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In this paper, a comprehensive theoretical treatment is developed for backward wave oscillators composed of a relativistic electron beam guided by a strong magnetic field through a slow wave structure consisting of a cylindrical waveguide with a sinusoidally varying wall radius. This analysis, equally applicable to traveling wave tube operation, includes both a linearized theory of small-amplitude perturbations and numerical simulations of the saturated, large-amplitude operating regime. The variation of device operating characteristics with system parameters is examined in detail. Comparisons of the analytic and numerical results with experiments and additional calculations show excellent agreement and justify a high degree of confidence in the validity of the theory.

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Extraordinary-mode stability properties of relativistic non-neutral electron flow in a planar diode with applied magnetic field are investigated within the framework of the macroscopic cold-fluid-Maxwell equations. The eigenvalue equation is derived for flute perturbations (kz=0) about the general class of relativistic planar equilibria characterized by electron density profile n0b(x), sheared velocity profile V0y(x) =−cE0x(x)/B0z(x), and relativistic mass factor γ0b(x) =[1−E02x(x)/B02z(s)]−1/2. The full influence of equilibrium self-electric and self-magnetic fields is retained in the analysis, and the cathode is located at x=0 and the anode at x=d. The exact eigenvalue equation is simplified for low-frequency perturbations in the guiding-center limit of strongly magnetized electrons with m→0. In this regime, it is shown that (∂/∂x)[n0b(x)/γ0b(x)]≤0 over the interval 0≤x≤d is a sufficient condition for stability of the relativistic electron flow to extraordinary-mode perturbations. A specific example of stable oscillations [rectangular profile for n0b(x)/γ0b(x)] is analyzed in detail. Finally, the exact eigenvalue equation is solved numerically for a wide range of electron density corresponding to weak and strong instability driven by velocity shear with ∂V0y/∂x≠0.

experiment to realize the optical tristability in which sodium vapor is used as a dispersive medium. By filling He gas at pressure higher than 200 Torr as a buffer gas, y ab for D x line at 589.6 nm becomes larger than 2 GHz, 6 and we can neglect hole burning effect and hyperfine pumping especially for off-resonant light. Furthermore, the buffer gas mixes the excited hyperfine and Zeeman structure completely. Thus the situation is very close to the model which we have used in this paper. To satisfy the inequality (13), 2KL must be of the order of unity or larger, which can be achieved by choosing N~ 10 12 cm" 3 , L = 10 cm, and | A| = 30y a6 . Then the absorption loss 2aL is about 0.1 and will be neglected. The required optical power density of a cw dye laser isIn current electron and light-ion-driven inertial-confinement fusion schemes, transmission lines capable of carrying power densities of the order of 1 TW/cm 2 at electric field levels exceeding 5 MV/cm are required. 1 These stresses, far exceeding the standoff capabilities of conventional insulators, necessitate the use of a magnetic field applied perpendicularly to the electric field in a gap to prevent breakdown by electrons. Known as magnetic insulation, this method of breakdown inhibition also finds useful application in the production of intense ion beams in vacuum diodes, in relativistic magnetrons, and in multiple-stage linear accelerators for charge-neutralized ion beams. An examination of the linear stability of the magnetically insulated state is of interest in helping to determine, as a function of of the order of 10 mW/mm 2 . 985 (1976). system parameters, the length of transmission line over which breakdown should be inhibited (or the time duration of the insulation), the quality of an ion beam which passes through an insulated electron layer, or the linear startup state of a magnetron device. In this paper, some results of the first solution of a fully relativistic and electromagnetic treatment of the stability of the magnetically insulated Brillouin-, or laminar-, flow state 2 are presented. As the name implies, electrons emitted from a cathode into this state are confined to a sheath near the cathode in which they drift laminarly along equipotentials at the local, self-consistent EXB drift velocity (which is sheared monotonically).It is found that TM waves propagating along the direction of electron flow are unstable to pertur-Presented herein is a fully electromagnetic and relativistic stability analysis of the Brillouin-flow equilibrium for magnetic insulation in planar geometry. Instability of TM waves propagating in the direction of the sheared electron flow is found. This instability occurs at short wavelengths at frequencies above the cyclotron and plasma frequencies relevant to the system. It is found that relativistic effects can make the maximum instability growth rate normalized to the cyclotron frequency substantially lower than the nonrelativistic value (0.06).