Analytical calculation of anode current in relativistic magnetron

An analytical expression for the anode current in a relativistic magnetron is derived. The anode current is described as the cathode-to-anode drift of the electron guiding centers in the crossed external dc and induced
rf
magnetic and electric fields. The drift of the electron guiding centers is analyzed in the frame of reference moving with the phase velocity of the induced
rf
electric field. The anode current determined by this drift is calculated under the assumption that the cathode of the relativistic magnetron operates in a space-charge-limited mode, where the external dc electric field at the cathode surface is zero.