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Cavity Control

Many thanks to R. Calaga and T. Mastoridis for help, material and comments. Cavity Control. P. Baudrenghien CERN BE-RF 6th Crab Cavity workshop (CC13 ) Dec 9-11, 2013. Content. Phasing the CC with the ACS Keeping the CC tilt aligned with the individual bunch centers …or not

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Cavity Control

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  1. Manythanks to R. Calaga and T. Mastoridis for help, material and comments Cavity Control P. BaudrenghienCERN BE-RF 6th Crab Cavity workshop (CC13) Dec 9-11, 2013

  2. 6th Crab Cavity workshop (CC13) Content • Phasing the CC with the ACS Keeping the CC tilt aligned with the individual bunch centers …or not • Impedance at the fundamental Same threshold as for the HOM or not? • Machine protection Mechanisms for fast CC field changes. LLRF mitigations • Operational scenario Filling and ramping with transparent CC. Physics with crabbing • Conclusions

  3. 6th Crab Cavity workshop (CC13) Phasing CC with the ACS Keeping the CC tilt aligned with the individual bunch centers …or not

  4. 6th Crab Cavity workshop (CC13) Phasing the CC with the bunch centre • A phase error (w.r.t. bunch centre) causes an offset of the bunch rotation axis. This results in a transverse offset Dxat the IP • 1 deg RF phase (7 ps) leads to Dx = 1mm (1/5h transverse beam size) • The stringent requirement concerns transverse emittance growth caused by RF phase noise at frequencies intersecting one of the betatron bands. Much larger offset can be accepted if static or at frequencies significantly below 3 kHz (first betatron band).

  5. 6th Crab Cavity workshop (CC13) A detour: Phase modulation in the Main cavities

  6. 6th Crab Cavity workshop (CC13) Present scheme • RF/LLRF is currently setup for extremely stable RF voltage (minimize transient beam loading effects). Less than 1 RF phase modulation over the turn with 0.35 A DC (7 ps) • To continue this way, we would need at least 300 kW of klystron forward power at ultimate intensity (1.7E11 ppb) • Klystrons saturate at 200 kW with present DC parameters (ultimately 300 kW). • Sufficient margin necessary for reliable operation, additional RF manipulations etc. • At 7 TeV, 1.1 A DC, the synchrotron radiation loss is 14 keVper turn, or 27 pW • All RF power is dissipated in the circulator loads • The present scheme cannot be extended much beyond nominal. Required klystron power for 1.15e11 ppb, 25 ns, 7 TeV, 1.7e11 ppb, 25 ns, 450 GeV, 1.7e11 ppb, 25 ns, 7 TeV P. Baudrenghien, T. Mastoridis, “Proposal for an RF Roadmap Towards Ultimate Intensity in the LHC", IPAC 2012

  7. 6th Crab Cavity workshop (CC13) Proposed RF phase modulation scheme • In physics • We will accept the modulation of the cavity phase by the beam current (transient beam loading) and adapt the voltage set point for each bunch accordingly • The klystron drive is kept constant over one turn (amplitude and phase) • The cavity is detuned so that the klystron current is aligned with the average cavity voltage • Needed klystron power becomes independent of the beam current. For QL=60k, we need 105 kW only for 12 MV total • Stability is not modified: we keep the strong RFfdbk and OTFB • The resulting displacement of the luminous region is acceptable • During filling • It is desirable to keep the cavity phase constant for clean capture. Thanks to the reduced total voltage (6 MV) the present scheme can be kept with ultimate. Modulation of the cavity phase by the transient beam loading in physics. 2835 bunches, 1.7 1011 p/bunch, 1.5 MV/cavity, QL=60k, full detuning (-7.8 kHz).

  8. 6th Crab Cavity workshop (CC13) Consequences for the CC • If the CC follows the phase modulation • Forcing the CC to follow the fast phase modulation (-10 degrees @ 400 MHz in the 3.2 ms long abort gap) results in huge power requirement • With the HiLumiparameters (2808 bunches, 2.2E11 p/bunch, 1.11 A DC, 3.2 ms long abort gap ), assuming 3 MV per crab cavity, 300 WR/Q, we need an absolute minimum of 170 kW per cavity. This minimum is achieved with a QL=44000 • With QL=500000, we need 950 kW

