SLAC

Feedback Systems for ILC:

- Experience with SLC Feedback

- ILC Simulations

Nan Phinney, SLC Program Coordinator

Feedback Integrated with Control System

• Uses BPMs. correctors and CPUs from control system, without dedicated hardware. Dedicated point-point communications system used for 120-hz, but 1-hz feedback uses communications backbone of control system.

• Integrates with machine physics application software. Example 1: In correlation plots, move anything and sample anything else. Move

feedback setpoints, sample feedback measured and calculated variables. Example 2: to phase klystrons, use energy feedback setpoint to move the energy,

and feedback energy calculation. Example 3: Emittance bumps. Optimize linac setpoint to minimize emittance.• Attach feedback setpoint to physical knob in control room, use feedback for

tuning (keeps beam stable while moving only position, for example).• Save/restore configurations of feedback setpoints, measurement references, etc.• Feedback calculations, measurements, control changes available in long-term

history plots.• Feedback problems can generate alarms, annunciators, etc. Logging system for

diagnostics (when did they turn the loop on? were actuators at limits? etc).

SLC History

SLC History:

– Explosion of loops: SLC+PEPII+ESA+FFTB+SPPS+NLCTA…

– Expansion of capabilities

– Essential for operation: improves luminosity, reproducibility, faster outage recovery, aids operator tuning, etc..

– Too many loops to keep track of, performance issues, design limitations

Energy Feedback Control in SLC

Actuators:Adjust RF phases, kink to maintain BNS phase. Pseudo energy actuator for linear calc.

States:Calc energy, position,angle. Control energy.

Measurements:BPMs, including at least one high-dispersion BPM.

Energy Feedback Control in SLC

Problems with SLC: Not cascaded, due to limited bandwidth. Probably not a major issue, because we don’t have very many energy loops. (LCLS solution: use cascade for multiple energy feedback loops.)Often we have one essential BPM (which has high dispersion), and other non-essential BPMs. Basic feedback design is non-ideal for this situation, because we want to automatically determine whether there enough good measurements to allow feedback control. SLC solution: Require all BPMs to have good status. or Set a flag that certain BPMs (with low dispersion) are non-essential.

Strange Design Issues with SLC:“Scavenger energy” feedback used hardware-based feed-forward to compensate for intensity fluctuations from the damping ring. (This was energy feedback on the beam that went to make positrons).End-of-linac energy feedback was configured to control 59-60 Hz oscillations using “timeslot” algorithm.In some cases, used linear klystron amplitude controllers; with Pulsed Amplitude Unit controllers to control different beams with varying amplitudes.

LCLS Energy Feedback: Juhao Wu. LCLS Energy Feedback: Juhao Wu. (PID feedback, controlling energy and bunchlength in the linac, with cascade.)

LCLS Energy Feedback: Juhao Wu. LCLS Energy Feedback: Juhao Wu. (PID feedback, controlling energy and bunchlength in the linac, with cascade.)

Observables: Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) CSR power bunch length: z,1 (at BC1), z,2 (at BC2)

Controllables: Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2)

Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

Observables: Energy: E0 (at DL1), E1 (at BC1), E2 (at BC2), E3 (at DL2) CSR power bunch length: z,1 (at BC1), z,2 (at BC2)

Controllables: Voltage: V0 (in L0), V1 (in L1), V2 (effectively, in L2)

Phase: 1 (in L1), 2 (in L2 ), 3 (in L3)

Courtesy of P. KrejcikCourtesy of P. Krejcik

Steering Feedback Control in SLC

Measurements:Horizontal and vertical BPMs. Usually limited to 1 or 2 sectors.

States:Position and angle at a specific fitted point in the beamline.

Actuators:Typically a minimal number of horizontal and vertical dipole correctors.

Steering Feedback in SLC, with cascade and with dispersion

States:- When we have multiple feedback loops, “cascaded” design eliminates overcompensation for beam perturbations.First 4 states are “adjusted” (i.e. subtract transported incoming position and angle).- If we have BPMs with dispersion, choose a feedback fit point with no dispersion, and add energy calculation.

