A method for the calculation of electron-beam contours in axially symmetrical magnetic fields, including the gun region

The focusing of high-density electron beams in axially symmetrical magnetic fields on the basis of laminar flow is calculated using an approximation method operating with power series. The method allows for any desired shape of the axial magnetic field, and includes the gun region, where there is an additional electric field. Brillouin flow as well as partially confined flow with a finite magnetic flux threading the cathode can be handled. One of the main results is the evidence that the different parameters, e.g. cathode diameter and rate of increase of the magnetic field, must not be chosen arbitrarily, since they depend very much on each other. The method is comparatively simple and well suited to gun design under various conditions.