Modulation instability of waves in a magnetized plasma

Modulation instability of finite-amplitude transverse waves in an ideal magnetized plasma with a non-zero sound speed has been investigated theoretically by use of an isentropic two-fluid model. In the first part of this thesis, a perturbation expansion is performed on a circularly polarized, transverse Alfven wave propagating parallel to the constant ambient magnetic field with arbitrary amplitude and with arbitrary frequency ω0. The result of the perturbation expansion is a sixth-order algebraic dispersion relation in terms of the frequency and wave number perturbations, w and k. The analysis is then limited to the case where ω much-lt ω0 much-lt ωce, ωce being the electron-cyclotron frequency. The resulting fourth-order dispersion relation is examined analytically and numerically and a surface is found that separates modulationally stable and unstable regions in parameter space. In the second part of this thesis, a reductive perturbation expansion of the two-fluid equations is used to derive a nonlinear Schrodinger equation, which describes the time evolution of a modulated, weakly nonlinear, elliptically polarized carrier wave propagating obliquely to the constant ambient magnetic field with frequency wo. Here, the author assumes that wo is negligible compared with ωce but nonnegligible with ωci, the ion-cyclotron frequency