Electrodynamics of particle or dust in periodic electric cusps with electric mirrors and its applications to planetary dust layers or rings and electric undulators

Summary form only given. Electrodynamics of particle or dust in an electric cusp (Kikuchi, 1998) is extended to the case of a longitudinal sequence of horizontal dipoles or double layers with vertically periodic electric-cusps formed by a cascade of quadrupoles. When a particle, uncharged or charged, is entering the first quadrupole-domain, it will be decelerated until it reaches the cusp centre. As soon as the particle passes through the cusp centre, it will be rapidly accelerated until it enters the next quadrupole-domain, repeating deceleration and acceleration alternately as its sequence lasts, finally being decelerated after going out of the last one. Particle trajectory and velocity for various cases above are obtained analytically and numerically with particular reference to ´electric undulators´ and ´planetary dust layer and ring formation´, taking into account gravity and horizontal electrification of planetary clouds.