Beam Dynamics Issues in SuperKEKB
D. ZhouWith contributions from
KEK: T. Ishibashi, K. Ohmi, K. Oide, Y. Ohnishi, K. Shibata, H.
Sugimoto, ...
Cornell Univ.: D. SaganIHEP: Y. Zhang
SLAC: Y. Cai
The 20th KEKB Accelerator Review Committee, Feb. 23, 2015

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan2

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan3

1. Impedance issues: LER

Clearing	  electrode

Grooved	  surfaces

From	  T.	  Ishibashi

Tested	  in	  KEKB

Ref.	  Y.	  Suetsugu	  et	  al.,	  NIMA	  598	  (2009)

Ref.	  Y.	  Suetsugu	  et	  al.,	  NIMA	  604	  (2009)4

1. Impedance issues: LER➤	  Pseudo-­‐Green	  wake	  funcBon	  	  	  	  	  	  ●	  σz=0.5mm	  	  	  	  	  	  ●	  Pumping	  ports	  and	  SR	  masks	  are	  negligible	  sources	  because	  of	  antechamber	  	  	  	  	  	  ●	  CSR	  and	  CWR	  (Wiggler	  radiaBon):	  CSRZ	  code	  with	  rectangular	  chamber

51. Impedance issues: LER➤	  Wake	  potenBal	  with	  nominal	  bunch	  length	  	  	  	  	  	  ●	  σz=5mm	  	  	  	  	  	  ●	  Main	  sources:	  Collimators,	  ResisBve	  wall,	  ARES	  cavity,	  Bellows,	  MO	  ﬂanges,	  Clearing	  electrodes	  	  	  	  	  	  ●	  CSR	  and	  CWR	  are	  not	  strong	  if	  no	  microbunching	  happens6

1. Impedance issues: Impedance budget➤	  Impedance	  budget	  with	  σz=5/4.9mm:	  	  	  	  	  	  ●	  Loss	  factors,	  resistance	  and	  inductance	  are	  calculated	  at	  nominal	  bunch	  lengths	  	  	  	  	  	  ●	  Bellows,	  ﬂanges	  and	  pumping	  ports	  contribute	  more	  impedance	  in	  HER	  than	  in	  LER	  Ref.	  D.	  Zhou	  et	  al.,	  IPAC14,	  TUPRI021
71. Impedance issues: MWI: LER➤	  SimulaBons	  with	  input	  of	  Pseudo-­‐Green	  wake:	  	  	  	  	  	  ●	  Use	  Warnock-­‐Cai’s	  VFP	  solver	  	  	  	  	  	  ●	  Collimators	  are	  important	  sources	  in	  bunch	  lengthening	  	  	  	  	  	  ●	  Simulated	  σz≈5.9mm	  @Design	  bunch	  current	  	  	  	  	  	  ●	  Simulated	  MWI	  threshold	  is	  around	  NPth=1.2E11	  	  	  	  	  	  ●	  Interplay	  between	  CSR	  and	  convenBonal	  wakes?

81. Impedance issues: MWI: HER➤	  SimulaBons	  with	  input	  of	  Pseudo-­‐Green	  wake:	  	  	  	  	  	  ●	  Use	  Warnock-­‐Cai’s	  VFP	  solver	  	  	  	  	  	  ●	  Simulated	  σz≈5.8mm	  @Design	  bunch	  current	  	  	  	  	  	  ●	  Simulated	  MWI	  threshold	  is	  around	  NPth=1.7E11	  	  	  	  	  	  ●	  Y.	  Cai’s	  comment:	  CSR	  should	  not	  be	  important	  in	  SuperKEKB	  (consider	  shielding	  and	  long	  bunch).

9Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan10

2. BB+LN: LER: Simplified IR➤	  Simpliﬁed	  la8ce	  (sler_simple001.sad)	  by	  H.	  Sugimoto	  	  	  	  	  	  ●	  No	  solenoid	  	  	  	  	  	  ●	  QC*	  magnets	  simpliﬁed:	  no	  oﬀset,	  dipole	  and	  skew-­‐quad	  correctors	  removed	  ➤	  No	  signiﬁcant	  lum.	  degradaBon	  at	  low	  current	  ➤	  Solenoid	  and	  high-­‐order	  terms	  in	  QC*	  are	  the	  main	  sources	  of	  la8ce	  nonlinearity11

2. BB+LN: Nonlin. X-Y coupling➤	  RealisBc	  la8ce	  ➤	  Y.	  Zhang’s	  idea:	  Look	  at	  the	  nonlinear	  X-­‐Y	  coupling

From	  Y.	  Zhang
122. BB+LN: Nonlin. X-Y couplingpy/σpypy/σpy➤	  RealisBc	  la8ce	  ➤	  Poincare	  map	  in	  y	  direcBon	  as	  funcBon	  of	  X	  oﬀset	  	  ➤	  Strong	  nonlinear	  X-­‐Y	  coupling	  in	  LER

From	  Y.	  Zhang
13

2. BB+LN: Nonlin. X-Y couplingpy/σpy➤	  Simpliﬁed	  LER	  la8ce	  (From	  H.	  Sugimoto)	  ➤	  Conﬁrm:	  solenoid	  and	  high-­‐order	  terms	  in	  QC*	  magnets	  cause	  nonlinear	  X-­‐Y	  coupling

From	  Y.	  Zhang
14

2. BB+LN: Nonlin. X-Y coupling➤	  Test	  by	  inserBng	  a	  map	  of	  H=K*x2y	  into	  the	  LER	  la8ce	  Phase	  advance	  from	  IPNormalized	  coordinates
Phase	  shir

skew-­‐sext.	  kick15

From	  Y.	  Zhang

2. BB+LN: Nonlin. X-Y coupling➤	  Test	  by	  inserBng	  a	  map	  of	  H=K*x2y	  into	  the	  LER	  la8ce	  ➤	  COD	  and	  oscillaBon	  amplitude	  in	  y	  are	  well	  suppressed	  as	  expectedpy/σpyw/o	  skew-­‐sext.	  map:py/σpyw/	  	  skew-­‐sext.	  map:

From	  Y.	  Zhang
16

2. BB+LN: Luminosity: LER➤	  RealisBc	  la8ce:	  lum.	  drops	  at	  low	  beam	  currents	  ➤	  Crab-­‐waist:	  	  	  	  	  	  ●	  To	  cancel	  beam-­‐beam	  driven	  resonances	  	  	  	  	  	  ●	  Work	  well	  at	  high	  currents,	  but	  not	  well	  at	  low	  currents17

2. BB+LN: Luminosity: LER➤	  Test	  by	  inserBng	  a	  map	  of	  H=K*x2y	  into	  the	  LER	  la8ce	  ➤	  Skew-­‐sext.	  map:	  	  	  	  	  	  ●	  To	  cancel	  the	  nonlinear	  terms	  from	  solenoid	  and	  QC*	  	  	  	  	  	  ●	  Work	  well	  at	  both	  low	  and	  high	  currents	  	  	  	  	  	  ●	  Interplay	  of	  SC	  and	  la8ce	  nonlin.	  also	  miBgated	  parBally18

2. BB+LN: LER: DA and lifetime➤	  Test	  by	  inserBng	  a	  map	  of	  H=K*x2y	  into	  the	  LER	  la8ce	  ➤	  Skew-­‐sext.	  map:	  	  	  	  	  	  ●	  cause	  loss	  in	  DA	  and	  lifeBme	  	  	  	  	  	  ●	  not	  perfect

19

From	  H.	  Sugimoto2. BB+LN: Quasi-strong-strong simulation

From	  H.	  Sugimoto20

2. BB+LN: Quasi-strong-strong simulation

From	  H.	  Sugimoto21

2. BB+LN: Quasi-strong-strong simulation

From	  H.	  Sugimoto22

2. BB+LN: Quasi-strong-strong simulation

From	  H.	  Sugimoto23

2. BB+LN: Quasi-strong-strong simulation

From	  H.	  Sugimoto24

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan25

3. SC effects: LER➤	  FMA	  shows	  betatron	  tunes	  of	  parBcles	  at	  the	  beam	  core	  are	  close	  to	  half-­‐integer	  with	  only	  SC	  considered.

