Space charge effects on the equilibrium of guided electron flow with gyromotion

The limiting current has been derived for electron beams with gyromotion propagating down a waveguide immersed in an external guide magnetic field, It has been found that the maximum current is strongly dependent on the pitch angle parameter α, where α = v⊥/v 1, the ratio of the velocity associated with the gyromotion and the velocity in the direction of propagation. The theory has been applied to the design of high power gyrotrons.