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

Zhang, Xin; Fu, Yichen; Qin, Hong

doi:10.1103/physreve.102.033302

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

Abstract

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. In this paper, 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. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.

Authors:

^[1];

^[1]

Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States)

Publication Date:: Tue Sep 01 00:00:00 EDT 2020

Research Org.:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1660496

Grant/Contract Number:: AC02-09CH11466

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. E

Additional Journal Information:: Journal Volume: 102; Journal Issue: 3; Journal ID: ISSN 2470-0045

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats


                    Zhang, Xin, Fu, Yichen, and Qin, Hong. Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm.  United States: N. p., 2020. 
Web.  doi:10.1103/physreve.102.033302.

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                    Zhang, Xin, Fu, Yichen, & Qin, Hong. Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm.  United States.  https://doi.org/10.1103/physreve.102.033302

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                    Zhang, Xin, Fu, Yichen, and Qin, Hong. Tue .  
"Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm".  United States.  https://doi.org/10.1103/physreve.102.033302.  https://www.osti.gov/servlets/purl/1660496.

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@article{osti_1660496,

  title        = {Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm},

  author       = {Zhang, Xin and Fu, Yichen and Qin, Hong},

  abstractNote = {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. In this paper, 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. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.},

  doi          = {10.1103/physreve.102.033302},

  journal      = {Physical Review. E},

  number       = 3,

  volume       = 102,

  place        = {United States},

  year         = {Tue Sep 01 00:00:00 EDT 2020},

  month        = {Tue Sep 01 00:00:00 EDT 2020}

}

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

Abstract

Citation Formats

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High Order Conformal Symplectic and Ergodic Schemes for the Stochastic Langevin Equation via Generating Functions
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Langevin approach to plasma kinetics with Coulomb collisions
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