1. progress of beam-beam compensation schemes
Frank Zimmermann
Thanks to
Kazunori Akai, Gerard Burtin, Jackie Camas,
Fritz Caspers, Ulrich Dorda, Wolfram Fischer,
Jean-Pierre Koutchouk, Kazuhito Ohmi,
Yannis Papaphilippou, Francesco Ruggiero,
Tanaji Sen, Vladimir Shiltsev, Jorg Wenninger,…

2. (1) need for beam-beam compensation
nominal LHC parameters are challenging & “at the edge”:
~20% geometric luminosity loss from crossing angle
chaotic particle trajectories at 4-6s due to long-range
beam-beam effects
if we increase #bunches or bunch charge, or reduce b*:
long-range beam-beam effects require larger crossing angle
but geometric luminosity loss would be inacceptable!

3. Piwinski angle
luminosity reduction factor
nominal LHC

4. Piwinski angles for lepton colliders & LHC
sz[mm]
sx[mm]
qc[mr]
Q= qcsz/(2 sx) Rq
DORIS-I 10
230 24
0.52
0.89
DAFNE
18-40
700 30
0.93-
0.76
KEKB 4
32.6 22
1.33
0.6
RHIC
140
177
~0.5
0.20
0.98
nominal LHC
75.5
16.6
0.285
0.65
0.84
ultimate
LHC
0.315
0.72
0.81

5. Impact of crossing angle?
Lepton colliders:
Strong-strong beam-beam simulations predict an
increase in the KEKB beam-beam tune shift limit
by a factor 2-3 for head-on collision compared with
the present crossing angle. This is the primary
motivation for installing crab cavities. The simulations
correctly predict the present performance. [K. Ohmi]
Hadron Colliders: RHIC operates with crossing angles of +/- 0.5 mrad due to limited BPM resolution and diurnal orbit motion. Performance of proton stores is very irreproducible and frequently occurring lifetime problems could be related to the crossing angle, but this is not definitely proven. [W. Fischer]
Tevatron controls crossing angle to better than 10 mrad, and for angles of mrad no lifetime degradation is seen [V. Shiltsev]

6. Experiment at SPS Collider
K. Cornelis, W. Herr, M. Meddahi,
“Proton Antiproton Collisions at a
Finite Crossing Angle in the SPS”,
PAC91 San Francisco
Q~0.45
qc=500 mrad
Q>0.7
qc=600 mrad
small emittance

7. to boost LHC performance further various approaches
have been proposed:
increase crossing angle AND reduce bunch length
(higher-frequency rf & reduced longitudinal emittance)
[J. Gareyte; J. Tuckmantel, HHH-20004]
2) reduce crossing angle & apply “wire” compensation
[J.-P. Koutchouk]
3) crab cavities → large crossing angles w/o luminosity loss
[R. Palmer, 1988; K.~Oide, K. Yokoya, 1989; KEKB 2006]
4) collide long intense bunches with large crossing angle
[F. Ruggiero, F. Zimmermann, ~2002]

8. beam-beam compensation with wires or crab cavities
baseline upgrade parameters invoke shorter or longer bunches
F. Ruggiero, F. Zimmermann, HHH-2004
beam-beam compensation with wires or crab cavities
would change the optimum beam parameters and
could greatly affect the IR layout

9. minimum crossing angle from LR b-b
“Irwin scaling”
coefficient
from simulation
note: there is a threshold - a few LR encounters
may have no effect! (2nd PRST-AB article
with Yannis Papaphilippou)
minimum crossing angle with wire
compensator
need dynamic aperture
of 5-6 s &
wire compensation not
efficient within 2 s
from the beam center
independent of beam current

10. (2) wire compensation “BBLR”
SPS studies
simulations
LHC situation
RHIC experiment
US LARP
pulsed wire

11. 1 wire models LHC long-range interaction
SPS experiment:
1 wire models LHC long-range interaction
extrapolation to LHC beam-
beam distance, ~9.5s, would
predict 6 minutes lifetime

