A coupled mode description of the backward–wave oscillator and the Kompfner dip condition

The start oscillation condition for the backward-wave oscillator and the operation of the traveling-wave tube amplifier at the Kompfner dip point are described from the point of view of the coupling of two modes of propagation. Growing waves are not involved. Two waves are sufficient when the tube is more than a half plasma wavelength long. Operation in this "large space charge" domain is inherently simpler than in the "low space charge" domain. The start oscillation condition and the Kompfner dip condition are simply expressed in terms of the coupling constant between modes, HL = (2n ± 1) π/2, where n is an integer. In addition, the uncoupled modes must have the same velocity. The result is also expressed in terms of the more familiar parameters CN and hL. The effect of loss in the circuit mode is calculated. When the two waves carry energy in opposite directions, growing waves result. This case is discussed briefly.