Theory of the high-power magnetron magnetron with intense electron flow

The magnetron has attracted much attention lately as a means of efficiently generating high-power electromagnetic radiation. Although there are successful applications of the magnetron, including the microwave oven, the theory of the magnetron is very primitive and ad hoc. A self-consistent theory of this device is essential for the development of a high power (>GW) high-efficiency magnetron. The major difficulties in developing such a description are the presence of the anode resonators and the intense self field of the electron flow at the cathode. Previously, in an effort to develop the first self-consistent theory of the magnetron, a linear stability analysis of the extraordinary mode in both a planar and a cylindrical magnetron was performed, using a macroscopic cold-fluid model for the electron flow. A closed analytic dispersion relation was found for each geometry in the limit of a tenuous electron flow. In this work, the authors have lifted this tenuous flow restriction by numerically solving the eigen-differential equation characterizing an intense electron flow at the cathode. In this way, the magnetron behavior over a wide range of physical parameter is explored