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We solve the problem of the electron beam current in a planar two-electrode gun with a moving magnetically insulated edge cathode under conditions of unbounded emissivity of the cathode edge. Current-voltage characteristics of the systems with both stationary and moving cathodes are compared. The dependences of the relative difference of the currents and electron motion energy on the accelerating voltage at different velocities of the cathode motion are found for the systems with stationary and moving cathodes. It is shown that the motion of the emitting edge with velocities exceeding 10 8 cm/s can change significantly the parameters of the electron beams in the guns with an accelerating voltage of up to 0.5 MV. The found relationships can be used as the basis for additional tools of diagnostics of the processes in the near-cathode plasma, and can be used approximately to describe moving virtual cathodes.Current characteristics of explosive-emission electron guns are calculated usually by the formulas obtained for the stationary systems, in which the motion of the emitting cathode plasma is not taken into account [1,2]. However, since the velocity of the emission-surface motion can reach rather high values (V 0 > 10 7 cm/s), the assumption of stationarity needs to be justified. For this purpose, this paper compares the current-voltage characteristics of the system with a flat stationary edge-type cathode and the system with a cathode which moves between two perfectly conducting planes along the trajectory of the beam electrons (Fig. 1). It is assumed that (i) the guiding magnetic field H 0 is uniform and so strong that one can neglect the transverse electron motion (V ⊥ = 0);(ii) the emissivity of the cathode edge is infinitely high; (iii) the beam is thin-walled, ribbon, and located in the symmetry plane, i.e., at the equal distances a from the bounding planes, whose potentials with respect to the cathode are identical and equal to U ;(iv) at a sufficient distance from the cathode edge, the beam passes into a uniform state, and the system is unbounded in the direction of the z axis.In the system of coordinates, which co-moves with the cathode, the dependence of the beam current I f on the accelerating voltage U is determined by the formulas [2]

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Beginning with 2005, the International Science and Technology Center (ISTC) funded a research program (grant No. 3169) for development of Ka-band gyroklystrons operating at combinations of high order modes. A number of versions differing in RF inputs and in sequences of operating modes have been tested at microsecond pulses [1,2]. In particular [2], a 35.4 GHz gyroklystron with the output rotating mode TE73 delivered 15 MW pulses with 33% efficiency and 30 dB gain.One of further modifications of the existing configuration is planned to operate at sequences of rotating modes with high azimuthal indexes m >> 1 and the radial index equal to 1. Operation at such whispering gallery modes would allow to expand the RF amplification band and approximate the gyro-klystron to a gyro-twystron.In such an amplifier, the electron-beam-modulation section is expedient to be fed with a wave arriving from a waveguide being coaxial relative to the tube axis [3] (Fig. 1). The drive RF signal would be injected to the structure from a horn (Fig. 2). In this case the azimuthal index m h of the excited coaxial waveguide mode would be excessively high; and to convert this mode into the counter-rotating operating mode with azimuthal index m, the inner wall of the coaxial waveguide would be corrugated with azimuthal index h m m m The above approach was used to preliminary design a 35.4 GHz gyro-twystron to operate at a sequence of TE modes with the common azimuthal index equal to 7. The junction between the feeding coaxial waveguide and the electron beam modulating section (Fig. 3) By analogy with present-day free-running gyromonotrons, future gyro-twystrons might operate at modes with azimuthal indexes up to 20-30.