  9. 6th Crab Cavity workshop (CC13) Consequences for the CC (cont’d) • Fixed CC phase • Keeping the Crab Cavity phase constant over the turn will result in a phase error df, with respect to the individual bunch center • This phase error causes an offset of the bunch rotation axis, resulting in a transverse displacement Dxat the IP • For aphase drift of 30 ps, the transverse displacement is 5 mm, approximately equal to the transverse beam size • Fortunately the filling patterns are identical for both rings (except for the first six or twelve bunches batch) and the phase errors will be equal for colliding pairs in IP1 (ATLAS) and IP5 (CMS) because the bucket numbering convention makes the bucket one of both rings (first bucket after the abort gap) “collide” in IP1 and IP5 • There will therefore be no loss of luminosity, only a modulation of the transverse position of the vertex over one turn. This is acceptable by the experiments

  10. 6th Crab Cavity workshop (CC13) Impedance at the fundamental “Best” parking position during filling/ramping Impedance reduction with cavities in operation (on resonance)

  11. 6th Crab Cavity workshop (CC13) Machine Impedance • The HighLumi LHC will accelerate 1.1 A DC current per beam (compared to 0.35 A DC in 2012) • The Crab Cavities will introduce a series of Narrow-Band resonators in the machine (fundamental plus HOMs) • Control of the fundamental is the responsibility of the LLRF. • At the fundamental one cavity presents a transverse impedance around 2.5 GW/m • At the fundamental frequency, the effective impedance can be reduced by an active RF feedback • But what is the max. impedance at the fundamental?

  12. E. Shaposhnikova, CC2010 Instability growth rate (1/2) • A resonant transverse impedance with resistive part ZT [Ohm/m] at resonant frequency ωr=2πfrwill drive coupled-bunch mode (n, m) fr=(n+pM+Qβ)f0+mfswith the growth rate f0 and fs are revolution and synchrotron frequency, M is number of (symmetric) bunches, Qβis betatron tune, ωξ = Qβω0ξ/η, ξis chromaticity, Formfactor F(x) for water-bag bunch: F(0)=1 (the worst mode m=0), F(x > 0.5) ≈ 0.5 6th Crab Cavity workshop (CC13)

  13. E. Shaposhnikova, CC2010 Instability growth rate (2/2) • Growth rate ~ 1/E → maximum at low energy • At 450 GeV, for nominal intensity and ZT =1 MOhm/m (ξ=0): minimum τinst= 0.15 [s] • Conditionτinst> τdgives ZT [MOhm/m] < 0.15 /(1-x/1.6)/τd , x = (fr -fξ)τ< 0.8 ZT [MOhm/m] < 0.3 (0.5+x)/τd ,x> 0.8 τd [s] is the damping time by transverse damper, τ is the bunch length, typically 1.0 ns < τ< 1.5 ns • For ultimate intensity factor 2/3 • Fortunately the situation looksbetter at the fundamental because • we can control the cavity tune vs. betatronband • we can act on the beam induced voltage via active RF feedback 6th Crab Cavity workshop (CC13)

  14. 6th Crab Cavity workshop (CC13) NB resonator, transverse • Transverse impedance of a transverse mode • The damping rate and tune shift of coupled-bunch mode l(rigid dipole only) can be computed from the cavity impedance • With w=(p M+l) wrev+wb.

  15. 6th Crab Cavity workshop (CC13) NB resonator, transverse • With 25 ns bunch spacing (M=3564), for a resonance around 400 MHz, with a BW much below 40 MHz, the infinite sum reduces to the two terms (p= ±10 -> p Mwrev = ± wRF) • The damping rate is computed from the difference between real impedance on the two ±(l wrev+wb) sidebands of the wRF • For example, with Qb=64.3, the damping rate of mode l=-64 is computed from the difference between the real part of the impedance at ±0.3 wrev • Negative damping rate -> instability

  16. 6th Crab Cavity workshop (CC13) During injection and filling, cavity detuned • With a positive non-integer tune (Qh=64.3, wb/wrev above an integer), the cavity should be tuned above the RF frequency to make the mode l=-64 stabilizing L=-64 stable L=-65 unstable + - - + • Real part of the cavity impedance with 1.5 kHz detuning (log scale) • Left: mode l=-64. The damping rate is computed from the difference in Real[Z] evaluated at +0.3 Frev and -0.3 Frev. STABLE • Right: mode l=-65. The damping rate is computed from the difference in Real[Z] evaluated at -0.7 Frev and +0.7 Frev. UNSTABLE but very low growth rate

