Equilibrium of braided flux ropes with helical symmetry

Solar corona loops consist of interwoven braided magnetic strands as observed by the Hi-C Imager [2] and in a new Caltech lab experiment. Braiding and strand-strand reconnection [1] are likely fundamental to loop dynamics. No braided MHD equilibrium model has been reported to our knowledge but would be vital to describe loop evolution. A possible equilibrium is conjectured to be helically symmetric with all strands either having the same J_z polarity or having alternating J_z polarity. Since actual solar corona loops are expected to have net current flowing between footpoints, a plausible presumption is that strands should all have the same J_z polarity. Using the helical JOKF MHD equilibrium [3] we can construct alternating-polarity solutions (i.e., zero net current flowing between footpoints). By combining different JOKF modes, we can also construct net current solutions with the same-polarity flux ropes at the center and reverse current flux ropes at large radius. However, we cannot find same-polarity JOKF solutions. Because of this failure of the JOKF approach, a Biot-Savart-based, multiple wrapped helical wire model is being investigated.

[1] E. N. Parker, ApJ 174, 499 (1972)

[2] J. W. Cirtain et al, Nature  493, 501 (2013)

[3] J. L. Johnson et al., Phys. Fluids 1, 281 (1958)