The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled, nevertheless current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions ($\sim 1,000 km$) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive ``bursty'' heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine bright in these wavelengths with little evidence of entangled features. The different regimes of weak and strong MHD turbulence that develop, and their influence on coronal heating scalings, are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in {\it stronger loop fields} and lead to {\it larger heating rates} than in weak field regions.Comment: 22 pages, 18 figures, uses emulateapj, for mpeg file associated to Figure 17e see (temporarily) http://www.df.unipi.it/~rappazzo/arxiv/jfl.mpg, ApJ, in pres
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.
Numerical simulations of a two-dimensional section of a coronal loop subject to random magnetic forcing are presented. The forcing models the link between photospheric motions and energy injection in the corona. The results show the highly intermittent spatial distribution of current concentrations generated by the coupling between internal dynamics and external forcing. The total power dissipation is a rapidly varying function of time, with sizable jumps even at low Reynolds numbers, and is caused by the superposition of magnetic dissipation in a number of localized current sheets. Both spatial and temporal intermittency increase with the Reynolds number, suggesting that the turbulent nature of the corona can physically motivate statistical theories of solar activity.
We present a series of numerical simulations aimed at understanding the nature and origin of turbulence in coronal loops in the framework of the Parker model for coronal heating. A coronal loop is studied via reduced magnetohydrodynamics simulations in Cartesian geometry. A uniform and strong magnetic field threads the volume between the two photospheric planes, where a velocity field in the form of a 1D shear flow pattern is present. Initially the magnetic field that develops in the coronal loop is a simple map of the photospheric velocity field. This initial configuration is unstable to a multiple tearing instability that develops islands with X and O points in the plane orthogonal to the axial field. Once the nonlinear stage sets in the system evolution is characterized by a regime of MHD turbulence dominated by magnetic energy. A well developed power law in energy spectra is observed and the magnetic field never returns to the simple initial state mapping the photospheric flow. The formation of X and O points in the planes orthogonal to the axial field allows the continued and repeated formation and dissipation of small scale current sheets where the plasma is heated. We conclude that the observed turbulent dynamics are not induced by the complexity of the pattern that the magnetic field-lines footpoints follow but they rather stem from the inherent nonlinear nature of the system.
Abstract. We have investigated a magnetohydrodynamic mechanism that accounts for several fundam6ntal properties of the slow solar wind, in particular its variability, latitudinal extent, and bulk acceleration. In view of the well-established association between the streamer belt and the slow wind, our model begins with a simplified representation of a streamer beyond the underlying coronal helmet: a neutral sheet embedded in a plane fluid wake. This wake-neutral sheet configuration is characterized by two parameters that vary with distance from the Sun: the ratio of the cross-stream velocity scale to the neutral sheet width, and the ratio of the typical Alfv6n velocity to the typical flow speed far from the neutral sheet. Depending on the values of these parameters, our linear theory predicts that three kinds of instability can develop when this system is perturbed: a tearing instability and two ideal fluid instabilities with different cross-stream symmetries (varicose and sinuous). In the innermost, magnetically dominated region beyond the helmet cusp, we find that the streamer is resistively and ideally unstable, evolving from tearing-type reconnection in the linear regime to a nonlinear varicose fluid instability. Traveling magnetic islands are formed which are similar to features recently revealed by the large-angle spectroscopic coronagraph on the joint European Space Agency/NASA Solar and Heliospheric Observatory (SOHO) [Brueckner et al., 1995]. During this process, the center of the wake is accelerated and broadened slightly. Past the Alfv6n point, where the kinetic energy exceeds the magnetic energy, the tearing mode is suppressed, but an ideal sinuous fluid mode can develop, producing additional acceleration up to typical slow wind speeds and substantial broadening of the wake. Farther from the Sun, the system becomes highly turbulent as a result of the development of ideal secondary instabilities, thus halting the acceleration and producing strong filamentation throughout the core of the wake. We discuss the implications of this model for the origin and evolution of the slow solar wind, and compare the predicted properties with current observations from SOHO. IntroductionThe solar wind has two distinct components: the fast wind
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