Main category
Natural Sciences (Mathematics)
Abstract
*Quadratic Helicity in MHD*
We discuss the definitions and properties of the helicity $\chi$ and of
the quadratic helicities \chi^{[2]} and \chi^{(2)} in MHD. A formula for
the practical computation of the quadratic helicity density $\chi^{(2)}$
is presented. We also explain why the examples of geodesic flows by P.
Dehornoy determine magnetic fields in a 3D domain $\Omega$ of minimal
magnetic energy with a constant helicity density and minimal quadratic
helicity: $\chi^{(2)} = \chi^2/Vol(\Omega)$. This is a joint result
with Simon Candelaresi and Alexandr Smirnov.
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