A method for the elimination of the spurious mode of backward-wave oscillations

For a given power output and voltage range, the minimum length of a backward-wave oscillator can be calculated from published data from any normal range of circuit loss and space charge regimes. As this circuit increases in length the rf oscillations become more insensitive to variations of beam current, but soon a point is reached where a new line appears in the spectrum at a slightly lower frequency. This new frequency corresponds to a second solution of the boundary value equation; and because the system is already in a state of oscillation, nonlinear mixing very rapidly fills the spectrum on either side of the main oscillation as the circuit length or the current is increased beyond that point. Thus, the optimum length of the circuit is a matter of compromise unless the starting current of the spurious mode can be appreciably increased or, as is indicated in this paper, can, in fact, be made infinite.