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Additional resources for Cosmic Electrodynamics: Electrodynamics and Magnetic Hydrodynamics of Cosmic Plasmas
The characteristic frequencies ω of processes under consideration must be small compared with the reverse times −1 τab between collisions of all distinct components. 86) for both a = b and a = b. The meaning of this conditions for a = b is that collisions between diﬀerent particles are numerous over the time interval 2π/ω, which ensures that motions of all plasma components are identical. In particular, the neutral component adjusts itself to motion of the charged components, if 2π/ω τia , τea .
Since a plasma is supposed to consist of collectively interacting charged and neutral particles, the inclusion of an external current needs some more clariﬁcation. Although, as a model of this current, one can always imagine well-isolated current-carrying wires embedded by a plasma; this example has little practical importance, while a current composed of free particles identical to the plasma particles is indistinguishable of the internal plasma current and so must not be treated as an external current.
In some cases, the population forming the external current cannot itself be described within the MHD approximation (as is often true for nonthermal particles), and requires a more general kinetic treatment, while its eﬀect on the main plasma can still be accounted within the MHD approach. , generalized Ohm’s law. 4 Ohm’s Law in a Partially Ionized Collisional Plasma In this section we examine partly ionized collisional plasmas, following Pikel’ner 1966; Bykov and Toptygin 2007. We consider the three-component medium (electrons e, ions i, neutral atoms a) and use Eqs.