Asymptotic velocity of relativistic E × B drift

We have obtained the asymptotic velocity of a relativistic charged particle in static and uniform electric and magnetic fields with arbitrary orientations of the fields and with an arbitrary ratio of a = |E|/|B|, where the particle is assumed highly relativistic and has a constant velocity. The obtained solution corresponds to the relativistic E × B drift velocity of the guiding-center, which has features different from those of the non-relativistic drift velocity. The latter is given by vD/c = E × B/|B|2, but in the relativistic case, an additional drift motion exists in the direction that is perpendicular to both B and vD. The dependence of drift velocity on the angle between B and E is also modified substantially.