2019/01/28 by Dieter H. Nickeler, D. H. Nickeler, M. Karlický +3 · 1 citation
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Classical mechanics #Cusp (singularity) #Geometry #Hessian matrix #Magnetic field #Mathematics #Physics #Quantum mechanics #Saddle point #Solar and Space Plasma Dynamics #Stellar, planetary, and galactic studies #Topology (electrical circuits) #astro-ph.SR #physics.flu-dyn #physics.plasm-ph #physics.space-ph
paper · pdf · doi:10.3847/1538-4357/ab020b
10 pages, 6 figures. Accepted for publication in ApJ
arxiv created 2019/01/28 · openalex created_date 2019/02/21 · openalex publication_date 2019/03/01 · arxiv updated 2019/03/06 · openalex updated_date 2026/08/05
Abstract Topological characteristics reveal important physical properties of plasma structures and astrophysical processes. Physical parameters and constraints are linked with topological invariants, which are important for describing magnetic reconnection scenarios. We analyze stationary nonideal Ohm’s law concerning the Poincaré classes of all involved physical fields in two dimensions by calculating the corresponding topological invariants of their Jacobian (here: particularly the eigenvalues) or Hessian matrices. The magnetic field is assumed to have a cusp structure, and the stagnation point of the plasma flow coincides with the cusp. We find that the stagnation point must be hyperbolic. Furthermore, the functions describing both the resistivity and the ohmic heating have a saddle-point structure, being displaced with respect to the cusp point. These results imply that there is no monotonous relation between current density and anomalous resistivity in the case of a two-dimensional standard magnetic cusp.