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

Xin Zhang1, Yichen Fu1, Hong Qin1

  • 1Princeton Plasma Physics Laboratory and Department of Astrophysical Sciences, Princeton University, Princeton NJ 08540, USA.

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|October 20, 2020
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Summary
This summary is machine-generated.

This study introduces a new numerical algorithm for simulating particle pitch-angle scattering, ensuring energy conservation and preventing unphysical artifacts in plasma simulations. The structure-preserving method achieves high accuracy and remarkable long-time stability.

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Area of Science:

  • Plasma Physics
  • Computational Physics
  • Numerical Analysis

Background:

  • Particle distribution functions are often simulated using the Langevin equation for pitch-angle scattering.
  • Current numerical methods can lead to unphysical artifacts like numerical heating due to lack of energy conservation.

Purpose of the Study:

  • To present a novel structure-preserving numerical algorithm for the Langevin equation for pitch-angle scattering.
  • To address the issue of energy conservation in numerical simulations of particle dynamics.

Main Methods:

  • Developed an algorithm leveraging the Cayley transform for structure preservation in velocity-space rotations.
  • The algorithm is explicitly solvable and preserves velocity norms to machine precision.
  • Utilized the Euler-Maruyama method for comparison of numerical convergence order.

Main Results:

  • The proposed algorithm preserves the norm of velocities down to machine precision.
  • Demonstrated the same order of numerical convergence as the stochastic Euler-Maruyama method.
  • Benchmarking against analytical solutions for particle beam pitch-angle scattering showed excellent agreement.

Conclusions:

  • The new algorithm accurately simulates pitch-angle scattering while conserving energy.
  • The structure-preserving approach offers remarkable long-time accuracy for plasma simulations.
  • This method mitigates numerical heating and spectral distortions common in existing treatments.