Twisted versus braided magnetic flux ropes in coronal geometry

I. Construction and relaxation

Department of Mathematical SciencesDurham University, Durham DH1 3LE, UK
e-mail: christopher.prior@durham.ac.uk

Received: 23 August 2015
Accepted: 21 November 2015

Abstract

We introduce a technique for generating tubular magnetic fields with arbitrary axial geometry and internal topology. As an initial application, this technique is used to construct two magnetic flux ropes that have the same sigmoidal tubular shape, but have different internal structures. One is twisted, the other has a more complex braided magnetic field. The flux ropes are embedded above the photospheric neutral line in a quadrupolar linear force-free background. Using resistive-magnetohydrodynamic simulations, we show that both fields can relax to stable force-free equilibria whilst maintaining their tubular structure. Both end states are nonlinear force-free; the twisted field contains a single sign of alpha (the force-free parameter), indicating a twisted flux rope of a single dominant chirality, the braided field contains both signs of alpha, indicating a flux rope whose internal twisting has both positive and negative chirality. The electric current structures in these final states differ significantly between the braided field, which has a diffuse structure, and the twisted field, which displays a clear sigmoid. This difference might be observable.