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Tune, Chromaticity, Coupling and Online b Measurements

Tune, Chromaticity, Coupling and Online b Measurements. LHC BI Review, Nov. 2001 A.J.Burns, SL-BI Thanks to: O.Berrig, P.Cameron (BNL), R.Jones, H.Schmickler & E. Vossenberg Ref: LHC Project Report 370, Feb. 2000. Requirements for Q, Q’ & |c|.

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Tune, Chromaticity, Coupling and Online b Measurements

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  1. Tune, Chromaticity, Coupling and Online b Measurements LHC BI Review, Nov. 2001A.J.Burns, SL-BI Thanks to: O.Berrig, P.Cameron (BNL), R.Jones, H.Schmickler & E. Vossenberg Ref: LHC Project Report 370, Feb. 2000

  2. Requirements for Q, Q’ & |c| • The “acceptable” tolerances for key beam parameters during accumulation and ramping [ref. O. Brüning, Chamonix 2000] : • dQ < 0.003 • dx < 1-2 [x = Q’ = DQ/(dp/p)] • |c| < 0.01 • The QH/QV tune separation at injection is 0.01. The tune split due to coupling must be less. • The requirement for x is very demanding and will need feedback for ultimate performance -- still some way to go. LHC BI Review, Nov.2001, A.J. Burns SL-BI

  3. Tune measurement overview LHC BI Review, Nov.2001, A.J. Burns SL-BI

  4. Emittance blowup from kicks 1999 simulation of series of single-kick (0.4 mm) Q meas. assuming : 50-turn damping time 128-turn FFTserrordQ= 3.10-4 20 mm PU noise level using 4 of 12 batches Measure every 5 sec duringsnap-back (but only every 4 min during injection) Conclusion: should aim for higher performance system compatible with low emittance blowup and strong transverse damping. LHC BI Review, Nov.2001, A.J. Burns SL-BI

  5. Beam excitation devices • Kicker magnets • AC-dipole • RF beam “tickler” • Transverse feedback kicker • Primarily, part of transverse feedback system, but should also be available to receive signal (e.g. noise, frequency sweep, resonant excitation, . . .) for oscillation measurements. • Operational scenario uncertain, e.g. will full gain (td ~ 50 turns) be maintained after damping of injection oscillations ? LHC BI Review, Nov.2001, A.J. Burns SL-BI

  6. Kicker magnets (1/2) • 1998 design -- 4 Q & 4 Aperture kickers • 9 ms base ½ sine pulse (+3rd harm. for MKQ) to kick essentially 1 LHC batch (was 243 bunches) • ‘MKA’ (rep. rate ~ 0.2 Hz) : • up to 8s @ 7 TeV {2.5 mm at b = 180m BPM} • ‘MKQ’ (rep. rate 2 Hz) : • 0.04-2.5s @ 450 GeV and 0.01-0.6s @ 7 TeV{50 mm - 3 mm} {3 mm - 0.2 mm} • To be constructed by SL/BT group LHC BI Review, Nov.2001, A.J. Burns SL-BI

  7. Kicker magnets (2/3) • 2001 (½ price) design -- 4 MKQA’s • for Ap. (86 ms base ½ sine) : • up to 8s @ 7 TeV  i.e. no change • all 12 batches kicked important change • for Q (16 ms base ½ sine +3rd harmonic) : • up to 3s @ 450 GeV & up to 0.85s @ 7 TeV • ~ 5 x 72 bunches kicked with 80-100% of peak value • 20-50 pulses at 2Hz possible every 10s • single magnet with dual pulse generators • certain aspects of design need 6-10 months prototyping work LHC BI Review, Nov.2001, A.J. Burns SL-BI

  8. 80-100% peak Kicker magnets (2/3)  • Can still consider variants of the Q-kick pulse (within max. 2.3 kV boundary) • 16 ms ½ sine pulse  80% more kick strength at centre, i.e. 1.55 s at 7 TeV. • 16 ms ½ sine + 3rd harm. • 1/3 shorter than 2/3 kick strength, i.e.  0.55 s at 7 TeV (~160 mm at BPM) • To remain on “official” schedule, choice should be fixed for Jan. 2002 =72 b  80-100% peak  80-100% peak LHC BI Review, Nov.2001, A.J. Burns SL-BI

