1. Orbit Response Matrix Studies
PEP-II MAC
14-Dec-2004
P. Tenenbaum

2. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
ORM Participants
M. Donald, K. Sonnad, C. Steier, PT, J. Turner, U. Wienands, A. Wolski, M. Woodley, G. Yocky
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

3. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Brief Introduction
“Orbit Response Matrix” (ORM) technique: method for deducing gradient errors in a storage ring
A subset of ring correctors is varied
The change in the closed orbit is measured
Orbit Response Matrix C defined as change in orbit at BPM i per unit excitation of corrector j,  i,j
Tune a model lattice until model of C matches measured C
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

4. Getting and Analyzing Data
Data acquisition driven by scripts on control system mainframe
both HER and LER scripts exist
Vary all selected correctors, read out all BPMs
Analysis tool = LOCO (“Linear Optics from Closed Orbits”)
Matlab application
Uses AT (Matlab “Accelerator Toolkit”) for accelerator model
HER: analysis performed on pepoptics (though some preprocessing occurs on my PC)
LER: analysis performed on Solaris LBL
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

5. Getting and Analyzing Data (2)
LOCO computes d(Cij)/dAk  fit parameters Ak
Result is a new design matrix, size = (sizeof C) x (# fit parameters)
Design matrix allows LOCO to estimate fit parameter values which minimize difference between measured and model C
Iterative
after 3-8 iterations χ2 reaches a minimum value
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

6. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Size of the Dataset
Size of C = # BPM channels x # Correctors
HER: 514 x 287 = 148,379
LER: 424 x 290 = 122,960
Each BPM channel and each corrector has 2 fit parameters (scale factor and coupling)
HER Design Matrix = 237 M values, 1.9 GByte!
LER: 176 M values, 1.4 GByte!
Before adding parameters for quad strengths!
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

7. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Size of the Dataset (2)
Computation time not limiting, but:
2 GByte is at or beyond the practical limit for a 32-bit application (Matlab) on a 32-bit OS
Strategies for Mitigation:
Iterate: fit BPM scale/coupling on 1 iteration, corrector scale/coupling on the next (LER)
Reduce: Cut some redundant (arc) correctors and single-view BPMs (HER)
Both work, though tests of cutting BPMs and correctors in LER were disappointing
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

8. MAC Recommendations from April 2004
“Maintain/Increase efforts to develop accurate and usable optics model of the rings.” (Priority 1)
“Identify sources of HER beta beat and fix or incorporate in the design optics.” (Priority 2)
“Optimize measurement-analysis-correction loop for both speed and effectiveness.” (Priority 2)
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

9. Progress on HER (since last MAC)
Took one new dataset, 10-June-2004
poor data quality
Main activities:
Optimization of the Fitting Procedure
Developing tools for information exchange
AT and MAD
AT and online characterizations
Scale-factor (“fudge”) configurations
Streamlining the analysis procedure
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

10. HER: Fitting Procedure
Which parameters to fit?
For the present, agreed to fit 1 scale factor per quad power supply
Total of 84 (compare to ~1,100 BPM/dipole pars)
limits memory usage and speeds execution
Trivial to translate to “PS fudge factor” configuration
Doesn’t fully answer the question, “What is wrong with my accelerator?”, but rather, “What’s the best way to fix my accelerator?”
Fit is performed using measured orbit
Online (MCC/pepoptics) tools generate starting model from PS, orbit data
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

11. HER: Information exchange
AT/MAD
Allow optics experts to use “fitted” optics as a starting point for MAD modelling
Error-catching – “When I run your AT optics in MAD my phase advance is different, something is wrong!”
AT/Characterization
Comparison to phase/coupling information gives confidence that AT/LOCO “know what they are talking about”
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

12. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
HER: AT/MAD
Point-to-point betatron phase advance comparison between AT and MAD, 10-June-2004 Fitted Optics
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

13. HER: AT/Characterization
Some examples of comparison: Fitted model tunes, C12bar versus measured from characterization process
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

14. HER: Scale Factor Configs
Done!
Software written – scale factors are included when computing optics starting from PS settings
Scale factor configs implemented
Procedure for generating more ~trivial
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

15. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
HER: Streamlining
Complete script / “cheat sheet”
Human intervention minimized
Execution speed test performed 08-Oct-2004, completed analysis in 3 hrs, 10 minutes (actual LOCO computation time was about 1 hour, 20 minutes)
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

16. Progress on LER (Since last MAC)
No additional ORM data taken
Main activities:
Optimization of the Fitting Procedure
AT/MAD interchange
transfer of fit parameters to MAD
comparison of AT/MAD models with fit parameters transferred
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

17. LER: Fitting Procedure
Similar to HER
one fit parameter per power supply, “effective fit”
exception: some PS fudges not well determined, set of fit parameters adjusted to avoid “fighting fudges”
Actual orbit used for fit (can be different from design)
Complication: sextupole feed-downs
Quality of fit is significantly better when normal and skew quad terms in sextupoles are used as fit parameters
But there’s no sensible way to implement this in the fudge config system
Leave out these terms, try to address through BBA and better orbit control
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

18. LER: AT/MAD comparison
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

19. LER: AT/Characterization
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

20. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Summary: Where we Are
HER: Getting close to a “turnkey” system
Expect to take and analyze data in a single shift
Fudge factors generated directly
LER: Procedures improved
Expect an overnight turnaround for analysis
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

21. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Further Improvements
HER: migrate tools on PT’s PC to pepoptics
Entire operation can be performed on central servers
Train additional people to perform analysis
LER: migrate tools from LBL Solaris workstation to pepoptics
Push to a similar state of “quick and simple” operation
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

22. P. Tenenbaum -- PEP-II MAC 14-Dec-2004 -- ORM
Improvements
Both rings
Consider migrating to 64-bit linux server running Matlab R14SP1 (64-bit version)
Allows up to 2 billion double-precision real numbers in a single matrix (recall that we already cannot cope with 200 million)
Expand fit parameter set
Go to 1 parameter/magnet?
Need to think about how to use this information even if we can get it
P. Tenenbaum -- PEP-II MAC 14-Dec ORM

23. Response to Recommendations
“Maintain/Increase efforts to develop accurate and usable optics model of the rings.” (Priority 1)
“Identify sources of HER beta beat and fix or incorporate in the design optics.” (Priority 2)
“Optimize measurement-analysis-correction loop for both speed and effectiveness.” (Priority 2)
We have increased our efforts. They have not yet reached fruition, but we anticipate that we will perform ORM early in Run 5 and put the results to work immediately.
Not yet done.
Much progress has been made here, although more remains to be done.
P. Tenenbaum -- PEP-II MAC 14-Dec ORM