A modular framework for simulations of Ionization Profile Monitors { Implementation and Benchmarking Dominik Vilsmeier June 15, 2017 Supervisors: Prof. Dr. Tilo Wettig Dr. Mariusz Sapinski (Universit¨atRegensburg) (GSI Helmholtz Centre for Heavy Ion Research) Abstract Simulations of electron and ion tracking in Ionization Profile Monitors are an important tool for specifying and designing new monitors. They are also essential for understanding the effects related to the ionization process, guiding field non-uniformities and influence of the beam fields which may lead to a distortion of measured beam profiles. Most of these effects cannot be treated analytically and therefore several simulation codes have been developed at different accelerator laboratories during the past years. Those existing codes are often tuned to the specific needs of a laboratory, are not well documented and lack a practical user interface. This work presents a novel, generic simulation tool with focus on the ability to test, maintain and extend the code. A complete documentation as well as facile usage were important aspects too. The application combines the features of existing codes in order to provide a common standard for IPM simulations. Because of its modular structure the application allows for exchanging the computational modules depending on the use case as well as for straightforward extensibility to new use cases. Future intended use cases are for example simulations of Beam Induced Fluorescence monitors based on gas jets or Electron Wire Scanners. The current set of algorithms includes several particle tracking methods (for instance Runge-Kutta 4th order or the Boris algorithm) and several bunch field evaluation algorithms (analytical solutions for specific cases as well as numerical Poisson solvers). The application and all involved methods have been tested and benchmarked against existing results. The code is well documented and includes a graphical user interface. It is publicly available as a git repository and as a Python package. Contents 1. Introduction6 2. Requirements & Use cases8 2.1. Use cases......................................8 2.1.1. Profile deformation due to beam space charge..............8 2.1.2. Profile deformation due to guiding field non-uniformities........8 2.1.3. Simulation of meta-stable excited states and their influence on the measured beam profile (BIF).......................9 2.1.4. Gas jets for IPM and BIF.........................9 2.1.5. Electron background............................9 2.1.6. Secondary electrons............................ 10 2.1.7. Electron Wire Scanner........................... 10 2.1.8. Correlations between electron and ion detection............. 10 2.1.9. Simulating multiple beams........................ 10 2.1.10. Studying trajectories of specific particles................. 11 2.2. Requirements.................................... 11 3. Components 13 3.1. Model & Manager................................. 13 3.2. Particle generation................................. 13 3.2.1. Ionization.................................. 16 3.3. Particle tracking.................................. 17 3.4. Devices....................................... 17 3.5. Guiding fields.................................... 18 3.6. Beams........................................ 19 3.6.1. Bunch trains................................ 19 3.6.2. Bunch shapes................................ 20 3.7. Beam fields..................................... 21 3.7.1. Bunch electric field models........................ 22 3.8. Output recorders.................................. 23 3.9. Auxiliaries...................................... 23 3.9.1. Simulation cycle.............................. 23 3.9.2. Particle Supervisor............................. 24 3.9.3. Setup.................................... 24 3.10. Configuration.................................... 25 3.11. Start & Setup.................................... 27 4. Available models 29 4.1. Particle Generation................................. 30 4.1.1. Single particle generation......................... 30 4.1.2. Manual generation of particles...................... 30 4.1.3. Ionize particles at a fixed z-position................... 30 4.1.4. Ionization cross sections.......................... 30 4.1.5. Electron gun (pending).......................... 32 4.1.6. Secondary electrons (pending)...................... 34 4.1.7. Gas jet (pending).............................. 34 4.2. Particle tracking.................................. 34 4.2.1. Runge-Kutta 4th order.......................... 34 4.2.2. Boris algorithm............................... 36 4.2.3. Analytical solutions............................ 36 4.3. Devices....................................... 37 4.3.1. Ionization Profile Monitor......................... 37 4.3.2. Beam Induced Fluorescence monitor (pending)............. 37 2 Contents 4.4. Guiding fields.................................... 38 4.4.1. Uniform fields................................ 38 4.4.2. Field maps................................. 38 4.5. Bunch electric field models............................ 38 4.5.1. Symmetric Gaussian (analytical, 2D)................... 38 4.5.2. Asymmetric Gaussian (analytical, 2D).................. 39 4.5.3. Parabolic ellipsoid (analytical, 3D).................... 40 4.5.4. Poisson solver based on Successive Over-Relaxation (numerical, 2D). 40 4.5.5. Poisson solver based on Finite Elements (numerical, 3D)........ 41 4.6. Output recorders.................................. 42 4.6.1. Mapping of initial to final particle attributes.............. 42 4.6.2. Studying trajectories............................ 42 4.6.3. Beam profiles in XML format....................... 42 5. Benchmarking 43 5.1. Particle tracking.................................. 43 5.1.1. Gyro motion................................ 43 5.1.2. E × B-drift................................. 44 5.1.3. Trajectories with beam fields....................... 46 5.2. Bunch electric field models............................ 48 5.2.1. LHC case.................................. 48 5.2.2. PS case................................... 51 5.3. Profile comparison................................. 51 5.3.1. LHC case.................................. 52 5.3.2. PS case................................... 52 5.3.3. SIS-18 measurements............................ 53 5.4. Performance..................................... 56 5.4.1. Particle tracking.............................. 56 5.4.2. Bunch electric field models........................ 57 6. Summary and Conclusions 59 References 61 Appendices 64 A. How to install the application 64 A.1. Installation..................................... 64 A.1.1. Via Anaconda (recommended)...................... 64 A.1.2. Manual installation (advanced)...................... 65 A.1.3. Verifying the installation......................... 67 A.1.4. Creating a desktop entry......................... 67 A.2. Updating the package............................... 67 A.2.1. For installations via Anaconda...................... 67 A.2.2. For manual installations.......................... 67 A.3. Uninstalling the package.............................. 68 B. How to use the application 68 B.1. Conventions..................................... 68 B.2. Via the command line............................... 68 B.3. Via the GUI..................................... 69 B.3.1. Configuration................................ 69 B.3.2. Simulation................................. 71 B.3.3. How can I test the current configuration?................ 72 B.4. Output....................................... 72 B.4.1. How can I check the output?....................... 72 B.5. Command line tools................................ 73 3 List of Figures 1. IPM sketch.....................................6 2. Package structure.................................. 14 3. Cross-dependency diagram............................. 15 4. Iteration flowchart................................. 15 5. Particle generation sub-package structure.................... 16 6. Particle tracking sub-package structure...................... 18 7. Devices sub-package structure........................... 18 8. Beams sub-package structure........................... 19 9. Beam field acquisition diagram.......................... 22 10. Configuration diagram............................... 27 11. Simulation flowchart................................ 28 12. Model overview................................... 29 13. Sketch of generating all particles at a fixed z-position.............. 31 14. Double differential cross section.......................... 32 15. Single differential cross sections with respect to energy............. 33 16. Single differential cross sections with respect to the scattering angle..... 33 17. Momentum shift for the Boris algorithm..................... 37 18. Results for the gyro motion and the E × B-drift test cases........... 45 19. Energy- and y-deviation for the gyro motion test case............. 45 20. Trajectories for the E × B-drift test case..................... 46 21. Trajectories for the LHC case........................... 47 22. Electric field estimation for large field gradients................. 48 23. Trajectories for the 3 kV PS case......................... 49 24. Trajectories for the 3 kV PS case with magnetic field.............. 49 25. Bunch electric field (LHC case).......................... 50 26. Charge density (LHC case)............................ 51 27. Longitudinal electric field from the Parabolic Ellipsoid model (LHC