Transport Window for Bunching Beams in a Final Stage of...
Transcript of Transport Window for Bunching Beams in a Final Stage of...
Transport Window for Bunching Beams in a Final Stage of Heavy Ion Inertial Fusion
Tokyo Institute of Technology, Department of Energy Sciences
Takashi KIKUCHI, Mitsuo NAKAJIMA and Kazuhiko HORIOKA
International Workshop on Recent Progress of Induction Accelerators (RPIA2002), October 29-31, 2002, Tsukuba, Japan
Background & Purpose
Intense Heavy Ion Beam (~10GeV ~10ns ~100kA) Generation & Transport are required for effective implosion.
Heavy Ion Inertial Fusion
BeamBunching
Induction Linear Accelerator
Final Beam Bunching
~100ns ~10ns
Accelerated Heavy Ion Beam
Focusing
Beam
Beam Irradiation for Implosion
Dynamics of Bunching BeamBunching Beam Transportability in Phase Advancing Condition
Researches:
Heavy Ion Beam Bunching by Induction LINAC
Bipolar Voltage Waveform
Apply Bunching Voltage at each Gapfor beam bunching
∆ββ
head
tail
Beam
t
V
Induction buncher consists of periodic lattice, acceleration gaps & FODO quadrupole.
apply to beam
Head & tail velocities are modulated. ∆β/β indicates Velocity Tilt.
Beam head is deceleratedBeam tail is accelerated
by
Beam bunch becomes short during transport.
Velocity Tilt Induced Instability
Head-to-Tail Velocity Tilt for Bunch Compression
Transverse Mismatch in terms of Quadrupole Lens
Beam Transport Instability
Prediction Resonance Effect by Phase Advance Modulation
Verify Simple Estimation of Instability using Particle-Core Model
Envelope OscillationResonance Instability
Beam Parameters
Ion SpeciesIon Number
Total ChargePulse Duration
Total Beam CurrentBeam Number
Current per BeamParticle Energy
Longitudinal Beam Length
Pb1+ (207.2 amu)2.5x1015
0.4mC250ns ⇒ 10ns1.6kA ⇒ 40kA
4400A ⇒ 10kA
10GeV ( β ~ 0.31 )
23m ⇒ 0.9m
by J.J. Barnard, et al., Physics of Fluid B 5, 2698 (1993).
Parameters in final stage of HIF driver system
Bunch Compression Ratio = 25
Envelope Calculation Result with Bunching
Transverse Behavior
Beam bunching causes current (perveance) increase.Radius Expansion
Longitudinal BehaviorBunching voltages apply velocity tilt to beam,bunch compression is caused.
Core/Particle Resonance
YX
Beam Core Oscillation
Particle Oscillations around CoreResonance
x
y
ωcore / ωparticle=integer
by J.-M. Lagniel, Nucl. Instrum. Methods Phys. Res. A345 (1994) 46.
Halo formation, larger orbit of particle, chaotic behavior, etc. are induced by resonance.
Beam Core
Halo Particles
Poincaré Maps
σ0=60˚ ∆β/β=0 σ0=60˚ ∆β/β=5%
Lager Orbitby Resonance
Particle Loss & Halo Formation
x [cm]
dx/d
s [m
rad]
x [cm]
Resonance reentrancedue to ∆β/β
Expression of Phase Advance in FODO Lattice
( ) θθθθθθθθθθσ sinhsin21coshsinsinhcoscoshcoscos 2
2
0
−−+=ll
LL
σo : Phase Advance without Space Charge [deg]θ : Focusing Strength of Lens [rad]L : Length of Drift Space (O in FODO) [m]ℓ : Length of Focusing Space (F or D in FODO)
from Transfer Matrix
F
ℓ
s
L
O ODkt
2
0 2coscos
++=
aLK lσσ
Calculate σ0
σ : Phase Advance Depressed by Space Charge
Estimate σ
( )σ
εsin
22 La t += l
Average Beam Radius
2
=l
θkℓ
ℓ ℓ
ℓ ℓ
Beam Envelope Calculation
Transverse Envelope Equation (K-V Distribution)
modulated by ∆β/β
3
2
2
2 ~2~XYX
KXkds
Xd tt
ε++
+−=
3
2
2
2 ~2~YYX
KYkds
Yd tt
ε++
+=
)(sXX ≡
γβ ~~1~ ∝tk
s : Transport Distance
32 ~~1~γβ
∝K
Velocity Tilt induces Beam Envelope Mismatch
3
2'
22
2
ZZKk
dsZd zzL
zε++−= = 0
Longitudinal Envelope Equationtk : Transverse Focusing Force: Transverse Perveance
zk : Longitudinal Focusing ForceLK : Longitudinal Perveance
K
)(sYY ≡ )(sZZ ≡
Transport Window Shrinking with Compression
Transport Window becomes small with longitudinal compression (K increase).
For Avoiding the Resonance Conditions ...
It is difficult that entire beam stability is maintained during compression.
Velocity Tilt ∆β/β
Phas
e A
dvan
ce σ
Phase Advance Dynamics with Compression
K/K0=1
K/K0=2
K/K0=3
from Envelope Calculation
at Z/3
The phase advance goes off Transport Window during compression.
Particle-Core Model (PCM) Calculation
Test Particle Equation in PCM
Beam Core
x
y
Test Particle
Beam cross section
calculated by Env. Eqs.
( ) ( )
( )
>−++
⋅
≤+
+−=Xx
XYxxKx
XxxYXX
K
xkds
xdx
222
2
2
~2)sgn(
~2
~
Poincaré plot at each slice with compression
–1 –0.5 0 0.5 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
–1
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
z/Z
λ/λ
0
(∆β
/β) / (∆
β/β
)max
123456
1 2 3
4 5 6From relation between velocity tilt & perveance, resonance effect is appeared at near center, rather than beam head.
PCM calculations are carried out at each sliced position.Each Poincaré plot is shown in
Summary
Resonance reentrance due to ∆β/β
Instability Growth
Simple Prediction of Phase Advance Modulation
Resonance Reentrance & Envelope Mismatch
decide Transport Window for Bunching Beam
Transport Window changes with Longitudinal Compression