Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Abstract

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorovlike spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity , which depends on the spectral index of total energy for given B 0 loop parameters, must vary from for weak fields to for strong fields at a given aspect ratio. The predictedheating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

Coronal heating by magnetic reconnection in loops with zero net current

“…Recently, the development of such current sheets, and a cascade of energy to small-scales, has been demonstrated numerically in reduced MHD simulations (Rappazzo et al 2007(Rappazzo et al , 2008. However, this relies on rather more complex patterns of footpoint motions, and has continual driving.…”

Wave turbulence in magnetized plasmas

“…Weak MHD turbulence is now invoked has a possible regime for some coronal loops since a very small ratio is found between the fluctuating magnetic field and the axial component (Rappazzo et al, 2007(Rappazzo et al, , 2008. Inspired by the observations and by recent direct numerical simulations of 3-D MHD turbulence (Bigot et al, 2008b), an analytical model of coronal structures has been proposed (Bigot et al, 2008c) where the heating is seen as the end product of a wave turbulent cascade.…”

Closed-Field Coronal Heating Driven by Wave Turbulence

“…In short, coronal heating theories are typically classified in two main groups; mechanism involving wave dissipation, known as 'alternating current' (AC) theories, and those involving the buildup of magnetic stresses, known as 'directcurrent' (DC) theories. Because of the immense complexity of realistic coronal plasmas, progress for a given theory typically evolves from analytic theory (Hollweg 1978;Parker 1972), to sophisticated modeling for idealized configurations (Rappazzo et al 2008;van Ballegooijen et al 2011;Pontin & Hornig 2015), to implementations suitable for 3D magnetohydrodynamic (MHD) models (van der Holst et al 2014;Bingert & Peter 2011). All the while our observational capabilities have improved, and work has strived to provide constraints to proposed mechanisms (Mandrini et al 2000;Warren et al 2011;Schmelz et al 2015).…”