The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows t
hat their magnetic fields have an asymmetric structure in the axial direction with variation length-scale $z_ell sim ell B_0/b$, where $B_0$ is the intensity of the strong axial guide field, $b$ that of the orthogonal magnetic field component, and $ell$ the scale of $mathbf{b}$. Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length $z_ell gtrsim L_z$, and increasingly more asymmetric for smaller variation scales $z_ell lesssim L_z$. The $critical$ $length$ $z_ell sim L_z$ corresponds to the magnetic field intensity threshold $b sim ell B_0/L_z$. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore fields with intensities below such threshold evolve quasi-statically, readjusting to a nearby equilibrium, without developing nonlinear dynamics nor dissipating energy. But stronger fields cannot access their corresponding asymmetric equilibria, hence they are out-of-equilibrium and develop nonlinear dynamics. The subsequent formation of current sheets and energy dissipation is $necessary$ for the magnetic field to relax to equilibrium, since dynamically accessible equilibria have variation scales larger than the loop length $z_ell gtrsim L_z$, with intensities smaller than the threshold $b lesssim ell B_0/L_z$. The dynamical implications for magnetic fields of interest to solar and stellar coronae are investigated numerically and the impact on coronal physics discussed.
The acceleration of charged particles is relevant to the solar corona over a broad range of scales and energies. High-energy particles are usually detected in concomitance with large energy release events like solar eruptions and flares, nevertheless
acceleration can occur at smaller scales, characterized by dynamical activity near current sheets. To gain insight into the complex scenario of coronal charged particle acceleration, we investigate the properties of acceleration with a test-particle approach using three-dimensional magnetohydrodynamic (MHD) models. These are obtained from direct solutions of the reduced MHD equations, well suited for a plasma embedded in a strong axial magnetic field, relevant to the inner heliosphere. A multi-box, multi-scale technique is used to solve the equations of motion for protons. This method allows us to resolve an extended range of scales present in the system, namely from the ion inertial scale of the order of a meter up to macroscopic scales of the order of $10,$km ($1/100$th of the outer scale of the system). This new technique is useful to identify the mechanisms that, acting at different scales, are responsible for acceleration to high energies of a small fraction of the particles in the coronal plasma. We report results that describe acceleration at different stages over a broad range of time, length and energy scales.
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 geome
try, where two magnetic field components are present: the strong guide field $B_0$, extended along the axial direction, and the dynamical orthogonal field $mathbf{b}$. 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 $ell_b$. We identify the magnetic intensity threshold $b/B_0 sim ell_b/L$. 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 $delta$ decreasing at least exponentially, after which the simulations become under-resolved.
We present simulations modeling closed regions of the solar corona threaded by a strong magnetic field where localized photospheric vortical motions twist the coronal field lines. The linear and nonlinear dynamics are investigated in the reduced magn
etohydrodynamic regime in Cartesian geometry. Initially the magnetic field lines get twisted and the system becomes unstable to the internal kink mode, confirming and extending previous results. As typical in this kind of investigations, where initial conditions implement smooth fields and flux-tubes, we have neglected fluctuations and the fields are laminar until the instability sets in. But previous investigations indicate that fluctuations, excited by photospheric motions and coronal dynamics, are naturally present at all scales in the coronal fields. Thus, in order to understand the effect of a photospheric vortex on a more realistic corona, we continue the simulations after kink instability sets in, when turbulent fluctuations have already developed in the corona. In the nonlinear stage the system never returns to the simple initial state with ordered twisted field lines, and kink instability does not occur again. Nevertheless field lines get twisted, but in a disordered way, and energy accumulates at large scales through an inverse cascade. This energy can subsequently be released in micro-flares or larger flares, when interaction with neighboring structures occurs or via other mechanisms. The impact on coronal dynamics and CMEs initiation is discussed.
