TY - UNPB
T1 - On self and mutual winding helicity
AU - Candelaresi, Simon
AU - Hornig, Gunnar
AU - MacTaggart, David
AU - Simitev, Radostin D.
PY - 2021/8/19
Y1 - 2021/8/19
N2 - The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly calculated relative helicity. Winding helicity, however, has several advantages, and we explore some of these in this work. In particular, we show, by splitting the domain into distinct subregions, that winding helicity can be decomposed naturally into "self" and "mutual" components and that these quantities can be calculated, in practice, for magnetic fields with complex geometries and topologies. Further, winding provides a unified topological description from which known expressions for self and mutual helicity can be readily derived and generalized. We illustrate the application of calculating self and mutual winding helicities in a simulation of an evolving magnetic field with non-trivial field line topology.
AB - The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly calculated relative helicity. Winding helicity, however, has several advantages, and we explore some of these in this work. In particular, we show, by splitting the domain into distinct subregions, that winding helicity can be decomposed naturally into "self" and "mutual" components and that these quantities can be calculated, in practice, for magnetic fields with complex geometries and topologies. Further, winding provides a unified topological description from which known expressions for self and mutual helicity can be readily derived and generalized. We illustrate the application of calculating self and mutual winding helicities in a simulation of an evolving magnetic field with non-trivial field line topology.
KW - math-ph
KW - math.MP
KW - nlin.CD
KW - physics.flu-dyn
KW - physics.plasm-ph
UR - https://arxiv.org/abs/2108.08888v1
M3 - Preprint
BT - On self and mutual winding helicity
PB - arXiv
ER -