Volume 585, January 2016
|Number of page(s)||5|
|Published online||05 January 2016|
Toroidal linear force-free magnetic fields with axial symmetry
Astronomical Institute of the Czech Academy of
Sciences, Boční II
1401, 141 00
Praha 4, Czech Republic
2 University Park, LSC, Houston, Texas, TX 77070, USA
Received: 11 September 2015
Accepted: 20 November 2015
Aims. Interplanetary magnetic flux ropes are often described as linear force-free fields. To account for their curvature, toroidal configurations must be used. The aim is to find an analytic description of a linear force-free magnetic field of the toroidal geometry in which the cross section of flux ropes can be controlled.
Methods. The solution is found as a superposition of fields given by linear force-free cylinders tangential to a generating toroid. The cylindrical field is expressed in a series of terms that are not all cylindrically symmetric.
Results. We found the general form of a toroidal linear force-free magnetic field. The field is azimuthally symmetric with respect to the torus axis. It depends on a set of coefficients that enables controlling the flux rope shape (cross section) to some extent. By varying the coefficients, flux ropes with circular and elliptic cross sections were constructed. Numerical comparison suggests that the simple analytic formula for calculating the helicity in toroidal flux ropes of the circular cross section can be used for flux ropes with elliptic cross sections if the minor radius in the formula is set to the geometric mean of the semi-axes of the elliptic cross section.
Key words: magnetic fields / magnetohydrodynamics (MHD) / solar wind
© ESO, 2016
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