Simulating pitch angle scattering using an explicitly solvable energyconserving algorithm
Abstract
Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitchangle scattering. This approach is frequently used in particlebased MonteCarlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a structurepreserving numerical algorithm for the Langevin equation for pitchangle scattering. Similar to the wellknown Boris algorithm, the proposed numerical scheme takes advantage of the structurepreserving properties of the Cayley transform when calculating the velocityspace rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic EulerMaruyama method. The numerical scheme is benchmarked by simulating the pitchangle scattering of a particle beam and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable longtime accuracy of the proposed algorithm.
 Publication:

Physical Review E
 Pub Date:
 September 2020
 DOI:
 10.1103/PhysRevE.102.033302
 arXiv:
 arXiv:2006.10877
 Bibcode:
 2020PhRvE.102c3302Z
 Keywords:

 Physics  Computational Physics;
 Physics  Plasma Physics
 EPrint:
 Updated to the final version after peer review at PRE. Added a new figure to include the time evolution of the Legendre components