Excitation of monotron oscillations in overmoded klystrons

Summary form only given, as follows. A general method for calculation of the start currents of modes of overmoded cavities in klystrons is described. The method is applicable to klystrons with an arbitraly geometry of electron beams and cavities with large transverse andior axial dimensions. When these dimensions are on the order of the wavelength or larger, the spectrum of mode frequencies is rather dense. Therefore, in addition to the desired mode, electrons can excite some parasitic modes. The conditions of self-excitation of various modes are formulated and applied to closed (gridded) and open (non-gridded) cavities. It is assumed that in closed cavities the field distribution can be described by sinusoidal functions, while for describing the field distribution in open cavities Hermite polynomials are used. In both cases, the coupling coefficients of the beam to the modes and corresponding real part of the gain function,which is analogous to the beam loading conductance taken with an opposite sign, can be calculated analytically. The formalism, in particular, is of immediate interest for sheet beam klystrons. As an example it was applied to one cavity of a sheet beam klystron. The cavity is of the extended interaction type, with 3 elements.Initial calculations with the real distribution indicate that the start current of the real cavity is higher than that evaluated with the use Self-Modulation and Chaos in Delayed-Feedback Klystron Oscillators.