The use of crab cavities in colliders to increase luminosity
Graeme Burt
Lancaster University / Cockcroft Institute
ILC Crab Cavity Collaboration• Cockcroft Institute :
– Graeme Burt (Lancaster University)– Richard Carter (Lancaster University)– Amos Dexter (Lancaster University)– Imran Tahir (Lancaster University)– Richard Jenkins (Lancaster University)– Philippe Goudket (ASTeC)– Peter McIntosh (ASTeC)– Alex Kalinin (ASTeC)– Carl Beard (ASTeC)– Lili Ma (ASTeC)– Mike Dykes (ASTeC)
• FNAL– Leo Bellantoni– Mike Church– Timergali Khabiboulline– Brian Chase
• CERN– Daniel Schulte– Andrea Latina
• SLAC– Chris Adolphson– Zenghai Li– Liling Xiao
Effect of the crossing angle on luminosity
Head-on collisionMaximum luminosity
Crossing angle introducedReduced luminosity due to crossing angle
Crossing angle with crab rotationEffective head-on collision
Transverse deflecting dipole mode
• The crab cavity imparts a transverse momentum to the bunch.
• The bunch continues to rotate outside the cavity.
IP
~0.12m/cell Separation from the Interaction Point ~15m
Crab Cavity
TM110 dipole mode cavity
• Use of the magnetic field of a TM110 dipole mode
• The field gives a phase-dependant transverse momentum kick to the beam
beam
●
magneticfield
elliptical cavity
electricfield
Magnetic field distribution of a TM110 mode
Effect of distance between crab cavity and focusing quadrupole
QF1 QD0
QF1 QD0
Position of the crab
cavity
Trajectory of a particle at one end of
the bunch
x1
Deflection x1>x2
x
2
Angle given by crab kick
Voltage Stability
crab is proportional to the maximum magnetic field in the cavity
voltage error induces errors in bunch rotation
crab
For optimum cell length
θerror
2c
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7 8
% l
um
ino
sit
y l
os
s
RMS cavity amplitude jitter [%]
Bunch arrival time Jitter
It is found that the crab cavity can correct for variation in bunch arrival time by providing a total transverse kick to early or late bunches, such that both bunch collide head-on.
IP
Late bunch without
transverse kick
Late bunch with transverse
kick
Collision point
Absolute cavity phase error
Phase error (deg) for 2% luminosity loss
Crossing angle
for cavity frequency
1.3GHz 3.9GHz
10mrad 6 19
20mrad 3 9
x IP displaced
IP
Collision point
Absolute cavity phase error is not a
major concern
Phase Jitter
Crabbed crossing angle with phase jitter Effective head-on collision
sinx r
Phase error (degrees)
Crossing angle 1.3GHz 3.9GHz
14mrad 0.03 0.1
Δx
Interaction point
electron bunch
positron bunch
0
1
2
3
4
5
6
7
0 0.02 0.04 0.06 0.08 0.1 0.12
% luminosity loss% luminosity loss
% l
um
ino
sit
y l
os
s
RMS cavity timing jitter [ps]
Cavity Alignment
0
0.2
0.4
0.6
0.8
1
1.2
-1.5 -0.5 0.5 1.5
Roll (deg)
Lu
min
osi
ty r
ed
uct
ion
fa
cto
r,S
PLACETsimulationsGeometricCalculations
If the cavity has a roll misalignment it will cause a small crossing angle in the vertical plane.
This will significantly reduce luminosity.
Higher Order Modes
frequency
TM010
accelerating mode
TM110h
crabbing mode
TM110v (SOM)
TE111 (HOM)
TM011 (HOM)Need to extract the fundamental mode
Beam-pipe cut-off
Higher order modes
Extraction of the lower order mode and the higher order modes is essential to minimise disruption of the beam.The cavity design should allow for as much LOM/HOM damping as possible.
Transverse Wakefield
• These results have been used to place damping requirements on the higher order modes.
• The collective effects have been simulated in MAFIA and the effects studied using a tracking code (PLACET).
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
0 50 100 150 200
Bunch number
Offs
et a
t th
e IP
(n
m)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
Percentage change in frequency
Ver
tical
Offs
et (
nm)
AnalyticalPLACET
• Collective Transverse Wakefields will kick the bunch similar to a phase error.
ILC CC System SpecificationCrossing angle 14 mrad
Number of cryovessels per IP 2
Number of 9-cell cavities per cryovessel 2
Required bunch rotation , mrad 7
Location of crab cavities from the corresponding IP, m 13.4 – 17.4
Longitudinal space allocated per cryovessel, m 3.8
RMS Relative Phase Stability, deg 0.095
RMS Beam Energy Jitter, % 0.33
X offset at IP due to crab cavity angle (R12), m/rad 16.3
Y offset at IP due to crab cavity angle (R12), m/rad 2.4
Amplitude at 1TeV CM, MV 2.64
Max amplitude with operational margin, MV 4.1