Study of Resonance Crossing in FFAG
Masamitsu Aiba (KEK)
Contents1. Introduction2. Crossing experiment at PoP FFAG3. Crossing experiment at HIMAC synchrotron4. Summary
Introduction• FFAG accelerator:
– For proton driver– For muon acceleration, phase rotation
• Resonance crossing– In scaling FFAG: tune variation due to
imperfection of scaling – In non-scaling FFAG: tune variation in wide range
• Dynamics of resonance crossing is important. Experimental study at PoP FFAG and HIMAC
Crossing experiment at PoP FFAG
sector number 8 (DFD triplet)k value 2.5
kinetic energy 50-500keVfmagnetic field 0.14-0.32T(F)
0.04-0.13T(D)average radius 0.81-1.14mbetatron tune 2.22-2.16(Hor.)
1.26-1.23(Ver.)revolution freq. 0.61-1.40MHz
RF voltage 5kVpp
Parameter list
PoP FFAG: radial sector type scaling FFAG
Experiment of resonance crossing withvarious driving term and crossing speed
Remodeling magnets
Crossing third order resonance during acceleration
0 50 100 150 200 250 300 350 400 450
2.20
2.25
2.30
2.35
2.40
3x=7 (
x=2.333)
hori
zont
al tu
ne
Beam Energy (keV)
After remodeling Before remodeling
4mm iron plates
Driving term
0 45 90 135 180 225 270 315 360
-20
-10
0
10
20
⑧⑦⑥⑤④③②①
current error
current error
septum
COD with current error
CO
D (
mm
)
azimuthal angle (deg.)
)33()( 32233 DxDDxxODxO Feed Down:Driving term with COD
Controlling COD
Driving term can be varied and controlled.
Beam measurementBeam scraping & intensity measurement
turn
intensity
Particle distribution in beam emittance was measuredbefore and after crossing.
Fast crossing
0 250 500 750 1000 1250 15000.0
5.0x10- 4
1.0x10- 3
1.5x10- 3
2.0x10- 3
2.5x10- 3
3.0x10- 3
3.5x10- 3
4.0x10- 3
dI/dW
(
mm
-m
rad.
-1 )
emittance ( mm- mrad.)
BeforeCrossingAfter
Fast crossing: no clear signal of a damage due to crossing
110 130 150 (keV)
40 60 80 100 120 140 160
0.0
0.2
0.4
0.6
0.8
1.0
current error -2%, speed1
Nor
. int
ensi
ty
r from 50keV (mm)
scrp. 868mm scrp. 888mm scrp. 908mm
Energy gain 1.6kV/turn = x 1.4×10-3
Current error –2%Scraping data
Particle distribution in beam emittance
Slow crossing
80 100 120 140 160 1800.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
inte
nsity
(-)
r from 50keV (mm)
scraper 888mm scraper 908mm scraper 928mm scraper 948mm
Slow crossing: a part of beam is transported to large amplitude
0 1000 2000 3000 40000.0
5.0x10-4
1.0x10-3
1.5x10-3
2.0x10-3
2.5x10-3
3.0x10-3
3.5x10-3
dI/d
a (
mm
-mra
d.)
emittance (mm-mrad.)
Crossing After 130 150 170 190 (keV)
Energy gain 0.13kV/turn = x 1.2×10-4
Current error –2%Scraping data
Particle distribution in beam emittance
“Particle trapping” modelReference: A.W.Chao and M.Month, NIM 121, P.129 (1974) “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER NONLINEAR RESONANCE”
Phase space topology during crossing third order resonance
p3
1Distance from resonance
This model explains the experimental result.
Assuming: nonlinear detuning (octupole) driving term (sextupole)
Trapping efficiency
,43 eNL
0012 aBNL
2
1
03 aApe
)(2
0160
OdB
)(8
2
0
2
1
Sipp edA
3
2
1 4
eNL
pL 3
1
eL 23
:2
4
32
12
sA
)exp( 1
s
TA
P
1,1
,1,
1
11
if
ifs
Nonlinear detuning:
Driving term:
Linear tune shift:
Nonlinear tune shift:
Excitation width:
s: the beam emittance of island center
the total area of islands
the adiabatic parameter
The adiabatic parameter means a speed of islands moving during crossing.
Crossing speed:
:
Trapping efficiency for third order resonance
*Assuming >>1 to derivethe trapping efficiency
Comparison of trapping efficiencies
500 600 700 800 900 1000 11000.0
0.2
0.4
0.6
0.8
1.0
error 2%, speed 0.13kV/turn, scraper 948mm
Nor
. int
egra
l (-)
num. of turn 0.0 0.1 0.2 0.30
5
10
15
20
25
30
35
trap
ping
eff
icie
ncy
(%)
energy gain (kV/turn)
current error theory: -2% theory: 0% theory: -3% exp.: -2% exp.: 0% exp.: -3% sim.: -2% sim.: 0% sim.: -3%
The experiment results are consistent to simulations.
Efficiency in experimentTrapping efficiencies
are about 3.
