Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy

TL;DR

This paper develops a criterion to determine when guiding-centre or full-orbit simulations are appropriate in complex 3D magnetic geometries, and demonstrates its application to tokamak and stellarator plasmas, improving simulation accuracy.

Contribution

It introduces a general criterion for guiding-centre accuracy in 3D magnetic fields, including effects of currents and shear, and shows how to implement it for switching between simulation models.

Findings

The criterion accurately predicts guiding-centre validity in complex geometries.

Full-orbit simulations reveal helical drift surfaces of fast ions in kinked equilibria.

Application to MAST plasma explains off-axis fast particle redistribution.

Abstract

To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates, and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (Mega Amp Spherical Tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation $\vec{B}(x,y,z) = B_0 [\sin(kx) \vec{e_y} + \cos(kx)\vec{e_z}]$, for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of NBI fast particles in the presence of MAST Long-Lived Modes (LLM).