Invited paper. A partly self–consistent theory of the gyrotron

Current theories on Single Cavity gyrotron oscillators assume a prescribed electro magnetic field, while travelling-wave amplifiers are treated in small signal without, space-charge. This paper describes theoretical work in progress to extend the existing theories. first it is shown that although space-charge mid electron beam fields (indistinguishable in a. relativistic theory) play a marginal role in present American or French gyrotrons, the limits of tube performance may ultimately be imposed by these effects. A short review of the literature on space-charge in gyrotrons is given Then a linear space-charge theory valid for wide electron beams is developed, and it is shown that unstable travelling spaec-charge waves exist in gyrotrons as in classical crossed-field devices. Values of gain parameters in TW amplifiers are given. Finally a set of circuit equations, similar to transmission line equations, is given that can be used to take beam fields into account either for oscillators or amplifiers. some calculations with a single mode lead to increased values of the efficiency, due to inter, action with the field propagating in the output horn.