Alfvén waves in a stochastic magnetic field
Abstract
Parametric amplification of Alfvén waves in a plasma, subjected to a spatially uniform but temporally stochastic magnetic field, is investigated. The analysis is made using Bogoliubov and Mitropoisky's asymptotic method and Stratanovich's method for stochastic differential equations. This enables us to obtain the probability distribution function for the evolution of the wave, under Markovian approximation. Thus, a complete statistical characterization of the wave can be obtained, if needed. It is shown that Alfvén waves with wavelengths larger than the radius of the plasma column are amplified with probability unity, if the power spectral density of the fluctuating field at twice the wave frequency is nonzero.
 Publication:

Journal of Plasma Physics
 Pub Date:
 April 1977
 DOI:
 10.1017/S0022377800020523
 Bibcode:
 1977JPlPh..17..147M
 Keywords:

 Magnetic Fields;
 Magnetohydrodynamic Waves;
 Parametric Amplifiers;
 Plasma Cylinders;
 Stochastic Processes;
 Asymptotic Methods;
 Coupled Modes;
 Differential Equations;
 Markov Processes;
 Power Spectra;
 Probability Distribution Functions;
 Statistical Analysis;
 Wave Amplification;
 Plasma Physics