Beam Dynamics Issue
in Nano Beam Scheme
K. Ohmi, D. Zhou (KEK)SuperKEKB MAC
Feb. 7-9, 2011

Contents• ✦Beam-beam effects

Nano-beam scheme✦ Synchro-beta effects✦ Tolerance for errors
Electron cloud effects•• Transverse impedance issues

Nano-beam scheme• KEKB with crab cavity targeted a high beambeam parameter >0.1.

• SuperKEKB goes toward Low emittance, lowbeta, moderate beam-beam parameter <0.1xs

Neglect paralleltranslation to x

Low emittance�approach

Φ: half crossing angle

σx /φ < σz
σx /φ < βyN2�L∝
φσz εy βyN βxξx ∝(φσz )2�Nβyξy ∝φσz εyKeepβyεyThen take limit

andσx /βyεy βy → 0• Bunch length is free.
• Small beta and small
emittance are required.

Super KEKB
εx=3/5 nm, εy=3/5 pm
βx=32/25 mm, βy=0.3mm

Current dependence of L and ξ
given by a weak-strong simulation

60.1

50.08
jn=2re` L/a Np fL/bunch (x1032 cm-2s-1)• Nano beam collision is reliable for small ξ<0.1 without Crab Waist.
• The gain of CW remarkably appear higher beam-beam parameter.
432
10CW11, i=0.523,0.558
NoCW, i=0.523,0.548
66.5

77.5

88.5

99.5 10 10.5

100.06
0.04
0.02
0CW11, i=0.523,0.558
NoCW, i=0.523,0.548
66.5

77.5

88.5

99.5 10 10.5

10Np (10 )Np (10 )νs=0.012

Crab waist is base line of SuperB.
Beam particles collide with the other beam attheir waist using sextupole magnets both sideof IP.

Characteristics of the collision• βy is small only interaction area

Beam particles with a large horizontal amplitude
collide high beta region✤ Issues on injection, collision offset, Touschek ....
Talk by Ohnishi, Iida✤ Crab waist recovers the issues, but✤

10x`y (mm)8Neglect paralleltranslation to xs

6420-6-4-20s(mm)246Crab waist and IR nonlinearity

CW sext

Quad’s Solenoid Quad’s

CW sext−axy 2 −HQ� s −HSol −HBB −HSol −HQ� s −axy 2MIR = eeeeeee−HQ� s −HSol −xp2y /2φ −HBB −xp2y /2φ −HSol −HQ� seeeeeee

dynamic aperture degradation is seen by• Strongcrab sextupole installation (H. Koiso).
do not know how to handle the nonlinear• We
terms of Q’s and Solenoid located at very high β.
waist is an option in (the) future for Super• CrabKEKB.

Study of synchro-beta resonance• Tune scan shows strong synchro-betaresonances.

•Beam-beam interaction contains x2z2
terms, which gives the synchro-beta effects.

• Weak-strong and strong-strong simulations
are performed to study the effects.

Luminosity in tune space given
by weak strong simulation
9• 2ν -nν =int
• Very strong
x

n=6

7
6

n=15
4

n=4

3
2

n=2

1
0
0.5

0.52

0.54

0.56

0.58

ix

Tune near half integer is better.

sresonances are seen.

iy=0.54
0.55
0.56
0.57
0.58
0.59
0.60

980.6

L x1035 (cm-2s-1)

L x10

35-2 -1(cm s )

8765

iy=0.54
0.55
0.56
0.57
0.58
0.59
0.60

4

Crab waist

321
00.5

0.52

0.54

0.56
ix

0.58

0.6Horizontal size and <xz>

• σx and <xz> behave harmful at the resonancetune.

• Synchro-beta resonance. Increasing horizontal
beam size enhances vertical hour glass.

Strong-strong beam-beamsimulation• Coherent instability should be studied bystrong-strong model

0.00025

1.2e+36i=(0.525,0.570)
i=(0.52,0.570)
i=(0.530,0.570)

0.00020.00015

8e+35

mx

6e+35

0.0001

4e+35

5e-05

2e+35
0001000

2000 3000
turn

01000

2000 3000
turn

4000
1e-06

4000

i=(0.525,0.570), e+e-8e-07
my (m)L (cm-2s-1)

1e+36

i=(0.525,0.570), e+e-6e-07
4e-07
2e-07
001000

2000
3000
turn

4000

Coherent beam-beam motion
on the s-β resonance
4e-08
3e-08

i=(0.525,0.570), e+
e-

2e-08

<xz>

1e-08
0-1e-08-2e-08-3e-08• 2ν -2ν =int
• Coherent head-tailxmodes-4e-08
2000 2005 2010 2015 2020 2025 2030
turn

Tune scan and Synchro-beta
resonances• Though some resonances degrades

luminosity, reliable tune area is a sufficientspace.

• When a horizontal offset exists, resonances2νx-(2n-1)νs can appear. The odd orderresonances were weak.
93-2 -1(cm s )

535

8
765

iy=0.54
0.55
0.56
0.57
0.58
0.59
0.60

4
321
0
0.5

0.52

0.54

0.56
ix

0.58

L x10

L x1035 (cm-2s-1)

iy=0.54
0.55
0.56
0.57
0.58
0.59
0.60

69

Δx=2σx
0.6

4

waist shift
Δs=Δx/2Φ

21
0

6x=2mx
0.5

0.52

0.54
ix

6x=2mx, e+- waist shift

80.56

L x1035 (cm-2s-1)7765

iy=0.54
0.55
0.56
0.57
0.58
0.590.60

432100.5

0.52

0.54
ix

0.56

Coupling-dispersion error tolerance• Collision offset• x-y coupling at the collision point• dispersion at the collision point• Their chromaticity• Correction of these errors are essential toachieve the high performance in KEKB. It
should be important also in SuperKEKB.