12. two wires model beam-beam compensation
SPS experiment:
two wires model beam-beam compensation
Qx=0.31
beam lifetime
no wire
2 wires
1 wire
vertical tune
lifetime is recovered over a large tune range, except for Qy<0.285

13. New Simulation Tool: BBTrack
Purpose of the code: Weak-strong simulations of long-range and head-on beam-beam
interactions and wire compensation.
Author: Ulrich Dorda, CERN
Programming language: FORTRAN90
Homepage :
Other codes, used in the past:
WSDIFF (F. Zimmermann, CERN)
Codes/Beam-Beam/wsdiff.htm
BBSIM (T. Sen, FNAL)

14. simulated stability region in x-y plane with1 & 2 SPS wires
19mm (8s) y
unstable
stable x
un-
stable
stable
-19mm (8s)
-19mm (8s)
19mm (8s)
-19mm
19mm
two wires
one wire
Yellow: stable with two wires & unstable with one
Green: unstable with one
wire & stable with two
U. Dorda

15. simulation of wire compensation
for the SPS experiment
stable
unstable
different initial betatron phases
one wire
1 sigma
unstable
stable
two wires
U. Dorda
8 sigma
3 sigma

16. unstable particles jump between phase-space ellipses when they approach the wire (or, in LHC, the other beam) x’ x
U. Dorda

17. sensitivity to 2nd wire’s
transverse position:
SPS data
BBSIM simulation
[T. Sen]
BBtrack simulation
[U. Dorda]

18. Long-Range Beam-Beam Compensation for the LHC
To correct all non-linear effects correction must be local.
Layout: 41 m upstream of D2, both sides of IP1/IP5
current-carrying
wires
Phase difference between BBLRC &
average LR collision is 2.6o
(Jean-Pierre Koutchouk)

19. simulated LHC tune footprint with & w/o wire correction
Beam
separation
at IP
MAD
(Jean-Pierre Koutchouk, LHC Project Note 223, 2000)

20. for future wire
beam-beam
compensators
- “BBLRs” -,
3-m long sections
have been reserved
in LHC at m
(center position)
on either side of
IP1 & IP5

21. tune footprints for starting amplitudes up to 6s in x and y
LR collisions at
IP1 & 5 for
nominal bunch
LR collisions at
IP1 & 5 for extreme
PACMAN bunch
long-range collisions only
without BBLR compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y

22. nominal bunch LR collisions at IP1 & 5 LR collisions & BBLR at IP1 & 5
compensated
long-range collisions only
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y

23. extreme PACMAN bunch LR collisions at IP1 & 5 LR collisions & BBLR at
overcompensated
long-range collisions only
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y

24. nominal bunch head-on & LR head-on, LR collisions in & BBLR IP1 & 5
LR compensated
4,10
-1,1
long-range & head-on IP1& 5
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y

25. PACMAN bunch head-on, LR & BBLR head-on & LR collisions in IP1 & 5
LR over-
compensated
long-range & head-on IP1& 5
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y

26. LHC tune scan for nominal bunch, 45 deg. in x-y-plane
red: unstable (strong diffusion), blue: stable
U. Dorda, BBTrack
long-range & head-on
10s
stability of nominal bunch improves for almost all tunes
long-range & head-on & wire compensation
0.3
0.8
10s Qy

27. LHC tune scan for PACMAN bunch, 45o in x-y-plane
red: unstable (strong diffusion), blue: stable
U. Dorda, BBTrack
long-range & head-on
10s
stability of extreme PACMAN bunch decreases for almost all tunes
long-range & head-on & wire compensation
0.3
0.8
10s Qy

28. tune scan for nominal bunch
wire compensation
LHC
without wire
wire increases dynamic aperture by ~2s
U. Dorda, BBTrack

29. tune scan for PACMAN bunch
without wire
LHC
wire “over-”
compensation
dc wire reduces dynamic aperture by ~2s
U. Dorda, BBTrack

30. 6-D effects? - nominal LHC optics:
IP5
IP5
up to
1 m
vertical
disper-
sion
in the
triplet
position
of BBLR
position
of BBLR
position
of BBLR
position
of BBLR
IP1
IP1
position
of BBLR
position
of BBLR

