Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods

Abstract

This paper investigates the subcycling of particle orbits in variational, geometric particle-in-cell methods, addressing the Vlasov-Maxwell system in magnetized plasmas. The purpose of subcycling is to allow different time steps for different particle species and, ideally, time steps longer than the electron gyroperiod for the global field solves while sampling the local cyclotron orbits accurately. The considered algorithms retain the electromagnetic gauge invariance of the discrete action, guaranteeing a local charge conservation law, while the variational approach provides a bounded long-time energy behavior.

Quasi-Helmholtz Decomposition, Gauss' Laws and Charge Conservation for Finite Element Particle-in-Cell

“…As before, we take recourse to the sequence W 0 ∇ −→ W 1 and note that ∇ W 0 (r) ∈ W 1 . In spirit of (12), it follows that one can write…”

“…We note the following. Given results from a standard MFEM solve, we can use (12) to partition into solenoidal and non-solenoidal components. That is, given coefficients Ēn we can obtain Ēn ns and Ēn s .…”

“…But more importantly, there is a well developed rigorous body of literature [6][7][8] on the mathematical foundation of FEM. Indeed, as is to be expected, FEM has made inroads into PIC modeling more of late with some excellent work rubrics of this approach [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . Of particular note in seminal work in 26 , wherein rubrics for charge conservation for FEM-PIC where developed.…”

A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

“…Structure-preserving particle-in-cell (PIC) algorithms preserve many of the geometric and topological mathematical structures of a point-particle kinetic plasma model, including its symplectic structure, symmetries, conservation laws, and cohomology (Villasenor & Buneman 1992;Esirkepov 2001;Squire et al 2012;Evstatiev & Shadwick 2013;Xiao et al 2013;Moon et al 2015;Qin et al 2015;Xiao et al 2015;He et al 2015;Crouseilles et al 2015;Qin et al 2016;He et al 2016;Burby 2017;Morrison 2017;Kraus & Hirvijoki 2017;Xiao et al 2018;Xiao & Qin 2019;Glasser & Qin 2020;Hirvijoki et al 2020;Wang et al 2021-07;Xiao & Qin 2021;Holderied et al 2021;Perse et al 2021;O'Connor et al 2021;Pinto et al 2021). One such structure, gauge symmetry, was first preserved in a PIC code in the Lagrangian formalism via a variational method (Squire et al 2012).…”

Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes

“…During the past ten years or so, numerical methods in kinetic plasma simulations have made quite a leap. We have seen the rise of structure-preserving, geometric particle-in-cell schemes [3][4][5][6][7][8][9][10][11][12][13][14] that are based on discretizing either the variational or Hamiltonian structure of the underlying kinetic model. Such schemes are superior in that they preserve not only the energy of the system but typically guarantee also a local algebraic charge conservation law and the preservation of the multisymplectic two-form.…”