What about Steering Feedback in Regions with Dispersion?

SLC Experience:When steering in dispersive region, always find fit point (effective position and angle calculation point) with zero dispersion.Example: In SLC ARCs, no convenient fit point with zero dispersion. But we chose an artificial fit point at end of linac, which the model thinks has zero dispersion. Then the feedback uses ARC BPMs (all with dispersion) to calculate the following states, back-transported to the end of the linac:X position, Y position, X angle, Y angle, energy.The feedback controls the positions and angles, but calculates the energy. Correctors in the ARC are calibrated to calculate the effect on the calculated state. It worked fine!

ILC Simulations:

Currently using calibration from BPMs in BDS to BDS correctors. Measure energy at reference point, and on every pulse. Measure dispersion at each BPM and subtract effect of energy changes on BPMs before applying feedback. It works, but not very robust.

Steering Feedback Control in SLC

Problems with SLC: Not fully cascaded, due to limited bandwidth. More loops were inserted later without full cascade design. Result: Mismash of rates and low gain factors, and poor performance!Cascade design was inappropriate for higher intensity regime, needed multi-cascade. (But simulated single cascade design works fine for ILC!). (Limited networking and CPUs were problems for SLC).Slow correctors, poorly modeled.Poor modeling of beam transport (bad model, needed calibration).Too many loops, inadequate automated detection of broken hardware.

Note: Solutions for some of these problems were demonstrated in beam tests using the SLC linac, and in simulations. Unfortunately, too late for SLC!

What is Cascade? (And why do I like it??)

Cascaded feedback communicates beam information to downstream feedback loop(s) to eliminate overcompensation due to multiple loops.

On each pulse:Beam goes by.Each loop receives digitized BPM readings.Each loop calculates beam states (position/angle for SLC, fitted corrector kicks in ILC simulations), and sends them to downstream loop(s).Each loop receives upstream states, optionally iterates on adaptive transport calculations, transports upstream states to this location, and subtracts transported state from our measured states. We control the “Adjusted state” vector, which equals states_at_this_location - (transport_matrix * upstream_states)

What is Cascade? (And why do I like it??)

Single Cascade: SLC-style, each loop sends beam information to single adjacent downstream loop. (Adequate for ILC in simulation, inadequate for later SLC running.)Multiple Cascade: NLC-style, each loop sends information to ALL downstream loops. (Adequate for all machines in simulation, tested prototype in SLC linac). Disadvantage: Requires longer-range beam transport calculations than single cascade, therefore more erroneous.Global Feedback: Should be ~mathematically equivalent to multiple cascade.BUT: Having separate feedback loops provides more operational flexibility. Can turn off one loop for tuning or due to broken hardware, etc. Can disable cascade, and lower feedback gains for preliminary startup, if beam transport has changed and no time to adapt or calibrate. >>> I am simulating SLC-style single cascade for ILC steering feedback.

Handling of Bad Measurements

- Pseudo-Median Filtering: If measurement far from expected and not between 2 previous, then filter (originally just one measurement, later for all together).

- Measurement limits.- Chi-squared residual limits (PEPII). When

residuals are large, try to guess which BPM is unreasonable, by excluding each measurement in turn, then mark the worst one SUSPECT.

Problem: chi-squared gets worse with time, esp if steering within range of feedback. Expected value is not same as measurement, so state jumps when measurement goes bad.

Partial Solution: Recalculate matrix taking meas -> states, excluding bad meas. (Doesn’t help for intermittent bad status, though).

Other solution: Save measurement references often. (But PEPII fears drifting orbit).

Assumes we have extra (redundant) BPM measurements. Calculate expected measurements, based on time-averaged state estimates which include actuator motion. Use expected value if a measurement has bad status.

Beam Test: set a single BPM limit so that it is alternating between good and bad status.

