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FFAG W.S. ’04 @ KEK. Resonance Crossing Experiment in PoP FFAG (preliminary report). M. Aiba (Tokyo Univ.) for KEK FFAG Group. Motivation of Experiment. Beam dynamics of resonance crossing is studied for non-scaling FFAG. - PowerPoint PPT Presentation
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Resonance Crossing Experimentin PoP FFAG (preliminary report)
M. Aiba (Tokyo Univ.) for KEK FFAG Group
FFAG W.S. ’04 @ KEK
Motivation of Experiment• Beam dynamics of resonance crossing is studied f
or non-scaling FFAG.• There are few study on resonance crossing. Especi
ally, experimental studies are only… (as far as I know)– Fifth integer (Particle Trapping)
@ CERN ISR (1975) by A. W. Chao et al.
– Half integer@ TRIUMF Cyclotron (‘80) by R. Baartman et al.
– Third integer, coupling resonance etc..@ HIMAC (under going) by S. Machida et al.
• PoP FFAG is good machine for beam study.
Basic Parameter of PoP FFAGnum. of sector 8
k value 2.5
kinetic energy 50keV~500keV
magnetic field 0.14~0.32T(F mag.)
0.04~0.13T(D mag.)
average radius 0.81~1.14m
betatron tune 2.22~2.16(Horizontal)
1.26~1.23(Vertical)
repetition 1kHz
frequency & voltage 0.61~1.40MHz/4kVpp
・ Crossing speed can be changed in wide range.・ It is necessary to introduce a variation of tune.
Remodel of Magnet4mm iron plates are inserted to all 8 magnets.
Iron plate
Relatively, a gap outside is more widen than inside.Therefore, k value decrease as increasing radius.
r
Schematic view of magnet cross section
Mainly, horizontal tune varies.
Variation of Tunes
1.5 2.0 2.5 3.01.0
1.5
2.0
2.5
F: 5000AT
D:2000AT
D:2500AT
D:2600AT
D:2900AT(D:2870AT@exp.)D:3000AT
tune variation with 4mm iron plate
verti
cal t
une
horizontal tune
Third order(normal)
Fourth order(normal)
Integer or Half integer
open circle: experimentcolored plot: calculation
3Nx=7 is focused here.
Longitudinal Beam Handling(1)
Crossing speed is one of important parameter! However, it is impossible to accelerate all particles with same energy gain because of synchrotron oscillation.
For clear observation of speed dependence, careful attentions are paid to longitudinal beam handling.
Beam chopper: 100nsec chopped beam (~ ±10deg. of RF phase)
Mountain-plot: Bunch monitor signal is transferred to mountain plot to check an amplitude of dipole oscillation.
Longitudinal Beam Handling(2)
-60 -45 -30 -15 0 15 30 45 600
2
4
6
8
10
bunc
h si
gnal
+ o
ffse
t(tu
rn*0
.1)
(V)
RF phase (deg.)
-60 -45 -30 -15 0 15 30 45 600
2
4
6
8
10
bunc
h si
gnal
+ o
ffse
t(tu
rn*0
.1)
(V)
RF phase (deg.)
Example of Mountain Plot (RF capture @ injection energy)
Dipole oscillation is perfectly suppressed.
Driving Term (1)
0 5 10 15 20
- 2500
- 2000
- 1500
- 1000
- 500
0
500
1000
1500
Δ 50GaussB~
field error with RF core (r=0.9m)
Δ BL=2*4.5E- 4 (T- m)Bz
(Gau
ss)
theta (deg.)
with core without core
Straight Section Defocus Focus0 45 90 135 180 225 270 315 360
- 6
- 4
- 2
0
2
4
6
r0=0.9mRF error:-17mrad.@130keV
CO
D (
mm
)
theta (deg.)
Magnetic field error with RF core COD due to RF core
RF cores disturb magnetic field of straight section. COD and octupole becomes sextupole driving term (feed down).
Core
Feed Down:)33()( 322333 DxDDxxODxOOx
(calculated with TOSCA) (calculated with TOSCA field & RK-tracking)
Driving Term (2)
COD with weak excited magnets
Error
Error
Septum
0 45 90 135 180 225 270 315 360
- 30
- 20
- 10
0
10
20
30
40
F:5000AT-4800AT / D:2870ATr0=0.88m
CO
D (
mm
)
theta (deg.)Septum
Error Error
Variable driving term can be introduced with changing coil current.
