### ビームテストの概要 ー ビームのふるまい ー 横方向 1．入射 2

```Crossing 3Nx=11
in KEK150MeV FFAG
M. Aiba (KEK)
For KEK FFAG Gr.
Crossing 3nx=11
• Characteristics of crossing 3nx=11 in KEK-FFAG
– Non structure resonance excited by COD(feed down)
– Affection depends on crossing direction due to nonlinearlity
• Particle Trapping
• Emittance Growth ←KEK-FFAG
Crossing direction dependence
Phase space topology with dominant nonlinearlity
〇  
1
p n
3
（distance from resonance）
1.(a)→(e)
“Particle trapping”
(Proposed A.W.Chao & M.Month)
2.(e) →(a)
“Emittance growth”
“Particle trapping”
60
60
40
40
20
20
0
-20
0
-20
-40
-40
-60
-60
-60
-40
-20
0
20
40
-60
60
-40
-20
0
20
40
60
20
40
60
x (m m )
x (m m )
“Emittance growth”
40
 = 9 .5 5 * 1 0
-3
40
L
-3
L
20
20
0
-2 0
0
-20
-40
-4 0
-6 0
 = - 2.87*10
-4 0
-2 0
0
20
x (m m )
40
60
エミッタンス増大は有限
-60
-40
-20
0
x (m m )
※変化を分かりやすくするため
150MeVと無関係なパラメータ
COD：correction scheme & measurement (1)
• Two additional dipole to correct COD
• RF 空洞: コアが漏れ磁場を吸収
• Dipole error：～0.02T-m
• COD：
40
C O D : -5 0 m rad . erro r
30
RF
C O D (m m )
20
10
0
-1 0
-2 0
-3 0
-4 0
0
30
60
MS ES
90 120 150 180 210 240 270 300 330 360
azim u th al an gle (de g.)
COD補正が必要
COD：correction scheme & measurement (2)
• Measurement：Change the excitation of correction
dipole and measure beam position
R F cavity uninstalled
R F cavity installed / suppression m ag. 0A
R F cavity installed / suppression m ag. 200A
50
R F cavity installed / suppression m ag. 340A
②
Black＝Cavity is not installed
Red＝RF is installed
Without dipole excitation
Green=
～0.01T-m
Blue=
～0.02T-m
①
40
current (nA )
③
30
20
10
0
4380
4400
4420
4440
4460
rad iu s (m m )
Dipole correction is effective
Emittance growth due to crossing
Analytical expression of growth ratio (assuming infinite slow crossing)
Gmax=
R  A /
1
R


1 2
2
R
1 4
s：Relative emittance
Crossing speed:
Nonlinear detuning:
   2
B 
 d  O ( )
0
16 n
0
Driving term:
R: the area of initial beam
A/: the area of islands
Ap 
Linear tune shift:
Nonlinear tune shift:
A

2

2

1
2
3
s4 :

1
  2
8n
L 
2
 d e
 ip 
S ( )
0
1
p n
3
 NL   12 B 0 a 0
1
Excitation width:
  3  NL 4  e ,
 e  3 A p a0 2
  3 L 2  e
Speed dependence of emittance growth
G ( )  1  G m exp(  /  )
2


 1  
 4   NL  e
3



Crossing speed: 
Nonlinear tune shift:  NL
parameter
Excitation width:
  12 B 0 a 0
1
 e  3 A p a0 2
600
550
500
D ata: D ata6 _B
M ode l: e xpde c ay- offse t
20
C h i^2
R ^2
= 5 .4 9 4 5 1
= 0 .9 9 9 2 7
15
P1
P2
P3
300
±0
2 7 6 .9 4 3 1 5
± 2 .1 4 1 9 8
0 .3 6 3 7 6 ± 0 .0 0 6 3 5
5
400
0
-5
-10
-15
1kV/turn
350
in itial
afte r c rossin g
10
450
300
1kV /turn
25
m ax. em ittance (  m m -m rad.)
-20
-25
0
1
2
3
ad iab atic p aram eter
4
Maximum growth 300⇒420
-25
-20
-15
-10
-5
0
x (m m )
5
10
15
20
25
Experiment data
Beam intensity during acceleration
0 .0 0 7
intensity (a.u.)
0 .0 0 6
Black：Suitable dipole
correction
0 .0 0 5
0 .0 0 4
0 .0 0 3
Red：70% dipole
correction
Crossing point
0 .0 0 2
1 .5
1 .6
1 .7
1 .8
1 .9
tim e (m sec)
2 .0
2 .1
2 .2

40
in jectio n
after cro ssin g
erro r: -5 m rad .
30
＝十分可能な値
20
10
0
-1 0
-2 0
-3 0
-4 0
4360
erro r: -1 0 m rad .
40
30
30
20
20
10
10
0
-1 0
4420
4440
4460
injection
after crossing
0
-10
-2 0
-20
-3 0
-30
-4 0
4400
r (m m )
in jectio n
after cro ssin g
40
4380
-40
4360
4380
4400
4420
r (m m )
4440
4460
4360
4380
4400
4420
r (m m )
4440
4460
```