Bunching Beam Dynamics in Final Stage of Heavy Ion Fusion Driver
T. Kikuchi, M. Nakajima, and K. HoriokaEnergy Sciences, Tokyo Institute of Technology (TIT)
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 : HIF
BeamBunching
Induction Linear Accelerator
Final Beam Bunching
~100ns ~10ns
Accelerated Heavy Ion Beam
Focusing
Beam Irradiation for Implosion
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.
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
x [cm] x [cm]
y [c
m]
dx/d
s [m
rad]
Beam Transport by PIC Simulation
x-y Real Map x-x’ Phase Map
Beam Transport in FODO Latticewithout compression
0m
x [cm] y [cm]
ρ[C
/m2 ]
Beam Transport by PIC Simulation
Particle Maps
x [cm]
y [c
m]
x [cm]dx
/ds [
mra
d]0m
444m148 lattice
KV envelopex [cm] y [cm]
ρ[C
/m2 ]
Charge Distribution
444m148 lattice
Estimation for Beam Compression Effect
Linear
RapidSlow
Slow
Rapid
Induction Buncher
We calculate about 3 compression schedules
from Longitudinal Envelope Calculation
x [cm] x [cm]
y [c
m]
dx/d
s [m
rad]
x-y Real Map x-x’ Phase Map
Estimation for Beam Compression Effect
Beam Transport in FODO Latticewith linear compression schedule
x [cm] y [cm]
ρ[C
/m2 ]
Estimation for Beam Compression Effect
Charge Distribution Change in x-y spacewith linear compression schedule
y [c
m]
from KV envelope
Linear Compression Schedule
Real map
x [cm]dx
/ds [
mra
d]
Phase map
at stagnation point444m,148 lattice
Emittance dilutiondue to Resonance effect (σ = 60deg)
Slow Compression Schedule
x [cm]y
[cm
]dx
/ds [
mra
d]
at stagnation point573m, 191 lattice Real map
Phase map
Emittance dilutionsmaller than linear case
y [c
m]
Rapid Compression Schedule
x [cm]dx
/ds [
mra
d]
Real map
Phase map
at stagnation point444m,148 lattice
Phase maps and EmittanceDilutions are changed by Compression schedules
*R.W. Hockney and J.W. Eastwood, Computer Simulation using Particles (McGraw-Hill, New York, 1981).
Mesh Size & Debye Length
Intense ion beams, non-neutral plasmas, will show collective phenomena.
H / λD = 0.23*
H : Spatial Mesh Size (H=∆x=∆y)λD : Debye Length
in Usual Plasma Simulations,
We try to calculate with changes of PIC mesh size H.
H / λD = 1.6 H / λD = 0.4 H / λD = 0.227 H / λD = 0.2
y [c
m]
x [cm]
dx/d
s [m
rad]
Real Map
Phase Map
H / λD < 0.23H / λD > 0.23
Calculations with H / λD Changes
Calculation results are quite different in H / λD < 0.23 or not
at 444m, 148 lattice, just x25 compression
Negative Feedback of Particle Loss
H / λD = 0.4 H / λD = 0.2y
[cm
]dx
/ds [
mra
d]
x [cm]
Real Map
Phase Map
Nf / Ni = 1 Nf / Ni = 0.7
Particle Loss causes mismatch increase
x [cm]
Large mismatch increases beam radius
Large beam radius causes beam loss
y [c
m]
dx/d
s [m
rad]
Nf : Final super particle numberNi : Initial super particle number
Seed of particle loss is Resonance & Plasma Oscillation
H / λD= 0.2
H / λD= 0.4
H / λD= 1.6
H / λD= 0.8
Calculations with H / λD Changes
in case of slow compression schedule
dx/d
s [m
rad]
x [cm]
Phase Map
No particle loss, but phase map is clearly different at H/λD< 0.23.
Summary
In high-current beams, collective behavior is important
Emittance dilution depends on compression schedules in intense ion beam bunching
resonance effects induced plasma oscillations important issue for emittance dilution in Final Beam Bunching