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Abstract
Context. Interplanetary flux ropes are often described by linear force-free fields. To account for their curvature, toroidal configurations valid for large aspect ratios are used. However, in some cases, flux ropes need to be approximated by a toroid with a low aspect ratio. Aims. The aim is to find an analytical description of a linear force-free magnetic field of toroidal geometry, not restricted to large aspect ratios. Methods. The solution is found as a superposition of fields given by linear force-free cylinders tangential to a generating toroid. Results. The obtained solution describes toroidal flux ropes with reasonable shapes and magnetic field values. The field is exactly linear force-free for arbitrary aspect ratios. The new solution can be applied for solar and interplanetary flux ropes, astrophysical objects, and laboratory plasma.
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