26

From	  H.	  Sugimoto

3. SC effects: LER➤	  FMA	  with	  beam	  distribuBon:	  10σx⨉10σy
LN	  +	  SCLN	  +	  SC	  +	  BB0.68

-2.0

-3.0

0.66

-3.0

-4.0

0.64

-4.0

0.62

-5.0

0.6

-6.0

0.58

-7.0

0.56

-8.0

-9.0

0.54

-9.0

-10.0

0.52
0.525

Fractional tune iy

0.56

-2.0

-5.0

0.54

-6.0
-7.0

0.52

-8.0

0.53 0.535 0.54
Fractional tune ix

0.545

10-3.0

y/my0

8

-5.0
-6.0

4

-7.0
-8.0

20
-10 -8-20 2x/mx0

4

68

-2.0
-3.0
-4.0
-5.0

6-6.0

40
-10 -8

-10.0

-4

-10.0

-7.0
-8.0

2-9.0

-60.545

8-4.0

60.53 0.535 0.54
Fractional tune ix

10-2.0y/my0

Fractional tune iy

0.58

0.50.525

sler_1684

1027-9.0-10.0-6-4-20 2x/mx04

6810

3. SC effects: LER➤	  Luminosity:	  Tune	  scan	  w/	  and	  w/o	  SC10Hor.	  tune	  scan

BBWS
SAD-sler-1682
SAD-sler-1684
SAD-sler-1684(w/ SC)

Lum. [1035cm-2s-1]

8BBWS

64200.5

10

0.51

0.52

0.53ix

0.54

0.55

0.56

BBWS
Vert.	  tune	  scan
SAD-sler-1684
SAD-sler-1684(w/ SC)

Lum. [1035cm-2s-1]

864

20
0.5

0.52

0.54

iy

0.56

0.58

0.628

3. SC effects: LER➤	  First	  try:	  opBcs	  matching	  w/o	  SC	  ➤	  Compensate	  linear	  SC	  tune	  shir	  =>	  Not	  successful	  ➤	  Next	  try:	  opBcs	  matching	  w/	  SC	  =>	  OngoingSpecific Lum. [1032cm-2s-1mA-2]

3BBWS
w/o SC
w/ SC (no optics matching)w/ SC (optics matching w/o SC)
Design

2.5
2
1.5
1
0.5
00

0.4

0.8

1.62
Ibunch(e )×Ibunch(e ) [mA ]+1.229-22.4

sler_16843. SC effects: LER➤	  Independent	  simulaBon	  (BBWS+SC)	  showed	  SC	  eﬀects	  are	  not	  serious,	  but:	  	  	  	  	  	  ●	  No	  la8ce	  nonlinearity	  	  	  	  	  	  ●	  Simple	  model	  for	  SC	  (Only	  consider	  tune	  spread	  due	  to	  SC)

30

From	  K.	  Ohmi

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan31

4. Lum. calculation: Detuned lattice➤	  Detuned	  la8ce:	  sler_1689_d4-­‐8/sher_5767_d4-­‐832

From	  Y.	  Ohnishi

4. Lum. calculation: Detuned lattice➤	  Assume:	  εx=1.75nm,	  coupling	  =	  2%	  ➤	  Space-­‐charge	  is	  not	  important	  ➤	  La8ce	  nonlinearity	  is	  not	  very	  important	  ➤	  L=1⨉1034cm-­‐2s-­‐1	  is	  promising	  ➤	  L=10⨉1034cm-­‐2s-­‐1	  is	  possible	  by	  increasing	  beam	  currents33

4. Lum. calculation: Detuned lattice➤	  Assume:	  εx=1.75nm,	  coupling	  =	  2%	  ➤	  Compare	  with	  the	  case	  of	  simpliﬁed	  IR	  ➤	  Solenoid	  not	  to	  cause	  lum.	  loss

34

4. Lum. calculation: Detuned lattice➤	  Assume:	  εx=1.75nm,	  coupling	  =	  1%	  ➤	  Space-­‐charge	  is	  not	  important	  at	  low	  currents	  ➤	  La8ce	  nonlinearity	  is	  not	  very	  important	  ➤	  Decreasing	  coupling	  =>	  Lum.	  gain	  but	  beam-­‐beam	  limit	  appears	  at	  lower	  beam	  currents35

