Particle motion and drift in non-uniform electric fields

Abstract

This paper analyzes the two-dimensional motion of a charged particle in constant mutually perpendicular electric and magnetic fields. The magnetic field is assumed to be uniform, and the electric field components are assumed to be linear functions of the Cartesian coordinates. Under these assumptions, the equations of particle motion can be solved analytically. This solution is used to study the stability of particle motion and to assess the accuracy of the guiding center approximation in the presence of electric field gradients. It is well known that if the gradient of a one-dimensional electric field is sufficiently large, the motion of the charged particles becomes unstable and the particles are effectively energized by the electric field. This paper, however, demonstrates that the instability threshold depends on the spatial derivatives of both electric field components and is, under certain conditions, very sensitive to both. The analytical solution is averaged over the gyroperiod to derive simple expressions for the drift speed and the position of the gyrocenter, which explicitly account for the electric field gradient. The results of this averaging are used to develop equations for tracing the particle gyrocenter location, which incorporate the effects of non-uniformity of the electric field. These equations are shown to be noticeably more accurate than those based on the standard E × B drift velocity, which is exact only for uniform electric and magnetic fields. Simple expressions for the local errors in the E × B drift velocity are also derived, which arise from the electric field gradients.