NSLS-II: Nonlinear Model Calibration for Synchrotrons
This tech note is essentially a summary of a lecture we delivered to the Acc. Phys. Journal Club Apr, 2010. However, since the estimated accuracy of these methods has been naive and misleading in the field of particle accelerators, i.e., ignores the impact of noise, we will elaborate on this in some detail. A prerequisite for a calibration of the nonlinear Hamiltonian is that the quadratic part has been understood, i.e., that the linear optics for the real accelerator has been calibrated. For synchrotron light source operations, this problem has been solved by the interactive LOCO technique/tool (Linear Optics from Closed Orbits). Before that, in the context of hadron accelerators, it has been done by signal processing of turn-by-turn BPM data. We have outlined how to make a basic calibration of the nonlinear model for synchrotrons. In particular, we have shown how this was done for LEAR, CERN (antiprotons) in the mid-80s. Specifically, our accuracy for frequency estimation was {approx} 1 x 10{sup -5} for 1024 turns (to calibrate the linear optics) and {approx} 1 x 10{sup -4} for 256 turns for tune footprint and betatron spectrum. For a comparison, the estimated tune footprint for stable beam for NSLS-II is {approx}0.1. Since the transverse damping time is {approx}20 msec, i.e., {approx}4,000 turns. There is no fundamental difference for: antiprotons, protons, and electrons in this case. Because the estimated accuracy for these methods in the field of particle accelerators has been naive, i.e., ignoring the impact of noise, we have also derived explicit formula, from first principles, for a quantitative statement. For e.g. N = 256 and 5% noise we obtain {delta}{nu} {approx} 1 x 10{sup -5}. A comparison with the state-of-the-arts in e.g. telecomm and electrical engineering since the 60s is quite revealing. For example, Kalman filter (1960), crucial for the: Ranger, Mariner, and Apollo (including the Lunar Module) missions during the 60s. Or Claude Shannon et al since the 40s for that matter. Conclusion: what's elementary in the latter is considered 'advanced', if at all, in the former. It is little surprise then that published measurements typically contains neither error bars (for the random errors) nor estimates for the systematic in the former discipline. We have also showed how to estimate the state space by turn-by-turn data from two adjacent BPMs. And how to improve the resolution of the nonlinear resonance spectrum by Fourier analyzing the linear action variables instead of the betatron motion. In fact, the state estimator could be further improved by adding a Kalman filter. For transparency, we have also summarized on how these techniques provide a framework- and method for a TQM (Total Quality Management) approach for the main ring. Of course, to make the ($2.5M) turn-by-turn data acquisition system that is being implemented (for all the BPMs) useful, a means ({approx}10% contingency for the BPM system) to drive the beam is obviously required.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source
- Sponsoring Organization:
- DOE - Office Of Science
- DOE Contract Number:
- DE-AC02-98CH10886
- OSTI ID:
- 1009503
- Report Number(s):
- BNL-94828-2010-IR; 39KC02000; TRN: US1101569
- Country of Publication:
- United States
- Language:
- English
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