Hamiltonian guiding center drift orbit calculation for plasmas of arbitrary cross section

TLDR

The authors develop a Hamiltonian guiding center drift orbit formalism that enables efficient calculation of particle trajectories in arbitrary magnetic field configurations and use it to study trapped particle precession and fishbone‑associated drift pumping. The formalism assumes the magnetic field is a small perturbation from a zero‑order equilibrium field with magnetic surfaces, which can be modeled analytically or from equilibrium codes, and a numerical code based on this formalism is used to study particle orbits in circular and bean‑shaped tokamak configurations. Finite banana‑width corrections to the toroidal precession rate are derived, and the bounce‑averaged trapped particle motion is expressed in Hamiltonian form.

Abstract

A Hamiltonian guiding center drift orbit formalism is developed which permits the efficient calculation of particle trajectories in magnetic field configurations of arbitrary cross section with arbitrary plasma β. The magnetic field is assumed to be a small perturbation from a zero-order ‘‘equilibrium’’ field possessing magnetic surfaces. The equilibrium field, possessing helical or toroidal symmetry, can be modeled analytically or obtained numerically from equilibrium codes. The formalism is used to study trapped particle precession. Finite banana width corrections to the toroidal precession rate are derived, and the bounce averaged trapped particle motion is expressed in Hamiltonian form. Particle drift-pumping associated with the ‘‘fishbone’’ oscillation is investigated. A numerical code based on the formalism is used to study particle orbits in circular and bean-shaped tokamak configurations.