Guiding-centre orbits for particles in cross-field devices

The motion of a particle driven by a slow RF wave inside crossed electrostatic and magnetostatic fields is examined. A time-scale separation exists in the synchronous frame, moving at the slow-wave phase velocity, where all fields appear static in time and the cyclotron motion is much faster than the guidingcentre drift. The averaging of the periodic gyromotion is performed systematically with canonical transformations up to second order in the smallwave amplitude. The first-order guiding-centre drift follows the equipotential surfaces of the transformed electric field. The second-order effects, due to the field-line curvature, and/or the nonlinear variation in the wave phase velocity, cause departures from the parapotential flow. The topology of the trajectories depends on the departure of the drift velocity from synchronism with the wave. Various flow topologies corresponding to different values of the control parameters are examined.