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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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)


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

wolfgang hofle cern ab/rf/fb

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