Technological aspects of crab cavities

Technological aspects of crab cavities CARE-HHH-Lumi-06, 16-20 Oct 06, Valencia, Spain J. Tückmantel, CERN Thanks to R. Calaga, F. Caspers, R. Tomas Garcia, F. Zimmermann, …

Frequency and Cavity Size Panofsky- Wenzel: Need gradient of Vz! TE modes: E- and B-deflection cancel (integrated) Dpx = -ie/w dVz/dx exp(-iwz/v) (Vz and Dp in quadrature; z = lag) Longitudinal interaction not desired: beam passage should be at zero of Vz

Crab cavity: RF phasing such that bunch centre gets zero kick ( -> beam and Vz in phase) BunchcentrelinesatIP: If not B.L. << lRF: lumi loss (transverse dimensions …) design and real kick for long bunches

4s-bunch length in coast: 30 cm 1 ns (present LHC) l800MHz = 37.5 cm (-> ±0.4): 800 MHz excluded for larger crossing angles Present LHC bunch spacing 25 ns -> 40 MHz Future bunch spacing under discussion • 12.5 ns -> 80 MHz (200 MHz incompatible) • 10/15 ns -> 100/66.6 MHz (200 MHz compatible) Next lower common denominator: 400 MHz (as main RF) If 400 MHz still too high: choice will exclude options

Minimum cavity dimensions: estimate by box-cavity Lowest w field map: round cavities: need more space for same f

For LHC IP4: beam-beam (centre) distance exceptionally spread to 42 cm (present design -> Rogelio) (required magnets already difficult for 7 TeV; 14 TeV ??) r400MHz,main = 345 mm fits next to opposite beam Oppos. beam in tube inside cryostat Accelerated beam 1/2 Lx ≤ 35 cm

Up-down and right-left symmetric cavity of classical sc. design with horizontal kick at 400 MHz excluded (with IP4 config.) (only vertical kick while horizontal (macroscopic) beam separation) • Re-entrant shape (lowers f): was ‘forbidden’ for sc. cavities: bad rinsing conditions (liquid cannot flow out easily); exists proposal for ILC cavity version (‘slighty’ re-entrant): experts not unanimous: test series pending (danger: field emission limiting performance!) • Other ‘adventurous shapes’: Danger of multipacting (MP)

‘Adiabatic deformation’ to get room for opposing beam: • (upward) displaced beam tube - lower kick efficiency - kick depends already in 1st order on vertical position (2nd for up-down sym. structures) • Beam still passes at Vz = 0 3D RF structure simulations if acceptable: beam dynamics Multipacting studies, …

Cavity fabrication • Standard: Niobium sheet metal -> spinning/deep drawing, welding, chemical treatment(s), rinsing, …, ‘witchcraft’ • Stiff cavities (vibration, vacuum forces on non-round cav.): Thicker material: Nb layer on (thick) copper is an option if specs can be met (e.g. by sputtering as for LEP2), + (OFHC) copper is a better thermal conductor than best Nb + no (earth-)magnetic shielding required (up to about 2 G) – steeper Q drop (… less adapted for very high fields)

Sergio Calatroni (…, R&D for LEP2 sputtering, …): • Bpeak is at iris: maximum damage during cavity forming -> sc. layer on it ? • angle of incidence (while sputtering) is steeper: Nb film forms under less favorable conditions (‘columnar film’) R&D to validate technology and performance

n-cell cavities • Higher real estate gradient (voltage/total length) • n times less couplers, tuners, controlers, …. • Each single-cell mode has n instances, each with different frequency, (R/Q), cell-to-cell-polarity, … - Crab cavity ‘HOM’ coupling scheme relies (partly) on frequency offset wrsp. to crab-mode: now (n-1) ‘close’ modes (with lower (R/Q) …); use power-coupler as damper ? - if vector feedback necessary for impedance reduction, ‘filter box’ is required (possibly with amplifiers -> maybe more noise)

Reference pick-up not on same cell as power coupler: direct cross-talk For well adjusted π-mode, 0-mode would auto-oscillate !! ‘filter’ has to turn 0-mode signal by 180º without perturbing π-mode signal (4-cell LEP2 cavities in SPS as injector: cable nl at fπ, (n–1/2)l at f 3π/4) …. phase noise (amplifiers) ? RF (power) system should cover whole pass-band !!

