XBAND CRAB CAVITIES FOR THE CLIC BEAM DELIVERY

X-BAND CRAB CAVITIES FOR THE CLIC BEAM DELIVERY SYSTEM Dr G Burt Cockcroft Institute / Lancaster Universtity P. K. Ambattu, A. C. Dexter, T. Abram - Lancaster V. Dolgashev, S. Tantawi - SLAC R. M. Jones - Manchester X-Band Workshop, CI, Dec 2008

Crab Cavity Function Crab cavities are required for ILC, LHC upgrade and CLIC The crab cavity is a deflection cavity operated with a 90 o 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. X-Band Workshop, CI, Dec 2008

TM 110 Dipole mode Electric Field Beam vertical horizontal Magnetic field • • • cross section Transverse magnetic and electric field components of the TM 110 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. X-Band Workshop, CI, Dec 2008

ILC Crab cavity Based on FNAL 3. 9 GHz CKM cavity 3. 9 GHz : compact longitudinally and transversely 3. 9 GHz cavity achieved 7. 5 MV/m (FNAL) Input coupler LOM coupler HOM coupler SOM coupler 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. X-Band Workshop, CI, Dec 2008

Transverse Kick for 3 Te. V CM To minimise required cavity kick R 12 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. X-Band Workshop, CI, Dec 2008

Phase synchronisation requirement for no more than 2% luminosity loss Crabbed crossing angle with phase jitter electron bunch Δx Luminosity reduction factor S is given as and positron bunch Interaction point Phase error (degrees) Crossing angle 20 mrad X-Band Workshop, CI, Dec 2008 12 GHz 30 GHz 0. 02 0. 06

The cavity cell structure t b Ri D Periodic boundary conditions 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. 498 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 Estimating voltage induced in crab cavity from one offset bunch rb ~ 0. 5 mm (hopefully not this bad) R/Q = 4000 Electric Field f=0 q = 0. 6 n. C w = 2 p 12 GHz Beam horizontal Magnetic field d. V = 190 V V = 2. 4 MV / cells ~ 160 k. V hence 16 offset bunches could shift amplitude by 2% X-Band Workshop, CI, Dec 2008

Group vel. vs iris radius and thickness Lines labelled in key correspond to differing iris thicknesses, 2 - 3 mm is preferred x-axis gives iris radius, 4 mm or above is preferred X-Band Workshop, CI, Dec 2008

Cavity Optimisation Lines labelled in key correspond to differing iris thicknesses, 2 - 3 mm is preferred x-axis gives iris radius, 4 - 5 mm is preferred X-Band Workshop, CI, Dec 2008

Short Wakes Short Range Wakes were calculated for several iris radii in ECHO 2 D. Assuming 30 cells, a 0. 25 mm horizontal beam offset and a 0. 5 Te. V 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 Frequency 11. 424 GHz Phase 120 deg Et/Epeak 0. 30 Et/c. Bpeak 0. 22 Group Vel. 3. 2% of c X-Band Workshop, CI, Dec 2008

TM 010 Wakefields in Crab cavities Higher order modes accelerating mode TM 110 v Need to extract the fundamental mode Same order mode 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. TM 110 h crabbing mode X-Band Workshop, CI, Dec 2008 TM 011 frequency TE 111 h TE 111 v

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 abs H field plots Crab, 11. 994 GHz Dipole, phi=120 deg, 11. 994 GHz, Q=5140 SOM, 10. 947 GHz Q=33 Dipole: Q 5729 LOM, 9. 12 GHz, Q=71 LOM: 239 LOM, 8. 11 GHz, Q=130 X-Band Workshop, CI, Dec 2008 HOM: 1900

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 TE 111 In order to have low fields in the matching cells we use the TE 111 mode in the matching cells and the TM 110 in the middle cells only. TM 110 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 k. A/m and a transverse gradient of 37 MV/m for 20 MW input power. X-Band Workshop, CI, Dec 2008

Coupler Design for CTF 3 tests H-field E-field X-Band Workshop, CI, Dec 2008