4. Lum. calculation: Detuned lattice➤	  LER:	  Tolerance	  for	  errors	  in	  various	  opBcs	  parameters	  at	  IP	  (Assume	  10%	  of	  lum.	  loss)

36

From	  K.	  Ohmi

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  ➤	  Summary	  and	  Future	  plan37

5. Benchmark of SAD: sher_5764➤	  OpBcs	  parameters	  at	  IP	  with	  δ=0	  	  	  	  	  	  ●	  In	  general,	  Bmad	  agrees	  well	  with	  SAD

Bmad:	  	  βx=0.02498209m,	  αx=-­‐4.959E-­‐5,	  νx=45.5299896,	  Dx=-­‐4.E-­‐8m,	  D’x=-­‐8.16E-­‐6,	  	  βy=2.941E-­‐4m,	  αy=-­‐6.791E-­‐5,	  νy=43.56852721,	  Dy=-­‐4.55E-­‐9,	  D’y=-­‐2.4E-­‐7,	  SAD:	  	  βx=0.025m,	  αx=-­‐1.34E-­‐12,	  νx=45.53,	  Dx=-­‐1.03E-­‐13m,	  D’x=-­‐3.11E-­‐13,	  	  βy=3.E-­‐4m,	  αy=-­‐3.545E-­‐13,	  νy=43.57,	  Dy=2.963E-­‐15,	  D’y=-­‐1.616E-­‐12,	  38

5. Benchmark of SAD: sher_5764➤	  OpBcs	  parameters	  at	  IP	  with	  δ=0.002	  	  	  	  	  	  ●	  In	  general,	  Bmad	  agrees	  well	  with	  SAD

Bmad:	  	  βx=0.32635028E-­‐01m,	  αx=0.65882408E-­‐01,	  νx=45.536646,	  Dx=-­‐0.47815350E-­‐03m,	  D’x=-­‐0.11870747E-­‐01,	  	  βy=0.31470442E-­‐03m,	  αy=0.13545109E-­‐01,	  νy=43.577108,	  Dy=0.64778741E-­‐06,	  D’y=0.23488780E-­‐02,	  SAD:	  	  βx=.032642757m,	  αx=.0658513493,	  νx=45.536688655,	  Dx=-­‐.0004781727,	  D’x=-­‐.01190317,	  	  βy=.00032006m,	  αy=.01341448,	  νy=43.57852356,	  Dy=6.27523687e-­‐07,	  D’y=.0022601526,	  39

5. Benchmark of SAD: FMA: sler_1684➤	  X-­‐Y	  space	  	  	  	  	  	  ●	  Bmad	  and	  SAD	  give	  similar	  DA	  in	  size	  	  	  	  	  	  ●	  Discrepancy	  is	  due	  to	  use	  of	  diﬀerent	  maps	  for	  high-­‐order	  nonlinear	  terms	  in	  elements	  such	  as	  solenoid
Bmad

SAD

40

5. Benchmark of SAD: FMA: sler_1684➤	  Tune	  space	  	  	  	  	  	  ●	  Discrepancy	  is	  due	  to	  use	  of	  diﬀerent	  maps	  for	  high-­‐order	  nonlinear	  terms	  in	  elements	  such	  as	  solenoid

yy

Bmad

SADxx41

5. Benchmark of SAD: luminosity calculation➤	  Compare	  with	  SCTR	  code	  (by	  K.	  Ohmi)	  	  	  	  	  	  ●	  Test	  on	  simpliﬁed	  la8ce	  (sler_simple001.sad)	  	  	  	  	  	  	  ●	  Discrepancy	  observed	  	  	  	  	  	  ●	  Need	  to	  compare	  in	  detail	  the	  nonlinear	  maps	  used	  in	  SAD,	  SCTR	  and	  Bmad.

