Activities per year
Abstract
Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergencefree field as the curl of a vector potential comes about because of homological considerations. With this in mind, we study gaugefreedom in magnetostatics and its effect on the comparison between magnetic configurations through key quantities such as the magnetic helicity. For this, we apply the Hodge decomposition of kforms on compact orientable Riemaniann manifolds with smooth boundary, as well as de Rham cohomology, to the representation of magnetic fields through potential 1forms in toroidal volumes. An advantage of the homological approach is the recovery of classical results without explicit coordinates and assumptions about the fields on the exterior of the domain. In particular, a detailed construction of a minimal gauge and a formal proof of relative helicity formulae are presented.
Original language  English 

Number of pages  15 
Specialist publication  arXiv preprint 
Publication status  Unpublished  6 Sep 2019 
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Activities
 1 Contribution or participation in a conference

Simons Collaboration on Hidden Symmetries and Fusion Energy
David Pfefferle (Participant)
28 Mar 2019 → 30 Mar 2019Activity: Conferences and workshops › Contribution or participation in a conference