Criterion to avoid trapping
2 3 4 5 6 7 8 9 10 110
5
10
15
20
25
30tr
appi
ng e
ffic
ienc
y (%
)
adiabatic parameter
current error -2% current error 0% current error -3%
Adiabatic parameter more than 7 will be harmless.
Crossing experiment at HIMACFlat bottom operation parameter
circumference 129.6msuper period / cell 6/12
particle carbon 6+inj. energy 6MeV/u
operation point (3.69, 2.13)
Crossing: Varying quadrupole strengthDriving term: SXFr*2 sextupole Nonlinear detuning: Second order effect of SXH sextupole
Crossing 3vx=11 in both directionObserving beam profile with Gas Sheet Monitor directly
SXFr
SXFr
SXH for all SPGas SheetMonitor
Crossing in a direction of tune decreasing
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)-40 -30 -20 -10 0 10 20 30 40
0
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
x=3.668 x=3.662 x=3.661 x=3.660
x=3.658 x=3.652 x=3.647Crossing speed:
4.6*10-6
Nonlinear detuning:2.52m-1
Driving term:0.019m-1/2
Beam profiles during crossing
Crossing in a direction of tune increasing
-40 -30 -20 -10 0 10 20 30 400.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
t
x (mm)-40 -30 -20 -10 0 10 20 30 40
0.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
tx (mm)
-40 -30 -20 -10 0 10 20 30 400.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
t
x (mm)
x=3.654 x=3.657
x=3.676 x=3.711
Crossing speed:4.6*10-6
Nonlinear detuning:2.52m-1
Driving term:0.019m-1/2
Beam profiles during crossing
Simulation – tune decreasing
-100 -50 0 50 100
-20-15-10-505
101520
x=3.647
x' (
mra
d.)
x (mm)
-60 -40 -20 0 20 40 600
100
200
300
400
500
x=3.660
Num
ber
of p
arti
cle
x (mm)
-50 -40 -30 -20 -10 0 10 20 30 40 50
-8-6-4-202468
x=3.668
x' (
mra
d.)
x (mm)-60 -40 -20 0 20 40 60
-15
-10
-5
0
5
10
15 x=3.660
x' (
mra
d.)
x (mm)
-60 -40 -20 0 20 40 600
100
200
300
400
500 x=3.668
Num
ber
of p
arti
cle
x (mm)-60 -40 -20 0 20 40 60
0
100
200
300
400
500 x=3.647
Num
ber
of p
arti
cle
x (mm)
Simulation – tune increasing
-40 -20 0 20 40-8
-6
-4
-2
0
2
4
6
8 x=3.654
x' (
mra
d.)
x (mm)
-100 -50 0 50 100
-20-15-10-505
101520
x=3.705
x' (
mra
d.)
x (mm)
-60 -40 -20 0 20 40 600
100
200
300
400
x=3.654
Num
ber
of p
artic
le
x(mm)-60 -40 -20 0 20 40 600
100
200
300
400
x=3.705
Num
ber
of p
artic
le
x (mm)
Difference due to crossing direction
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
-40 -30 -20 -10 0 10 20 30 400
1000
2000
3000
4000
5000
6000
7000
8000
coun
t
x (mm)
x=3.668 x=3.647
-40 -30 -20 -10 0 10 20 30 400.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
t
x (mm)
x=3.654
-40 -30 -20 -10 0 10 20 30 400.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
coun
t
x (mm)
x=3.711
Tune decreasing
Tune increasing
The effect due to crossing depends upon crossing direction.
In one direction: “particle trapping”In other direction: “emittance growth”
Crossing without sextupoles (1)
Crossing speed:8.5*10-6
Nonlinear detuning:0 m-1
Driving term:0 m-1/2
Beam profiles during crossing (tune decreasing)
“Particle trapping” occurred even when all magnets are linear elements.
Possible source for nonlinear components:allowed poles, fringing field …
-60 -40 -20 0 20 40 600
1000
2000
3000
4000
5000
6000
7000
8000
Cou
nt (
A.U
.)
x (mm)-60 -40 -20 0 20 40 60
0
1000
2000
3000
4000
5000
6000
7000
8000
Cou
nt (
A.U
.)
x (mm)
-60 -40 -20 0 20 40 600
1000
2000
3000
4000
5000
6000
7000
8000
Cou
nt (
A.U
.)
x (mm)
Crossing without sextupoles (2)
In tune decreasing In tune increasing
Beam intensity during crossing
Beam loss due to crossing 3Nx=11
Crossing speed:5.5*10-6
Nonlinear detuning:0 m-1
Driving term:0 m-1/2
*Data acquired by Machida and Uesugi
Summary
• Experiment at PoP FFAG (crossing 3x=7)– “Particle trapping” due to resonance crossing was obser
ved.– Trapping efficiency are understood qualitatively.– Adiabatic parameter more than 7 was harmless.
• Experiment at HIMAC (crossing 3x=11)– Difference due to crossing direction was clearly observ
ed.– Even sextupoles are not excited, the effect of crossing
was “particle trapping”.
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