Dispersion equation for stochastically perturbed MHD waves. Propagation in infinite medium and thin flux tube

The purpose of this work is to study the effect of noise on wave propagation in ionized plasmas. The route undertaken is to work in the MHD framework in an A-Langevin equation approach, i.e., to include a stochastic term in the equation of motion. We considered two cases amply described in the literature for the deterministic approach: waves propagating in an infinite medium and waves propagating in a thin plasma flux tube, respectively; a stochastic term was then added in the equation of motion. The general approximation is that the stochastic term is seen as constant in regard to the fluid, i.e., the characteristic timescale of noise is much smaller than any characteristic timescale of the fluids. Results show that the additional term does have an influence on the stability of the system.