Feedback Simulations with Amplifier Saturation, Transient and Realistic

Filtering

Mauro Pivi, Claudio Rivetta, Kevin Li

Webex CERN/SLAC/LBNL13 September 2012

Simulation Code Development

• Realistic single-bunch feedback system have been implemented in 3 simulation codes: Head-Tail, C-MAD, WARP.

• At SLAC (by Rivetta, Pivi, Li):– Feedback implemented firstly in C-MAD– Developed and tested then translated in

HeadTail

Plans for codes utilization

The feedback system is simulated with:• HeadTail which comes with different options for the

SPS: electron cloud, TMCI and advanced impedances model for the SPS.

• For benchmarking, C-MAD parallel code: electron cloud instability, Intra-Beam Scattering IBS. Allows uploading the full SPS lattice from MAD for increased realistic simulations.

HeadTail-CMAD codes comparison

• Initial beam offset of 2 mm, no electron cloud• Feedback Bandwidth 200MHz

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Verti

cal b

eam

pos

ition

(m) HeadTail

CMAD

Following simulation results

• For our feedback simulations, here:– To reduce the statistical noise, used bunch slices

with same constant charge (rather than slices with constant distance).

– Kicker bandwidth 500MHz, cloud density of 6e11 e/m3, gain = 15 (equivalent to Kevin’s 0.5)

– Bunch extent: ±4 sz (as feedback input matrices)

Feedback system design

Saturation in the Receiver: ± 250mV

Saturation in the Amplifier: defined by DAC ± 200mV

Corresponds to kicker signal: ± 4e-5 eV-sec/m

Feedback system and electron cloud: reference simulation run

*equivalent to 0.5 for Kevin

parameter valueKicker bandwidth 500 MHzCloud density 6×1011 e/m3

Feedback gain 15*

Emittance evolution Vertical displacement - each slice

Rivetta, Pivi

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• Set high electron cloud density

Momentum signal delivered by kicker is within saturation limits ± 4e-5 ev-sec/m

Central bunch slice # 32: DAC Voltage is within the saturation values ± 200mV

Central bunch slice # 32: kicker signal

Rivetta, Pivi

Feedback system and electron cloud: reference simulation run

Rivetta, Pivi

(above) Vertical slice positions(central) ADC Voltage at Receiver, well within saturation ± 250mV(below) Yout=fir(Yin) in Volts

Each of 64 bunch slices is shown

Feedback system and electron cloud: reference simulation run

Next• Set Amplifier saturation (or DAC saturation)• Introduce a transient in the bunch

Set Amplifier saturation and beam with initial offset

parameter valueKicker bandwidth 500 MHzCloud density no cloud

Set:• No electron cloud • Amplifier saturation corresponds to

saturation limits for DAC ± 200 mV• “Transient” or initial beam offset 500 um

Rivetta, Pivi

• Without electron cloud, the feedback damps the oscillation• The question was: with an electron cloud, will it still dump?

Vertical displacement Kicker signal constrained

See also Claudio presentation:

Set Amplifier Saturation and beam with initial offset

*equivalent to 0.5 for Kevin

parameter valueKicker bandwidth 500 MHzCloud density 6×1011 e/m3

Feedback gain 15*

Emittance Vertical displacement - each slice

Set:• Turn electron cloud ON • Saturation limits for DAC ± 200 mV• “Transient” or initial beam offset of

500 um (representing position jitter)

Rivetta, Pivi

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Set Amplifier saturation (DAC 200 mV), and a beam with initial offset 500um

Rivetta, Pivi

Constrained kicker saturation limits ± 4e-5 eV-sec/m

DAC Control Voltage when saturation is set to ± 200mV

Bunch slice # 32: kicker signal

• Effective Damping of emittance and vertical motion with DAC saturation limits

Rivetta, Pivi

(above) Vertical slice positions(central) ADC Voltage at Receiver, well within saturation ± 250mV

Each of 64 bunch slices is shown

Set Amplifier saturation (DAC 200 mV), and a beam with initial offset 500um

Shift of beam signal due to realistic Filter

Even more shift at kickershift at filter processing

measured

See also Claudio presentation:

• Note: All previous simulations (also Kevin’s) did not include a realistic Filter yet, but an ideal one.

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• We included a realistic filter in the feedback system• Not compensating the signal shift internally in the feedback

results in an unstable beam.

Shift of beam signal due to realistic Filter

Beam unstable!

EmittanceVertical displacement - each slice

kicker signal exceeds saturation limits

• Including a realistic filter results in a shift (+ distortion) of the beam signal by ~ +7 slices

• Beam unstable• We compensated by shifting back the beam

signal at kicker by shifting -7 slices• Transparent process for beam: all internal

processing inside feedback system

Compensation of shifted beam signal due to Filter

compensate shift at kickershift at filter processing

measured

See also Claudio presentation:

Compensation of shifted beam signal due to Filter

Rivetta, Pivi

Compensation of shifted beam signal due to Filter

*equivalent to 0.5 for Kevin

parameter valueKicker bandwidth 500 MHzCloud density 6×1011 e/m3

Feedback gain 15*

Emittance growth Vertical displacement - each slice

turns

Rivetta, Pivi

Compensation of shifted beam signal due to Filter

Momentum signal delivered by kicker is within saturation limits of ± 4e-5 ev-sec/m

Rivetta, Pivi

• Effective damping of emittance and beam motion

Simulation plan

M. Pivi, C. Rivetta, K. Li, SLAC/CERN

Support for proof of principle

prototype design

final design

LHC Long Shutdown

What we didn’t include, in these simulations

• Although the codes have full features capabilities

• In these results we are not showing issues:– Noise: both in the receiver and amplifier– Limitations in the bunch sampling– Other processing algorithms– Realistic SPS lattice

• Step by step adding more physics and more reality into simulations

Summary• Successful implementation of a realistic single-

bunch feedback system into codes and very promising initial results

• Preliminary studies to include: -Amplifier Saturation (DAC)-Beam transient -Compensation of shift due to realistic Filtering

• Simulation plan to support the feedback prototype, the final design and construction

Code comparison

(M. Pivi et al. SLAC) (G. Rumolo et al. CERN) (J-L Vay et al. LBNL)