Abstract
Starting from the Liouville equation and utilizing the multiple time-scale method, we derive the equations which govern the dynamics of a many-species plasma in presence of neutrals and with an arbitrary ionization ratio. The plasma is supposed to be in equilibrium and the collisions between neutral and charged particles are taken to be elastic; thus the temperature of the plasma is quite low, of the order of a few eV. We emphasize the importance of a parameter μ(μ ⋍ ν e,M ω p , where ν e,M is the electron-neutral-molecule elastic collision frequency and where ω p is the electron plasma frequency), such that for μ ⪢ 1 our equations become those of the Lorentz plasma, while for μ ⪡ 1 we have the case of a fully ionized plasma. The domain of applicability of these limiting equations is discussed.
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