Magneto-Hydrodynamics

To proceed beyond the basic inferences of Chap. 1 , we will not only need a representative thermodynamic model (Fig. 1.4 ), but also a theoretical framework that is simple, yet complete enough, with which to confront hypothetical scenarios with critical data. The initial framework we adopt is magnetohydrodynamics (MHD). As the name implies, this is a fluid approximation describing the plasma as a collisionally coupled single fluid of ions and electrons, and so we may not expect to apply it without great care on scales below the mean free paths. The fluid treatment seems rather safe in the low-temperature, high-density chromosphere where scale heights exceed mean free paths by six orders of magnitude. However, in the corona, mean free paths of 200 km are typical in structures whose scale heights are just 50 Mm. The associated Knudsen numbers of 0.004 for typical particles are Knudsen number uncomfortably large, they scale as particle energy \(\varepsilon ^2\) . As we argued in Sect. 1.7 , this energy dependence confounds attempts to justify a fluid treatment, without some care and fore-knowledge of the risks it entails.