Editors' Choice: Definition of the Spatial Propagator and Implications for Magnetic Field Properties
Edmondson, J.K. & Démoulin, P., Definition of the Spatial Propagator and Implications for Magnetic Field Properties, Sol Phys (2019) 294: 76. https://doi.org/10.1007/s11207-019-1452-4
Editor's Choice (Research Article)
First Online: 12 June 2019
We present a theoretical framework to analyze the 3D coronal vector magnetic-field structure. We assume that the vector magnetic field exists and is a priori smooth. We introduce a generalized connectivity phase space associated with the vector magnetic field in which the basic elements are the field line and its linearized variation: the Spatial Propagator. We provide a direct formulation of these elements in terms of the vector magnetic field and its spatial derivatives, constructed with respect to general curvilinear coordinates and the equivalence class of general affine parameterizations. The Spatial Propagator describes the geometric organization of the local bundle of field lines, equivalent to the kinematic deformation of a propagated volume tied to the bundle. The Spatial Propagator’s geometric properties are characterized by dilation, anisotropic stretch, and rotation. Extreme singular values of the Spatial Propagator describe quasi-separatrix layers (QSLs), while true separatrix surfaces and separator lines are identified by the vanishing of one and two singular values, respectively. Finally, we show that, among other possible applications, the squashing factor [Q] is easily constructed from an analysis of particular sub-matrices of the Spatial Propagator.
Justin K. Edmondson is an Adjunct Research Scientist at the Department of Climate and Space Science and Engineering of the University of Michigan, Ann Arbor, and Aerospace Engineer in the US Department of the of Navy. His research interests are in mathematical hydrodynamics and magnetohydrodynamics in astrophysical contexts.
Pascal Démoulin is Astronome Adjoint at LESIA, Observatoire de Paris in Meudon, France. He is an expert on magnetohydrodynamics (MHD) and solar eruptive events.
Solar Physics Editor's Choice:
In each volume of Solar Physics, a few papers are marked as “Editors’ Choice”. The primary criteria is original, high quality research that is of wide interest within the community.