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,…
(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!
 cs z
R 
; 
2s x
1  2
1
luminosity reduction factor
nominal LHC
Piwinski angle
Piwinski angles for lepton colliders & LHC
sz[mm] sx[mm] c[mr]  csz/(2 sx) R
DORIS-I 10
230
24
0.52
0.89
DAFNE
18-40
700
30
0.39-0.86
KEKB
4
32.6
22
1.33
177
16.6
~0.5 0.20
0.285 0.65
0.98
0.84
16.6
0.315 0.72
0.81
RHIC
140
nominal 75.5
LHC
ultimate 75.5
LHC
0.930.76
0.6
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 10-20 mrad no lifetime degradation is seen.
[V. Shiltsev]
Experiment at SPS Collider
~0.45
c=500 mrad
K. Cornelis, W. Herr, M. Meddahi,
“Proton Antiproton Collisions at a
Finite Crossing Angle in the SPS”,
PAC91 San Francisco
>0.7
c=600 mrad
small emittance
to boost LHC performance further various approaches
have been proposed:
1) 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]
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
minimum crossing angle from LR b-b
k par N b 3.75mm 
  d da

c 

3
* 
11
s
2
x
32
 
b 
10
“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
need dynamic aperture
compensator

of 5-6 s &
c  8
b*
independent of beam current
wire compensation not
efficient within 2 s
from the beam center
(2) wire compensation “BBLR”
SPS studies
simulations
LHC situation
RHIC experiment
US LARP
pulsed wire
SPS experiment:
1 wire models LHC long-range interaction
d
  5 ms  
s 
5
extrapolation to LHC beambeam distance, ~9.5s, would
predict 6 minutes lifetime
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
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 : http://ab-abp-bbtrack.web.cern.ch/ab-abp-bbtrack/
Other codes, used in the past:
WSDIFF (F. Zimmermann, CERN)
http://care-hhh.web.cern.ch/CARE-HHH/Simulation Codes/Beam-Beam/wsdiff.htm
BBSIM (T. Sen, FNAL)
http://waldo.fnal.gov/~tsen/BBCODE/public
simulated stability region in x-y plane with1 & 2 SPS wires
19mm
(8s)
unstable
y
stable
x
unstable
stable
-19mm
(8s)
-19mm (8s)
one wire
Yellow: stable with two
wires & unstable with one
19mm (8s)
-19mm
two wires
19mm
Green: unstable with one
wire & stable with two
U. Dorda
simulation of wire compensation
for the SPS experiment
unstable
stable
different initial
betatron phases
one wire
1 sigma
unstable
stable
two wires
0
3 sigma
8 sigma
U. Dorda
unstable particles jump between phase-space
ellipses when they approach the wire (or, in
LHC, the other beam)
x’
x
U. Dorda
sensitivity to 2nd wire’s
transverse position:
• SPS data
• BBSIM simulation
[T. Sen]
• BBtrack simulation
[U. Dorda]
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)
simulated LHC tune footprint with
& w/o wire correction
•.16s
•.005s
•.016s
Beam
separation
at IP
MAD
(Jean-Pierre Koutchouk, LHC Project Note 223, 2000)
for future wire
beam-beam
compensators
- “BBLRs” -,
3-m long sections
have been reserved
in LHC at 104.93 m
(center position)
on either side of
IP1 & IP5
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
LR collisions at
IP1 & 5
nominal bunch
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
LR collisions
at IP1 & 5 extreme
PACMAN bunch
LR collisions
& BBLR at
IP1 & 5
overcompensated
long-range collisions only
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y
head-on & LR
collisions in
IP1 & 5
nominal bunch
head-on, LR
& BBLR
LR compensated
4,10
-1,1
long-range & head-on collisions @ IP1& 5
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y
head-on & LR
collisions in
IP1 & 5
PACMAN bunch
head-on, LR
& BBLR
LR overcompensated
long-range & head-on collisions @ IP1& 5
with & without compensation
U. Dorda
BBTrack
tune footprints for starting amplitudes up to 6s in x and y
LHC tune scan for nominal bunch, 45 deg. in x-y-plane
red: unstable (strong diffusion), blue: stable
0
U. Dorda, BBTrack
long-range & head-on
10s
0
stability of nominal bunch improves for almost all tunes
long-range & head-on & wire compensation
0.3
10s
0.8
Qy
LHC tune scan for PACMAN bunch, 45o in x-y-plane
red: unstable (strong diffusion), blue: stable
0
U. Dorda, BBTrack
long-range & head-on
10s
0
stability of extreme PACMAN bunch decreases for almost all tunes
long-range & head-on & wire compensation
0.3
10s
0.8
Qy
tune scan for nominal bunch
wire compensation
LHC
without wire
wire increases dynamic aperture by ~2s
U. Dorda, BBTrack
tune scan for PACMAN bunch
without wire
LHC
wire “over-”
compensation
dc wire reduces dynamic aperture by ~2s
U. Dorda, BBTrack
6-D effects? - nominal LHC optics:
IP5
IP5
position position
of BBLRof BBLR
position position
of BBLRof BBLR
IP1
IP1
position
of BBLR
position
of BBLR
up to
1m
vertical
dispersion
in the
triplet
chromaticity from LRBB & wires
 rp N b  4 3
 6 d x x  3d x2 d y y  3d x d y2 x  d y3 y n LR
Q'  
 4 N  d
 rp N b  4 D
B. Erdelyi & T. Sen, 2002
 3
 