31. chromaticity from LRBB & wires
B. Erdelyi & T. Sen, 2002
d: beam-beam or beam-wire distance in s
D: dispersion
h: dispersion in s
nLR: number of LR encounters
e.g., d=9.5, nLR=30, D=0.6 m, b=3000 m → Q’~0.25
chromaticity from long-range collisions or wire is a small effect

32. Long-Range BB Experiment in RHIC, 28 April 2005,
Wolfram Fischer, et al., 1 Bunch per Ring
Beam lifetime vs transverse separation -
Initial test to evaluate the effect in RHIC.
collision at main IP
10 min.
lifetime
collision at s=10.65m
(1) Experiment shows a measurable effect. (2) The beam loss is very sensitive to working point.

33. Long-Range BB Experiment in RHIC, 28 April 2005,
Wolfram Fischer et al.,
1 Bunch per Ring
… more data sets
collision at s=10.65m
Some time stamps have to be adjusted (used
time of orbit measurement, not orbit change); parameters other than the orbit were changed - not shown. Scan 4 is the most relevant one.
collision at s=10.65m

34. BBTrack simulation for RHIC with a single long-range collision
puzzling:
BBTrack simulation for RHIC with
a single long-range collision
predicts no effect,
consistent with earlier studies
for the LHC

35. US LHC Accelerator Research Program Task Sheet
Task Name: Wire compensation of beam-beam interactions
Date: 23 May 2005
Responsible person (overall lead, lead at other labs):
Tanaji Sen (FNAL, lead), Wolfram Fischer (BNL)
Statement of work for FY06:
Statement of work for FY07:
CERN Contacts
J.P. Koutchouk, F. Zimmermann
Design and construct a wire compensator (either at BNL or FNAL)
Install wire compensator on a movable stand in one of the RHIC rings
Theoretical studies (analysis and simulations) to test the compensation and robustness
Beam studies in RHIC with 1 bunch / beam at flat top & 1 parasitic interaction.
Observations of lifetimes, losses, emittances, tunes, orbits for each b-b separation.
Beam studies to test tolerances on: beam-wire separation w.r.t. b-b separation,
wire current accuracy, current ripple
Beam studies with elliptical beams at the parasitic interaction, aspect ratio close
to that of the beams in the LHC IR quadrupoles
Compensation of multiple bunches in RHIC with pulsed wire current.
Requires additional voltage modulator

36. not to degrade lifetime for the PACMAN bunches,
the wire should be pulsed train by train
LHC
bunch filling
pattern
example excitation patterns (zoom)

37. specifications for pulsed wire compensator
88.9 ms+/ ms
23.5 ms+/-0.02 ms
(variation with beam
energy is indicated)
high repetition rate & turn-to-turn stability tolerance

38. approaches towards solution:
earlier design for pulsed LHC orbit correction
by Corlett & Lambertson (LBNL)
[was expensive 10 years ago]
fast kicker developments for ILC (KEK, UK)
fast switching devices for induction rf (KEK)
contacts with industry
collaboration with US LARP
advice by Fritz Caspers and other CERN
colleagues
start paper study [Ulrich Dorda]
if promising solution is found, possibly lab test
test in RHIC (2007?)

39. merits of wire compensation
long-range compensation was demonstrated
in SPS using 2 wires (lifetime recovery)
simulations predict 1-2s gain in dynamic
aperture for nominal LHC
allows keeping the same – or smaller –
crossing angle for higher beam current
→no geometric luminosity loss
challenges & plans
further SPS experiments (3rd wire in 2007)
demonstrate effectiveness of compensation
with real colliding beams (at RHIC)
study options for a pulsed wire

40. (3) Crab Cavities

41. Super-KEKB crab cavity scheme
2 crab cavities / beam / IP
Palmer for LC, 1988
Oide & Yokoya for storage rings, 1989
first crab cavities will be installed
at KEKB in early 2006

