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We present a comprehensive study of MHD waves and instabilities in a weaklyionised system, e.g., an interstellar molecular cloud. We determine all thecritical wavelengths of perturbations across which the sustainable wave modescan change radically (and so can their decay rates), and various instabilitiesare present or absent. These critical wavelengths are essential forunderstanding the effects of MHD waves (or turbulence) on the structure andevolution of molecular clouds. Depending on the angle of propagation relativeto the magnetic field and the physical parameters of a cloud, there arewavelength ranges in which no wave can be sustained as such. Yet, for otherdirections of propagation or different properties of a model cloud, there mayexist some wave mode(s) at all wavelengths. For a typical cloud,magnetically-driven ambipolar diffusion leads to removal of any support againstgravity that most short-wavelength waves (or turbulence) may have had, andgravitationally-driven ambipolar diffusion sets in and leads to cloudfragmentation into stellar-size masses, as first suggested by Mouschovias threedecades ago -- a single-stage fragmentation theory of star formation, distinctfrom the hierarchical fragmentation picture. Phase velocities, decay times, andeigenvectors (the densities and velocities of neutral particles and the plasma,and components of the magnetic field) are determined as functions of thewavelength of the disturbances and are explained physically. Comparison of theresults with nonlinear analytical or numerical calculations is also presented,excellent agreement is found, and confidence in the analytical, linear approachis gained to explore phenomena difficult to study through numericalsimulations. Mode splitting and mode merging, which are impossible insingle-fluid systems for linear perturbations, occur naturally in multifluidsystems.

Hydromagnetic Waves in Weakly Ionised Media. I. Basic Theory, and Application to Interstellar Molecular Clouds