Magnetic reconnection at the interface between coronal holes and loops, so-called interchange reconnection, can release the hotter, denser plasma from magnetically confined regions into the heliosphere, contributing to the formation of the highly var
iable slow solar wind. The interchange process is often thought to develop at the apex of streamers or pseudo-streamers, near Y and X-type neutral points, but slow streams with loop composition have been recently observed along fanlike open field lines adjacent to closed regions, far from the apex. However, coronal heating models, with magnetic field lines shuffled by convective motions, show that reconnection can occur continuously in unipolar magnetic field regions with no neutral points: photospheric motions induce a magnetohydrodynamic turbulent cascade in the coronal field that creates the necessary small scales, where a sheared magnetic field component orthogonal to the strong axial field is created locally and can reconnect. We propose that a similar mechanism operates near and around boundaries between open and closed regions inducing a continual stochastic rearrangement of connectivity. We examine a reduced magnetohydrodynamic model of a simplified interface region between open and closed corona threaded by a strong unipolar magnetic field. This boundary is not stationary, becomes fractal, and field lines change connectivity continuously, becoming alternatively open and closed. This model suggests that slow wind may originate everywhere along loop-coronal hole boundary regions, and can account naturally and simply for outflows at and adjacent to such boundaries and for the observed diffusion of slow wind around the heliospheric current sheet.
Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets w
here energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a system where energy is deposited at unresolved small-scales. Methods. Fully compressible three-dimensional magnetohydrodynamic simulations are carried out to understand the thermodynamics of coronal heating in the magnetically confined solar corona. Results. We show that temperature is highly structured at scales below observational resolution and nonhomogeneously distributed so that only a fraction of the coronal mass and volume gets heated at each time. Conclusions. This is a multi-thermal system where hotter and cooler plasma strands are found one next to the other also at sub-resolution scales and exhibit a temporal dynamics.
The fundamental assumptions of the adiabatic theory do not apply in presence of sharp field gradients as well as in presence of well developed magnetohydrodynamic turbulence. For this reason in such conditions the magnetic moment $mu$ is no longer ex
pected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width $Delta mu$ (defined as the half peak-to-peak difference in the particle magnetic moment) and the bounce frequency $omega_b$. We perform test-particle simulations to investigate magnetic moment behavior when resonances overlapping occurs and during the interaction of a ring-beam particle distribution with a broad-band slab spectrum. We find that magnetic moment dynamics is strictly related to pitch angle $alpha$ for a low level of magnetic fluctuation, $delta B/B_0 = (10^{-3}, , 10^{-2})$, where $B_0$ is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function $f(alpha)$. This is a transient regime during which magnetic moment distribution $f(mu)$ exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance $<(Delta z)^2 >$ grows linearly in time as in normal diffusion. With strong fluctuations $f(alpha)$ isotropizes completely, spatial diffusion sets in and $f(mu)$ behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
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 which developes in the coronal loop is a simple map of the photospheric velocity field. This initial configuration is unstable to a multiple tearing instability which 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.
The plasma density enhancements recently observed by the Large-Angle Spectrometric Coronagraph (LASCO) instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft have sparked considerable interest. In our previous theoretical study o
f the formation and initial motion of these density enhancements it is found that beyond the helmet cusp of a coronal streamer the magnetized wake configuration is resistively unstable, that a traveling magnetic island develops at the center of the streamer, and that density enhancements occur within the magnetic islands. As the massive magnetic island travels outward, both its speed and width increase. The island passively traces the acceleration of the inner part of the wake. In the present paper a few spherical geometry effects are included, taking into account either the radial divergence of the magnetic field lines and the average expansion suffered by a parcel of plasma propagating outward, using the Expanding Box Model (EBM), and the diamagnetic force due to the overall magnetic field radial gradients, the so-called melon-seed force. It is found that the values of the acceleration and density contrasts can be in good agreement with LASCO observations, provided the spherical divergence of the magnetic lines starts beyond a critical distance from the Sun and the initial stage of the formation and acceleration of the plasmoid is due to the cartesian evolution of MHD instabilities. This result provides a constraint on the topology of the magnetic field in the coronal streamer.
The Parker or field line tangling model of coronal heating is investigated through long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photosp
heric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy and characterized by current sheets elongated along the axial magnetic field. Increasing the value of the axial magnetic field different regimes of MHD turbulence develop with a bearing on coronal heating rates. In physical space magnetic field lines at the scale of convection cells appear only slightly bended in agreement with observations of large loops of current (E)UV and X-ray imagers.