SLC Fast Feedback Measurement Handling

-Each BPM has lower and upper reasonability limits.

- Pseudo-median filtering limits.

-Residual cuts (PEP2).

-Count number of bad measurements. Some measurements don’t count. If too many are bad, assume there is no beam. If bad for too long, disable control.

-Optionally may re-invert matrix to omit bad measurements.

Feedback timescales for Luminosity Optimization: SLC experience

A.F.A.R.A! (As Fast As Reasonably Achievable) Fast response to upstream tuning, supports higher order optimizations. Want < 30 minutes to optimize all, from untuned state (10-30 minutes

typical SLC running) Typical SLC optimization scenario: optimize 10 parameters every 2

hours, plus on user request:2 beams: X&Y waist; X&Y eta; couplingEstimated < 2% luminosity loss due to dithering

Possible NLC optimization scenario: optimize 10-13 parameters every 2 hours, plus on user request: 2 beams: X&Y waist; X&Y eta; coupling; crab cavity

phase(?) 1 beam: compressor phase(?)

Luminosity Optimization in the SLC: Original Scan method: Minimize beam

width-squared from deflection scans (subject to meas error ~20-40%

luminosity)

Dither Method: Maximize luminosity while moving

multiknob up and down by small amounts, average 1000’s

of pulses

Bhabha

BSM

Luminosity Optimization in the SLC: Comparative Resolution of Scan Method vs Dither Method

Dither

Scan

Fast Feedback Architecture

Fast Feedback Architecture, cont’dMatlab control system simulation

Alpha Computer

(VMS)

Feedback Calibration/ModelingFeedback matrices are designed offline through automated program which is currently implemented in matlab m-files using control toolbox and signal processing toolbox.User can choose to generate matrices using online model, or calibration (measured matrices).Choice between linear calibration (scan) and dither-style calibration (move back and forth and fit a line to 2 points).

LQG Feedback algorithms (Linear Quadratic Gaussian): Optimal (Modern) Control Theory.State-space formalism, Kalman filter, Predictor-corrector.

What does this mean to us? Optimal controller: minimizes RMS of signal, given

inputs of noise spectrum and plant response. Predictor-corrector theory: Feedback knows about

its own actuator movement, so it does not repeatedly try to fix the same error (overcorrection). Feedback responds to UNEXPECTED changes.

SLC Feedback Algorithms (Himel)

Control Design (FDESIGN) Inputs:• Plant noise model:

Low-pass, white, harmonic oscillator, bandpass, etc.(harmonic oscillator dangerous in simulation)

• Actuator Response Model:Time delay (N pulses or feedback iterations.)

or Exponential Response (dangerous!)• Sensor Noise• Plant Transport Matrices:

States => MeasurementsActuators => States

But: In practice in the SLC, we always use the same basic design. Exponential response with selected speed, usually 6 exponential pulses.

And: It is not trivial to put a real-time optimizer (adaptive control) onto the complicated matrices we are using.

SLC Feedback Algorithms, cont’d

Feedback timescales: NLC vs SLC feedback design response:

(It helps to assume a faster control system: low-latency BPMs, fast IP kickers/correctors)

Problem: DC offset in feedback.

Theoretical DC offset proportional to command change (LQG algorithm). If estimate of command change is large (erroneously), DC offset is significant.

(NLCTA: stepping motor irregularities. SLC IP: flawed normalization kept beams slightly out of collision! – later fixed.)

Solution:-> no DC offset in simplistic exponential algorithm (also used by Schlarb for TTF feedback systems). This algorithm is just a low-pass filter with a proportional feedback, with a gain factor. Easy to parametrize for optimization, and nearly identical in practice to SLC design.

