Hydrodynamic model of the penetration of a magnetic field into a plasma with two ion species

Magnetic field propagation in a two ion species planar plasma opening switch

“…Here µ is a viscosity. More details of the derivation appear in [13], which also contains a more complete dissipative model than we employ here. In the following, it will be assumed that the temperature is low, and pressure will be neglected.…”

“…The dimensionless radial width is L x = 2.4L, and the vertical length is L y = 5L, similar to the experiments [9,10,11]. Dissipation is added to the equations: the viscosity had the same magnitude as resistivity, µ = η = 2.5 ×10 −2 v A L. Rather than using collisional diffusion coefficients [13], the values of η, µ are compatible with anomalous microturbulent diffusion in the experiments [9,10,11]. A small diffusion was added to the density equations, with χ = 10 −3 v A L, in order to provide some numerical smoothing.…”

“…However, the density pileup appears to be the dominant effect. It was pointed out in [13] that in the limit µ Z >> Z, the difference velocity v D is larger than the Hall velocity v H , and it may make a larger contribution to the magnetic field evolution (14), (15). Since the literature has emphasized v H , we will consider v H and v D separately.…”

“…In this paper, three fluid equations of motion [8,13,14,15] are applied to the POS. We employ the formulation by Gordeev [13] which decomposes the velocity into an MHD part and a difference velocity between the two ion species.…”

A nonlinear oblique derivative boundary value problem for the heat equation Part 1: Basic results

“…Formal studies of this system were made by the authors of [8] in the case where the diffusion along z is suppressed.…”