Brillouin flow in a magnetron diode as the kinetic model limit

Two classes of approaches that have received the most attention to describe the important space charge dynamics in a magnetron are Brillouin flow and the double-stream kinetic model. It is supposed that in the first case electrons move parallel to the electrode surfaces and in the second case they move in cycloidal orbits performing a single turn. Precise analysis of electron dynamics in fully selfconsistent kinetic equilibria in a smooth-bore magnetron shows that for a given external magnetic field and a voltage there exists a multiplicity of natural equilibrium states, differing as to structure of electron trajectories and emission current density. The value of emission current density differs from one to another type of equilibrium and can aspire to zero under the same condition of space charge limited flow due to a large number of revolutions of electrons around the cathode. The greater the number of revolutions the closer the main parameters of the kinetic flow to the Brillouin one. The comparison of analytical calculations and the results of computer simulation of transient processes of Brillouin flow formation from initially kinetic flow are presented