# Presentation: 707741

## 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. (PID feedback, controlling energy and bunchlength in the linac, with cascade.)

*Observables: *
* **Energy: E**0** (at DL1), E**1** (at BC1), E**2** (at BC2), E**3** (at DL2)*
* **CSR** power            bunch length: ****z,1** (at BC1), ****z,2** (at BC2)*
*Controllables: *
* **Voltage: V**0** (in L0), V**1** (in L1), V**2** (**effectively**, in L2)*
* **Phase: ********1** (in L1), ********2** (in L2 ), ********3** (in L3)*

*Courtesy 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; coupling
Estimated < 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(?)

_**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; coupling**
**Estimated < 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’d

- Matlab control
-  system simulation

- Alpha Computer (VMS)

## Feedback Calibration/Modeling

- Feedback 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 => Measurements
- Actuators => 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)

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

## SLC LQG algorithm

_**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.**

**COMMAND        STATE VALUE**

***SLC LQG algorithm***

***New 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.
- 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).
- 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

- 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).
- Slow correctors;  and  improper  modeling  of  slow
-          correctors. Design  feedback  system  to  run   reasonably   if
- correctors are slow (LJH made improvement Aug1999). (Should not be a problem for ILC 5 hz).
- Concerns about corrector nonlinearity around  zero. Questions about hysteresis.  (Approach so far: Ignore it!).

## SLC Feedback problems, to sort out for ILC 

- 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).
-  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.).
- 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 

- 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?
- 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!).
- 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 

- 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...?
- 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).
- 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**_

**Maintain collisions**

**Maintain small beams **

## (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

- Y beam position, um

- 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

- Y norm emittance, m-rad

- Y beam position, um

## 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 feedback
- without 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

- Y Position, m

## Linac Feedback

- Emittance 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 feedback

- Single-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*

*+ Component*
*jitter*

*+ 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 Simulations

- Jitter 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 Simulations

- For 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:  0.33
- IP 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 Simulations

- Move 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-beam Integrated Feedback Simulations

- Beam-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).

## Ground Model B:  Jitter in Feedback Simulations

- IP e- average:                X: 0.30     Y:   10.6            X:  0.012   Y:  0.29
- IP 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: 0.92
- difference:
- Luminosity (without
- bunch-bunch fbk) ratio
- /ideal:                                0.20                                  0.84
- Y Beamsize                   e-:   1.06    e+:  1.05        e-: 1.02    e+: 1.005
- ratio /ideal:

- For 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 Simulations

- Move 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 Simulations

- Move 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 train
- straightener,
- 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 multiple
- error 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).