Self-excitation conditions in overmoded klystrons

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 arbitrary geometry of electron beams and cavities with large transverse and/or 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.