The two-dimensional mathematical model of electron interaction with UHF field in a magnetron and high-voltage UHF oscillations breakdown

The described model does not contain any suppositions about the form of the electron spike, since this form is defined by the solution of strict equations. Both in the model and in real magnetrons the form of the electron spike and all the electron characteristics in some regimes largely depend on the emission characteristics of the cathode, in particular, on the current of the secondary electron emission. In a two-dimensional model an adequate setting of the coefficient of the secondary electron emission presents a certain difficulty, in particular, because in real magnetrons the energy of the electrons bombarding the cathode may considerably depend on their axial velocity. Another difficult problem consists in defining an adequate bombardment energy of spiral cathodes often used in magnetrons since, strictly speaking, it requires a three-dimensional solution