n LR
b
 4 N  d

)
d: beam-beam or beam-wire distance in s
D: dispersion
: 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
Long-Range BB Experiment in RHIC, 28 April 2005,
Wolfram Fischer, et al., 1 Bunch per Ring
collision at main IP
10 min.
lifetime
Beam lifetime vs
transverse separation Initial test to evaluate
the effect in RHIC.
collision at s=10.65m
(1) Experiment shows a
measurable effect.
(2) The beam loss is very
sensitive to working point.
collision at s=10.65m
Long-Range BB Experiment
in RHIC, 28 April 2005,
Wolfram Fischer et al.,
1 Bunch per Ring
… more data sets
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
puzzling:
BBTrack simulation for RHIC with
a single long-range collision
predicts no effect,
consistent with earlier studies
for the LHC
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:
 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
Statement of work for FY07:
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
CERN Contacts
J.P. Koutchouk, F. Zimmermann
not to degrade lifetime for the PACMAN bunches,
the wire should be pulsed train by train
LHC
bunch filling
pattern
example excitation patterns (zoom)
specifications for pulsed wire compensator
88.9 ms+/-0.0002 ms
23.5 ms+/-0.02 ms
(variation with beam
energy is indicated)
high repetition rate & turn-to-turn stability tolerance
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?)
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
(3) Crab Cavities
Super-KEKB crab cavity scheme
RF Deflector
( Crab Cavity )
HER
LER
Electrons
Positrons
1.44 MV
Head-on
Collision
Crossing Angle
(11 x 2 m rad.)
1.41 MV
2 crab cavities / beam / IP
1.41 MV
Palmer for LC, 1988
Oide & Yokoya for storage rings, 1989
1.44 MV
first crab cavities will be installed
at KEKB in early 2006
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
bunch shortening rf voltage:
  ||,2rmsc 3C  1   ||,2rmsc 3C 
 c4
Vrf  
 4 

4
*4
E
2

f
s
E
2

f
0
.
7
16
s
 0 rf  z  0 rf 
x
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:
Vcrab
cE0 tan  c / 2)
cE0


c
e2f rf R12
e4f rf R12
proportional to crossing angle & independent of IP beam size;
scales with 1/R12; also inversely proportional to rf frequency
R12 & R22(R11) from MAD
nominal LHC optics
|R12,34|~30-45 m
|R22,44|~1
(from crab cavity to IP)
voltage required for Super-LHC
crab cavity voltage for different c’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
~1.5 MV@500 MHz
K. Ohmi, HHH-2004
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)
(axial view)
Absorbing
material
Notch filter
Absorbing
material
inner conductor
Coaxial beam pipe
Cooling for
inner conductor
~1.5 m
"Squashed cell"
Squashed Crab cavity for B-factories
(K. Akai et al., Proc. B-factories, SLAC-400 p.181 (1992).)
Courtesy K. Akai
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;
 c 1 c 2 3 
1   c
x' ( z ) 
z
z  ...
2

R12  2
2 6  rf 
 rf 
6c
2s z
 2 775 MHz )
1.2 GHz probably too high; 400 MHz reasonable;
800 MHz perhaps ok
noise
amplitude noise introduces small crossing
angle; e.g., 1% jitter → 1%c/2 cross. angle –
tolerance ~0.1% jitter from emittance growth
phase noise causes beam-beam offset;
tolerance on LHC IP offset random variation
xmax~10 nm
→ tight tolerance on left-right crab phase and
on crab-main-rf phase differences
crab 
xmax 4
rf  c
 <0.012o (t<0.08 ps)
at c=1 mrad & 400 MHz
 <0.04o (t<0.28 ps)
at c=0.3 mrad & 400 MHz
comparison of timing tolerance with others
KEKB
sx*
100 mm
SuperKEKB
70 mm
c
+/- 11
mrad
6 ps
+/-15
mrad
3 ps
t
ILC
Super-LHC
0.24 mm
11 mm
+/-5 mrad
+/- 0.5
mrad
0.08 ps
0.03 ps

IP offset of 0.2 sx*
IP offset of
0.001 sx*
→ not more difficult than ILC crab cavity
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
Impedance of Super-KEKB Crab Cavity Design
K. Akai
horizontal
longitudinal
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?)