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 Alfvén speed VA and plasma β are computed. The results are scale-invariant.
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机译：研究了在指定压力pa的环境介质中非无力平衡磁通绳的结构。磁通绳是一种自组织的磁化等离子体结构，由电流的局部通道和由该电流产生的磁场组成。提出了一种解析方法来获得满足c –1 J×B –？p = 0的一维平衡解，但要满足以下条件：（1）所有物理量都是非奇异且连续的;（2）压力p（r）在物理上是允许的-实数和非负数，以及（3）磁场分布具有“最小复杂度”。该解由两个参数表征：B * p p Bpa /（8πpa）1/2，其中，是在横截面半径a上平均的环形（轴向）场，而Bpa是极向（方位角）场在当前通道的边缘（r = a）。对压力的物理约束定义了B * t -B * p空间中的平衡边界，超过该边界则不存在物理解。用受不同物理约束支配的许多解决方案系列说明了该方法。研究了pa≠0的无力极限，并发现其特征在于等离子β=∞。计算局部Alfvén速度VA和血浆β。结果是尺度不变的。
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