Theory of pulse–particle interaction in one dimension

Abstract

Interaction of charged particles with various types of one-dimensional pulses is investigated systematically. Gaussian pulses of arbitrary velocity and polarization, both electrostatic and electromagnetic, are considered. The pulses range from ordinary wave packets to impulses. Analytic expressions are obtained for velocities of charged particles interacting with those traveling pulses, and are compared with numerical counterparts. Dependence of the interaction on pulse size, initial particle velocity, and external magnetic field is investigated. For many nonrelativistic pulses traveling along an external magnetic field, the interaction can be divided into two types, i.e., transit-time acceleration and reflection in the wave frame. In the absence of the magnetic field, transit-time acceleration is significant only for impulses with sizes of less than one wavelength. On the other hand, with a magnetic field (transit-time) cyclotron acceleration becomes possible for pulses of sizes greater than one wavelength. With larger amplitudes the wave-frame reflection becomes increasingly important, typically occurring at the pulse head or tail. However, it tends to be suppressed by external magnetic fields. Compact expressions are obtained for final velocities of the particles for the two types of interaction. Both types of acceleration mechanism may be important in dissipating relatively large-amplitude waves.