Theoretical Study of the Saturated Stage of a Relativistic Magnetron

The saturated stage of a magnetron or a cross-field amplifier is when the device has powered up and is steadily delivering power. Theoretical studies of this stage had suggested that when the dc current would become sufficiently large in comparison with the rf current, then no steady state solution could be expected to exist. Attempts were made to develop a numerical code which would allow one to numerically solve for a stationary solution of the saturated stage, if it existed. However the high order of the ordinary differential equations and their singular nature had prevented any solutions from being found. It has been suggested that a hybrid method involving single particle orbits could be used. Here one would assume that a stationary solution did exist and then one would solve for the particle orbits in that stationary solution. From those orbits, one then could obtain the corresponding fluid quantities by averaging and thereby bypassing any need to solve the high order, singular differential equations. Other work completed under this contract included studies of integrable systems, particularly those integrable optical systems which govern intense laser beams and stability, and also Bose-Einstein condensates. Prepared in cooperation with DCMA Orlando, 3555 Maguire Blvd, Orlando, FL.