Inviscid fluid motions induced by an electric current source. Part 1: Preliminary analysis

The flow induced by an electric current source and its influence on the current density in an incompressible, inviscid medium were studied. The inviscid and viscous problems have no length or velocity scale and the solutions can be put in a similarity form. Detailed analytic study of the inviscid problem shows that the MHD equations, under the usual approximations, lead to solutions which have weak singularities at the axis of symmetry. The result is that in a neighborhood of the axis of symmetry of order of the Debye length the space charge density can not be neglected, so that in the equation of Euler the Coulomb force and the Lorentz force and in Ohm's law the convection current density and the current density become of equal order. This does not necessarily imply that this problem is not self-similar and that a different near and far field will occur. It might also be an explanation for the physically unrealistic phenomena which appear in the viscous problem.