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

TL;DR

This paper introduces a new class of structure-preserving geometric algorithms for guiding center dynamics based on the slow manifolds of the classical Pauli particle, offering improved stability and accuracy in plasma physics simulations.

Contribution

It reveals that the classical Pauli Hamiltonian can be used to develop stable geometric algorithms for guiding center dynamics, overcoming previous issues with parasitic modes.

Findings

Algorithms exhibit long-term stability and accuracy.

Applicable to other degenerate Lagrangians.

Reveals classical Pauli Hamiltonian's utility in plasma physics.

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.