FIG.38 (a) Potential grating with a

FIG.38 (a) Potential grating with a cyclotron orbit superimposed. When the electron is close to the two extremal points Y ± lcycl, the guiding center at Y acquires an E × B drift in the direction of the arrows. (The drift along nonextremal parts of the orbit averages out, approximately.) A resonance occurs if the drift at one extremal point reinforces the drift at the other, as shown. (b) Numerically calculated trajectories for a sinusoidal potential (ǫ = 0.015). The horizontal lines are equipotentials at integer y/a. On resonance (2lcycl/a = 6.25) the guiding center drift is maximal; off resonance (2lcycl/a = 5.75) the drift is negligible. Taken from C. W. J. Beenakker, Phys. Rev. Lett. 62, 2020 (1989). FIG.39 Energy-orbit center phase space. The two parabolas divide the space into four regions, which correspond to different types of classical trajectories in a magnetic field (clockwise from left: skipping orbits on one edge, traversing trajectories, skipping orbits on the other edge, and cyclotron orbits). The shaded region is forbidden. The region at the upper center contains traversing trajectories moving in both directions, but only one region is shown for clarity. Taken from C. W. J. Beenakker et al., Superlattices and Microstructures 5, 127 (1989).