Stability of the Steady-State-Stimulated Brillouin Scattering

Abstract

It is discussed whether steady-state-stimulated Brillouin scattering (SBS) can exist in homogeneous plasmas. For the case when the damping of the ion-sound waves is more important than their convection, the general solutions of the associated perturbed equations are presented and the influence of various boundary conditions is discussed. Steady-state SBS in semi-infinite plasmas is nearly always unstable. The same is true for SBS with reflective boundary conditions, although the physical mechanism is different. By a Hopf bifurcation a (regular) nonstationary state (limit cycle) can appear with a possible consecutive transition to chaos.

Chaotic stimulated Brillouin scattering in a finite-length medium

“…This has not yet been done. For no temporal dephasing (A = 0), Blaha et aL [3] showed that this fourth order system reduces to two second order equations, one each for the real and imaginary parts. These second order equations can then each be transformed into Legendre equations and the time evolution of perturbations can be found in terms of associated Legendre functions.…”

“…The dynamics of Stimulated Brillouin Scattering (SBS) in a homogeneous finite medium has captured considerable interest both in laser-plasma interactions [1][2][3][4] and in optical fibers [5][6][7][8][9][10]. SBS is a three wave interaction (3WI) that results from a parametric coupling between electromagnetic (light) and acoustic waves.…”