Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation

Abstract

We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low's Lagrangian or on a Hamiltonian with a non-canonical Poisson bracket. The useful property of this variational principle is that it allows independent transformations of particle coordinates and velocities, i.e., transformations in particle phase space. With such transformations, a finite degree-of-freedom drift-kinetic action is obtained through time-averaging of the finite degree-of-freedom fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads to a self-consistent, macro-particles and fields numerical model. Since the computational particles utilize only guiding center coordinates and velocities, there is a large computational advantage in the time integration part of the algorithm. Numerical comparison between the time-averaged fully-kinetic and drift-kinetic charge and current, deposited on a computational grid, offers insight into the range of validity of the model. Being based on a variational principle, the algorithm respects the energy conserving property of the underlying continuous system. The development in this paper serves to further emphasize the advantages of using variational approaches in plasma particle simulations.

arXiv comment8 pages, 3 figures; this version with minor modifications

References in corpus (6)

• An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
• The Energy Conserving Particle-in-Cell Method
• Variational formulation of particle algorithms for kinetic plasma simulations
• Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
• Variational Integrators in Plasma Physics
• Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations

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• Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of Charged Particles
• Hamiltonian structure of the guiding center plasma model
• A low-frequency variational model for energetic particle effects in the pressure-coupling scheme
• Variational mean-fluctuation splitting and drift-fluid models
• Charge-conserving, variational particle-in-cell method for the drift-kinetic Vlasov-Maxwell system