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SLC LQG algorithmNew exponential algorithm

time (2 days) time (2 days)

SLC Feedback problems, to sort out for ILC (From NLC, Hendrickson/Phinney rev April 4, 2000)New comments in BLUE.1) Multiple feedback loops without working cascade. Cascade flaws: 1. It's not running everywhere. (Need networks, want all loops

running at same rate. 2. Nonlinear transport with wakefields. (OK, not an issue for ILC). 3. Improper adaptive beam transport calculations at low intensity with large BPM errors. (Algorithm flaw in least

squares fit: Need algorithm, or calibration).2) General strategy for multiple loops; cascade/ global feedback? What about multiple feedbacks running different rates with different gains? This was a headache with SLC and if ILC wants it, should simulate it as a system. Aliasing problems are exacerbated with slower feedbacks. (For ILC, I like all linac plus BDS

cascaded at 5 hz with 36-pulse time constant; IP feedback at 5 hz with 6-pulse time constant). Use lower gains to compensate for feedback imperfections.

SLC Feedback problems, to sort out for ILC

3) DC offsets. Mostly caused by design flaws in special-purpose feedback systems, especially with nonlinear actuators and pseudo-actuators. All are believed fixed now. Also when matrices are loaded in database, if they don't fit and we don't notice, get dc offset. Also seen in pepii: Sparse matrices were too sparse, leading to DC offsets in HER orbit feedback.

(Simple low-pass algorithm fixes the DC offset problem which is inherent in the LQG design).

4) Slow correctors; and improper modeling of slow correctors. Design feedback system to run reasonably ifcorrectors are slow (LJH made improvement Aug1999). (Should not be a

problem for ILC 5 hz).5) Concerns about corrector nonlinearity around zero. Questions about

hysteresis. (Approach so far: Ignore it!).

SLC Feedback problems, to sort out for ILC 6) Questions about BPMs: What is the sensitivity? Do BPM offsets change with time? What about BPMs which have flaky and/or unreasonable readings? Impact of these on feedback performance. Also when BPMs drift in and out of filtering or limits, the feedback can have a 2-state condition with bad results. (See ideas below). 7) Self-diagnosing feedback. System should have an automated way

to detect bad BPMs; broken correctors. Also to diagnose/detect misbehaving feedback loops. (Ideas: steer often to avoid bad chi-squared. For 5-Hz feedback, have enough time and CPU to re-invert the matrix to omit bad measurements, on every pulse. Look at MIA and other procedures which may automatically be able to detect and disable flaky BPMs, and to at least detect and report broken correctors.).

8) Calibration/adaption strategy. Should we adapt to realtime changes in beam transport/correctors? Should we calibrate? Dither calibration? Or offline calculation? (Adaption would need better algorithms to handle problem with the least squares issue and BPM noise; ILC simulations by LJH assume calibration is used. Need to check expected phase changes and timescale for calibration/adaption).

SLC Feedback problems, to sort out for ILC 9) Noise spectrum design. Does feedback system amplify noise where

there's a lot? Should feedback adapt to changing input noise spectrum? Or can we design a feedback that responds robustly with noise frequency changes? (Maybe a watchdog checks...?). What is the expected incoming noise spectrum? Like SLC, mostly white and some low frequency? Or does ILC need to do better with high frequency noise?

10) For steering feedbacks, worry about bunch tilt and wakefield effects. (Need to look at BPMS which aren't in the feedback region and make sure they're flat?) (LJH 5-HZ simulations use extended configuration, which works great for bunch tilt and emittance preservation. But I haven’t compared it to SLC-style limited range distribution, and should!).

11) What about feedbacks which have dispersion? Some difficulties in SLC (RTL and FF) in feedback loop that steer the beam when energy changes; and/or which think a steering change is energy and control that... Also questions about steering feedbacks if the fit point has non-zero dispersion? Should it resteer the beam when the energy changes?

(No! Very important for ILC BDS! If we re-steer in response to tiny energy changes, the beamsize explodes! Need to measure dispersion originally, measure energy exactly corresponding to the reference orbit, and constantly compensate each BPM measurement for energy fluctuations using energy measurement and dispersion.)

SLC Feedback problems, to sort out for ILC 12) Feedback problems in the final focus, when we didn't have

enough BPMs with phase advances to detect position vs angle. Should there be criteria for this? Should feedback design at least warn us??? Similar issue when correctors are poorly chosen.. Maybe we want some upfront check that feedback components are reasonable...?

13) Dithering feedback for phase ramp optimization: Didn't have a small enough DAC bit size to dither noninvasively. Need small bit size for dithering. (Worked fine for SPPS operation, and we finally got it commissioned).

14) There is a question whether the feedback philosophy we chose, ie. hold position/angle/energy at a particular location, is actually optimal. One could have chosen to minimize the rms orbit in a region, or some related more global algorithm. What we chose makes tracking easier and histories more comprehensible. Need a better idea whether it makes any difference or what the tradeoffs are. (LJH for NLC/ILC simulations I control effective kick at each actuator; then I can distribute actuators as needed. I demonstrated that it worked better for NLC linac, should demonstrate for ILC. But this distribution is the best I have found for BDS feedback in ILC, and the only thing I got working! ).

PEPII B Factory Beam-based Feedback (Lesson: It is really hard, when you have slow BPMs, slow/buggy correctors, and buggy CPU/software. ((Are “modern”, intelligent controllers always good??)))BPMs:- Sometimes periodically forget their firmware in presence of radiation.- Not real-time response.- Heavy BPM user acquisition can lock out feedback.Corrector Power Supply Controllers:- Multi-cpu intelligent controllers. Not real-time response. Periodically perform “long” status checks, locking out feedback system for seconds at a time. Some correctors move in closed bump and some fail, resulting in non-closed bump, luminosity dips and sometimes beam losses! - Previous problems where power supply controller system froze, sometimes needed reset, requiring dumping the ring and refilling.CPU:Using TCPIP communications. Previous buggy TCPIP software would cause micro to freeze, requiring reboot.

These problems are worse for feedback system, because it is a frequent and taxing user of the control system, therefore often blamed for problems.

Strategies for stabilization of nanometer-sized beams (?? from old NLC ideas)

Linac alignment Mover steering ~30 minutes

Control Final focus aberrations

Luminosity optimization feedback with ‘dithering’

~30 minutes

Stabilize linac beam, preserve emittance

Interpulse feedback with correctors

Seconds - minutes

Stabilize beam in final focus

Interpulse feedback with correctors

Seconds

Keep beams near collision

Interpulse feedback (correctors/kickers)

Control DC-0.5 Hz, operate at 5Hz

Keep beams in collision

Interbunch feedback (Font)

few hundred nanoseconds

Function Technique Timescale

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(NLC) Linac Feedback Loop Layouts: Orbit Flattening

Simulated Experiment:

Kick the beam orbit and let it propagate down the machine. Compare uncorrected to different feedback configurations: Longer distribution of devices -> better orbit. (But, tradeoff is

operational robustness: need longer-range transport matrices.)

Uncorrected orbit along the linac: y vs z

‘NLC’-style feedback: longer device distribution flattens the orbit

‘SLC’-style feedback: short device distribution

Red arrows show feedback loop regions; magenta lines are correctors,

red marks are feedbk BPMs

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Z along linac, km

(NLC) Linac Feedback Layouts: EMITTANCE preservation

Simulated Experiment, cont’d:Kick the beam orbit. Compare emittance growth for: Uncorrected, ‘SLC’-style layout, ‘NLC’-style layout. -> SLC-style feedback

emittance is larger than uncorrected. NLC-style feedback with distributed layout has much lower emittance! ‘NLC’ bunch profile is flat.

Z along linac, km Z along bunch, um

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5-Hz Integrated Feedback Simulations Linac feedback distribution: 5 distributed loops per beam, each with 4

horizontal and 4 vertical dipole correctors, and 8 BPMs (X&Y). Based on SLC experience and NLC simulations by LJH.

BDS feedback distribution: 1 BDS loop per beam, 9 BPMs and 9 dipole correctors, both horizontal and vertical. Based on NLC simulations by Seryi.

