X-Band Workshop, CI, Dec 2008

X-BAND CRAB CAVITIES FOR THE CLIC BEAM DELIVERY

SYSTEM

Dr G BurtCockcroft Institute / Lancaster

Universtity

P.K. Ambattu, A.C. Dexter, T. Abram - LancasterV. Dolgashev, S. Tantawi - SLAC

R. M. Jones - Manchester

X-Band Workshop, CI, Dec 2008

Crab Cavity Function

The crab cavity is a deflection cavity operated with a 90o phase shift.

A particle at the centre of the bunch gets no transverse momentum kick and hence no deflection at the IP.

A particle at the front gets a transverse momentum that is equal and opposite to a particle at the back.

The quadrupoles change the rate of rotation of the bunch.

Crab cavities are required for ILC, LHC upgrade and CLIC

X-Band Workshop, CI, Dec 2008

• Transverse magnetic and electric field components of the TM110 dipole mode combine to give the overall transverse momentum kick.

• The net transverse momentum kick is phase dependent.

• If the beam has an offset it can be accelerated or retarded by the longitudinal electric field and hence delivers or extracts power from the cavity.

Beam

Magnetic field

cross section

horizontal vertical

Electric Field

TM110 Dipole mode

X-Band Workshop, CI, Dec 2008

ILC Crab cavity

Based on FNAL 3.9 GHz CKM cavity

3.9GHz : compact longitudinally and transversely

3.9GHz cavity achieved 7.5 MV/m (FNAL)

To minimise wakefields for the short time structure of the ILC bunches, the number of cells must be optimised against overall length. Crab cavity needs extraction of LOM (avoid unwanted energy spread), SOMs and HOMs.

Input coupler

HOM coupler

LOM coupler

SOM coupler

X-Band Workshop, CI, Dec 2008

Transverse Kick for 3 TeV CM

MV4.21012225

103105.110

R

cEV

9

8122

12

ormax

To minimise required cavity kick R12 needs to be large hence put the cavity close to IP (25 metres suggested)

At 20 MV/m transverse gradient this is only 12 cm which is 10-30 cells depending on the cavity design and gradient.

This is about 3 MW RF for a SW design probably more for TW.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-120 -70 -20 30 80

X-Band Workshop, CI, Dec 2008

Phase synchronisation requirement for no more than 2% luminosity loss

Crabbed crossing

angle with phase jitter

sincx r

Phase error (degrees)

Crossing angle 12 GHz 30 GHz

20 mrad 0.02 0.06

Δx

Interaction point

electron bunch

positron bunch

2

x

2

4

xexpS

Luminosity reduction factor S is given as

and

X-Band Workshop, CI, Dec 2008

The cavity cell structuret

D Cell length

t Iris thickness

b Equator radius

a Iris radius

Phase advance per cell, φ radians

Length of the cell, D mm (11.994 GHz)

2π/3 (TW) 8.332

5π/6 (TW) 10.415

π (SW) 12.498Periodic boundary

conditions

b

D

Ri

Four independent cell parameters – but one fixed by frequency and one fixed by phase advance

hence investigative plots only vary iris thickness and iris radius

X-Band Workshop, CI, Dec 2008

Beam-loading Issues

• Beam-loading is typically large and depends on bunch offset

• Beam-loading might at worst vary randomly

1cos

2b d

i

r RV q

c Q

Estimating voltage induced in crab cavity from one offset bunchrb ~ 0.5 mm (hopefully not this bad)R/Q = 4000 = 0q = 0.6 nCw = 2 12 GHz

V = 190 VV = 2.4 MV / cells ~ 160 kVhence 16 offset bunches could shift amplitude by 2%

Beam

Magnetic field

horizontal

Electric Field

X-Band Workshop, CI, Dec 2008

Group vel. vs iris radius and thickness

Group Vel (% of c) 2/3 mode

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

2 3 4 5

Iris Radius (mm)

