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