Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm

Zhang, Xin ; Fu, Yichen ; Qin, Hong
Issue date: 2020
Rights:
Creative Commons Attribution 4.0 International (CC BY)
Cite as:
Zhang, Xin, Fu, Yichen, & Qin, Hong. (2020). Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm [Data set]. Princeton Plasma Physics Laboratory, Princeton University. https://doi.org/10.11578/1814935
@electronic{zhang_xin_2020,
  author      = {Zhang, Xin and
                Fu, Yichen and
                Qin, Hong},
  title       = {{Simulating pitch angle scattering using
                an explicitly solvable energy-conserving
                 algorithm}},
  publisher   = {{Princeton Plasma Physics Laboratory, Pri
                nceton University}},
  year        = 2020,
  url         = {https://doi.org/10.11578/1814935}
}
Description:

Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo 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 novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space 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 Euler-Maruyama method.

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# Filename Filesize
1 README.txt 403 Bytes
2 ARK_DATA.zip 805 KB