Ambipolar diffusion, interstellar dust, and the formation of cloud cores and protostars. I. Basic physics and formulation of the problem

We formulate the problem of the self-initiated formation and contraction of cloud cores due to ambipolar diffusion in axisymmetric, self-gravitating, isothermal, magnetic molecular cloud models, accounting for a cosmic abundance of interstellar grains (both charged and neutral). The basic microscopic and macroscopic effects of grains are discussed. The magnetohydrodynamic equations for a multicomponent plasma are derived, the dimensionless free parameters are obtained, and their meaning is explained physically. The ion and electron fluids combine to form a system of "quasiparticles," each having an effective charge Z_eff = e(n_i - n_e)/n_i (where n_i and n_e are the number densities of ions and electrons, and e the electronic charge). Electrostatic attraction between quasiparticles, which are attached to the magnetic field, and negatively charged grains couples the grains to the field even at densities at which grain-neutral collisions would normally decouple the grains from the field. Also, neutral grains can couple to the magnetic field through (inelastic) charge capture. The numerical method of solution, the results, and their application to the formation of cores and protostars in molecular clouds are presented in following papers.