“…Usually, following Komaki et al [9], planar-channeling RCE is treated in the ion rest frame (x, y, z) which x axis is directed along the beam and z axis is perpendicular to the channel. One of the results of the paper [8] is that RCE on a single (k, l) resonance can be most conveniently treated in a special coordinate system, where its X axis is determined by the Lorentz transformation of the corresponding harmonic of the field into its both scalar ϕ( r ′ , t ′ ) and vector A( r ′ , t ′ ) components in the ion rest frame while the Z axis remains perpendicular to the channeling plane. To show the main idea of [8] in this short presentation, we neglect here all effects of the vector potential induced in the ion rest frame and, using the dipole approximation for the electric field in this frame, take a projection of its vector E on the channeling plane for the direction of axis X.…”