Large-signal field analysis of an O-type travelling-wave amplifier. I - Theory

A rigorous method of analyzing the large-signal behavior 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 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.