FFAG-ERIT R&D

06/11/06Kota Okabe (Kyoto Univ.)

for FFAG-DDS group

Neutron source for BNCTFFAG-ERIT scheme

Requirements from BNCT(Boron Neutron Capture Therapy): 　In order to remedy the tumor of 10cm2, 2*1013 neutrons are needed.If we assume that remedy time is 30 minutes => Flux cm2 sec.

Accelerator as a neutron source ; Energy is low, but beam current is very large (I > 40mA [CW])

ERIT : Emittance-Energy Recovering Internal Target

The stored beam is irradiated to the internal target, it generates the neutron in the storage ring. The beam energy lost in the target is recovered by re-acceleration.

Technically hard and expensive

Feature of ERIT schemeBeam current reduced by storage the beam in the ring.

Overview of FFAG-ERIT accelerator system

Emittance growth in storage ring

• Using an internal target in the ring, the beam emittance can be increased in 3-D directions by multiple scattering and straggling. In this reason, the storage ring require to large acceptance.

• In ERIT scheme, however, the beam emittance growth can be cured by Ionization Cooling effect.

Ionization cooling (1)

The rate equation of beam emittance passing through a target material is,

LongitudinalLongitudinal

HorizontalHorizontal

VerticalVertical

€

dεy

ds= −

1

β 2E

dE

dsεy +

β y E s2

2β 3mpc2LR E

€

dεx

ds= −

1

β 2E

dE

ds1−

D ′ ρ

ρ 0

⎛

⎝ ⎜

⎞

⎠ ⎟εx +

β x E s2

2β 3mpc2LR E

€

d σ E2

ds= −2

∂(dE /ds)

∂E 0

+dE

ds

1

pcβD

′ ρ

ρ 0

⎛

⎝ ⎜

⎞

⎠ ⎟ σ E

2 +d ΔE 2

rms

ds

Cooling term

Heating term

E

EΔ+

E

EΔ−

0

Wedge Target Acceleration Cavity

When the wedged target is placed at

dispersive point, can be possible.

€

∂(dE /ds)

∂E

Ionization cooling (2)

Energy loss rate dE/dx from Bethe-Bloch formula (9Be target)

In the light orange area (5~11MeV) the neutron is stable generated

For example, target thickness ~ 5 m

Energy loss : ΔEt ~ 35 keV

10 MeV proton beam

Energy loss : ΔEt ~ 46.8 keV

7 MeV proton beam

Requirement for FFAG storage ring

• Large acceptancemomentum acceptance dp/p ~ 5 [%] (from RF bucket height)transverse acceptance > 1000 [ mm mrad]

• Length of straight section (to install large RF cavity(width 54cm))The numbers of sectors is few, length of the straight section iseasy to guarantee.

• To be the compact which can be installed in the hospitalMean radius (r0) ~ 2 [m]

Spiral sector type FFAG

Magnetic field calculation (TOSCA)

Lattice parameters Cell num. = 8Open sec. angle = 45 degOpen F angle = 13.5 degPacking fac. = 0.3Average radius = 1.8 m

Spiral sector type FFAG

7MeV proton beam

The size of the accelerator becomes small compared with the radial sector type.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.0

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

horizontal tune

vertical tune

structure

3rd

2nd

1st

Operating point

Spiral angle and k value optimization

26o, k = 2

30o, k = 2

35o, k = 2

26o, no clamp, k = 2

35o, k = 1.7Optimized parameter

K value = 1.7,Spiral angle = 34 deg(With field clamp)x ~ 1.68, y ~ 1.20

We optimize k value and spiral angle.

Acceptance study

Gap 14 [cm]

Horizontal Vertical

~7000π mm-mrad ~1400π mm-mrad

Gap 14 [cm] ~7000π [mm-mrad], ~1400π [mm-mrad]

Gap 17.5 [cm]

~6100π [mm-mrad], ~3200π [mm-mrad] Gap 20.0 [cm]

~7000π [mm-mrad], ~2400π [mm-mrad]

Hori. Acceptance, Vert. acceptance

Ionization cooling simulation

Initial condition Transverse

Hori. emittance = 15 pi [mm mrad], Vert. emittance = 15 pi [mm mrad],

Matched twiss para.Longitudinal

dE = 0, Inial RF phase 10 deg. (moved from synchronous phase.)

ICOOL

•　 Using TOSCA field map•　 Fluctuations in the energy : Vavilov distributions•　 Multiple scattering : Moliere distribution• Particle num. = 1000• Be target is rectangle (no wedge). Target thickness = 5 m

RF amplitude Vrf = 400 kV, (mom. Acceptance ~ 4%)

Surviving turn numberResult of magnet gap 14 [cm]

Mean surviving turn num.　 192 turn

Suv.rate = particle num. (at turn) / initial particle num

RMS emittance and energy spread

An analytical solution and the simulation results are corresponding well while a little the beam loss.

Particle of the large amplitude is lost as the turn number increases.

Emittance is saturated

Vertical acceptance - dependent

~1400π [mm-mrad] ~2400π [mm-mrad] ~3200π [mm-mrad]

Vertical beta function@target ~ 1.35 [m]

Discussion

• From simulation results, the most cause of beam loss is heating of the vertical direction.

• It is difficult to achieve strong focusing the vertical direction in the spiral type lattice.

In this reason, radial sector type suitable for ERIT?

Radial sector type

Magnetic field calculation (TOSCA)

FDF latticeF-Mag. = 6.4[deg],D-Mag. = 5.1 [deg], F-D gap 3.75[deg], F-Clamp gap = 1.9[deg],Clamp thick = 4[cm]Mean radius = 2.35[m]

11MeV proton beamx ~ 1.75, y ~ 2.23FD ratio ~3

Vertical beta function & acceptance

Vertical acceptance ~ 3000π [mm-mrad] Vertical beta function@target ~ 0.83 [m]

Tracking results used TOSCA field.

(Horizontal acceptance > 7000π [mm-mrad])

Surviving turn number

Mean surviving turn num. 　 810 turns

RMS emittance and energy spread

An analytical solution and the simulation results are corresponding well while beam loss is few.

Vertical beta function - dependent

y = 0.83[m] : y = 2.22, Mean surviving turn num. 　 810 turny = 0.75[m] : y = 2.32, Mean surviving turn num. 　 910 turn

Summary• It is important to suppress overheating of the vertical direct

ion to increase the surviving turn number.

• Radial sector is more suitable than the spiral sector type for controlling the heating of the vertical direction.

• The surviving turn number exceeded 900 turns for radial sector type by controlling the tune.

• It might have to care for the longitudinal and horizontal direction trying increase the number of turns any further.