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,

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, …

J.T., 17/10/06

Frequency and Cavity Size

Panofsky-

Wenzel:

Need gradient of Vz!

TE modes: E- and B-deflection cancel (integrated)

px = -ie/  dVz/dx   exp(-iz/v)

(Vz and p in quadrature; z = lag)

Longitudinal interaction not desired:

beam passage should be at zero of Vz

ExBybeamyzxEzbeamByxyzx-deflection

J.T., 17/10/06

Crab cavity: RF phasing such that bunch centre gets zero kick

( -> beam and Vz in phase)beam 1beam 2collision direction

design and real kick for long bunches

Bunch centre lines at IP:

If not B.L. <<RF: lumi loss

(transverse dimensions …)

design kickobtained kicklong bunch

J.T., 17/10/06

4-bunch length in coast: 30 cm 1 ns (present LHC)

800MHz = 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

J.T., 17/10/06

Minimum cavity dimensions: estimate by box-cavitydefl.LxLyLz

beamEzdefl.cavitywallcavitywallxz

€

Ez =A⋅ (sinkxx) ⋅ (coskyy); Ex =Ey =0Lowest field map:

€

kx =2π / Lx; ky =π / Ly; kz =0

€

2 =c2 (kx2 + ky

2 + kz2 )⇒ f 2 =c2 (1/ Lx

2 + 1/(2Ly)2)

round cavities: need more space for same f

J.T., 17/10/06

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

J.T., 17/10/06

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)

J.T., 17/10/06

opposite beamkicked beam

‘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

1) 3D RF structure simulations

2) if acceptable: beam dynamics

3) Multipacting studies, …

J.T., 17/10/06

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)

J.T., 17/10/06

Sergio Calatroni (…, R&D for LEP2 sputtering, …):accel.E peakdefl.B peaksputter direction

• 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

J.T., 17/10/06

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)

J.T., 17/10/06

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 n at fπ, (n–1/2) at f 3π/4) …. phase noise (amplifiers) ?

RF (power) system should cover whole pass-band !!

–+referencefilter0-mode π-mode

Reference pick-up not on same cell as power coupler:

direct cross-talk

J.T., 17/10/06

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 ???

J.T., 17/10/06

AB12 from power splitter L1 L2 21AB load β to cavity loadαTαTβ

Ferrite amplitude and Phase Modulators with hybrids

AB12 L1 L2 from power splitter cavity  LC 

Cav. reflection absorbed

Cav. reflection not completely absorbed, more complex in application

J.T., 17/10/06

Set-functionBalanced Power SplitterVector SummingX+–TunerX+–TunerX+–Tuner

One problem: precision of vector sum calibration (esp. ampliude)

‘fast delta’: transmitter; ‘slow delta’: device ‘X’

J.T., 17/10/06

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

J.T., 17/10/06

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.

J.T., 17/10/06

‘H’OM dampingThe 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)

J.T., 17/10/06

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)

J.T., 17/10/06

Transient beam loading: beam in phase with crab-field: ‘no’ phase error induced, only amplitude error

bunch head movement(centred beam)‘optical’ distance : πVz

Both systems give kick in same direction (same polarity) !!!off axis beamVz

Off axis beam: one system increases, one decreases field:

amplitude difference error induced

J.T., 17/10/06

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 (E=0 in coast)

J.T., 17/10/06

€

(R/Q)⊥ =12Vz

2(x) /(U ) /(kx)2 =47.5Ω (circuitΩ !!) ↔ 95linacΩ

2-cell cavity with 5 MV nominal kick (-> Rama’s design)

€

(R/Q)||=(R/Q)⊥(kx)2

k= / c

€

I g,r =c⋅V⊥

2(R/Q)⊥ ⋅ ⋅xQext±I b

⎛

⎝⎜

⎞

⎠⎟

€

Pg,r = 12(R / Q)⊥ 2 / c2 ⋅x2 Qext⋅I g,r

2

Optimum Qext (i.e. Ir=0)

€

Qext,opt=c⋅V⊥

2(R/Q)⊥ ⋅I b ⋅ ⋅x

model current (tuned cav.)

measurable RF power

€

Pg,r,min= ⋅V⊥ ⋅I b

cxMinimum installed power:

Maximum beam excursion:(for optimum Qext !)

€

Pg,r c

⋅V⊥ ⋅I b=xmax

€

px =e

dVz

dx⇒ V⊥ =

c

dVz

dx⇒

c

V⊥x=Vz

J.T., 17/10/06

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,r,x=0 =V⊥

2

8 (R/Q)⊥⋅

1Qext

=65kW

Pg

Pr

displacement [m]

100…150 kW/cav.

tetrode

klystron(noisy)

J.T., 17/10/06

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

πbunch center on axiscrab 1crab 2I P

J.T., 17/10/06

πoptics errorbunch center on axis

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)

πamplitude errorbunch center on axis

J.T., 17/10/06

πbunch center on axisbunch center off axis at IP

Independent phase shifts of two crab systems:

Bunch centre off-axis at IP and later

Common phase shift of two crab systems (shifted tilt point):

Bunch centre off-axis at IP, perfect again after crab 2

πbunch center off axisbunch center off axis at IP

J.T., 17/10/06

Noise table (F. Zimmermann, Arcidosso Ohmi-san)

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)

KEKB Sup. KEKB ILC Sup. LHCx*[ ]µm 100 70 0.24 11θc[ ]mrad 22 30 10 1 [ ]t ps 0.6 0.3 0.03 0.002 =z c· [ ]t µm 180 90 9 0.6

RF is ‘blind’ concerning mechanical displacements by zas vibrations, drifts

J.T., 17/10/06

Questions by F. Caspers

What are phase noise properties of power amplifier (caution AMPM  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?)

J.T., 17/10/06

Questions by F. Caspers (cntd.)

Where is the limit between jitter and drift? is betatron frequency decisive ? Coherence-length ? how stable is β-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 !!

J.T., 17/10/06

C1C2noisyklystronnoisyklystronreferenceC1 and C2 have ‘individual klystron noise’

Proposal F. Caspers, similar J. Frisch, SLAC (ILC)

C1C2referenceC1 and C2 have (partly) ‘coherent klystron noise’

φ

φ

???? Does this really help or not ???????? Does this really help or not ????

J.T., 17/10/06

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

J.T., 17/10/06

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, ….)

J.T., 17/10/06

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

RF power

J.T., 17/10/06

The ‘bunch sliding’ during 7 TeV-ramp up to coast.

Possibly redone during coast (if beam changes conditions)

End injection, V = 1MV/cavAdapted on flat bottom

Half ramp, V risingflat top reached, V=2 MV/cav

Adapted for coast

J.T., 17/10/06

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

RF power

J.T., 17/10/06

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

.... and after 3 more yearsof R&D we may reach v = 2 c