Cosmic Rays: Climate, Weather and Applications by Ho-ming Mok

By Ho-ming Mok

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APPLICATIONS OF MAGNETOHYDRODYNAMICS The MHD equations are a set of highly coupled equation describing the complicated electromagnetic interactions between particles and fields. For instance, charge current is the source of magnetic field according to the Maxwell's equation but the presence of magnetic field influences the current of charged particles as described by the generalized Ohm's law Plasma Physics 43 and the momentum transfer equation. The determination of the behaviour of a specific physical variable in the set of equations requires decoupling of it from other variables.

It is known as the Krook collision term (some text refer it as the BKG collision term after Bhatnagar, Gross and Krook in 1954) and the model is called Krook model or relaxation model. More elaborated understanding on the nature of collision term requires discussions on the correlation between the interacting particles. 106) Since the distribution function f k (x, v, t) describes the probability of a particle of species k staying at a point in the phase space at a moment of time t, if the k type particle does not interact with the l type, their distributions will not depend on each other.

Thus, the net number of particles entering or leaving the phase space element Δ V by following their trajectories in the time interval Δ t is zero. This is known as Liouville’s theorem and it is only valid for the cases that the processes of particle collisions, particle loss and production and radiation losses can be neglected. For non-zero particle collisions, some particles will scatter in or out the phase space volume element d3xd3v by collisions rather than exactly obeying the Liouville’s theorem.

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