Nonlinear theory of stimulated backscattering in a bounded dissipative plasma

Abstract

The anomalous reflectivity, k2, of a bounded plasma, dissipative for the excited electrostatic wave, is investigated. Quantitatively, the phenomenon is controlled by three characteristic lenghts: L, the length of the plasma, La, the longitudinal absorption length, and L0, the basic gain length. When the parametric decay instability is convective, L0/La≡β⩾2, Tang’s approximation is shown to apply. With α2=2LLa/L02, and ε2= (radiation noise/incident signal), it is found that when Γ=ε2 exp(α2) ≲0.1, k2 is negligible. When Γ≳0.1, then k2≃1−α−2 ln(1/4ε2). In the regime of absolute instability, β<2, with zero noise, it is found that the reflectivity in implicit form is κL/L0=F (π/2, k)+(1/2) F (tan−1 A, k). F is the elliptic integral of the first kind, κ2=1−β2/4 kc2, kc2=1−k2, A=2B/kc(1−B2), B=β/2kcκ. As a function of L/L0, the reflectivity saturates at 1−β2/4.