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Simulation of Longitudinal Beam Dynamics

Fachgebiet Theoretische Elektrotechnik und Numerische Feldberechnung PD Dr. Markus Clemens. DESY Beam Dynamics Meeting. Simulation of Longitudinal Beam Dynamics. Sebastian Lange, Markus Clemens Chair for Theory in Electrical Engineering and Computational Electromagnetics

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Simulation of Longitudinal Beam Dynamics

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  1. Fachgebiet Theoretische Elektrotechnik und Numerische Feldberechnung PD Dr. Markus Clemens DESY Beam Dynamics Meeting Simulation of Longitudinal Beam Dynamics Sebastian Lange, Markus Clemens Chair for Theory in Electrical Engineering and Computational Electromagnetics Faculty of Electrical Engineering, Helmut-Schmidt-University, Hamburg Email: sebastian.lange@hsu-h.de DESY Hamburg, March 05, 2007

  2. Introduction • Overview LiTrack • Optimization • State of LSC Impedance Extension • Summary and Next Steps

  3. Introduction Example 1

  4. Introduction Example 2

  5. Introduction • Overview LiTrack • Optimization • State of LSC Impedance Extension • Summary and Next Steps

  6. Attributes of Original LiTrack Code • Longitudinal phase space single bunch tracker • RF acceleration • Bunch compression up to 3rd order • Cavity wakes • Random distributions Original Reference: P. Emma and K.L.F. Bane, LiTrack: A FAST LONGITUDINAL PHASE SPACE TRACKING CODE WITH GRAPHICAL USER INTERFACE, PAC ’05 / SLAC-PUB-11035

  7. Extensions to LiTrack • Set up by energy and momentum derivatives (“knobs”) • Minimization of the longitudinal rms emittance • Constrained minimization of the longitudinal rms emittance (SQP- local convergent) • Penalty emittance minimization (GA - global convergent) • Hybridization of both algorithms • Systematic distribution • Longitudinal space charge impedance (in the works) • Manual / Documentation (draft available / under construction)

  8. The New GUI • Linac definitions by pics • Clearly arranged panels • New introduced menu bar • Parameter/target choice • Optimization for more than one BC system.

  9. Energy adjustment Momentum chirp adjustment Symmetry tuning Precision adjustment of tails The Knob Panel Known from specification: Reference: M. Dohlus and T. Limberg, BUNCH COMPRESSION STABILITY DEPENDENCE ON RF PARAMETERS

  10. The GUI Pictograms Mark, no action General Bunch Compression Chicane (low angle approx.) RF Linac FIT-point (Peak current, energy, skewness, correlation coefficient and rms emittance ) End of track

  11. Introduction • Overview LiTrack • Optimization • State of LSC Impedance Extension • Summary and Next Steps

  12. General Problem Description • Optimization aims: • Minimal longitudinal rms emittance • subject to requirements • Peak current • Energy • Symmetric current profile • Positive correlation in phase space • Bounds on the design variable • Nonlinear Constrained Optimization • Nonlinear Constraints Approximation of the start values SQP

  13. Start Values by Genetic Algorithms • Determination of start values: • Global optimization (GA) • Subject to Constraints • Positive correlation, else • Bounds on the design variable GA Start values SQP Result

  14. Start population SQP GA Schema of Hybridization Start population inthe space of bounds Minimization of the penalty problem Result Start value Constrained optimization of thereal problem • Analogy to Hill-Climb-Algorithm: • GA finds the hill • SQP searches the crest Result

  15. Result 1 - Without Cavity Wakes Time needed: 6.8 s

  16. Result 1- With Cavity Wakes Time needed:79.3 s

  17. Result 1 – Start Values by GA Without Wakes Time needed:4.5 min

  18. Result 2 – Without Wakes - GA Results

  19. Result 2 – Without Wakes - SQP Results Time needed: 7.6 min

  20. Introduction • Overview LiTrack • Optimization • State of LSC Impedance Extension • Summary and Next Steps

  21. Model Assumptions • RF-Sections • Constant energy gradient • Compressors / Drifts • Constant energy • Beta function • from component list • in sections constant • Beam size

  22. Analytical Modes of LSC Analytical Integration • Possible alternatives to analytical model : • Numerical Integration • Adaptive Simpson quadrature • Adaptive Lobatto quadrature

  23. Beta Function Reference: W. DeckingXFEL Componentlist 3.3

  24. Introduction • Overview LiTrack • Optimization • State of LSC Impedance Extension • Summary and Next Steps

  25. Summary and Next Steps • Summary • Extension by knobs • Optimization of bunch compression system • New convenient GUI • Implementation of systematic distribution • Implementation of LSC impedance (in the works) • Documentation ((permanently) under construction) • Future Work • Implementation of LSC impedances and wakes • Sensitivity analysis and search for insensitive working points • Improvement of the actual optimization design Acknowledgement to Martin Dohlus and Torsten Limberg for guidance and many helpful discussions!

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