A Magnetic Velocity Verlet Method

TL;DR

This paper introduces a modified velocity Verlet method tailored for charged particle motion in magnetic fields, improving energy and magnetic moment conservation over traditional methods, and demonstrates its effectiveness through various magnetic field scenarios.

Contribution

It presents a novel magnetic velocity Verlet method that better conserves energy and magnetic moments in charged particle simulations compared to existing algorithms.

Findings

Enhanced energy conservation in magnetic particle simulations

Accurate trajectory generation in magnetic mirror and dipolar fields

Successful modeling of mirror motion with magnetic monopoles

Abstract

We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup, and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.