A theory of corrugated plasma resonators excitation by relativistic electron beams

Excitation of corrugated resonators with plasma filling with high-current relativistic electron beams is theoretically investigated. Considered is a case of a weak corrugated resonator, for which a problem can be solved analytically. The excitation conditions for a direct and a reverse waves, their frequencies and gains, as well as starting excitation currents of the resonator at a given value of the coefficient of wave reflection from the resonator face planes are found. The maximum efficiency of the generator is estimated. On the basis of the investigation of the obtained approximated dispersion relation, taking into account the first decelerated harmonic of proper electromagnetic waves, it is shown that in a corrugated infinite plasma waveguide, as well as in a smooth one there are E-waves of two types: high-frequency and low-frequency ones. Low-frequency waves are pure plasma ones and they are analogous to waves existing in the smooth waveguide. High-frequency E-waves in the corrugated waveguide in contrast to the smooth one are slowered down, and under the particular condition the phase velocity of these waves can become smaller than the longitudinal electron beam velocity. It is emphasized that in the corrugated waveguide simultaneous excitation of direct and reverse high-frequency E-waves can be obtained. In the case of an infinite wave-guide a wave with a greater increase increment would be practically excited, it is a direct wave, as a rule. Excitation of a reverse wave can be realized in a limited waveguide being a corrugated resonator. Although the starting current with the decrease of the corrugation depth increases, the generation efficiency considerably falls down. Therefore, the transition to systems with a very small corrugation depth is not very profitable, not to mention that it leads to a considerable increase of the optimum generator length