Current Sheets Formation in Tangled Coronal Magnetic Fields

Abstract

We investigate the dynamical evolution of magnetic fields in closed regions of solar and stellar coronae. To understand under which conditions current sheets form, we examine dissipative and ideal reduced magnetohydrodynamic models in cartesian geometry, where two magnetic field components are present: the strong guide field B 0 , extended along the axial direction, and the dynamical orthogonal field b. Magnetic field lines thread the system along the axial direction, that spans the length L, and are line-tied at the top and bottom plates. The magnetic field b initially has only large scales, with its gradient (current) length-scale of order ℓ b . We identify the magnetic intensity threshold b/B 0 ∼ ℓ b /L. For values of b below this threshold, field-line tension inhibits the formation of current sheets, while above the threshold they form quickly on fast ideal timescales. In the ideal case, above the magnetic threshold, we show that current sheets thickness decreases in time until it becomes smaller than the grid resolution, with the analyticity strip width δ decreasing at least exponentially, after which the simulations become under-resolved.

Coronal heating and nanoflares: current sheet formation and heating

“…In the absence of current layers, the motions result in an increase of magnetic energy and the possible formation of current layers, but no significant heating. This is in agreement with the results found by Rappazzo & Parker (2013) who show that an initial configuration with a large-scale magnetic field develops small scales only above a magnetic intensity threshold.…”

Resistive Magnetohydrodynamics Simulations of the Ideal Tearing Mode

“…Our simulations provide further proof of the existence of such an instability, which is expected to set in during current sheet collapse arising in any turbulent scenario of plasma dynamics Servidio et al 2009;Rappazzo & Parker 2013).…”

Coronal Heating Topology: The Interplay of Current Sheets and Magnetic Field Lines

“…The imposed large-scale velocity at the boundaries z=0, and L twists the field lines and, once the twist exceeds a small critical threshold, the orthogonal magnetic field line tension is no longer balanced. Thus, as proposed by Parker (1972Parker ( , 1994, the magnetic field b transitions to non-equilibrium (Rappazzo & Parker 2013;Rappazzo 2015), bringing about turbulent dynamics that transfers energy towards the small scales where it is dissipated in nanoflares (Parker 1988). Line-tying keeps the velocity field in the computational box smaller than the magnetic field (far from equipartition).…”

“…Although the aforementioned studies include at most a weak guide magnetic field, the formation of current sheets with the exponentially thinning widths have been observed in fully nonlinear 2D and 3D MHD simulations (Sulem et al 1983;Frisch et al 2003;Krstulovic et al 2011;Brachet et al 2013), and line-tied simulations with a strong guide field and vanishing initial velocity (Rappazzo & Parker 2013). Although kinetic simulations with a strong guide field are still computationally challenging, we expect that the overall phenomenology and current sheet structure is not substantially modified in the strong guide field case of interest to the solar corona and inner heliosphere.…”