High Order Explicit Lorentz Invariant Volume-preserving Algorithms for Relativistic Dynamics of Charged Particles

Abstract

Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct structure-preserving algorithms, but without exquisite considerations, it can easily break the Lorentz invariance of continuous systems. In this paper, we introduce a Lorentz invariant splitting technique to construct high order explicit Lorentz invariant volume-preserving algorithms (LIVPAs) for simulating charged particle dynamics. Using this method, long-term stable explicit LIVPAs with different orders are developed and their performances of Lorentz invariance and long-term stability are analyzed in detail.

References in corpus (15)

• A comprehensive comparison of relativistic particle integrators
• Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields
• Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system
• Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
• Explicit symplectic algorithms based on generating functions for charged particle dynamics
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields
• Formation of current singularity in a topologically constrained plasma
• Variational Integrators in Plasma Physics
• A Symplectic Multi-Particle Tracking Model for Self-Consistent Space-Charge Simulation
• Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics
• A Spectral Canonical Electrostatic Algorithm
• 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