Linac and BDS feedbacks “Cascaded” system of 6 loops per beam: loops don’t overcompensate beam perturbations, but can be independently disabled for operational convenience. SLC-style “single cascade” (each loop communicates beam information to single adjacent downstream loop).

Linac and BDS loops have exponential response of 36 5-Hz pulses.

IP deflection (X&Y), not cascaded, exponential 6 pulses (like SLC). Matlab/liar/dimad/guinea-pig platform. Upgraded liar/dimad for energy and

current jitter, and dispersion measurements. Ground motion models (Seryi). Study effects of component jitter, energy,

current, kicker jitter. Problems: BDS beamsize very sensitive; using dispersion compensation and perfect energy measurement.

Linac Feedback Layout, similar to NLC.

-5 Hz.-Time response design similar to SLC.- 5 loops, cascaded. - 4 correctors per plane, per loop.-16 BPMs per plane, per loop,distributed.

Linac feedback: Can preserve emittance between steering.Can minimize bunch-bunch jitter from long-range wakefields.Can improve “banana-bunch” shape at IP.

Feedback Simulations, ILC LINAC + BDS

Emittance growth in linac ~100% after 30 min “KEK”ground motion + jitter for 10 seeds, 6% with feedback (3% with feedbackwithout jitter).

5 distributed linac loops

IP loop

1 BDS loop

BPM readings after 30 minutes ground motion

Each linac loop has 4 X correctors and 4 Y correctors, distributed in 2 sets. Each linac loop has 16 X BPMs and 16 Y BPMs, distributed in 2 sets.The BDS feedback has 9 X correctors, 9 Y correctors, 9 X BPMs and 9 Y BPMs (Seryi).The IP feedback has an X corrector and a Y corrector, and BPMs for deflection measurement.

Feedback Simulations, ILC LINAC“Banana-bunch” shape is seen at end of LINAC after 30 minutes of “K” ground motion. Fixed with feedback.

Z along bunch, m

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Linac FeedbackEmittance growth as a function of time (5-hz pulses), after linac feedback is turned on (after 30 minutes of “K” ground motion). This was using 6-pulse time constant. 36 pulses were used in later simulations.

Beamsize growth effects, with feedbackSingle-beam studies of beamsize growth, with 5-hz feedback in LINAC and BDS. Perfect initially, add 30 minutes “KEK” ground motion”, let feedback converge -> 5% beamsize growth.

Increase energy spread for undulator (.15% end of linac; this effect needs more study!) -> 14%.

Add component jitter (25 nm BDS, 50 nm linac) -> 15%.

Add 5-Hz “KEK” ground motion -> 18%.

Add kicker jitter (.1 sigma), current jitter (5%), energy jitter (.5% uncorrelated amplitude on each klystron, 2 degrees uncorrelated phase on each klystron, 0.5 degrees correlated phase on all klystrons, BPM resolution .1 um. -> 21%

30 min ground.

+ Undulator

+ Componentjitter

+ 5 Hz ground.

+ Kicker, current,energy jitter, BPM resol.

(Note: results are with respect to design beamsizes, which vary slightly with # of particles in guinea pig).

Beam Jitter in Feedback SimulationsJitter in the linac, as a fraction of beamsize. Plots are for a single seed, simulations with all jitter sources included.

Y jitter vs z along linac

Y jitter vs z, blows up at the IP

Beam Jitter in Feedback SimulationsFor 10 seeds, move the ground 30 minutes with model “K”, apply ground motion and sample for 200 pulses while feedback converges. The following are average beam jitter as a ratio of perfect simulated beamsize, for the last 20 pulses, after feedback has converged.

