Description:
The first-order linearized set of Maxwell-Lorentz equations are used as basis for the derivation of a power conservation theorem describing the balance between the rf kinetic power and the rf electromagnetic power in the electron beam. The theorem applies to laminar electron beams in which the electron flow is irrotational and the thermal velocity distribution at the cathode surface is neglected. The kinetic power flow is given in terms of the longitudinal rf kinetic potential or the Chu potential, the longitudinal part of the rf beam current and the equivalent longitudinal surface current on the beam boundary. This surface current embodies the effect of the transverse rf motion in the beam. A short discussion of the application of the theorem to thin beams is given.