  9. AC dipole • Technique (from BNL) for exciting large (several sT) transverse oscillations without emittance blowup • sine wave frequency outside tune spread; and amplitude ramped over 10’s of msec. • potential applications : • dynamical aperture & resonance driving terms • phase advances and bfunctions •  source of sextupolar fieldsand impedance measurements • tune measurement (see JPK talk) • To reach high sT at 7 TeV, speciallydesigned magnet needed (details inJPK talk) LHC BI Review, Nov.2001, A.J. Burns SL-BI

  10. Turn n 5.079 MHz excitation withSPS damper (Head-Tail PU) {117.17 x frev(43.35 kHz)}  Turn n+3 RF beam “tickler” • Beam exciter for Resonant BPM tune measurement • Objective: maintenance of betatron oscillations at a sufficiently low amplitude to minimise emittance blow-up on beams for physics ( few mm) • Associated with notch filter in transverse feedback to avoid damping oscillations •  2m long stripline couplerdriven by 0.5-1 kW RFcommercial amplifier withBW 0-20 + (n x 40) MHz. LHC BI Review, Nov.2001, A.J. Burns SL-BI

  11. Tune measurement devices • BPM system • Dedicated tune couplers • Resonant BPM • Schottky monitor LHC BI Review, Nov.2001, A.J. Burns SL-BI

  12. BPM system • 500 button monitors in each ring measuring in both transverse planes • Summing FFTs from all BPMs after a kick should give a good tune accuracy. • A more complete analysis retaining the phase information  integer part of Q also. • BUT, at best, BPM digitisation  1 bit ~ 20 mm. So will need ~ mm amplitude kicks (e blowup) LHC BI Review, Nov.2001, A.J. Burns SL-BI

  13. Tune couplers • Combined 15 mm stripline coupler + 4-button assemblies • Planned (1996) as the dedicated Q-meas. devices (4 installed for Q-meas, 8 for transverse feedback) • Higher (~ x 5) transfer impedance than button  larger output signal • Equipped with special electronics, should be more sensitive than 500 BPMs for sub-mm oscillations. • e.g. 16-bit ADCs, possibly limited aperture with C.O. removal, full turn integration, . . . • Question: does this device need to provide bunch-by-bunch or batch-by-batch Q-measurement ? LHC BI Review, Nov.2001, A.J. Burns SL-BI

  14. Resonant BPM (1/4) • Stripline coupler with external cabling that resonates the D signal at a sideband of a bunch freq. harmonic • (to simplify, let bunch freq.= 40.0 MHz, not 40.08 MHz) • e.g. choose excitation freq. fex = 17 + (N x 40) MHz • N.B. the beam “sees” only 17 MHz • to excite within the tune resonance: • fex = K x frev + ft , where K = integer,frev = revolution freq. (~11 kHz), ft = fractional tune frequency (~3 kHz) • each bunch then “sees” only ft resonant excitation • BPM should resonate at sidebands fC = (M x 40) ± 17 MHz • e.g. 97, 103, 137 MHz LHC BI Review, Nov.2001, A.J. Burns SL-BI

  15. Resonant BPM (2/4) • Choice of resonant frequency : • For optimum response, fC should be ~ freq. corresponding to stripline length, L = l/4 (e.g. 200 MHz for L = 37.5 cm) • Mechanical constraints  L  75 cm (i.e. fC 100 MHz) • Lower frequencies also correspond to lower cable losses. • Performance with other bunch spacings : • Any bunch spacings = N x 25 ns are compatible (since 40 MHz harmonics will still be present; but N should be small). • The resonance effect depends on the accumulation of signals from consecutive bunches. Individual (or a few) pilot bunches will not produce a resonant response. LHC BI Review, Nov.2001, A.J. Burns SL-BI

