Abstract: I will describe in detail a package we developed recently that uses a fully geometrical method to derive perturbation equations
about a spatially homogeneous background.
Based on the expansion (10), the perturbation equations
could be obtained from (1)-(6) in the form:
The linearized perturbation equations
are conveniently solved by a two-dimensional Fourier transform in the xy-plane and a Laplace transform in time, which result in ordinary differential equations in z for the transformed velocity and pressure perturbations, which can be solved analytically.
and aerodynamic derivatives complete the discussion of modeling.
Thus the linearized perturbation equations
governing the motion of hydromagnetic thermally conducting two components of the partially-ionized plasma are given by
Substituting expressions (5) and (6) in the system (4), and after neglecting second order terms, yields the system of governing perturbation equations