The Brillouin flow in a smooth-bore magnetron fed by split cathode

Explosive emission from an axial cathode of a relativistic magnetron produces plasma, the radial expansion of which can cause pulse shortening. In a split cathode fed magnetron, the electron source and its explosive plasma are outside the space where the high power microwave producing interaction occurs. This electron source is a longitudinal annular electron column expanding radially. This expansion simulates the radial emission from an axial cathode. A mathematical model and numerical simulations are presented which enable to calculate the parameters of this electron column, its density, angular velocity, and potential distributions. The Hull Cutoff and Buneman-Hartree modified conditions applicable to the split cathode magnetron are formulated.