STRUCTURE OF NON-FORCE-FREE MAGNETIC FLUX ROPES IN AN AMBIENT MEDIUM

Abstract

The structure of non-force-free equilibrium magnetic flux ropes in an ambient medium of specified pressure pa is studied. A flux rope is a self-organized magnetized plasma structure consisting of a localized channel of electric current and the magnetic field arising from this current. An analytic method is developed to obtain one-dimensional equilibrium solutions satisfying c –1 J × B – ∇p = 0 subject to the requirements that (1) all physical quantities be nonsingular and continuous, (2) pressure p(r) be physically admissible—real and non-negative, and (3) the magnetic field profile have minimum complexity. The solutions are shown to be characterized by two parameters, and B* p ≡ Bpa /(8πpa )1/2, where is the toroidal (axial) field averaged over the cross-sectional radius a and Bpa is the poloidal (azimuthal) field at the edge of the current channel (r = a). The physical constraint on pressure defines equilibrium boundaries in the B* t -B* p space beyond which no physical solutions exist. The method is illustrated with a number of families of solutions governed by distinct physical constraints. The force-free limit with pa ≠ 0 is investigated and is found to be characterized by plasma β = ∞. The local Alfven speed VA and plasma β are computed. The results are scale-invariant.