  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.
