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