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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 forcefree 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 forcefree 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 forcefree 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.
Original language  English 

Article number  55 
Pages (fromto)  11 
Number of pages  11 
Journal  Astrophysical Journal 
Volume  884 
Issue number  1 
Early online date  10 Oct 2019 
DOIs  
Publication status  Published  10 Oct 2019 
Keywords
 Sun: Corona
 Sun: Heliosphere
 magnetic fields
ASJC Scopus subject areas
 Astronomy and Astrophysics
 Space and Planetary Science
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 2 Finished

Complex Magnetic Fields: An Enigma of Solar Plasmas (joint with Durham University)
Hornig, G., Pontin, D. & WilmotSmith, A.
Science and Technology Facilities Council
1/04/13 → 30/06/16
Project: Research