Self-consistent stationary MHD shear flows in the solar atmosphere as electric field generators

Abstract

Context. Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria. Aims. Within a physically simplified, but exact mathematical model, we study the electric currents and corresponding electric fields generated by shear flows. Methods. Starting from exact and analytically calculated magnetic potential fields, we solved the nonlinear MHD equations selfconsistently. By applying a magnetic shear flow and assuming a nonideal MHD environment, we calculated an electric field via Faraday's law. The formal solution for the electromagnetic field allowed us to compute an expression of an effective resistivity similar to the collisionless Speiser resistivity. Results. We find that the electric field can be highly spatially structured, or in other words, filamented. The electric field component parallel to the magnetic field is the dominant component and is high where the resistivity has a maximum. The electric field is a potential field, therefore, the highest energy gain of the particles can be directly derived from the corresponding voltage. In our example of a coronal post-flare scenario we obtain electron energies of tens of keV, which are on the same order of magnitude as found observationally. This energy serves as a source for heating and acceleration of particles.

An Optimization Principle for Computing Stationary MHD Equilibria with Solar Wind Flow

“…We are aware that non-ideal effects as, e.g., caused by turbulence, can lead to a violation of ideal Ohm's law and play an important role for coronal heating and solar wind expansion (see Cranmer et al, 2015, for a review article). For special cases (2.5D, incompressible flow and no gravity) stationary solutions of resistive MHD have been found (see, e.g., Throumoulopoulos, 1998;Throumoulopoulos and Tasso, 2000;Nickeler et al, 2014). Studying turbulence and resistivity is well outside the scope of this work, however.…”

An optimization principle for computing stationary MHD equilibria with solar wind flow

“…We are aware that nonideal effects as, e.g., caused by turbulence, can lead to a violation of ideal Ohm's law and play an important role for coronal heating and solar wind expansion (see Cranmer et al, 2015, for a review article). For special cases (2.5D, incompressible flow and no gravity) stationary solutions of resistive MHD have been found (see, e.g., Throumoulopoulos, 1998;Throumoulopoulos and Tasso, 2000;Nickeler et al, 2014). Studying turbulence and resistivity is well outside the scope of this work, however.…”

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

“…In 2D, the search of the Poincaré class of the total electric field is linked to the Poincaré class of the resistivity. It is well known that for exact and analytical reconnection solutions, it is not sufficient to assume any non-ideal term or non-idealness or for example a constant resistivity (Priest et al 1994;Craig & Henton 1995;Watson & Craig 1998;Throumoulopoulos & Tasso 2000;Titov & Hornig 2000;Nickeler et al 2012Nickeler et al , 2014. For the classical role of reconnection in 2D it is inevitable that the plasma flow can cross both magnetic separatrix branches, as this scenario constitutes the reconnection solution.…”