Beam simulations forthe nano beam scheme
K. Ohmi, D. Zhou,Y. Seimiya,Y. Susaki
15-17 Feb., 2010
MAC for KEKB and SuperKEKB

Early studies with weak-strong simulations

15σxe,p/2Φ<βy••L

2.74x1035

7.86x1035

8.00x1035

L(CW)

8.09x1035

9.67x1035

8.69x1035

Parameter choice for the nano beam scheme• HourGlass effect degrades the performance.
• Crab waist recovers the degradation.
σxp/2Φ

σxe,p/2Φ<βyσxe/2ΦCurrent dependence• If the condition is satisfied, NoCW is not
60.1

50.08jn=2re` L/a Np f

L/bunch (x1032 cm-2s-1)

bad for ξ<0.1.

4
321
0CW11, i=0.523,0.558
NoCW, i=0.523,0.548
66.5

7

7.5

88.5
10Np (10 )99.5 10 10.5

0.06
0.04
0.02
0CW11, i=0.523,0.558
NoCW, i=0.523,0.548
6

6.5

7

7.5

88.5
10Np (10 )99.5 10 10.5

Tune scan with/without crab waist•No crab waist

crab waist

0.5

0.5
6e+35
5.5e+35e+35
4.5e+34e+35
3.5e+3 0.55
3e+35
2.5e+32e+35
1.5e+31e+35
5e+34
0.6

iy

iy

0.55

6e+35
5.5e+35e+35
4.5e+34e+35
3.5e+33e+35
2.5e+32e+35
1.5e+30.6

0.65

0.65
0.5

0.55

0.6
ix

0.65

0.5

0.55

0.6
ix

0.65

•Crab waist gives better performance.
•Synchro-beta resonance is seen in both cases.
•More systematic studies

Tentative strong-strong simulation• PIC collision if the separation of two slices is closer
than 5σx, otherwise Gaussian approximation.

• 6000 PIC, 34000 Gaussian approximation per collision(200x200 slices).

1.2e+36CW
NoCW

1.1e+365σx

L (cm-2s-1)

1e+369e+35
8e+35
7e+35
6e+35
5e+35
0

1000 2000 3000 4000 5000 6000
turnComplete Strongstrong simulation• Multi-mesh• Shifted Green function• The code has been developed. Theexecution time is huge. Expect next
supercomputer in KEK or new type ofcomputers.

Errors and noise
tolerances• The tolerances are evaluated with the weakstrong simulation.

• Collision offset and waist deviation• x-y coupling and their chromatic aberrations• Fast noiseTolerance	  of	  collision	  condi.on
Horizontal	  collision	  oﬀset	  and	  waist• Horizontal	  oﬀset	  and	  waist	  are	  related	  to	  each	  other.

9988

L (1035 cm-2s-1)

L (1035 cm-2s-1)• The	  cross	  point	  of	  the	  waist	  is	  only	  one	  in	  x-­‐z	  plane	  for	  the	  crab	  waist	  scheme.	  
76543 NoCW
CW
2050

100 150 200 250 300 350 400swaist µm

76543
21 NoCW
CW
0-20 -10

waist

010 206x (µm)3040e-­‐	  waist

No	  crab	  waist

e+	  waist

crab	  waist 1050X-­‐Y	  coupling	  w/	  crab	  waist

X-­‐Y	  coupling	  w/o	  crab	  waist

Chroma.c	  X-­‐Y	  w/	  crab	  waist	  Chroma.c	  X-­‐Y	  w/o	  crab	  waist

Ver.cal	  dispersion	  and	  it’s	  chroma.city

w/	  crab	  waist

w/o	  crab	  waist

Ver.cal	  momentum	  dispersion,	  ηy’	  w/	  crab	  waist

w/o	  crab	  waist

Beam	  noise• Turn	  by	  turn	  noise
9NoCW
CW

8
L (1035 cm-2s-1)

L (1035 cm-2s-1)

8.5
7.5
76.5
65.5
mx=6-10µm

5
4.5
00.2

1800.40.6bx (µm)

102

46by (nm)

810

NoCW
CW

my (nm)

120

120
100

100
mx does not change

80

80

60

60
40

my=60nm140

mx does not change

140

NoCW
CW

160

NoCW
CW

160

my (nm)

