Simulating Heavy Ion Beams Numerically using Minimum Entropy Reconstructions

• Applicant: Professor Dr. Martin Frank
• Subject Area: Mathematics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 316995219

• Final Report Year: 2021

Final Report Abstract

The aim of this project was to develop a novel tool for the simulation of heavy ion beams as they are decelerated in thick targets. We wanted to characterize the spatial and energy distributions of all primary particles and secondary fragments in a target. This is relevant because ion beams are used in various fields: atomic physics (e.g. atomic collisions, ion capture), nuclear physics (e.g. the study of the structure of nuclei), electronics (e.g. deposition of elements), material science and chemistry (e.g. analysis of damage on the walls of a tokamak), biology (e.g. the study of the toxicology of cellular tissues by ion analysis). Simulations of heavy ion beams are challenging for two main reasons. First, beams are difficult to capture with a method that uses a computational grid. Grids are used to make problems solvable on computers: The solution is approximated on grid points. Second, the simulations rely on measurements of the stopping power, and therefore must be regarded as uncertain. The stopping power quantifies how much radiation is absorbed by the material depending on energy and material composition. In this project we developed new entropy-based discretization schemes which allow both a sub-grid resolution and at the same time a very detailed reconstruction that can capture beams. In addition, we used similar methods to characterize the uncertainties in the particle distribution due to uncertain stopping powers.

Publications

• Maximum-principle-satisfying second-order Intrusive Polynomial Moment scheme, The SMAI Journal of Computational Mathematics 5 (2019) 23-51
  J. Kusch, G.W. Alldredge, M. Frank
  (See online at https://doi.org/10.5802/smai-jcm.42)
• Filtered stochastic galerkin methods for hyperbolic equations, Journal of Computational Physics 403 (2020) 109073
  J. Kusch, R.G. McClarren, M. Frank
  (See online at https://doi.org/10.1016/j.jcp.2019.109073)
• Intrusive acceleration strategies for uncertainty quantification for hyperbolic systems of conservation laws, Journal of Computational Physics 419 (2020) 109698
  J. Kusch, J. Wolters, M. Frank
  (See online at https://doi.org/10.1016/j.jcp.2020.109698)
• Realizability-preserving discretization strategies for hyperbolic and kinetic equations with uncertainty, doctoral thesis, 2020
  J. Kusch
  (See online at https://doi.org/10.5445/IR/1000121168)
• Oscillation mitigation of hyperbolicity-preserving intrusive uncertainty quantification methods for systems of conservation laws, Journal of Computational and Applied Mathematics (2021) 113714
  J. Kusch, L. Schlachter
  (See online at https://doi.org/10.1016/j.cam.2021.113714)