Channeling continuum model derivation by method of averaging

Abstract
Derivations of the axial- and planar-channeling continuum models from the perfect-string and perfect-plane models by the Krylov-Bogoliubov method of averaging are discussed. For the first time, error bounds are obtained relating the perfect crystal trajectories to the continuum-model trajectories. Details are presented for the axial case, because this case is easier to treat and the generalization to planes is straightforward.