Group Vel (% of c) 5p/6 mode

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

2 3 4 5

Iris Radius (mm)

2Li = 1 mm

2 mm

3 mm

4 mm

5 mm

6 mm

7 mm

8 mm

Frerquency Separation (%) mode

-0.08

-0.06

-0.04

-0.02

0.00

2 3 4 5

Iris Radius (mm)

Note Changeof Parameter

Lines labelled in key correspond to differing iris thicknesses, 2 - 3 mm is preferredx-axis gives iris radius, 4 mm or above is preferred

X-Band Workshop, CI, Dec 2008

Cavity Optimisation

Cavity Q 2/3 mode

0

2000

4000

6000

8000

10000

2 3 4 5

Iris Radius (mm)

2Li=1 mm

2 mm

3 mm

4 mm

5 mm

6 mm

7 mm

8 mm

R/Q (W/m) 2/3 mode

0

1000

2000

3000

4000

5000

2 3 4 5

Iris Radius (mm)

Lines labelled in key correspond to differing iris thicknesses, 2 - 3 mm is preferredx-axis gives iris radius, 4 - 5 mm is preferred

E trans /E max 2/3 mode

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 3 4 5

Iris Radius (mm)

2Li=1 mm

2 mm

3 mm

4 mm

5 mm

6 mm

7 mm

8 mm

X-Band Workshop, CI, Dec 2008

Short Wakes

y = 7760.3x-1.9278

0

500

1000

1500

2000

2500

1 2 3 4 5 6

Iris radii (mm)

Tra

nsv

ers

e K

ick

(V/p

C/m

)

Short Range Wakes were calculated for several iris radii in ECHO 2D.

Assuming 30 cells, a 0.25 mm horizontal beam offset and a 0.5 TeV energy beam the luminosity loss is 2% for a 5 mm iris.

Longitudinal wake would be ~0.6 MV for 30 cells.

X-Band Workshop, CI, Dec 2008

Cavity Design

10

12

14

16

18

20

22

24

0 45 90 135 180

Phase (degrees)

Fre

qu

en

cy

(G

Hz)

.

Dipole 1

Dipole 2

Dipole 3

Dipole 4

Dipole 5

Light Line

Frequency 11.424 GHz

Phase 120 deg

Et/Epeak 0.30

Et/cBpeak 0.22

Group Vel. 3.2% of c

X-Band Workshop, CI, Dec 2008

frequency

TM010accelerating mode

TM110hcrabbing mode

TM110vSame order mode

TE111h

TM011Need to extract the fundamental mode

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/SOM/HOM damping as possible.

Wakefields in Crab cavities

TE111v

X-Band Workshop, CI, Dec 2008

Ways of polarising

• Elliptical cells (requires CNC diamond tipped milling machine)

• Squash cells

• Coupling slots

• Stubs (problems at high fields)

• Couplers (need to avoid coupling to operating mode)

X-Band Workshop, CI, Dec 2008

Mode Damping

LOM, 8.11 GHz, Q=130

Crab, 11.994 GHz

SOM, 10.947 GHz Q=33

abs H field plots

Dipole, phi=120 deg, 11.994 GHz, Q=5140

LOM, 9.12 GHz, Q=71

Dipole: Q5729

LOM: 239

HOM: 1900

X-Band Workshop, CI, Dec 2008

SOM detuning

• Elliptical Damped Detuned structures (EDDS)

• Ellipticity of each cell is altered to detune the SOM throughout the structure.

X-Band Workshop, CI, Dec 2008

Structure Design

In order to have low fields in the matching cells we use the TE111 mode in the matching cells and the TM110 in

the middle cells only.

TE111

TM110

X-Band Workshop, CI, Dec 2008

Travelling wave simulation

The structure has a peak electric field of 110 MV/m

and a peak magnetic field of 350 kA/m and a transverse gradient of 37 MV/m for 20

MW input power.

X-Band Workshop, CI, Dec 2008

Coupler Design for CTF3 tests

E-field

H-field