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Transcript of Technological aspects of crab cavities CARE-HHH-Lumi-06, 16-20 Oct 06, Valencia, Spain J....
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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, …
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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
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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
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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
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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
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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
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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)
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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, …
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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)
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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
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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)
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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
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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 ???
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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
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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’
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J.T., 17/10/06
CW mode(problem much ‘older’ than ‘pulsed sc. Cavity problem’, both related)
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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.
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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)
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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)
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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
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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)
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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
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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)
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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
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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
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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
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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
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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?)
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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 !!
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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 ????
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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
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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, ….)
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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
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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
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J.T., 17/10/06
Bunches ‘slide’ to ‘individual’ z-position not to overloadRF system in coast (2 MV/cavity)
RF power
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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:
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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