The role of magnetic moment in the collisionless pitch-angle scattering of runaway electrons

TL;DR

This paper derives a new, more accurate expression for the magnetic moment of relativistic runaway electrons, improving modeling of their collisionless pitch-angle scattering in tokamaks by including second-order corrections.

Contribution

It introduces a second-order correction to the magnetic moment expression, enhancing the guiding-center theory for relativistic runaway electrons with high parallel momentum.

Findings

New magnetic moment expression conserves better than standard.

Explains collisionless pitch-angle scattering observed in simulations.

Provides simplified guiding-center equations for highly relativistic electrons.

Abstract

Recently, the validity of the guiding-center approach to model relativistic runaway electrons in tokamaks has been challenged by full-orbit simulations that demonstrate the breakdown of the standard magnetic moment conservation. In this paper, we derive a new expression for the magnetic moment of relativistic runaway electrons, which is conserved significantly better than the standard one. The new result includes one of the second-order corrections in the standard guiding-center theory which, in case of runaway electrons with $p_{\parallel}\gg p_{\perp}$, can peculiarly be of the same order as the lowest-order term. The better conservation of the new magnetic moment also explains the collisionless pitch-angle-scattering effect observed in full-orbit simulations since it allows momentum transfer between the perpendicular and parallel directions when the runaway electron is accelerated by an electric field. While the derivation of the second-order correction to the magnetic moment in general case would require the full extent of the relativistic second-order guiding-center theory, we exploit the Lie-perturbation method at the limit $p_{\parallel}\gg p_{\perp}$ which simplifies the computations significantly. Consequently, we present the corresponding guiding-center equations applicable to the highly relativistic runaway electrons.