Synthesis of electrodes for axisymmetric systems

The electrodes needed to extract a tubular stream of charged particles from a conical cathode in an axial magnetic field are found in two stages, by a development of the methods of Dryden and of Harker. These methods have been extended by the use of spherical co-ordinates and of iteration, to include all contributions to space-charge density where the trajectories cross one another. Examples are given of designs in which the electric field at the cathode is zero, corresponding to limitation of the emitted current by space charge rather than by the cathode temperature.