  17. 6th Crab Cavity workshop (CC13) L=-65 small growth rate • If we can keep the cavity properly detuned, the impedance at the fundamental is not a serious problem for stability • The detuning amplitude should be set to keep the beam induced kicks (for an off-centered trajectory) within reasonable bounds L=-64 large damping rate Growth rate (per cavity) with cavity parked idling at 1.5 kHz detuning. Assuming beta function at location of crabbing equal to average Operation with idling cavities seems feasible if they are properly detuned

  18. In physics, with the crabbing on, we must have an active RF feedback for precise control ofthe cavity field The RF feedback reduces the peak cavity impedance and transforms the high Q resonator into an effective impedance that covers several revolution frequency lines The actual cavity tune has no big importance for stability anymore The growth rates and damping rates are much reduced, and we have no more dominant mode 6th Crab Cavity workshop (CC13) While crabbing Comparison of the modulus of the cavity impedance without and with RF feedback. Real part of the effective impedance with RF feedback. Reduced from 2.5 GW/m to 6 MW/m

  19. 6th Crab Cavity workshop (CC13) • Growth rate (per cavity) in physics, with RF feedback • Left: cavity on tune • Right: cavity detuned by -100 Hz • Assuming beta function at location of crabbing equal to average Note: RF feedback could also be used during filling and ramping

  20. 6th Crab Cavity workshop (CC13) Tentative conclusion (impedance at the fundamental) • Filling and ramping • The cavity must be tuned above the RF frequency • For stability, the detuning should be very small. But this may lead to excessive beam induced voltage if the beam is off-centered, resulting in crabbing oscillations over the full turn. Acceptable? • The growth rates are small and correspond to low-frequency modes, where the damper gain is maximum • The RF feedback could be used but it may not be needed • Crabbing • The cavity will be on-tune • The RF feedback is needed for precision of the kicks and reduction of TX noise • It will reduce the growth rate to values compatible with the damper. The unstable modes correspond to low frequency transverse oscillations

  21. 6th Crab Cavity workshop (CC13) Machine Protection Fast failure of one Crab Cavity Mechanisms Can the LLRF help?

  22. 6th Crab Cavity workshop (CC13) Mechanism for fast failure • Case 1: • The “predictable” case: A problem with power hardware supplying one cavity (such as TX trip, arcing in waveguide, circulator or load,…) resulting in switching off the TX. The cavity stored energy will flow out, through the waveguide and circulator, and will be dissipated into the circulator’s load. The cavity field will decay to zero with a time constant t With a QL equal to 106, the time constant is 800 ms. Assuming three cavities with a total voltage of 9 MV, and a single TX trip, the field would drop from 9 MV to 8.15 MV in the three turns delay (267 ms) until the beam dump is fired

  23. 6th Crab Cavity workshop (CC13) Mechanism for fast failure (cont’d) • Case 2: • In the case of a quench, the stored energy is dissipated in the cavity walls and the main coupling (QL) has no effect on the field evolution. Lessons must be learnt from the SM18 and SPS tests. • Case 3: • In the case of an arc in the main coupler, the stored energy will be dissipated through the arc. Again lessons must be learnt from the SM18 and SPS tests. Better understanding of the field evolution in case of a quench or arcing needed

  24. 6th Crab Cavity workshop (CC13) LLRF mitigation: Coupled feedback • The LLRF can help minimizing the losses during the 3 turns transient till the beam is dumped. The idea is to implement a coupled feedback, acting on all CC cavities, and keeping crabbing and un-crabbing equal • In the case of a crabbing cavity trip, it would ramp the un-crabbing voltage down, tracking the total crabbing voltage

  25. 6th Crab Cavity workshop (CC13) The Crab Cavity systems (IP1 and IP5)

  26. 6th Crab Cavity workshop (CC13) Operational scenario

  27. 6th Crab Cavity workshop (CC13) Operational scenario • Tune control is ON at all time. RF feedback is ON during crabbing and can be ON during filling/ramping although it may not be strictly needed • During filling, ramping or operation with transparentcrab cavities, we detune the cavity (1.5 kHz?) but keep a small field requested for the active Tuning system. As the crabbing kick is provided by three cavities we can use counter-phasing to make the total field invisible to the beam. The RF feedback is (probably) not necessary for stability during filling/ramping. It could be used with the cavity detuned to keep the Beam Induced Voltage zero if the beam is off-centered. If so, we can use the demanded TX power as a measurement of beam loading to guide the beam centering.

