Linear Theory On Enhancement And Stopping Of Radiation From A Finite Length Plasma-filled Backward Wave Oscillator

The linear theory of enhanced radiation from a high-power plasma-filled backward wave oscillator (BWO) with sinusoidally corrugated slow wave structure with length L has been developed and analyzed numerically. We assume a localized source of small signal in the structure. In infinitely long case, the absolute instability of the signal grows up at the complex frequency and wavenumber of the saddle point of the dispersion relation, D (k, w ) =0, of the plasma BW0. For finite L case, oscillation is affected by the round trip reflection coefficient R, 0 < R < 1, at both ends. If L large, among various roots, main contribution comes from a pair of waves propagating in opposite directions; one is the growing roots, k
₊
, with the highest spatial growth rate that determine the oscillation, while the other is the evanescent root, k , with the smallest damping rate propagating in the opposite direction to the growing wave, creating a positive feedback in the structure. In addition to D(k
₊
,W)=0, D(k ,W)=0, the condition [ 2] that a physical-quantity at any given z and t must be unique imposes another relation; k
_-
- k =-[2 Π N+iln(R)]/L, where N is an arbitrary integer coming from an infinite number of sheet of Riemann surface of logarithm function. Among various choices of N, we confine ourselves to the case of N = + 1, when the pair roots are located most closely each other.