Trajectories of Charged Particles in Radial Electric and Uniform Axial Magnetic Fields

The trajectories of charged particles were determined over a wide range of parameters characterizing the motion in cylindrical low-pressure gaseous discharges and plasma-heating devices which have steady radial electric fields E perpendicular to uniform steady magnetic flelds B. Three radial distributions of E were considered: E ¿ r, constant E, and E ¿ r-1. These distributions are characteristic of the fields measured in a modified Penning discharge, in two NASA Lewis Bum-out-type plasma-heating devices, and that estimated for the Ixion device, respectively. The plasmas of such ¿ × B¿ devices are often characterized by their high ratios of drift energy to mean particle energy, finite gyroradius effects, and sizeable electric field changes in the distance covered by a cyclotron radius. Such particle motions are not amenable to simple guiding center theory. From numerical calculations of the actual trajectories it was concluded that the differences between cyclotron frequency and qB/m, and between azimuthal drift and a guiding center approximation (including ¿ × B¿ and centrifugal force terms) are appreciable. The net cyclotron motion obtained by subtracting the actual drift from the trajectories, however, has a nearly circular contour over which the speed is quite constant.