An analysis of nonaxisymmetric E×B equilibrium flow in a crossed-field apparatus is made. The apparatus consists of a conducting circular-cylindrical cathode encompassed by either a corrugated conducting anode or by a periodically biased, circular-cylindrical wall. A uniform magnetic field is directed parallel to the cathode axis. With the aid of perturbation theory, the guiding-center approximation, and the assumption of a constant electron density in the electron layer, we determine equipotential surfaces, electron trajectories, and the corrugated boundary of the electron layer. An interesting result is the appearance of vortex structures in regions of negative potential near the cathode surface. The scaling properties of the width and potential depth of the vortex are studied for the small-amplitude corrugation regime. For sufficiently thin electron layers, results are shown to be applicable to relatively high-density regimes as well as to low-density regimes.
This paper presents exact analytic conditions for absolute instability in the cyclotron resonance maser for the case of a cold beam, lossless circular waveguide, and infinite interaction length in the axial direction. The conditions are expressed in terms of the parallel beam velocity, the applied magnetic field strength, and the strength of the coupling between the beam and waveguide modes. The results are applicable to both the gyrotron and cyclotron autoresonance maser operating regimes.
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