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Abstract
For the quadratic helicity χ(2) we present a generalization of the Arnol’d inequality which relates the magnetic energy to the quadratic helicity, which poses a lower bound. We then introduce the quadratic helicity density using the classical magnetic helicity density and its derivatives along magnetic ﬁeld lines. For practical purposes we also compute the ﬂow of the quadratic helicity and show that for an α2dynamo setting it coincides with the ﬂow of the square of the classical helicity. We then show how the quadratic helicity can be extended to obtain an invariant even under compressible deformations. Finally, we conclude with the numerical computation of χ(2) which show cases the practical usage of this higher order topological invariant.
Original language  English 

Article number  102128 
Journal  Physics of Plasmas 
Volume  24 
DOIs  
Publication status  Published  Oct 2017 
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Dive into the research topics of 'Calculations for the Practical Applications of Quadratic Helicity in MHD'. Together they form a unique fingerprint.Projects
 1 Finished

Dynamics of Complex Magnetic Fields: From the Corona to the Solar Wind (Joint with University of Durham)
Hornig, G. (Investigator) & Pontin, D. (Investigator)
Science and Technology Facilities Council
1/04/16 → 30/09/19
Project: Research