Tune, Chromaticity, Coupling and Online b Measurements

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 lt 0.003
• dx lt 1-2 x Q DQ/(dp/p)
• c lt 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.

3
Tune measurement overview
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? error dQ 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.

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 ?

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 _at_ 7 TeV 2.5 mm at b 180m BPM
• MKQ (rep. rate 2 Hz)
• 0.04-2.5s _at_ 450 GeV and 0.01-0.6s _at_ 7 TeV50 mm
  - 3 mm 3 mm - 0.2 mm
• To be constructed by SL/BT group

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Kicker magnets (2/3)

• 2001 (½ price) design -- 4 MKQAs
• for Ap. (86 ms base ½ sine)
• up to 8s _at_ 7 TeV ? i.e. no change
• all 12 batches kicked ? important change
• for Q (16 ms base ½ sine 3rd harmonic)
• up to 3s _at_ 450 GeV up to 0.85s _at_ 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

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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
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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 10s of msec.
• potential applications
• dynamical aperture resonance driving terms
• phase advances and b functions
• ? source of sextupolar fieldsand impedance
  measurements
• tune measurement (see JPK talk)
• To reach high sT at 7 TeV, speciallydesigned
  magnet needed (details inJPK talk)

10
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.

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Tune measurement devices

• BPM system
• Dedicated tune couplers
• Resonant BPM
• Schottky monitor

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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)

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 ?

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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

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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.

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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 Q200 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.

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Resonant BPM (4/4)

• RD 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).

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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 ?)

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Chromaticity measurement

• Classical method
• Measure tune for different beam momenta (by
  changing fRF within limit dp/p lt 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
• RD 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)

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Head-tail phase-shift method
Head
Tail
1 Synchrotron Period
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Head-tail simulation
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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 ?

2000
2001
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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-qVmin 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

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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. ? 4p
  DQ/(Dk L)
• Measurement at LEP
• k modulated at 0.25 Hz? DQ 0.005 (lt for LHC)
• lt 5.10-5 noise on 0.25 HzFourier component of
  PLLtune measurement? rms error on b lt 1
• measured colliding beams

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Final remarks

• A comprehensive Transverse Diagnostics Toolkit
  will be available for running the LHC.

• Weve being saying this for years, but its 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