N cavities with one transmitter One mother with N children: while looking for one, the other N-1 do what they want …. N degrees of freedom with 1 knob -> add knobs (at a price) Possibility: • Ferrite phase and amplitude modulators (as tested at CERN for SPL at 352 MHz) • Serrodyne (ferrite) phase shifter ( <- F. Caspers), www: 8-140 GHz commercially available ??? 400 MHz ???

Ferrite amplitude and Phase Modulators with hybrids Cav. reflection not completely absorbed, more complex in application Cav. reflection absorbed

One problem: precision of vector sum calibration (esp. ampliude) ‘fast delta’: transmitter; ‘slow delta’: device ‘X’

CW mode (problem much ‘older’ than ‘pulsed sc. Cavity problem’, both related)

N cavities of n cells with one transmitter LEP2: 8 cavities of 4 cells on one transmitter Basically each cavity had a ‘scalar’ amplitude measurement; assuming cavities in phase: (digital) sum was used for control. ‘Once there was a time’ when a vector sum feedback was tried: relatively low gain, ‘a pain to set up’, and caused frequent trips: operational people were happy when switched off again. Combination of ‘problems’ • each cavity needs a ‘filter box’ -> unique ‘reference signal’ • vector sum calibrated for crab-mode, not very good for others: rely on low (R/Q) of other pass-band modes.

‘H’OM damping The Problem: • Keep ‘workhorse mode’ field inside cavity • Get the other fields out of the cavity (strong damping) Mode distinction: • By frequency • By field configuration Two methods: • Lumped circuit Coupler with filter, …. -> line outside cryostat -> dump power outside (LHC sc. main RF) • Transport away from cold area -> dump inside cryostat (cooling)

KEK/Cornell cavity uses symmetrized (no crab-mode pick-up) coaxial coupler -> some MP problems • option: resonant (enhances coupling) lumped circuit coupler in coupling port (as LHC main RF ‘dipole mode coupler’) • first distinction on E-minimum (antenna) or B-minimum (loop) of crab-mode, but always couples to TM0 modes (as coaxial) (coupler with filter (!) has to be superconducting !) R&D necessary (CERN’s main expert Ernst Haebel retired)

Transient beam loading: beam in phase with crab-field: ‘no’ phase error induced, only amplitude error Both systems give kick in same direction (same polarity) !!! Off axis beam: one system increases, one decreases field: amplitude difference error induced

RF power / Qext considerations Longitudinal Vz and beam are in phase: strong interaction Ideally beam passes at Vz zero-crossing -> no RF power In reality: LHC orbit can be / is displaced -> -> ‘static’ adaptation by physically moving the cavity/cryostat (remote controlled set-up with low intensity beam, dumped) -> keep a ‘dynamic’ range for ‘online’ orbit changes • the crab RF system has to deliver / absorb power; • the main RF has to absorb / deliver complement (DE=0 in coast)

2-cell cavity with 5 MV nominal kick (-> Rama’s design) model current (tuned cav.) measurable RF power Optimum Qext (i.e. Ir=0) Minimum installed power: Maximum beam excursion: (for optimum Qext !)

A 500 W solid-state amplifier per cavity (Ib,ult=1A) would • allow up to ±12 µm ‘excursion’ • at a Qext,opt=5·108 -> BW < 1 Hz (untunable) For a ‘reasonable’ Qext=1·106 (BW =400 Hz) • to keep the field up for a perfectly centered beam Pg 100…150 kW/cav. tetrode Pr klystron (noisy) displacement [m]

Kick errors (‘additive’) Perfect case: bunch centre and bunch line on axis (after crab 2) Always respected: Keep beam 1 and beam 2 RF wise separate: no common high power equipment

Optic transfer function not π between 2 crab system: Bunch centre on axis, bunch line oscillates Mutual amplitude deviation between 2 crab system: Bunch centre on axis, bunch line oscillates (absolute amplitude error: non-zero crossing angle)

