Equilibrium analysis of a flowing two-fluid plasma

Abstract

An improved formalism for a flowing two-fluid equilibrium with constant density is developed. This extends the usual single-fluid model. In this generalization, the magnetic field is replaced by two quantities, the generalized vorticities of each species. Criteria are found for when the single-fluid model is adequate and when the more general two-fluid model is necessary. The two-dimensional equilibria with purely azimuthal ion flow are studied analytically and numerically. Spherical torus and compact toroid equilibria are found that are relevant to the current experiment. The ion flow and plasma beta as well as the size parameter are found to play a major role in the question of whether two-fluid corrections are needed.

On nonexistence of tokamak equilibria with purely poloidal flow

“…It turns out that in cases ͑i͒ and ͑ii͒, as well as in case ͑iii͒ for incompressible flows, the nonexistence statement holds. It should be noted that there are a number of papers on equilibria with flow within the framework of MHD, 2-4,6-17 the two-fluid model, 7,14,[17][18][19][20][21] and for anisotropic pressure. [22][23][24][25] Certain derivations and equations therein are related to the present work.…”

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas

“…[15][16][17] Indeed, for a two-fluid equilibrium, two Grad-Shafranov-like coupled equations were written by using as unknowns two flux functions of the two Ertel surfaces. The writers apparently did not consider whether these flux functions remain intact during the evolution of the plasma.…”

Nearby-fluids equilibria. I. Formalism and transition to single-fluid magnetohydrodynamics

“…16 It employs three reference scales: ͑1͒ global length scale L, e.g., the outboard separatrix radius; ͑2͒ magnetic field, B R , e.g., the poloidal field at the outboard separatrix; and ͑3͒ density, n R , e.g., the average density inside the 16 It employs three reference scales: ͑1͒ global length scale L, e.g., the outboard separatrix radius; ͑2͒ magnetic field, B R , e.g., the poloidal field at the outboard separatrix; and ͑3͒ density, n R , e.g., the average density inside the…”