Motion of relativistic particles in axially symmetric and perturbed magnetic fields in a tokamak

Abstract

An extensive comparison is given between an analytical theory for the computations of particle orbits of relativistic runaway electrons [M. de Rover et al., Phys. Plasmas 3, 4468 (1996)], and numerical simulations. A new numerical scheme is used for the computer simulations of guiding center orbits. Furthermore, simulations of the full particle motion, including the gyration are performed to check the guiding center approximation. The behavior of drift surfaces and particle orbits in axially symmetric magnetic fields, as predicted in the companion paper are confirmed. This includes the smaller minor radius of a drift surface compared to a magnetic flux surface with identical rotational transform, and the decrease of the minor radius of a drift surface with increasing particle energy. Magnetic islands and drift islands appear when the axial symmetry of the magnetic field is broken by harmonic perturbations. In the numerical simulations the amplitudes of the perturbations have been chosen to increase towards the plasma edge. The analytic theory gave predictions of the width of the drift islands that are in good agreement with the numerical simulations. When overlap of the magnetic perturbations introduces stochasticity, the Hamiltonian theory shows that drift islands can exist in the region of stochastic magnetic field lines, which is also confirmed by the numerical simulations.