42. history of s.c. crab cavity developments
CERN/Karlsruhe sc deflecting cavity for separating
the kaon beam, 1970’s, 2.86 GHz*
Cornell 1.5 GHz crab cavity 1/3 scale models 1991*
KEK 500 MHz crab cavity with extreme polarization,
1993-present, for 1-2 A current, 5-7 mm bunch
length
FNAL CKM deflecting cavity, 2000-present*
KEK 2003 new crab cavity design for Super-KEKB,
10 A beam current, 3 mm bunch length,
more heavily damped (coaxial & waveguide)
Daresbury is studying crab cavities for ILC, 2005
Cornell is interested in developing crab cavities
for Super-LHC
*H. Padamsee, Daresbury Crab
Cavity Meeting, April 2004

43. bunch shortening rf voltage:
unfavorable scaling as 4th power of crossing angle and
inverse 4th power of IP beam size; can be decreased by
reducing the longitudinal emittance; inversely proportional
to rf frequency
crab cavity rf voltage:
proportional to crossing angle & independent of IP beam size;
scales with 1/R12; also inversely proportional to rf frequency

44. R12 & R22(R11) from MAD nominal LHC optics |R12,34|~30-45 m |R22,44|~1
(from crab cavity to IP)

46. voltage required for Super-LHC

47. crab cavity voltage for different qc’s & rf frequencies
crossing angle
0.3 mrad
1 mrad
8 mrad
800 MHz
2.1 MV
7.0 MV
56 MV
400 MHz
4.2 MV
13.9 MV
111 MV
200 MHz
8.4 MV
27.9 MV
223 MV

48. KEKB crab cavity Squashed cell operating in TM2-1-0 (x-y-z)
K. Ohmi, HHH-2004
~1.5 MHz
KEKB crab cavity
Squashed cell operating in TM2-1-0 (x-y-z)
Coaxial coupler is used as a beam pipe
Designed for B-factories (1〜2A)
~1.5 m
Courtesy K. Akai

49. longitudinal space & crab frequency
longitudinal space required for crab cavities scales roughly linearly with crab voltage;
desired crab voltage depends on rf frequency);
achievable peak field also depends on rf
frequency; 2 MV ~ 1.5 m, 20 MV ~ 15 m
frequency must be compatible with bunch spacing; wavelength must be large compared with bunch length;
1.2 GHz probably too high; 400 MHz reasonable;
800 MHz perhaps ok

50. noise amplitude noise introduces small crossing
angle; e.g., 1% jitter → 1%qc/2 cross. angle –
tolerance ~0.1% jitter from emittance growth
phase noise causes beam-beam offset;
tolerance on LHC IP offset random variation
Dxmax~10 nm
→ tight tolerance on left-right crab phase and
on crab-main-rf phase differences
Df <0.012o (Dt<0.08 ps)
at qc=1 mrad & 400 MHz
Df <0.04o (Dt<0.28 ps)
at qc=0.3 mrad & 400 MHz

51. comparison of timing tolerance with others
KEKB
Super-KEKB
ILC
Super-LHC
sx*
100 mm
70 mm
0.24 mm
11 mm qc
+/- 11 mrad
+/-15 mrad
+/-5 mrad
+/- 0.5 mrad Dt
6 ps
3 ps
0.03 ps
0.08 ps
IP offset of
0.001 sx*
IP offset of 0.2 sx*
→ not more difficult than ILC crab cavity

52. impedance of crab cavities
transverse impedance is an issue
due to large beta function
rise time due to 1 crab cavity =
rise time from ~10 normal rf cavities
with the same voltage

53. horizontal longitudinal Impedance of Super-KEKB Crab Cavity Design
K. Akai
horizontal
longitudinal

54. merits of crab cavities
practical demonstration at KEKB in early 2006
avoids geometric luminosity loss, allowing
for large crossing angles (no long-range
beam-beam effect)
potential of boosting the beam-beam tune
shift (factor 2-3 predicted for KEKB)
challenges & proposed plans
design & prototype of Super-LHC crab cavity
(Cornell is interested)
demonstration that noise-induced emittance
growth is acceptable for hadron colliders
(installation & experiment at RHIC?)