Guiding-center transformation of the radiation-reaction force in a nonuniform magnetic field

TL;DR

This paper derives a guiding-center transformation for the radiation-reaction force acting on charged particles in nonuniform magnetic fields, enabling simplified analysis of particle dynamics affected by radiation losses in plasma physics.

Contribution

It introduces a novel guiding-center transformation of the radiation-reaction force applicable to nonuniform magnetic fields using Lie-transform and Poisson bracket methods.

Findings

Transformation valid when gyroradius is much smaller than magnetic field nonuniformity scale

Applicable to planetary magnetic fields and magnetic confinement fusion plasmas

Facilitates kinetic modeling of radiation effects on charged particle dynamics

Abstract

In this paper, we present the guiding-center transformation of the radiation-reaction force of a classical point charge traveling in a nonuniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field nonuniformity length scale, so that the guiding-center Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation-reaction force is obtained with the Poisson bracket formalism originally introduced by [A. J. Brizard, Phys. Plasmas 11 4429 (2004)], where it was used to eliminate the fast gyromotion from the Fokker-Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-center radiation-reaction force include tracing of charged particle orbits in complex magnetic fields as well as kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g., for runaway electron dynamics in tokamaks.