Topological Structures of Velocity and Electric Field in the Vicinity of a Cusp-type Magnetic Null Point

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 non-ideal Ohm's law concerning the Poincaré classes of all involved physical fields in 2D 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 2D standard magnetic cusp.

The Reversibility Of Magnetic Reconnection

“…Magnetic separatrices along the lines z = ± √ α B x divide space into upstream (|z| > √ α B |x|) and downstream (|z| < √ α B |x|) regions. Similar configurations have previously been investigated as models of reconnection 16,17 .…”