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, B^*_t \equiv \bar{B}_t/(8\pi p_a)^{1/2} and B* p ≡ Bpa /(8πpa )1/2, where \bar{B}_t 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 Alfvén speed VA and plasma β are computed. The results are scale-invariant.
- Publication:
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The Astrophysical Journal
- Pub Date:
- December 2012
- DOI:
- 10.1088/0004-637X/761/2/179
- Bibcode:
- 2012ApJ...761..179C
- Keywords:
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- interplanetary medium;
- Sun: corona;
- Sun: coronal mass ejections: CMEs;
- Sun: helioseismology;
- stars: magnetic field;
- Sun: magnetic topology