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, Markus Clemens Chair for Theory in Electrical Engineering and Computational Electromagnetics Faculty of Electrical Engineering, Helmut-Schmidt-University, Hamburg DESY Beam Dynamics Hamburg, Meeting March 05, March

2 Introduction Overview LiTrack Optimization State of LSC Impedance Extension Summary and Next Steps Beam Dynamics Meeting March

3 Introduction Example 1 Beam Dynamics Meeting March

4 Introduction Example 2 Beam Dynamics Meeting March

5 Introduction Overview LiTrack Optimization State of LSC Impedance Extension Summary and Next Steps Beam Dynamics Meeting March

6 Attributes of Original LiTrack Code Longitudinal phase space single bunch tracker RF acceleration Bunch compression up to 3 rd 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 Beam Dynamics Meeting March

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) Beam Dynamics Meeting March

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. Beam Dynamics Meeting March

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

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 Beam Dynamics Meeting March

11 Introduction Overview LiTrack Optimization State of LSC Impedance Extension Summary and Next Steps Beam Dynamics Meeting March

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 Beam Dynamics Meeting March

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 Beam Dynamics Meeting March

14 Schema of Hybridization Start population Start population in the space of bounds GA Minimization of the penalty problem Result Start value SQP Constrained optimization of the real problem Result Analogy to Hill-Climb-Algorithm: GA finds the hill SQP searches the crest Beam Dynamics Meeting March

15 Result 1 - Without Cavity Wakes Time needed: 6.8 s Beam Dynamics Meeting March

16 Result 1- With Cavity Wakes Time needed: 79.3 s Beam Dynamics Meeting March

17 Result 1 Start Values by GA Without Wakes Time needed: 4.5 min Beam Dynamics Meeting March

18 Result 2 Without Wakes - GA Results Beam Dynamics Meeting March

19 Result 2 Without Wakes - SQP Results Time needed: 7.6 min Beam Dynamics Meeting March

20 Introduction Overview LiTrack Optimization State of LSC Impedance Extension Summary and Next Steps Beam Dynamics Meeting March

21 New Standardized Distribution Gaussian Distribution Uniform Distribution Equidistant on z Gaussian on δ Number of particles: n 2 Beam Dynamics Meeting March

22 Model Assumptions RF-Sections Constant energy gradient Compressors / Drifts Constant energy Beta function from component list in sections constant Beam size Beam Dynamics Meeting March

23 Analytical Modes of LSC Analytical Integration Possible alternatives to analytical model : Numerical Integration Adaptive Simpson quadrature Adaptive Lobatto quadrature Beam Dynamics Meeting March

24 Beta Function Reference: W. Decking XFEL Componentlist 3.3 Beam Dynamics Meeting March

25 Introduction Overview LiTrack Optimization State of LSC Impedance Extension Summary and Next Steps Beam Dynamics Meeting March

26 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! Beam Dynamics Meeting March

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