Instabilities in the Smooth-Anode Cylindrical Magnetron

A magnetically focused space-charge cloud of the type found in the smooth-anode magnetron is examined to determine whether a perturbation of the equilibrium condition will grow. A field analysis is carried out in which radial admittances are matched at the edge of the cloud. The solutions for the characteristic frequencies are complex, indicating that the disturbance grows with time. These instabilities occur at multiples of the Larmor frequency. The solutions indicate that electrons oscillate with increasing swings, a process which absorbs energy. Instability therefore gives rise to some anode current even when the tube is ``cut off'' though rf power is not made available by the process.