Power Flow in Electron Beam Devices

This paper discusses power flow in devices in which electrons are constrained to move in the z direction only. Besides the electromagnetic power flow given by Poynting's vector, there is a kinetic power flow per unit area in the z direction. In a linear system equivalent to the electron beam at low levels of operation this power flow is PR = ---(- J0+J)(u02+2u0v). Here -J0 and J are the dc and instantaneous ac convection current densities and u0 and v are the dc and instantaneous ac velocities. The electromagnetic power must be calculated including all fields due to the presence of the beam. In the case of space-charge waves, the electromagnetic power flow adds to or subtracts from the kinetic power flow. If the electric field is purely longitudinal, H is zero, and the electromagnetic power flow is zero.