DENSITY PROFILE AND CURRENT FLOW IN A CROSSED-FIELD AMPLIFIER

Assuming tile averaged (background) electron distribution in a crossed -field device, such as a magnetron or crossed-field amplifier, to be s lowly varying between the cathode and the anode, we develop a WKB appr oximation for the cold-fluid plasma equations of a planar magnetron. I n this approximation, we can give general expressions for the solution of linearized, high-frequency oscillations in such a device in terms of two integrals. Assuming also that the high-frequency wave in the sl ow-wave structure drives the response in the electron plasma, we are t hen able to show that the current drawn by a crossed-field device will be proportional to the power propagating in the slow-wave structure. Thus the device will operate as a linear amplifier. we also show, in t he same approximation, that tile averaged electron sheath that forms w hen tile device is operating is independent of the current being drawn . Thus the current will not be limited by the sheath, but only by the ability of the cathode to emit electrons. In tile process, we also obt ain expressions for the linear growth rate and the value of the quasil inear diffusion coefficient at the diocotron resonance,in terms of par ameters of the background electron sheath.