Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Abstract

Since variational symplectic integrators for the guiding center was proposed [1,2], structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

References in corpus (16)

• On Landau damping
• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
• 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 high-order symplectic integrators for charged particles in general electromagnetic fields
• Explicit symplectic algorithms based on generating functions for charged particle dynamics
• Toroidal regularization of the guiding center Lagrangian
• Simulations of relativistic-quantum plasmas using real-time lattice scalar QED
• Slow manifold reduction for plasma science
• The geometric theory of charge conservation in particle-in-cell simulations
• Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics
• Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
• Guiding center dynamics as motion on a formal slow manifold in loop space
• Projected Variational Integrators for Degenerate Lagrangian Systems
• Constructing current singularity in a 3D line-tied plasma

Cited by in corpus (6)

• Hybrid simulation of energetic particles interacting with magnetohydrodynamics using a slow manifold algorithm and GPU acceleration
• Self-consistent simulation of resistive kink instabilities with runaway electrons
• Normal stability of slow manifolds in nearly-periodic Hamiltonian systems
• Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
• Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
• Verification and validation of gyrokinetic and kinetic-MHD simulations for internal kink instability in DIII-D tokamak