Parametric instability of hydromagnetic waves with oblique propagation

The parametric excitation of Alfvén waves by two magnetosonic waves, which propagate obliquely to the static magnetic field, is analysed. The theoretical model used is the uniform, unbounded, ideally conducting and compressible one-fluid plasma, with suitable resonance conditions. Our consideration is restricted to determining the conditions under which some initially small perturbation grows, so that the magnetosonic pump wave is regarded as constant. It is found that, both in the case of the standing and the propagating pump, the growth rates of the excited waves depend not only on the pump power but also on β, and that the threshold pump intensities are proportional to β. In the case of the standing pump, the threshold pump intensity of the oscillating instability is zero at perfect matching. The parametric excitation of Alfvén waves by two magnetosonic waves, which propagate obliquely to the static magnetic field, is analysed. The theoretical model used is the uniform, unbounded, ideally conducting and compressible one-fluid plasma, with suitable resonance conditions. Our consideration is restricted to determining the conditions under which some initially small perturbation grows, so that the magnetosonic pump wave is regarded as constant. It is found that, both in the case of the standing and the propagating pump, the growth rates of the excited waves depend not only on the pump power but also on β, and that the threshold pump intensities are proportional to β. In the case of the standing pump, the threshold pump intensity of the oscillating instability is zero at perfect matching.