Interstellar magnetic fields influence all stages of the process of starformation, from the collapse of molecular cloud cores to the formation ofprotostellar jets. This requires us to have a full understanding of thephysical properties of magnetized plasmas of different degrees of ionizationfor a wide range of densities and temperatures. We derive general equationsgoverning the magneto-hydrodynamic evolution of a three-fluid medium ofarbitrary ionization, also including the possibility of charged dust grains asthe main charge carriers. In a companion paper (Pinto & Galli 2007), wecomplement this analysis computing accurate expressions of the collisionalcoupling coefficients. Over spatial and temporal scales larger than theso-called large-scale plasma limit and the collision-dominated plasma limit,and for non-relativistic fluid speeds, we obtain an advection-diffusion for themagnetic field. We derive the general expressions for the resistivities, thediffusion time scales and the heating rates in a three-fluid medium and we usethem to estimate the evolution of the magnetic field in molecular clouds andprotostellar jets. Collisions between charged particles significantly increasethe value of the Ohmic resistivity during the process of cloud collapse,affecting in particular the decoupling of matter and magnetic field andenhancing the rate of energy dissipation. The Hall resistivity can take largervalues than previously found when the negative charge is mostly carried by dustgrains. In weakly-or mildy-ionized protostellar jets, ambipolar diffusion isfound to occur on a time scale comparable to the dynamical time scale, limitingthe validity of steady-state and nondissipative models to study the jet'sstructure.
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