Do current and magnetic helicities have the same sign?

Russell, A.J.B., Demoulin, P., Hornig, G., Pontin, D.I. and Candelaresi, S. (2019) Do current and magnetic helicities have the same sign? Astrophysical Journal, 884(1), 55. (doi: 10.3847/1538-4357/ab40b4)

Abstract

Current helicity, H c , and magnetic helicity, H m , are two main quantities used to characterize magnetic fields. For example, such quantities have been widely used to characterize solar active regions and their ejecta (magnetic clouds). It is commonly assumed that H c and H m have the same sign, but this has not been rigorously addressed beyond the simple case of linear force-free fields. We aim to answer whether H m H c ≥ 0 in general, and whether it is true over some useful set of magnetic fields. This question is addressed analytically and with numerical examples. The main focus is on cylindrically symmetric straight flux tubes, referred to as flux ropes (FRs), using the relative magnetic helicity with respect to a straight (untwisted) reference field. Counterexamples with H m H c < 0 have been found for cylindrically symmetric FRs with finite plasma pressure, and for force-free cylindrically symmetric FRs in which the poloidal field component changes direction. Our main result is a proof that H m H c ≥ 0 is true for force-free cylindrically symmetric FRs where the toroidal field and poloidal field components are each of a single sign, and the poloidal component does not exceed the toroidal component. We conclude that the conjecture that current and magnetic helicities have the same sign is not true in general, but it is true for a set of FRs of importance to coronal and heliospheric physics.

• Item Type: Articles
• Additional Information: The University of Dundee Solar MHD Group gratefully acknowledge support from STFC under consortium grants ST/K000993/1 and ST/N000714/1. This paper was prompted by discussions during a research visit of P.D. to the University of Dundee, which was kindly funded by the Northern Research Partnership (which is supported by The Scottish Funding Council) and organized by Dr. Miho Janvier.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Candelaresi, Dr Simon
• Authors: Russell, A.J.B., Demoulin, P., Hornig, G., Pontin, D.I., and Candelaresi, S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Astrophysical Journal
• Publisher: American Astronomical Society
• ISSN: 0004-637X
• ISSN (Online): 1538-4357
• Published Online: 11 October 2019
• Copyright Holders: Copyright © 2019 The American Astronomical Society
• First Published: First published in Astrophysical Journal 884(1): 55
• Publisher Policy: Reproduced under a Creative Commons License