Velocity and Position Spread of Electron Beam in Gyrotrons

In the gyrotron, the phenomenon that electron velocity spread coupled with beam radius spread may occur, which is quite different from the traditionally considered uncoupled ones. In this paper, the formation of such spatial velocity spread is investigated. It is found that the inhomogeneous electric and magnetic fields in the cathode region are responsible for this problem. This phenomenon is much more visible in low-voltage, high-frequency gyrotrons, in which the beam Larmor radius may be significantly smaller than the beam radius spread.