Driving Term (3)
dsesSeG lsix
i xx
)3()(3237,0,3 )(
24
2
0 1 2 30.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
G3,
0,7 (
10-8m
^3/2
)excitation error (%)
:Fourier amplitude of 3Nx=77,0,3G
x :horizontal beta-function:coefficient of sextupole)(sS
x :horizontal tune
x
x
dss
)( :phase advance
:phase factor
Due to the relation of phase between fixed and variable driving term, Fourier amplitude is not proportional to variable driving term.
Beam Size Measurement During acceleration, an orbit shifts to outer radius. Using a scraper and an intensity monitor, beam size, before and after crossing, can be measured.
turn
Results (1) –data of driving term 0.18*10-8(m^3/2)
40 50 60 70 80 900.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 1, scraper 300mm
Nor
. int
egra
l (-)
num. of turn
50 60 70 80 90 1000.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 1, scraper 320mm
Nor
. int
egra
l (-)
num. of turn
70 80 90 100 110 1200.0
0.2
0.4
0.6
0.8
1.0 error 2%, speed 1, scraper 340mm
Nor
. int
egra
l (-)
num. of turn
80 90 100 110 120 1300.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 1, scraper 360mm
Nor
. int
egra
l (-)
num. of turn
130 140 150 160 170 180 190 200 210 220 2300.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 3, scraper 300mm
Nor
. int
egra
l (-)
num. of turn
180 190 200 210 220 230 240 250 260 270 2800.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 3, scraper 320mm
Nor
. int
egra
l (-)
num. of turn
230 240 250 260 270 280 290 300 310 320 3300.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 3, scraper 320mm
Nor
. int
egra
l (-)
num. of turn
290 300 310 320 330 340 350 360 370 380 3900.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 3, scraper 320mm
Nor
. int
egra
l (-)
num. of turn
300 400 500 600 7000.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 5, scraper 300mm
Nor
. int
egra
l (-)
num. of turn
300 400 500 600 700 800 9000.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 5, scraper 320mm
Nor
. int
egra
l (-)
num. of turn
500 600 700 800 900 1000 11000.0
0.2
0.4
0.6
0.8
1.0error 2%, speed 5, scraper 340mm
Nor
. int
egra
l (-)
num. of turn
Speed0.13kV/turn
Speed0.49kV/turn
Speed1.6kV/turn
Scraper pos.r=908mm
Scraper pos.r=908mm
Scraper pos.r=908mm
Scraper pos.r=928mm
Scraper pos.r=948mm
Scraper pos.r=928mm
Scraper pos.r=948mm
Scraper pos.r=968mm
Scraper pos.r=928mm
Scraper pos.r=948mm
Scraper pos.r=968mm
Results(2)-trapping efficiency
speed (kV/ turn)driving term(10̂ - 8*m̂ 3/ 2) 0.13 0.21 0.49 1.04 1.56
0.18 12% 9% 0% 0% 0%1.1 17% 12% 0% 0% 0%1.6 23% 16% 0% 0% 0%
The result can be understood qualitatively.
Large driving term Large trapping efficiency
Slow Crossing Large trapping efficiency
Particle Trapping
Particle Trapping: When a non-linear detuning is very larger than a driving term, some particles are trapped by islands during crossing resonance.
Reference: “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER RESONANCE”, A.W. Chao and Melvin Month, NIM 121(1974) pp129-138
Phase space topology for third integer resonance
?Opposite Crossing?
- 40 - 30 - 20 - 10 0 10 20 30 40
0
1000
2000
3000
4000
5000
6000
7000
8000 135msec
count
x (mm)- 40 - 30 - 20 - 10 0 10 20 30 40
0
1000
2000
3000
4000
5000
6000
7000
8000 142msec
count
x (mm)
- 40 - 30 - 20 - 10 0 10 20 30 40
0
1000
2000
3000
4000
5000
6000
7000
8000 150msec
coun
t
x (mm)- 40 - 30 - 20 - 10 0 10 20 30 40
0
1000
2000
3000
4000
5000
6000
7000
8000 155msec
count
x (mm)
- 60 - 40 - 20 0 20 40 60
0
50000
100000
150000
200000
250000
300000
350000
count
x (mm)
60msec 100msec 120msec 150msec 205msec 210msec
Crossing 3Nx=11
HIMAC experiment
Num. of Cell =12
Particle trapping (tune decreases)
Growth? (tune decreases)
SummaryBeam study in PoP FFAG was carried out to study a dynamics of resonance crossing.
Tune crosses 3Nx=7, then…
There seems no effect, when crossing speed is fast enough.Particle trapping is observed. The dependence of trapping efficiency on crossing speed and driving term can be understood qualitatively.
Opposite crossing does not become trapping.
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