On axisymmetric double adiabatic MHD equilibria with plasma flow

Abstract

Abstract. The stationary equilibrium of an axisymmetric plasma characterized by toroidal and poloidal flows is considered within the framework of ideal double adiabatic magnetohydrodynamic equations. The problem is reduced to a nonlinear partial differential equation for the poloidal magnetic flux function, containing six surface functions, plus a nonlinear algebraic Bernoulli equation defining the plasma density. Ellipticity conditions and bifurcations of its solutions are discussed in the limit of small beta, appropriated for tokamak-like equilibria. Possible connections with the L-H transition are suggested.

On nonexistence of tokamak equilibria with purely poloidal flow

“…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. We will prefer, however, to present the study in a self-contained way because explicit reference to the content of the aforementioned papers for the three models employed would make a common notation difficult and the manuscript inconvenient to read.…”

Adiabatic plasma rotations and symmetric magnetohydrodynamical stationary equilibria: analytical and semi-numerical solutions

“…This is not the only type of motion compatible with mass continuity equation, though. It is possible to show that the most general such motion consists of a combined toroidal and poloidal rotation, although the equations are far more difficult to solve [9,22,23].…”

“…Let R 0 denote a characteristic radius of the system. Since we have g=g 33 =R 2 , the corresponding representations for the magnetic induction, (21), and plasma density, (22), are…”

Resistive axisymmetric equilibria with arbitrary flow

“…We further assume that part of the pressure gradient that varies within a magnetic flux tube has no " component, 17 i.e.,…”

“…16 Further, we show that in a field-reversed ͑FRC͒ axisymmetric configuration with no toroidal magnetic field, both toroidal and poloidal equilibrium flows can coexist with finite resistivity, which is not found to be the case with ideal equilibrium. 17 We consider the equilibrium resistive MHD equations with plasma flow. The equations are…”