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<p>A multi-species Fokker–Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3436_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">H</mi> </math></EquationSource> </InlineEquation>-Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potential. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values.</p>

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A Nonlinear, Conservative, Entropic Fokker–Planck Model for Multi-species Collisions

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Evan Habbershaw,
  • Cory D. Hauck,
  • Jingwei Hu,
  • Jeffrey R. Haack

摘要

A multi-species Fokker–Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an \(\mathcal {H}\) H -Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potential. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values.