Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system

Abstract

Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretizing its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g., $10^9$, degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.

Revised submission with more detailed derivation and a new application. 16 pages and 6 figures

Cited by in corpus (48)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Structure and structure-preserving algorithms for plasma physics
• Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
• Explicit symplectic algorithms based on generating functions for charged particle dynamics
• Hamiltonian integration methods for Vlasov-Maxwell equations
• Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
• Metriplectic Integrators for the Landau Collision Operator
• Finite-dimensional collisionless kinetic theory
• A quantum-inspired method for solving the Vlasov-Poisson equations
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm
• Conservative discretization of the Landau collision integral
• High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields
• 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
• Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
• Simulations of relativistic-quantum plasmas using real-time lattice scalar QED
• A Symplectic Multi-Particle Tracking Model for Self-Consistent Space-Charge Simulation
• Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger-Maxwell systems
• The geometric theory of charge conservation in particle-in-cell simulations
• Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
• Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics
• Multi-scale Full-orbit Analysis on Phase-space Behavior of Runaway Electrons in Tokamak Fields with Synchrotron Radiation
• A symplectic particle-in-cell model for space-charge beam dynamics simulation
• Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of Charged Particles
• Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field
• Symplectic model reduction methods for the Vlasov equation
• Hamiltonian Particle-in-Cell methods for Vlasov-Poisson equations
• Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System
• Quasi-Helmholtz Decomposition, Gauss' Laws and Charge Conservation for Finite Element Particle-in-Cell
• The Accurate Particle Tracer Code
• High Order Explicit Lorentz Invariant Volume-preserving Algorithms for Relativistic Dynamics of Charged Particles
• Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods
• Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
• Reducing Noise for PIC Simulations Using Kernel Density Estimation Algorithm
• Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes
• Multispecies structure-preserving particle discretization of the Landau collision operator
• Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
• A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
• Time simulation of the nonlinear wave-particle interaction in meters long traveling-wave tubes
• Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics
• Meshless Methods for Magnetohydrodynamics with Vector Potential
• Variational Schemes and Geometric Simulations for a Hydrodynamic-Electrodynamic Model of Surface Plasmon Polaritons
• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe
• A structure-preserving finite element framework for the Vlasov-Maxwell system
• Symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects
• Symmetries and Local Conservation Laws of Variational Schemes for the Surface Plasmon Polaritons
• Discrete Gravity with Local Lorentz Invariance