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Recently, the validity of the guiding-center approach to model relativisticrunaway electrons in tokamaks has been challenged by full-orbit simulationsthat demonstrate the breakdown of the standard magnetic moment conservation. Inthis paper, we derive a new expression for the magnetic moment of relativisticrunaway electrons, which is conserved significantly better than the standardone. The new result includes one of the second-order corrections in thestandard guiding-center theory which, in case of runaway electrons with$p_{\parallel}\gg p_{\perp}$, can peculiarly be of the same order as thelowest-order term. The better conservation of the new magnetic moment alsoexplains the collisionless pitch-angle-scattering effect observed in full-orbitsimulations since it allows momentum transfer between the perpendicular andparallel directions when the runaway electron is accelerated by an electricfield. While the derivation of the second-order correction to the magneticmoment in general case would require the full extent of the relativisticsecond-order guiding-center theory, we exploit the Lie-perturbation method atthe limit $p_{\parallel}\gg p_{\perp}$ which simplifies the computationssignificantly. Consequently, we present the corresponding guiding-centerequations applicable to the highly relativistic runaway electrons.

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