Download - Wolfgang Hofle CERN AB/RF/FB
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 1/17
Wolfgang Hofle
CERN AB/RF/FB
LHC Transverse DamperLimits on damping times
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 2/17
2. Saturation limit due to available kick strength and size of injection error
4. Constraints from noise properties of damper system
1. Stability of FB loop with kickers in one location
3. Saturation limit imposed by necessity to damp kicks from tune kicker
Conclusions
Effects limiting the achievable damping times
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 3/17
If tunes are close to integer or half-integer, two kickers are required with phase advance in between them to guarantee stability (see SPS vertical damper, fixed target beam Qv=26.58, one kicker moved in 2001/2002 shutdown to cure intermittent feedback instability when tune is too low at very high gain)
Damping times faster than 10 turns difficult to achieve and require generally also two kickers with phase advance in between them or even a larger number of kickers distributed around rind (“fast damper system” as was planned for UNK, Russia)
In LHC, kickers are installed in one location, hence ~10 turns damping will be an absolute limit in practice for this configuration
1. Stability of FB loop
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 4/17
Design specification: 3.3 can be damped in 38 turns at injection in absence of instability
Instability rise-times of 208 turns as quoted in the LHC design report or 190 turns (E. Métral 8/2/2008) can be easily handled at 450 GeV, provided these fast instabilities are limited to ~ 1MHz
At 20 MHz capabilities are a factor 10 lower in power, however if instabilities are intercepted early enough and do not start from large “seeds” the gain at high frequency can be boosted
2. Saturation at injection
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 5/17
LHC ADT Loop – Digital Processing Module
Serdes Chip Sync Gain BalanceNotch
FilterPhaseShifter
Delay (à 1 Turn )incl . Fine Delay
Serdes Chip Sync
Observation
FIR Phase Comp . DAC
(_ /_ )PU 1
Gigabit Serial Link
(_ /_ )PU 2
fREV(PU1)
Interpolation80 MHz
ON /OFFa1ON/OFF
Delay
b2
Factor 0. 5÷1
VME , Timing
Gain Function via reference voltage
~ 20 dB
80 MHz Clock Domain
Switch/Change b1
ON /OFF
Gigabit Serial Link
Function Delay
Function Phase
_
b2 = sin(_)
b1 = cos (_ ) not exact , calculation in
VME
fREV
fREV(PU1)
+1/-1
Gain Equalizationdynamically changing FIR Low Pass
~ 20 MH z
last edit: 4/18/2008
change sign per bunch
Gain BalanceNotchFilter
PhaseShifter
ON /OFFa2ON/OFF
Factor 0. 5÷1
Switch/Change
PerturbationVME,
Timing
Damper Signal Processing
G. Kotzian / V. Rossi
high gain at low frequency for injection dampingadapt gain vs. frequency to instability rise-time after injection damping and during the cycle
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 6/17
Tune kicker can kick by 2 at 450 GeV and 0.5 at 7 TeV
Damper must be able to cope with these oscillations, i.e. not saturate
Limits the damping to 23 turns (using same reasoning as for injection damping)
3. Saturation at during ramp & at 7 TeV
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 7/17
Normal operating range of feedback is with high gain such that
D << F
i.e. coherent oscillations are damped faster than they convert into an increase of emittance
must distinguish
“monitor noise” : noise entered at level of ADC, due to ADC and analog front-end“kicker noise” : noise added after DAC and gain adjustment
Emittance blow-up effect on beam of kicker noise is reduced by an increase in FB gainmonitor noise is increased by an increase in FB gain
4. Constraints from noise in the damper system
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 8/17
Pick-up 1
Kicker+ fixed gain amplification
Signal processing
beam signal
Pick-up 2
gain gadjustable
kicker and monitor noise entering FB loop
kicker noise
monitor noise
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 9/17
