The theory of the steady-state operational regime of a high-voltage magnetron diode

The determination of the parameters for a spinning Brillouin flow is discussed. A 'coaxial diode' with a longitudinal magnetic field is considered, taking into account the condition for the motion of the electrons as a balance of radial forces. This balance condition makes it possible to obtain a suitable equation for the potential within the electron layer, and equations are derived for the unambiguous determination of the relativistic Brillouin flow. For the further study of the steady-state regime, it is necessary to solve a system of three equations numerically. However, some interesting results can be obtained analytically. Formulas are presented which, under certain conditions, provide a good approximation to the correct values. The electron density throughout the layer is shown in graphs along with the variation of the potential in the cathode-anode space, and the dependence of the basic parameters on the external magnetic field. It is found that the diode geometry has a significant effect on the parameters of the steady-state electron flow.