  28. 6th Crab Cavity workshop (CC13) Operational scenario (cont’d) • ON flat top • We reduce the detuning while keeping counter-phasing so that the total voltage is zero. We switch the RF feedback ON (if OFF during ramp) to compensate for the beam loading as each cavity moves to resonance. The RF feedback also keeps the cavity impedance small (beam stability). • Once the cavity detuning has been reduced to zero, we drive counter-phasing to zero.Any luminosity leveling scheme is possible by synchronously changing the voltage or phase in each crab cavity as desired.

  29. 6th Crab Cavity workshop (CC13) conclusions

  30. 6th Crab Cavity workshop (CC13) Conclusions • Phase modulation of the ACS voltage is compatible with crabbing • There seems to be no major issue of transverse coupled-bunch instability caused by the cavity fundamental resonance • During filling and ramping, operation may be possible with cavities idling at detuned position. The effect of beam loading must be studied • During crabbing operation the RF feedback reduces the effective impedance, so that the growth rate is compatible with the damper’s performances • In both cases, the dominant modes are at very low frequencies, where the damper’s gain is highest • Fast failure (drop in cavity field) can be caused by quench or arcing in the main coupler. The dynamics must be studied. LLRF mitigations are proposed • The operational scenario did not change since last CC2012, except for the possibility to fill and ramp with RF feedback off.

  31. Thank you for your attention 6th Crab Cavity workshop (CC13) Crabs can adapt To new challenging conditions

  32. 6th Crab Cavity workshop (CC13) Back up slides From the DaresburyHiLumi-LARP workshop Nov 2013

  33. 6th Crab Cavity workshop (CC13) Transverse: Betatron Comb filter We can further reduce the growth rate by selectively correcting the effective impedance on the betatron lines • One-turn delay filter with gain on the betatron bands • To keep 10 dB gain margin, the gain on the betatron lines is limited to ~ 6 linear (16 dB) • 2 N Poles on the betatron frequencies • Reduction of noise PSD where the beam responds • Reduction of the effective cavity impedance thereby improving transverse stability • Zeros on the revolution frequency lines • No power wasted in transient beam loading compensation with off centered beam • Betatron comb filter response with a=31/32 and non-integer Q=0.3. Observe the high gain and zero phase shift at (n ±0.3) frev

  34. 6th Crab Cavity workshop (CC13) RF feedback on Crab Cavities • The transverse impedance of a resonator is [Lee] • Assume 300 W R/Q and QL=106, the shunt impedance is 2.5 GW/m per cavity • With strong RF feedback, the minimal effective transverse impedance scales with the loop delay T • Assume 1ms loop delay, we get Rmin= 6.3 MW/mper cavity • The impedance is reduced by 400 linear • For HOM the budget is only 1 MV/m per cavity

  35. 6th Crab Cavity workshop (CC13) RF Power vs. QL • Candidate TX: 50-100 kW tetrode as used in the SPS 352.2 MHz system in the 1990’s • TX linked to the cavity via a circulator. 3 MV RF. R/Q = 300 W. 1.1 A DC current, 1 ns 4s bunch length (1.8 A RF component of beam current). Cavity on tune. • Yellow trace: beam centered • Blue trace: x=+1 mm offset • Red trace: x=-1 mm offset For 1 mm offset, the range of acceptable QL (P < 30 kW) is • 2.5 105< QL <1.8 106 for R/Q=300 W • 8 104< QL <6 105 for R/Q=900 W Low values preferred for tuning (microphonics).

  36. 6th Crab Cavity workshop (CC13) Proposed layout

  37. 6th Crab Cavity workshop (CC13) LHC layout Main (ACS) RF system Crab Cavity RF Crab Cavity RF

  38. 6th Crab Cavity workshop (CC13) TX and LLRF in new service galleries • We have ~300 m distance between crabbing and un-crabbing cavities • We propose to dig-out a short gallery running parallel to the tunnel on both sides of IP1 and IP5 for the RF power (TX) and LLRF electronics • Such a gallery exists in IP4 (ex LEP klystron gallery)

  39. 6th Crab Cavity workshop (CC13) LLRF challenges

  40. 6th Crab Cavity workshop (CC13) Challenges • Fine-phasing of the CC kick with the individual bunch centre • Reduce the cavity impedance at the fundamental to prevent transverse Coupled-Bunch instabilities • Prevent transverse emittance blow-up caused by RF noise • Manage beam loss following a klystron trip or cavity quench

  41. 6th Crab Cavity workshop (CC13) The Crab Cavity systems (IP1 and IP5)

