Finite-dimensional collisionless kinetic theory

Abstract

A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.

12 pages, 2 columns. V2 includes funding acknowledgments

References in corpus (6)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Effects of the $g$-factor in semi-classical kinetic plasma theory
• A general theory for gauge-free lifting
• Second order Gyrokinetic theory for Particle-In-Cell codes
• Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
• Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation

Cited by in corpus (25)

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• Structure and structure-preserving algorithms for plasma physics
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• Explicit Structure-Preserving Geometric Particle-in-Cell Algorithm in Curvilinear Orthogonal Coordinate Systems and Its Applications to Whole-Device 6D Kinetic Simulations of Tokamak Physics
• Detection and Prediction of Equilibrium States in Kinetic Plasma Simulations via Mode Tracking using Reduced-Order Dynamic Mode Decomposition
• Gauge-free electromagnetic gyrokinetic theory
• Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
• Hamiltonian Particle-in-Cell methods for Vlasov-Poisson equations
• Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System
• Energy and momentum conservation in the Euler-Poincaré formulation of local Vlasov-Maxwell-type systems
• Quasi-Helmholtz Decomposition, Gauss' Laws and Charge Conservation for Finite Element Particle-in-Cell
• Hamiltonian structure of the guiding center plasma model
• Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes
• Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
• Collisional Gyrokinetics Teases the Existence of Metriplectic Reduction
• Accelerating Particle-in-Cell Kinetic Plasma Simulations via Reduced-Order Modeling of Space-Charge Dynamics using Dynamic Mode Decomposition
• Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold
• A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
• Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
• Towards a classification of bifurcations in Vlasov equations
• Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations
• Charge-conserving, variational particle-in-cell method for the drift-kinetic Vlasov-Maxwell system
• Improved accuracy in degenerate variational integrators for guiding center and magnetic field line flow