Shadowing of the operating mode by sidebands in gyrotrons with diode-type electron guns

In gyrotrons operating in high-order modes, during the startup process, the shadowing of the operating mode by two sidebands may take place. By "shadowing,"we mean the situation when, during the voltage rise, one of the parasitic modes is excited first, and this excitation prevents the excitation of the desired mode. Then, the oscillations of the first parasitic mode, whose frequency is higher than the frequency of the desired operating mode, can be replaced by excitation of the second parasitic mode, whose frequency is lower than the operating one. As a result, the desired mode remains in the "shadow"of these parasitic modes and is never excited. This paper describes such effect in gyrotrons with diode-type electron guns. This paper consists of two parts. First, the problem is studied in a generalized approach, which means that the results are valid to gyrotrons operating at arbitrary voltages and in any modes. By using this approach, it is possible to determine the critical density of the mode spectrum, above which the shadowing occurs. This study is carried out for the cases when the interaction between modes is synchronous and when it is nonsynchronous. Second, this paper contains the analysis of a typical Megawatt-class gyrotron with a diode-type electron gun. It is studied whether the moving of this gyrotron to operating in higher-order modes will lead to the shadowing of the desired mode or other, more complicated, dynamic, and/or stochastic processes will take place.