10 - Non-ideal MHD

Summary

Three models of a partially ionised fluid are considered by examining together three sets of (M)HD equations for the neutral, ionised, and electron components of a fluid. The first assumes low ionisation and isothermality leading to the one-fluid, isothermal model where all three non-ideal terms–resistance, the Hall effect, ambipolar diffusion–appear in the induction equation. New quantities introduced include: the ambipolar force density; coupling, rate, and ambipolar coefficients; and resistivity, all helping to determine the relative role of each non-ideal term. For resistive MHD, the Sweet–Parker model for magnetic reconnection, and dynamo theory are discussed. For the Hall effect, a two-fluid, isothermal model is introduced that refines the Sweet–Parker model to give a reconnection time scale in better keeping with observations of solar flares. Finally, the section on ambipolar diffusion derives the full two-fluid, non-isothermal model applicable for a fluid with arbitrary ionisation. Here, exchange terms are introduced to account for mass, momentum, and energy transfers when neutrals ionise or ions recombine.