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

Evan Habbershaw; Cory D. Hauck; Jingwei Hu; Jeffrey R. Haack

doi:10.1007/s10955-025-03436-7

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

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

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

Abstract

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 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.

Original language	English
Article number	59
Journal	Journal of Statistical Physics
Volume	192
Issue number	5
DOIs	https://doi.org/10.1007/s10955-025-03436-7
State	Published - May 2025

Funding

This manuscript has been authored, in part, by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://energy.gov/downloads/doe-public-access-plan). This work was supported, in part, by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). J. Hu\u2019s research is partially supported by AFOSR grant FA9550-21-1-0358, and DOE grant DE-SC0023164.

Keywords

Conservation laws
Dougherty
Entropy
Fokker–Planck
Lenard–Bernstein
Moment equations
Multi-species kinetic models
Plasma physics

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10.1007/s10955-025-03436-7

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abstract = "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 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.",

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

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Keywords

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