Initiation and Stationary Operating States in a Crossed-Field Vacuum Electron Device

摘要

Previous studies of crossed-field electron vacuum devices, such as magnetrons and crossed-field amplifiers (CFA), have centered on their initial growth, as an indication of their operating modes. In such an analysis, one assumes a growth rate, and solves the equations for the density profile, the operating frequency, and the growth rate. What one obtains here are the conditions for the initial operation of the device. However, eventually the RF fields will have saturated, and the device then will enter into either a stationary operating regime, or some other mode, which could in general be some non-operating mode. To study this regime of operation, we return to the classical planar magnetron equations and study what the form of the solution will be for these stationary solutions. What we find is that upon saturation, as the growth rate vanishes, its effect is replaced by second-order velocity terms, and in particular, the second-order vertical velocity. What we will do here is to derive and present the magnetron equations when the growth rate vanishes, and discuss the solutions of the RF equations about the resonance points. Lastly, we shall consider what implications these results may have for relativistic and nonrelativistic crossed-field devices.