A higher-order finite-element implementation of the nonlinear Fokker–Planck collision operator for charged particle collisions in a low density plasma

Hardman, Michael R.; Abazorius, M.; Omotani, J.; Barnes, M.; Newton, S. L.; Cook, J. W. S.; Farrell, P.E.; Parra, F. I.

doi:10.1016/j.cpc.2025.109675

Title: A higher-order finite-element implementation of the nonlinear Fokker–Planck collision operator for charged particle collisions in a low density plasma

Journal Article · 19 May 2025 · Computer Physics Communications

DOI: https://doi.org/10.1016/j.cpc.2025.109675 · OSTI ID:2567501

^[1]; Abazorius, M. ^[2]; Omotani, J. ^[3]; Barnes, M. ^[2]; Newton, S. L. ^[3]; Cook, J. W. S. ^[4]; Farrell, P.E. ^[5]; Parra, F. I. ^[6]

Tokamak Energy Ltd., Abingdon (United Kingdom); Univ. of Oxford (United Kingdom); United Kingdom Atomic Energy Authority (UKAEA), Abingdon (United Kingdom)
Univ. of Oxford (United Kingdom)
United Kingdom Atomic Energy Authority (UKAEA), Abingdon (United Kingdom)
United Kingdom Atomic Energy Authority (UKAEA), Abingdon (United Kingdom); Univ. of Warwick, Coventry (United Kingdom)
Univ. of Oxford (United Kingdom); Charles Univ., Prague (Czech Republic)
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinear Fokker–Planck collision operator written in terms of Rosenbluth potentials in the Rosenbluth–MacDonald–Judd (RMJ) form. The Rosenbluth potentials may be obtained either by direct integration or by solving partial differential equations (PDEs) similar to Poisson's equation: we optimise for performance and scalability by using sparse matrices to solve the relevant PDEs. We represent the distribution function using a tensor-product continuous-Galerkin finite-element representation and we derive and describe the implementation of the weak form of the collision operator. We present tests demonstrating a successful implementation using an explicit time integrator and we comment on the speed and accuracy of the operator. Finally, we speculate on the potential for applications in the current and next generation of kinetic plasma models.

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

Sponsoring Organization:: Engineering and Physical Sciences Research Council (EPSRC); European Union (EU); USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 2567501

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 314; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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