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On the validity of ideal MHD equations for different collisional regimes

This paper is devoted to clarify the discrepancy between the experimentally found, rather wide and theoretically predicted, very restricted range of validity of the ideal MHD (IMHD) equations. In the first part of the paper, the standard derivation for a collision-dominated plasma is critically reviewed, leading to even stronger limitations, than those known in the literature. In the second part of the paper, the validity range of the IMHD equations on the Alfvén timescale is, based on a multiple timescale approach, analysed for different collisional regimes. It turns out that the IMHD equations are unrestricted valid for a (strongly magnetized) weak-collisional plasma. For an intermediate- and high-collisional plasma, the adiabaticity is violated essentially due to the work done by the friction forces. However, for both collisional regimes the full set of IMHD equations is obtained for the slow-flowing case, i.e., for plasmas with a magnetic Mach number of the relative velocity |ui − ue|/vA << 1.