Modeling of an A6 relativistic magnetron with analytics and numerics



D. J. Kaup


Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Phys. Scr.


Physics, Multidisciplinary


We report on recent results in our studies of relativistic magnetrons, in regard to their stability at high power levels. Experimentally, these devices have proven to be very difficult to operate, typically cutting off too quickly after they are initialized, and therefore not delivering the power levels expected. This analysis is based on our model of a crossed-field device, consisting only of its two dominant modes, a DC background and an RF oscillating mode. This approach has produced generally quantitatively correct values for the operating regime and major features of nonrelativistic devices. It has also predicted that such devices would have an operating range localized within about 20% of the Hartree voltage (the lowest voltage at which the device would operate), in agreement with generally known experimental results. It has also indicated the reason for ultralow noise operation is related to increased vertical electron velocities near the cathode. Here we have performed a fully electromagnetic, relativistic analysis of a magnetron of the A6 cylindrical configuration. We will also demonstrate that when the device should generate maximum power, it enters a regime where the DC background could become potentially unstable. In particular, we had earlier shown that when a nonrelativistic planar device enters the saturation regime (which is after the initial growth ceases and when the device steadily delivers power), that the DC electron density distribution could become unstable if the vertical DC velocity would ever become equal to the magnitude of the vertical RF velocity. Basically what happens is that the electrons would not be able to execute more than a couple of gyrations before striking the anode and thereby not have time to fully synchronize with the RF wave in the slow-wave structure before that, with the result that coherence would be lost, and chaotic motion would tend to ensue. Although that prediction was made for a nonrelativistic planar device, the same general principle can also be expected to generally hold also for a relativistic cylindrical device. And perhaps with an even slightly lower threshold, due to the centrifugal force present in a cylindrical device, which is absent in a planar device. In any case, we find that for the highest power levels of our model of the A6, the DC vertical velocity does become just less than, but definitely on the order of the magnitude of the vertical RF velocity. Consequently, any localized surge in the currents near the cathode, could easily destroy the smooth upward flow of the electrons, drive the DC background unstable, and thereby shut down the operation of the device.

Journal Title

Physica Scripta



Publication Date


Document Type




First Page


Last Page


WOS Identifier