the energy driver for ICF system.
However, the required parameters o f heavy ion beam
are several GeV particle en er g y ,100 kA total current，andaround 10 ns short pulse duration, so that the beam
parameters are far from those o f conventional particle
accelerator. To this end, the beam dynamics and control
are important research issue. In the final stage o f 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, w e should transport and compress thebunch o f 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 charge
oscillation [6-8]. The instability has threshold on strengtho f the space charge effect. W hen the tune depression islower than 0.4, the beam transport may be unstable due tothe instability induced by the space charge effect. In theregion o f the final beam bunching, the intense heavy-ion
beam just becom es the space-charge-dominated beam,and passes through the threshold.
In this study, we investigate the beam dynamics during
the longitudinal bunch com pression in the final beam
bunching. Numerical simulation using particle-in-cell(PIC) method is carried out for the consideration o fparticle behaviour. The emittance growth is calculated andis compared with various types o f initial particle
distribution.
T R A N S V E R S E P A R T IC L E B E H A V IO U R

In this study, the beam dynamics simulation requires
fully three-dimensional numerical scheme. From theviewpoint o f the computational cost, such fullcalculations are difficult. W hile the longitudinal bunch
length is o f the order o f meter, the scale o f the transverse
cross section is only a few cm in the regime o f final beam
bunching [9]. A s a result, the sm all-scale phenomena w ill
be dominated by the transverse beam dynamics. W e dealwith the particle dynamics in the transverse cross sectiono f the beam by multi-particle simulation, and the effect o flongitudinal compression is introduced as the beam
current increase [10].
The PIC method is used for descriptions o f the1x-yreal space

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Q.
Ox-x1
phase space(QQ(DZ30 t
Figure 1 : Norm alized charge density in initial K V 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

Zox-yQ>
N*real space

CDQ.

O$cSx-x'phase space

CDDCDI3(IiFigure 2: Normalized charge density in initial W B beam on real (top) and phase (bottom) spaces,condition, (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 o f which was evaluated by assuming linearincrease o f the beam current. The charge and mass o f thesuper particles are increased and the ratio performs thereweighting o f 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 lengtn is assumed as 450 m with
FODO unit o f 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 (W B) [12], Gaussian (GA) [12], andsemi-Gaussian (SG) [13] distributions are given as theinitial condition.
Figure 1 shows the charge density maps o f 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 F i g . 1,localized charge distribution in real space and the dilutiono f the beam particle in phase space are indicated during

tial

the final beam bunching. A lso, qualitatively similar
behaviours with KV beam are observed in W B
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 o f SG beam, the behaviours are almost the same asGA case.
E M IT T A N C E G R O W T H

W e define the average o f unnormalized transverse rms
emittance as s= (sx rms+ s y5rms)/2. The initial emittance isassumed at £i=ex,rms=8y,rms= 10 mm mrad. At each initial
distribution, the evolution o f the emittance ratio 8/£i?
wmch indicates the ratio o f the average emittance andinitial one at each lattice period, is shown in Fig. 5. A sshown in Fig. 5, the emittance abruptly increases after 80l.p. in the case o f initial KV beam. A s similar to the resulto f KV distribution, the emittance at initial W B beam issteeply increased over 90 l.p. The initial GA and SG
beam cases cause the gradual increase o f 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, W B, GA, and SG distributed beams, respectively.
The space-charge-dominated beam plays as nonneutral
plasma, and the collective behaviour causes the1IHHS I—HBphase space

Figure 3: Normalized charge density in initial GA beam on real (top) and phase (bottom) spaces,condition, (b) at 87 l.p” (c) at 96 l.p” (d) at 108 l.p., and (e) at last (150 l.p.), respectively.

atNormalized Charge D e n s ity so i,—.
■I. . . . . .
i— J ニi -IB—ni ti

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

zo目x-yNCDQ.
Oreal space(SCDx-x
phase spaceoCD13(fi0 尽
Figure 4: Norm alized 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 Lp” and (e) at last (150 l.p.)，respectively.
restructuring o f the space charge distribution. The
localized particle distribution in the beam interior isobserved in F ig s .1 and 2, and the abrupt increase o f
emittance is also confirmed as shown in Fig. 5. Unstablebeam transport caused by azimuthally symmetric fluteperturbation is known as one o f instabilities due to thespace charge effect [7,8]. At each mode number o f theflute perturbation, the dispersion relation in KV
distribution can give growth rate o f the instability. These
analytical considerations suggested that the emittance
growths observed by the particle simulations in the caseo f KV and W B beams are attributed to the instability due
to the collective behaviour o f space-charge-dominatedbeam during the final beam bunching [14].
C O N C L U S IO N

In HIF driver system, the transverse beam dynamics
was investigated during the final beam bunching. Thetransverse PIC simulation with the increase o f the beam
current, as a model o f the longitudinal bunch compression,
was carried out for the study o f the beam transport.
A s a result, the numerical simulations indicated that thebeam is bunched accompanied by the restructuring o fcharge density distribution and emittance growth during
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1.05

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0.95

020

40

60

80

100

120

140

Lattice Period S
Figure 5: Emittance ratio at each initial
distribution as a function o f lattice period.

particle

the final beam bunching. The initially K V 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-buncmng region without
instability excited by space charge oscillation.
ACKNOW LEDGM ENT

A part o f these calculation results was derived by theuse o f the Special Application Server B in RIKEN
Computer and Information D ivision.
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