Acceleration of particles in a constant magnetic field and an electric field perpendicular to it, increasing with time

Abstract

The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.