On the parametric instability of magnetoacoustic waves in a plane plasma waveguide

Modulation instability of magnetoacoustic waves in a plane plasma waveguide as well as parametric interaction of normal modes of the system in the MHD approximation are investigated. A new waveguide mode corresponding to space homogeneous oscillations of a plasma across a magnetic field has been discovered. Shown is a possibility for wave interaction in two cases: interaction of magnetoacoustic modes with different transverse indexes and decay of a magnetoacoustic wave to a waveguide mode packet wide in wave numbers is shown. Increment of parametric instability for the first case and change of initial pulse shape in the second case has been determined in the approximation of the given field. Equations for wave amplitudes in the given field of the highest frequency wave have been derived and solved. Evaluations for a semiconductor plasma are given