Charge-conserving, variational particle-in-cell method for the drift-kinetic Vlasov-Maxwell system
arXiv:1910.03441
Abstract
This paper proposes a charge-conserving, variational, spatio-temporal discretization for the drift-kinetic Vlasov-Maxwell system, utilizing finite-elements for the electromagnetic fields and the particle-in-cell approach for the Vlasov distribution. The proposed scheme is fully electromagnetic, dealing with fields instead of potentials, and includes the effects of polarization and magnetization in the Gauss and Ampère-Maxwell laws, a consequence of reducing the full particle dynamics to drift-center dynamics. There is, however, no need to invert the Gauss law: it is satisfied automatically at every time-step as a result of a discrete Noether symmetry, and the electric field is updated directly from the Ampère-Maxwell equation. The method provides an update for the magnetic field that is fully explicit, involving only local operations. The update for particles is implicit for each particle individually, also leading to local operations only. The update for the electric field is linearly implicit due to the presence of a finite-element mass matrix and polarization and magnetization effects in the Ampère-Maxwell equation, hence involving a sparse matrix inversion once at every time step. Because the scheme deals with the electromagnetic fields and not the potentials, it also provides the first serious attempt at constructing a structure-preserving numerical scheme for the mixed kinetic-ion--drift-kinetic-electron Vlasov-Maxwell model. Consequently, the proposed method could be used to simulate electromagnetic turbulence in fusion experiments or space plasmas that exhibit a strong background magnetic field while retaining all of the ion physics, most of the necessary electron physics, yet eliminating perhaps the biggest obstacle in reaching macroscopic transport time scales in kinetic simulations, namely the electron cyclotron time scale.
arXiv comment15 pages
References in corpus (17)
- An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
- The Energy Conserving Particle-in-Cell Method
- GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
- Exactly Energy Conserving Semi-Implicit Particle in Cell Formulation
- Structure and structure-preserving algorithms for plasma physics
- Variational formulation of particle algorithms for kinetic plasma simulations
- Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
- An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm
- Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
- Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations
- A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations
- Finite-dimensional collisionless kinetic theory
- Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
- Variational principles for the guiding-center Vlasov-Maxwell equations
- Gauge-free electromagnetic gyrokinetic theory
- Projected Variational Integrators for Degenerate Lagrangian Systems
- Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation