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Toroidal Flux Ropes with Elliptical Cross Sections and Their Magnetic Helicity

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Abstract

Axially symmetric constant-alpha force-free magnetic fields in toroidal flux ropes with elliptical cross sections are constructed in order to investigate how their alphas and magnetic helicities depend on parameters of the flux ropes. Magnetic configurations are found numerically using a general solution of a constant-alpha force-free field with an axial symmetry in cylindrical coordinates for a wide range of oblatenesses and aspect ratios. Resulting alphas and magnetic helicities are approximated by polynomial expansions in parameters related to oblateness and aspect ratio. These approximations hold for toroidal as well as cylindrical flux ropes with an accuracy better than or of about 1%. Using these formulae, we calculate relative helicities per unit length of two (probably very oblate) magnetic clouds and show that they are very sensitive to the assumed magnetic cloud shapes (circular versus elliptical cross sections).

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Acknowledgements

We acknowledge the use of data from OMNIWeb and the PIs who provided them. This work was supported by projects 14-19376S and 17-06065S from GA ČR and by the AV ČR grant RVO:67985815.

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Authors and Affiliations

  1. Astronomical Institute, Academy of Sciences of the Czech Republic, Boční II 1401, 141 00, Praha 4, Czech Republic

    M. Vandas

  2. University Park, LSC, Houston, TX, USA

    E. Romashets

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  1. M. Vandas
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  2. E. Romashets
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Correspondence to M. Vandas.

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Vandas, M., Romashets, E. Toroidal Flux Ropes with Elliptical Cross Sections and Their Magnetic Helicity. Sol Phys 292, 129 (2017). https://doi.org/10.1007/s11207-017-1149-5

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