A GENERAL METHOD FOR TREATING

Abstract

MHD models are extensively used in the analysis of magnetic fusion devices, industrial processing plasmas, and ionospheric/astrophysical plasmas. MHD is the extension of fluid dynamics to ionized gases, including the effects of electric and magnetic fields. So, the general method presented in the part one can be extended to some special (but usual) cases in magneto-plasma dynamics, considering an adiabatic but non-isentropic flow (taking into account the flow vorticity effects, as well as those of the associated Joule-Lenz heat losses) in an external magnetic field, obtaining new first integrability cases (similar to the “D. Bernoulli” ones): a) assuming a continuous medium; b) making no distinction between the intensity of the magnetic field and the magnetic induction of the medium (in the Gaussian system of units), since for all conducting fluids the magnetic permeability is approximately equal to 1 (see [1 - 3]); c) assuming that the value of the electric conductivity of the fluid medium is uniform and isotropic throughout and independent on the magnetic field intensity. There always are some space curves (Selescu) along which the vector equation of motion admits a first integral in the general case. In the particular case of a fluid having an infinite electric conductivity (the highly ionized plasma), these curves also are the isentropic lines of the flow, in both cases enabling the treatment of any 3-D flow as a “quasi-potential” 2-D one. Like the part one, this work also deals with the unsteady non-isentropic flows, giving a first integral for the equation of motion in the general case.