BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gunnar Hornig (Dundee University - UK) DTSTART:20230616T160000Z DTEND:20230616T170000Z DTSTAMP:20260423T023017Z UID:GEOTOP-A/60 DESCRIPTION:Title: Magnetohydrodynamic relaxation\, helicity and minimum energy states in m agnetised plasmas\nby Gunnar Hornig (Dundee University - UK) as part o f GEOTOP-A seminar\n\n\nAbstract\nDuring the turbulent relaxation of a pla sma with a high magnetic Reynolds number\, the magnetic energy is typicall y dissipated faster than the magnetic helicity. Hence one can attempt to d escribe the result of such a relaxation as a state that minimises the ener gy while preserving the magnetic helicity. Mathematically the relation bet ween magnetic helicity and energy is defined by an inequality\, $|H(B)| \\ le (2/C) E(B)$\, a result that was first shown in a classical paper by V.I . Arnold (1974) for simply connected domains. The formula shows how a non- trivial magnetic field topology (a non-zero helicity) forms a lower bound for the magnetic energy. The formula contains a constant C\, which is the smallest possible eigenvalue of the curl operator in a magnetically closed domain. The corresponding eigenfield is a state of maximum helicity for a given energy. We will discuss under which circumstances these maximum hel icity (minimum energy) states can be reached\, show how Arnold’s formula can be applied to non-simply connected domains\, and how one can modify A rnold’s formula to find lower bounds for the energy even if $H(B)=0$.\n\ nReferences:\n\nArnold\, V.I.\, The asymptotic Hopf invariant and its appl ication\, Sel. Math. Sov.\, 5\, 327 (1986)\n\nCandelaresi\, S.\, Pontin\, D. I.\, Hornig\, G.\, & Podger\, B. Topological Constraints in the reconne ction of vortex braids\, Physics of Fluids\, (33)\, 056101 (2021)\n\nYeate s\, A.R.\, Hornig\, G. and Wilmot-Smith\, A.L. Topological Constraints on Magnetic Relaxation\, Phys. Rev. Lett.\, 105\, 085002 (2010)\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/60/ END:VEVENT END:VCALENDAR