  42. 6th Crab Cavity workshop (CC13) RF Noise

  43. 6th Crab Cavity workshop (CC13) Cavity RF Noise • RF feedback noise sources: • The RF reference noise nref • The demodulator noise (measurement noise) nmeas • The TX (driver) noisendr(process noise). It includes also the LLRF noise not related to the demodulator • The Beam Loading IbDx • We get Main coupler • Beam Loading response = effective cavity impedance Zeff(s) • Equal to ~1/KG in the CL BW • Increase of K decreases Zeff within the CL BW • Within the CL BW, TX noise and beam loading are reduced by the Open Loop gain KG • Closed Loop response CL(s) • Equal to ~1 in the CL BW • Increase of K increases the BW • Within the BW, reference noise and measurement noise are reproduced in the cavity field

  44. 6th Crab Cavity workshop (CC13) Scaling the ACS noise to CCs Noise in the 10Hz-1kHz range is not an issue as the first betatron band is around 3 kHz TX noise is important in the band extending to 20 kHz. It is reduced by loop gain and scales as 1/Sqrt[QL]. Tetrodes are less noisy than klystrons In the 10kHz-400 kHz range the noise level is defined by the demodulation of the antenna signal. The noise BW increases with the loop gain • ACS SSB phase noise Power Spectral Density in dBc/Hz. First betatron band In the transverse plane the first betatron band is at 3 kHz. Reference noise is not an issue. The performances will be defined by TX noise and measurement noise

  45. 6th Crab Cavity workshop (CC13) Scaling the ACS to crab • The beam will sample the noise spectrum in all betatron side-bands • Assume a SSB phase noise of L= -135 dBc/Hz or S= 6.3E-14 rad2/Hz, thensumming the noise PSD from DC to + 300 kHz over all betatron bands, we get 300/11 x 2 x 6.3E-14 rad2/Hz =3.4E-12 rad2/Hz from DC to the revolution frequency • A “copy” of the LHC ACS design (300 kW klystron !) would generate 3.7E-8 rad2 white noise, that is 2E-4 rad rms or 1.1E-2 degrms phase noise @ 400 MHz

  46. 6th Crab Cavity workshop (CC13) Resulting transverse emittance growth • Simulations are numerous. In the longitudinal plane I have used • For the CC I use an early analysis indicating that 2 nm rms white noise would lead to 1% emittance growth per hour.(R. Calaga et al., small angle crab compensation for LHC IR upgrade, PAC07). • The 2E-4 rad rmscorrespond to 10 nm rms • Scaling emittance growth with the noise power, leads to a predicted 10% emittance growth per hour, from a “copy” of the LHC ACS design • Improvements are expected because • The damper gain can be increased compared to the PAC07 figures • The CC TX (50 kW tetrode) will be less noisy than the ACS klystron • And an additional reduction (16 dB?) will come from the betatroncomb A simplified analysis is needed to pilot the LLRF developments, such as a very low-noise demodulator. Measurements of TX noise are also urgent.

  47. 6th Crab Cavity workshop (CC13) Trade-off • A weak coupling (large QL) • Reduces the effect of TX and LLRF noise. Good • But we want to keep BW sufficient so that microphonics are located within the cavity BW • A large feedback gain • Limits the effect of TX and LLRF noise. Good • Increases the integrated effect of measurement noise by increasing the BW. Bad • Trade-off required • Will depend on the TX noise

  48. 6th Crab Cavity workshop (CC13) LLRF HARDWARE

  49. 6th Crab Cavity workshop (CC13) LLRF Hardware • Very close synergy with the 800 MHz Harmonic cavities in the SPS and the Linac4 352.2 MHz system • On-going commissioning of the Linac4 prototype with the RFQ • Commissioning of the 800 MHz version at SPS restart (2nd half 2014) • Hardware must be tuned for 400 MHz and firmware must be developed to have prototypes ready for the SM18 test by 2015, in advance for the planned 2016 installation

  50. 6th Crab Cavity workshop (CC13) Interconnection with the paired cavity(ies) Coupled feedback Gain increased on the betatron bands Measurement of bunch phase modulation Field control fully integrated with the rest of the LHC by using standard FGCs • For each Crab Cavity we have a Cavity Controller including: • An RF Feedback Loop for noise and beam loading control • A TX Polar Loop to reduce the TX noise and stabilize its gain/phase shift • A Tuner Loop to shift the cavity to a detuned position during filling and ramping. Then smoothly bring the cavity on-tune with beam for physics • A field Set Point for precise control of the cavity field.

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