Investigation of the series determining the space charge field in the nonlinear analytical theory of bunching

A system of equations describing nonlinear bunching in a multiresonator klystron is derived. The derivation is based on the expansion of the variable component of the electron transit angle in a Fourier series according to the time of transit into the drift space. A method for improving the convergence of series determining the space charge field is proposed, and the application of the improved series is illustrated by the example of a double-resonator klystron.