42

From	  K.	  Ohmi

Outline➤	  Impedance	  issues	  -­‐	  updates	  ➤	  Interplay	  of	  beam-­‐beam(BB)	  and	  la8ce	  nonlinearity(LN)	  ➤	  Space	  charge(SC)	  eﬀects	  in	  LER	  ➤	  Luminosity	  calculaBon	  for	  detuned	  la8ces	  ➤	  Benchmark	  of	  SAD	  and	  Bmad	  ➤	  Summary	  and	  Future	  plan43

6. Summary➤	  Impedance	  issues	  	  	  	  	  	  ●	  Impedance	  model	  updated	  	  	  	  	  	  ●	  MWI	  simulaBon	  updated	  ➤	  BB+LN	  	  	  	  	  	  ●	  Nonlinear	  amplitude-­‐dependent	  X-­‐Y	  coupling	  idenBﬁed	  	  	  	  	  	  ●	  Solenoid	  and	  high-­‐order	  terms	  in	  QC*	  magnets	  are	  the	  main	  sources	  of	  LN	  	  	  	  	  	  ●	  MiBgaBon	  methods	  to	  be	  invesBgated	  ➤	  Space	  charge	  	  	  	  	  	  ●	  To	  be	  invesBgated	  	  	  	  	  	  ●	  OpBcs	  matching	  with	  SC	  (need	  to	  upgrade	  SAD?)	  ➤	  Lum.	  calculaBon	  for	  detuned	  opBcs	  	  	  	  	  	  ●	  SC	  and	  LN	  likely	  not	  to	  cause	  lum.	  loss	  	  	  	  	  	  ●	  L=1⨉1034cm-­‐2s-­‐1	  is	  promising,	  L=10⨉1034cm-­‐2s-­‐1	  is	  possible	  ➤	  Benchmark	  of	  SAD	  	  	  	  	  	  ●	  Successful	  and	  need	  more	  eﬀorts
44

6. Summary➤	  Interplay	  of	  various	  issues	  	  	  	  	  	  ●	  Luminosity	  <=	  Emizance	  <=	  Beam-­‐beam,	  La8ce	  nonlinearity,	  Space	  charge,	  Impedances,	  Electron	  cloud,	  Intra-­‐beam	  scazering,	  etc.	  	  	  	  	  	  ●	  =>	  Dynamic	  aperture	  and	  lifeBme	  =>	  Beam	  commissioning	  =>	  InjecBon,	  Detector	  back	  ground,	  Alignments,	  etc.	  =>	  Tolerance	  for	  hardwares	  =>	  …
Latticenonlinearities

Beam-beam

Luminosity

Background

Emittance

Machine errors& correction

Space charge

Electron cloud

Lifetime

Intra-beam
Instabilities
Impedance

Alignment
45

Collimation
Dynamic
aperture

Linac, injection, e+/esources, damping
ring, ... ...

7. Future plan➤	  Detailed	  analysis	  of	  la8ce	  nonlinearity	  under	  an	  internaBonal	  collaboraBon	  program	  	  	  	  	  	  ●	  Cornell	  Univ.:	  D.	  Sagan	  (Bmad+PTC)	  	  	  	  	  	  ●	  SLAC:	  Y.	  Cai	  	  	  	  	  	  ●	  IHEP:	  Y.	  Zhang	  	  	  	  	  	  ●	  KEK:	  E.	  Forest,	  A.	  Morita,	  K.	  Ohmi,	  Y.	  Ohnishi,	  K.	  Oide,	  H.	  
Sugimoto,	  D.	  Zhou,	  etc.	  

➤	  CollaboraBon	  with	  CEPC/FCC-­‐ee	  teams	  ➤	  High-­‐priority	  tasks:	  	  	  	  	  	  ●	  Global	  or	  local	  correcBon	  schemes	  for	  laz.	  nonlin.	  	  	  	  	  	  ●	  SC	  compensaBon	  schemes	  	  	  	  	  	  ●	  Bezer	  understand	  beam-­‐beam	  physics	  for	  nano-­‐beam	  scheme	  	  	  	  	  	  ●	  More	  benchmark	  studies	  for	  SAD	  	  	  	  	  	  ●	  …	  …	  ➤	  RecommendaBons	  are	  welcome!	  
46

Thanks for your attention!

47