Large-signal field analysis of an O-type travelling-wave amplifier. Part 1: theory

A rigorous method of analysing the large-signal behaviour of a travelling-wave amplifier is presented, starting from the Maxwell equations in the Eulerian form and the electron ballistic equation in the Lagrangian form. The key step in the method is a representation of the field components as functionals of the electron-arrival time through a Green´s function sequence for the slow-wave circuit. Substitution of this functional representation for the axial electric field component into the electron ballistic equation reduces the latter to a fixed-point problem for an operator in an appropriate function space. The fixed point, and therefore the solution for the electron-arrival time and hence the solution for the electromagnetic field components, can be obtained by standard successive approximation techniques. The calculation of the TWT gain, comparison of the results of the present theory with those of the existing ones etc., on the basis of such a successive approximation solution for the field components, will be deferred to a later paper.