  16. Resonant BPM (3/4) • Q-values for such a resonator are ~ few 100 • depending on feedthrough and cable quality and frequency • The Q-value of a resonant circuit determines the resonant width, transient behaviour and steady state stored energy. • For Q=200 at 100 MHz: • The full width at 70% of the voltage peak is 500 kHz • the 1/e rise/decay time is 640 ns  • signal decays 30% between each set of 72 bunches, 80% in 1ms between batches and 99% in 3ms dump gap at end of turn • The choice of Q is thus a trade-off between steady state signal magnitude and rise/decay time. LHC BI Review, Nov.2001, A.J. Burns SL-BI

  17. Resonant BPM (4/4) • R&D started this year with investigations of different resonant circuits using a spare 200 MHz SPS coupler. • Some measurements with beam were made at the end of the run with an identicaldevice in the SPS. • A more completesetup will be testedin the 2002 run. • The final aim is a PLL tune measurement system such as developed at RHIC using a similar resonant BPM (right). LHC BI Review, Nov.2001, A.J. Burns SL-BI

  18. Schottky monitor • Used with success at CERN in SPS p-pbar collider • Measurements on LHC bunched beam may be problematical ( F.Caspers’ talk) • Budget line included in LHC BI budget • Manpower should be committed to this topic soon (collaboration with PS division ?) LHC BI Review, Nov.2001, A.J. Burns SL-BI

  19. Chromaticity measurement • Classical method: • Measure tune for different beam momenta (by changing fRF within limit dp/p < 10-3). • In LEP, PLL tune measurement with 0.3 Hz fRF modulation. • Available in LHC, but has drawbacks (esp. with nominal beams) • limited speed, incompatibility with Q-loop, orbit changes • R&D on new method (Rhodri Jones et al.): • Head-tail phase shift measurement (see following slides) • Other methods used (but not promising for LHC): • Amplitude of synchrotron sidebands (low QS, lattice resons.) • Width of tune resonance (Q’ not only contribution) • Further methods to be investigated (e.g. O. Brüning) LHC BI Review, Nov.2001, A.J. Burns SL-BI

  20. Time Head-tail phase-shift method Tail Head 1 Synchrotron Period LHC BI Review, Nov.2001, A.J. Burns SL-BI

  21. Head-tail simulation LHC BI Review, Nov.2001, A.J. Burns SL-BI

  22. Head-tail measurement (SPS) • Measurements on test setup in the SPS since 1997. • 2001: new 60cm coupler now allows measurement of “head” and “tail” (previously “head” and “centre”) • Amongst questions still be answered :What is kick amplitude (e blowup) required to obtain a reasonable (~ 0.5 unit) precision in Q’ ? 2001 2000 LHC BI Review, Nov.2001, A.J. Burns SL-BI

  23. qH |c| qV Time Coupling measurements • Linear coupling of H and V betatron motion needs to be controlled (i.e. minimised) • “Closest Tune Approach” • H and V tunes tracked (via PLL)during linear ramp of quadrupolefamily |qH-qV|min = |c| • “Feed-forward” correction • Alternative methods : • Beam is kicked in one plane coupling obtained from timeevolution of H & V oscillations. • Measurement of full BeamTransfer Function in one plane with excitation in other plane LHC BI Review, Nov.2001, A.J. Burns SL-BI

  24. k Dk time DQ=0.005 Online b measurement • Objective : Provide real b value at profile monitor to convert beam-size to emittance : e = s2/b • Measure change in tune, DQ, resulting from change Dk in quadrupole strength b at quad.  4pDQ/(Dk L) • Measurement at LEP : • k modulated at 0.25 HzDQ = 0.005 (< for LHC) • < 5.10-5 noise on 0.25 HzFourier component of PLLtune measurement rms error onb < 1% • measured colliding beams LHC BI Review, Nov.2001, A.J. Burns SL-BI

  25. Final remarks • A comprehensive “Transverse Diagnostics Toolkit” will be available for running the LHC. • We’ve being saying this for years, but it’s still true • All Q & Q’ measurements (kicks, noise, chirps, BTF..) can be used on setup beams to give “feed forward” corrections (even though they increase emittance). • Presently emphasis is on developing low e blowup methods for use on physics beams (resonant BPM based PLL, “AC-dipole” technique, . .) In 2002, the TD part of the Beam Instrumentation should be reviewed by the BI Specification team LHC BI Review, Nov.2001, A.J. Burns SL-BI

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