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

100 150 200 250 300 350 400
swaist µm

7654321 NoCW
CW
0-20 -10waist

010 206x (µm)3040e-­‐	  waist

No	  crab	  waist

e+	  waist

crab	  waist 1550

Ver.cal	  oﬀset• tolerance	  ~0.5σy	  (20%)• 0.2σy=0.01μm	  (5%)
7.25

7.3
my=0.05 (µm)

7.1
76.9
6.8
6.7
6.6

No CW

7.2
L (1035 cm-2s-1)

L (1035 cm-2s-1)

7.2

NoCW

7.15
mpy=200 (µrad)

7.1
7.05
76.95
6.9
6.85
6.8

0

0.005

0.01by (µm)

0.015

0.02

0204060by’ (µrad)

80

16100

X-­‐Y	  coupling	  w/	  crab	  waist• D.	  Zhou	  &	  K.	  Ohmi

Beam	  noise• Turn	  by	  turn	  noise
9NoCW
CW

8L (1035 cm-2s-1)

L (1035 cm-2s-1)

8.5
7.5
7
6.5
65.5
mx=6-10µm

54.5
0

0.2

0.4
0.6bx (µm)

1801

my=60nm0246by (nm)810810NoCWCW

140mx does not change120

my (nm)

140

NoCW
CW

160

NoCW
CW

160

my (nm)

0.8

98.5
8
7.5
76.5
65.554.5
4

120
100

100
mx does not change

80

80

60

60
40

40
00.2

0.4
0.6
bx (µm)

0.8

1

02

46

δy	  nm)bx ((µm)

18

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±0.23

Δx	  (μm)	  collision	  oﬀset	  	  	  	  	  	  	  	  	  	  	  	  	  10	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  10Δs	  (μm)	  	  	  waist	  error	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  100	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  100Δy,Δy’(μm,μrad)	  collision	  oﬀset	  	  	  0.02	  (100)δx	  (μm)	  turn	  by	  turn	  noise	  	  	  	  	  	  	  0.5	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  0.5δy	  (nm)	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4The	  degrada.on	  is	  roughly	  quadra.c
σx=6-­‐10μm	  	  σy=50	  nmElectron cloud instability• ω σ /c is very high in low emittance rings.
ez• Single bunch instability• Coupled bunch instability

Threshold	  of	  the	  strong	  head-­‐tail	  instability	  (Balance	  of	  growth	  and	  Landau	  damping)• Stability	  condi.on	  for	  ωeσz/c>1
U=3λ p r0 β

Z ⊥ (ωe )ν s γ ωeσ z cZ0=ωe =λ p re c 2σ y (σ x + σ y )3λ p r0 β

νs

KQ λe
L=1γ ωeσ z c 4π λ p σ y (σ x + σ y )• Since	  ρe=λe/2πσxσy,2γν s ωeσ z c
ρe ,th =3KQr0 β L

Origin	  of	  Landau	  damping	  is	  momentum	  compac.on

ν sσ z = ασδ L• Q=min(Qnl,	  ωeσz/c)	  	  	  	  	  	  	  • 	  Qnl=10	  in	  this	  presenta.on,	  depending	  on	  the	  nonlinear	  €interac.on.	  
• K	  characterizes	  cloud	  size	  eﬀect	  and	  pinching.	  Parameters
SuperKEKB
3016
4.09
3.6
3.2
3.5
6
0.8
0.025643

SuperKEKB{/Symbol s}_y0.0002
0.000150.0001••

Y.	  Susaki,	  K.	  Ohmi,	  IPAC10

5e-05
0•
•

1.2e11
1.4e11
1.6e11
1.8e112.e11
2.2e112.4e112.6e11

01000

2000 3000
turn

4000

5000

Simulation ρth=2.1x1011 m-3.(νs=0.012)
Analyticρth=2.7x1011 m-3.
11-3Targetρe~1x10 m
Take care of high β section. Effects areenhanced. �ρe βy ds/L = 1011 × 10 m−2

23Es.ma.on	  of	  cloud	  density	  and	  coupled	  bunch	  instability• Ante-­‐chamber,	  δ2,max=1.2	  without	  special	  structure	  like	  grooveρe=2.2x1011 m-3• Wake	  ﬁeld	  and	  growth	  rate	  of	  the	  couplied	  bunch	  instability.
Growth time is 40
turns. It should be
suppressed atρe=1x1011 m-3.

• Suetsugu-­‐san	  es.mates	  the	  density	  based	  on	  measurements	  and	  is	  designing	  the	  chamber	  to	  achieve	  density.

Fast head-tail instability due tomask impedance• Y. Suetsugu & D. Zhou

Gdfidl2D round modelrectangular cross sec.

V maskd=2mmΦ

Beam tilt due to the impedance
=�

β∗

��
i

1
βy (i)y0 (i)eE� ∞ρ(z � + z)Wy1 (z � )dz �0D. Zhou & A. Chao

One mask
Round model• Round model impedance: 1/10 of instability threshold.
• For the case of the impedance corresponding theinstability threshold, tolerance of the orbit shift is 0.05
mm for 10% beam size increase.

Summary• Tune scan and synchro-beta resonance forthe beam-beam performance is done.
Reliable tune area was a sufficient space.

• The tolerance for optics errors at IP wasdetermined.

• Target electron cloud density to avoid
instabilities was determined.

• Mask estimation and design will be updated.