0.8

9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4

0

0.2

0.4

0.6

0.8

1

40

1702

4

6810

Summary	  –	  tolerance	  for	  parameters	  with	  20%	  luminosity	  degrada.on
Parameter

w/	  crab	  waist

w/o	  crab	  waist

r1*	  (mrad)±5.3±3.5

r2*	  (mm)±0.18±0.13

r3*	  (m-­‐1)±44±15r4*	  (rad)±1.4±0.4∂r1*	  /∂δ (rad)±2.4±2.1∂r2*	  /∂δ (m)±0.086±0.074∂r3*	  /∂δ (m-­‐1)±1.0×104±8400∂r4*	  /∂δ (rad)±400±290ηy*	  (µm)±62±31ηyʹ′*	  ±0.73±0.23Δx	  (μm)	  collision	  oﬀset	  	  	  	  	  	  	  	  	  	  	  	  	  10	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  10Δs	  (μm)	  	  	  waist	  error	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  100	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  100δx	  (μm)	  turn	  by	  turn	  noise	  	  	  	  	  	  	  0.5	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  0.5δy	  (nm)	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4

19

20

Microwave instability in Nanobeam Collision• Integrated horizontal beam-beam force along
bunch length is Bassetti-Erskine type for triGaussian distribution in x-y-z plane.

• When Micro-wave instability arises, transverse
beam-beam force is distorted and fluctuated.

xsModel wake field
l0, W’0 (x105 m-1), 6b (x10-4)• Low Q resonator model (Y. Cai)
5l0
W’06b432
10Ne=5.x1010-1-2-3-0.015 -0.01 -0.005• Threshold of the micro-wave instability is 0.5mA
0z (m)

0.005

0.01

0.015

(Nb=3.3x1010)
9

0.95

8.5

0.9

7.5

mb (mm)mz (mm)

87
6.5

0.85
0.8
0.75

60.7

5.5
50

0.2

0.4

0.6 0.8
I (mA)

1

1.2

1.4

0.65
00.2

0.4

0.6 0.8
I (mA)

11.2

1.4Simulation result of collision under microwave instability• Longitudinal profile of the strong beam.
0.009

5000 turn
10000 turn
15000 turn20000 turn
30000 turn

0.008
0.007

N0.006

The resonator modelis mild for instability.

0.005
0.004
0.003
0.002
0.001
0-6

-4

-2

0z/mz

246

• Luminosity and the beam size of the weak beam. No remarkableeffect except for the bunch lengthening in this impedance model.
1e+36mx,y (µm)

L (cm-2s-1)

8e+35
6e+35
4e+35
2e+35
00

5000 10000 15000 20000 25000 30000
turn

8.88.6
8.4
8.2
8
7.8
7.6
7.4
7.2
76.8

mx
100 x my05000 10000 15000 20000 25000 30000
turnElectron	  cloud	  issue• Threshold	  of	  the	  fast	  head-­‐tail	  instability,	  ρe=1-­‐2x1011	  cm-­‐3.
0.00021.2e11
1.4e11
1.6e11
1.8e112.e11
2.2e112.4e112.6e11

my0.00015
0.0001

Dispersion	  makes	  to	  degrade	  the	  1/2	  density.

5e-05
0010002000 3000
turn

4000

5000

• Ante-­‐chamber,	  Solenoid,	  coa.ng	  and	  grove.	  
The	  density	  is	  reduced	  3-­‐6x1010	  cm-­‐3.	  	  (Y.	  
Suetsugu)
24

Summary• Tenta.ve	  strong-­‐strong	  simula.on	  did	  not	  show	  diﬃcul.es	  in	  the	  nano	  beam	  collision.
• Crab	  waist	  gives	  befer	  performance	  and	  loose	  tolerances.	  We	  should	  consider	  the	  crab	  waist.
• True	  strong-­‐strong	  simula.on	  is	  prepared.
• Errors	  and	  noise	  tolerances	  are	  evaluated.	  The	  tolerance	  may	  be	  feasible	  for	  the	  beam	  dynamical	  issues,	  if	  the	  design	  lahce	  is	  realized.	  
• All	  the	  diﬃcul.es	  are	  transferred	  to	  lahce	  design	  and	  dynamic	  aperture	  issues.
• Show	  stopper	  will	  be	  in	  the	  lahce	  design	  and	  dynamic	  aperture	  issue,	  if	  exist.
• The	  word	  “	  show	  stopper”	  is	  used	  for	  bad	  thing.	  E.	  Forest	  said	  this	  was	  european	  english.
25