Common phase shift of two crab systems (shifted tilt point): Bunch centre off-axis at IP, perfect again after crab 2 Independent phase shifts of two crab systems: Bunch centre off-axis at IP and later

Noise table (F. Zimmermann, Arcidosso  Ohmi-san) RF is ‘blind’ concerning mechanical displacements by Dz as vibrations, drifts F. Caspers (… , stochastic cooling, … ): “ …. to measure 0.03 ps might be possible at the limit of today’s technology, but 0.002 ps (@400 MHz) is out of range” Josef Frisch, SLAC: 0.003º@357MHz (0.025 ps) was done … To control means to measure at least with the same quality (provided ‘actuator’ does not inject new noise)

Questions by F. Caspers • What are phase noise properties of power amplifier (caution AMPM conversion!!) systems typically used to drive such cavities. CW amplitude foreseen; beam-loading transients to be ‘recovered’ by transmitter ? • To what precision can it be measured ? (0.025 ps possible, which technical reliability ?, need 10x • To which precision can it be controlled ? ???? • Which technology to be used (klystrons , solid state?)

Questions by F. Caspers (cntd.) • Where is the limit between jitter and drift? is betatron frequency decisive ? Coherence-length ? how stable is b-freq in practice ? Spectrum ? • How about the (blow-up) impact of amplitude noise (AM/PM conversion). • What are the phase noise properties of the beam itself ? (e.g. from power supply ripple, parametrically excited modulation etc etc..) phase different from bunch to bunch “is planned” (and unavoidable in any case): each bunch pairing is different !!

Proposal F. Caspers, similar J. Frisch, SLAC (ILC) ???? Does this really help or not ????

Problems with this proposal: • How to build a RF vector-feedback (impedance !) around? (slow changes ( kHz) can be handled by individual amp&phase modulators for each cavity, but not coupled bunch) • For each ‘pair’ a bulky HIGH POWER LINE has to run along the tunnel between Crab 1 and Crab 2 • Ideally klystrons at IP (where ?), else asymmetric design

Bunch to bunch positions are fixed but not ‘regular’ in coast • Beam and RF are in quadrature: each bunch ‘turns’ RF vector • For ‘regular beam’: detune cavity such that it drifts back automatically till next bunch (react. beam loading compensation) • Beam with gaps: ‘half detuning’ to make the best out of it: RF has to fight keeping bunches in regular position (and only partly succeeds due to limited loop gain) In coast at full voltage: RF system comes to limits -> let bunches drift (<< B.L.) on ‘easier’ positions (status depends on individual bunch charges, ….)

RF power Already after injection (1 MV/cavity) bunches have ‘individualized’ z-position (due to technical limitation of RF vector feedback)

End injection, V = 1MV/cav Adapted on flat bottom Half ramp, V rising flat top reached, V=2 MV/cav The ‘bunch sliding’ during 7 TeV-ramp up to coast. Possibly redone during coast (if beam changes conditions) Adapted for coast

RF power Bunches ‘slide’ to ‘individual’ z-position not to overload RF system in coast (2 MV/cavity)

Summary • At 400 MHz horizontal kick with present horizontal beam-beam distance not possible -> need different cavity shapes or more beam-line separation (-> Rogelio) • Nb/Cu technology might be an option: need R&D to verify film quality for this shape • n-cell (low n !!) cavities and N cavities per transmitter possible (space, $$$), but more complex installation with probably higher noise • Limited beam excursions in LHC cannot be exploited for low power consumption: system BW too low -> Qext 106 -> 100-150 kW / 2-cell cavity (wasted) • Role of different type of noise (amplitude, phase; does coherence between both crab systems help) has to be analyzed in more detail to find best technical options • Is the fact that each bunch has its ‘private phase’ a real problem or only a nuisance ? • The announced required noise level is about 10 below present technology. This is no reason for despair, but caution should be kept when extrapolating technology:

One should not overrate technical advancement potentials: Reliability is cornerstone for integrated luminosity in LHC

Technological aspects of crab cavities