End Linac e- average: X: 0.032 Y: 0.70 X: 0.016 Y: 0.33IP e- average: X: 0.28 Y: 12.5 X: 0.12 Y: 3.4 IP avg 2beam diff: X: 0.33 Y: 15.8 X: 0.17 Y: 3.7

IP maximum 2beam X: 1.57 Y: 49.0 X: 0.72 Y: 15.9 difference: (777 nm) (197 nm)

Luminosity (without bunch-bunch fbk) ratio /ideal: 0.17 0.38

Y Beamsize e-: 1.24 e+: 1.07 e-: 1.22 e+: 1.08 ratio /ideal:

All Jitter Sources 5 Hz ground only

Beam Jitter in Feedback SimulationsMove the ground 30 minutes with model “K”, apply ground motion and all other jitter sources, and sample for 200 pulses while feedback converges. The following shows the vertical beam position at the interaction point for both electrons and positrons, for a single seed.

2 beams, 5-Hz linac, BDS and IP deflection feedback. Perfect initially, feedback turned on after 30 minutes of “KEK” ground motion. 5 Hz ground motion, added component jitter, kicker, energy, current jitter. No angle feedback, no intratrain feedback. For the first ~20 seconds, IP feedback cannot keep up with large BDS steering changes. After 20 seconds, beams kept in collision but luminosity is poor (~17% in preliminary simulations, ~71% with perfect intratrain IP feedback).

2-beam Integrated Feedback SimulationsBeam-size jitter in steady-state.

Beam sizes decrease after feedback is turned on. (Note seed-dependent beamsize from ground motion; in this seed, e- becomes smaller).

End Linac e- average: X: 0.029 Y: 0.61 X: 0.0005 Y: 0.01IP e- average: X: 0.30 Y: 10.6 X: 0.012 Y: 0.29IP avg 2beam diff: X: 0.32 Y: 12.4 X: 0.11 Y: 0.31

IP maximum 2beam X: 0.98 Y: 33.9 X: 0.13 Y: 0.92difference:

Luminosity (withoutbunch-bunch fbk) ratio/ideal: 0.20 0.84

Y Beamsize e-: 1.06 e+: 1.05 e-: 1.02 e+: 1.005ratio /ideal:

Ground Model B: Jitter in Feedback SimulationsFor 5 seeds, move the ground 30 minutes with model “B”, apply ground motion and sample for 200 pulses while feedback converges. The following are average beam jitter as a ratio of perfect simulated beamsize, for the last 20 pulses, after feedback has converged.

All Jitter Sources 5 Hz ground only

Ground Model B: Jitter in Feedback SimulationsMove the ground 30 minutes with model “B”, apply ground motion, and sample for 200 pulses while feedback converges. The following shows the vertical separation of the 2 beams at the interaction point, for the case with all jitter sources compared to ground motion only.

Ground Model B: Jitter in Feedback SimulationsMove the ground 30 minutes with model “B”, apply ground motion, and sample for 200 pulses while feedback converges. The following shows the luminosity as the feedback converges.

“Standard” Wakefields (RJones):Standard wakefields, after 30 minutes “K” ground motion.Oscillation over first ~30 bunches up to 2-3*beamsize.5 different ground motion seeds shown. Train-straightener can fix completely.

“Rogue” Wakefields (RJones):Possibility of undamped HOM: Check bunch-bunch jitter end-of-linac.Need to check > 200 bunches. But this is unrealistically pessimistic, because probably not all structures have rogue modes. (Frisch/RJones suggest: in future, mix rogue and standard structures in the linac).

“Rogue” Wakefields (RJones):Possibility of undamped HOM: Check bunch-bunch jitter end-of-linac.30 min ground motion, without steering feedback, then 30 5-hz pulses.

With a trainstraightener, bunch-bunch position jitter is still significant.

Detrending approximates the effect of long-timescale bunch-bunch position feedback at end of the linac: results are good. -> Rogue wakes not a serious problem for bunch-bunch jitter.

“Bunch-bunch jitter”Looking at bunch-bunch positionjitter at end of linac, in presence of multipleerror sources. Note, kicker jitter appears to limit: TDR specification says .1 sigma, which results in ~.1 sigma bunch-bunch jitter at end of linac. (OK).