BPMC - Coupler type pick-ups
8 Dedicated Pick-ups BPMC @ Q7L, Q7R, Q9L, Q9R 50 couplers of 150 mm length on one end short circuited
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 10/17
Length of electrodes 150 mm
Frequency domain: maximum of transfer impedance ZT = 6.46 @ 500 MHz
BPMC - Coupler type pick-ups
Peak voltage (beam centered) for ultimate beam @ collision: ~140 V -> very large
Peak sensitivity: 0.264 / mm => 8.1 V/mm peak in time domain after ideal hybrid
L=150 mmBeam
= 2 L/c ~ 1 ns
^
|ZT ()|
…
ZT = 6.46
Frequency Domain
ZT () = ZT j sin() e -j/2^
^
500 MHz
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 11/17
LHC Beam Parameters Injection Collision
Beam Energy 450 GeV 7000 GeV
479.6 7461
RMS bunch length in cm 11.24 7.55
FREV in kHz 11.245 11.245
FRF in MHz (h=35640) 400.789 400.790
Range of intensities for LHC beam and expected pick-up signal levels (ZT = 3.23 ; ZT () = 6.46 )
Pilot Nominal beam Ultimate beam
Particles per bunch 5x109 1.15x1011 1.7x1011
Number of bunches 1 2808 2808
Circulating current (DC) in A 9 x 10-6 0.582 0.860
Bunch peak current @ injection in A 0.9 19.6 29.0
Bunch peak current @ collision in A 1.3 29.2 43.1
Peak Voltage from PU @ inj. in V 2.8 63.4 93.6
Peak Voltage from PU @ coll. in V 4.1 94.3 139.4
^
Signal levels from pick-up
Intensity range to be covered: factor 50
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 12/17
G. Kotzian
Realistic simulation model is being developed to include actual characteristics of hardware
BPMCable (650 m for Q9) BP IQ demod
RF=400.8 MHz
Bunch synchronous sampling @ 40 MHz and digitization with 16 bitnormalization () after calculation of sqrt(I*I+Q*Q) in digital part
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 13/17
G. Kotzian
Simulation results, bunch to bunch oscillations
Simulation model enables us to study imperfections of hardware and also propagate noise or interferences throughsystem and evaluate their impactbunch synchronous sampling with a 40 MHz clock rateongoing study
Simulations using simulink/matlab
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 14/17
G. Kotzian
Some simulation results, single bunch
Signal from pick-up
Response of BP filter to signal from pick-up
Base band signal after LP
Base band signal after LP
Simulations using simulink/matlab
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 15/17
Ohmi calculated that (numerical simulations, LHC Project Report 1048):
10 turns damping with a monitor resolution of 0.6 % of (i.e. at 7 TeV 1.8 m at our pick-ups) gives a luminosity life time of 1 day
with a transverse synchrotron radiation damping time for the emittance of 26 hours
-> no blow-up at all
Hence, we can use damper if we have a m resolution
Numerical simulations (Ohmi) on blow-up by damper noise
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 16/17
Available signal from pick-ups compared to thermal noise
Digitization with effective 14 bit: 16384 discrete levels, assume 1 m -> 4 steps then 14 bit are sufficient to cover +/- 2 mm
Large margin with respect to thermal noise: To use this margin we should limit orbit variations at the pick-ups to less than +/- 2 mm (Q7 and Q9 left and right of IP4)
Power available from pick-up @400 MHz (+/- 20 MHz): 433 pW (nominal beam)to be checked with final measurements of all cables etc.
Thermal noise at 290 K: kBT = 4x10-21 W/Hz; in 40 MHz BW: 0.16 pW
Assume bunches oscillate with 1 m rms (bunch-to-bunch)
Wolfgang Hofle AB/RF LHC Coll WG - April 18, 2008 17/17
Conclusions
Normal operating range of FB at 7 TeV should be at gains corresponding to 20-40 turns damping times
Good control of orbit in damper pick-ups essential for high gain and low noise operation of damper systems
Limit on damping time will come from the available kick strength at 7 TeV and the size of the largest oscillation that one wants to damp, take tune kicker, with 0.5 kicks-> 23 turns limit on damping time
If oscillations can be intercepted at the 1 m level noise is not expected to limit the achievable damping times