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We formulate the problem of the formation and collapse of nonaxisymmetricprotostellar cores in weakly ionized, self-gravitating, magnetic molecularclouds. In our formulation, molecular clouds are approximated as isothermal,thin (but with finite thickness) sheets. We present the governing dynamicalequations for the multifluid system of neutral gas and ions, includingambipolar diffusion, and also a self-consistent treatment of thermal pressure,gravitational, and magnetic (pressure and tension) forces. The dimensionlessfree parameters characterizing model clouds are discussed. The response ofcloud models to linear perturbations is also examined, with particular emphasison length and time scales for the growth of gravitational instability inmagnetically subcritical and supercritical clouds. We investigate theirdependence on a cloud's initial mass-to-magnetic-flux ratio (normalized to thecritical value for collapse), the dimensionless initial neutral-ion collisiontime, and also the relative external pressure exerted on a model cloud. Amongour results, we find that nearly-critical model clouds have significantlylarger characteristic instability lengthscales than do more distinctly sub- orsupercritical models. Another result is that the effect of a greater externalpressure is to reduce the critical lengthscale for instability. Numericalsimulations showing the evolution of model clouds during the linear regime ofevolution are also presented, and compared to the results of the dispersionanalysis. They are found to be in agreement with the dispersion results, andconfirm the dependence of the characteristic length and time scales onparameters such as the initial mass-to-flux ratio and relative externalpressure.Comment: 30 pages, 7 figures Accepted by Ap

Formation and Collapse of Nonaxisymmetric Protostellar Cores in Planar Magnetic Interstellar Clouds: Formulation of the Problem and Linear Analysis