Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering

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 with p∥>>⊥, 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∥>>⊥, 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. In conclusion, 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∥Gtp⊥ which simplifies the computations significantly. Consequently, we present the corresponding guiding-center equations applicable to runaway electrons.