When is it appropriate to treat astrophysical plasma as a two temperature fluid and under what conditions can it be treated as a one temperature fluid?
Hi Biplob,
this question concerns time scales of collisions. Since you ask about temperatures you imply that the collisions are quite efficient so that temperatures can be defined for each species (i.e. they are close to being fully relaxed). Basically, if electron-ion collisions are faster than any time scale of interest then you have a single fluid. The time scales for energy equilibration between electrons and electrons is short, tau_e say. Then if temperatures of the ions and electrons are not too dissimilar to start with then the time for ion-ion collisions to equilibrate is about sqrt(m_ion/m_e) tau_e, the time for electron-ion collisions about (m_ion/m_e) t_e, where m is the mass of the ion or electron. See Braginskii 1965 Rev Plasma Phys vol 1.
These are just the first considerations, they describe the "relaxation" of the different plasma components described by Coulomb collisions. These collisions will have to work against agents that tend to heat the different species- each species has its own energy equation, and so if there are dynamically significant things (turbulence, high frequency Alfven waves for example) that heat, say, ions preferentially over the electrons, then the safest approach is a multi-fluid one. In other words, if you are unsure (i.e. you are not sure that collisions dominate) it is perhaps a good idea to look at a multi-fluid approach.
If the plasma is very tenuous and/or dynamic then you may even end up having to solve Boltzmann equations instead of fluid equations- very nasty nonlinear things. But even then (see Parker's "Conversations on electric and magnetic fields in the cosmos") sometimes the fluid approaches work to describe certain aspects of the physics, depending on the question you want to answer.
good luck
phil
ps. I answered the second part of the question starting with "When is it appropriate to treat astrophysical plasma..", I am not sure I understand the first part. Phil
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