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Register a new userCurrent Sheet Statistics in Three-Dimensional Simulations of Coronal Heating
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In a recent numerical study [Ng et al., Astrophys. J. {bf 747}, 109, 2012], with a three-dimensional model of coronal heating using reduced magnetohydrodynamics (RMHD), we have obtained scaling results of heating rate versus Lundquist number based on a series of runs in which random photospheric motions are imposed for hundreds to thousands of al time in order to obtain converged statistical values. The heating rate found in these simulations saturate to a level that is independent of the Lundquist number. This scaling result was also supported by an analysis with the assumption of the Sweet-Parker scaling of the current sheets, as well as how the width, length and number of current sheets scale with Lundquist number. In order to test these assumptions, we have implemented an automated routine to analyze thousands of current sheets in these simulations and return statistical scalings for these quantities. It is found that the Sweet-Parker scaling is justified. However, some discrepancies are also found and require further study.
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We simulate a coronal mass ejection (CME) using a three-dimensional magnetohydrodynamic (MHD) code that includes coronal heating, thermal conduction, and radiative cooling in the energy equation. The magnetic flux distribution at 1 R$_s$ is produced by a localized subsurface dipole superimposed on a global dipole field, mimicking the presence of an active region within the global corona. Transverse electric fields are applied near the polarity inversion line to introduce a transverse magnetic field, followed by the imposition of a converging flow to form and destabilize a flux rope, producing an eruption. We examine the quantities responsible for plasma heating and cooling during the eruption, including thermal conduction, radiation, adiabatic effects, coronal heating, and ohmic heating. We find that ohmic heating is an important contributor to hot temperatures in the current sheet region early in the eruption, but in the late phase adiabatic compression plays an important role in heating the plasma there. Thermal conduction also plays an important role in the transport of thermal energy away from the current sheet region throughout the reconnection process, producing a ``thermal halo and widening the region of high temperatures. We simulate emission from solar telescopes for this eruption and find that there is evidence for emission from heated plasma above the flare loops late in the eruption, when the adiabatic heating is the dominant heating term. These results provide an explanation for hot supra-arcade plasma sheets that are often observed in X-rays and extreme ultraviolet wavelengths during the decay phase of large flares.
Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfv{e}n waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of $k_{perp}^{-1.3}$. The kinetic code shows a spectral slope of $k_{perp}^{-1.5}$ for smaller simulation domain, and $k_{perp}^{-1.3}$ for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.
Context. The recent discovery of much greater magnetic flux cancellation taking place at the photosphere than previously realised has led us in our previous works to suggest magnetic reconnection driven by flux cancellation as the cause of a wide range of dynamic phenomena, including jets of various kinds and solar atmospheric heating. Aims. Previously, the theory considered energy release at a two-dimensional current sheet. Here we develop the theory further by extending it to an axisymmetric current sheet in three dimensions without resorting to complex variable theory. Methods. We analytically study reconnection and treat the current sheet as a three-dimensional structure. We apply the theory to the cancellation of two fragments of equal but opposite flux that approach each another and are located in an overlying horizontal magnetic field. Results. The energy release occurs in two phases. During Phase 1, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating a plasma jet as it does so. During Phase 2 the fluxes cancel in the photosphere and accelerate a mixture of cool and hot plasma upwards.
The spreading of the X-line out of the reconnection plane under a strong guide field is investigated using large-scale three-dimensional (3D) particle-in-cell (PIC) simulations in asymmetric magnetic reconnection. A simulation with a thick, ion-scale equilibrium current sheet (CS) reveals that the X-line spreads at the ambient ion/electron drift speeds, significantly slower than the Alfven speed based on the guide field $V_{Ag}$. Additional simulations with a thinner, sub-ion-scale CS show that the X-line spreads at $V_{Ag}$ (Alfvenic spreading), much higher than the ambient species drifts. An Alfvenic signal consistent with kinetic Alfven waves develops and propagates, leading to CS thinning and extending, which then results in reconnection onset. The continuous onset of reconnection in the signal propagation direction manifests as Alfvenic X-line spreading. The strong dependence on the CS thickness of the spreading speeds, and the X-line orientation are consistent with the collisionless tearing instability. Our simulations indicate that when the collisionless tearing growth is sufficiently strong in a thinner CS such that $gamma/Omega_{ci}gtrsimmathcal{O}(1)$, Alfvenic X-line spreading can take place. Our results compare favorably with a number of numerical simulations and recent magnetopause observations. A key implications is that the magnetopause CS is typically too thick for Alfvenic X-line spreading to effectively take place.
The magnetic fields of interplanetary coronal mass ejections (ICMEs), which originate close to the Sun in the form of a flux rope, determine their geoeffectiveness. Therefore, robust flux rope-based models of CMEs are required to perform magnetohydrodynamic (MHD) simulations aimed at space weather predictions. We propose a modified spheromak model and demonstrate its applicability to CME simulations. In this model, such properties of a simulated CME as the poloidal and toroidal magnetic fluxes, and the helicity sign can be controlled with a set of input parameters. We propose a robust technique for introducing CMEs with an appropriate speed into a background, MHD solution describing the solar wind in the inner heliosphere. Through a parametric study, we find that the speed of a CME is much more dependent on its poloidal flux than on the toroidal flux. We also show that the CME speed increases with its total energy, giving us control over its initial speed. We further demonstrate the applicability of this model to simulations of CME-CME collisions. Finally, we use this model to simulate the 12 July 2012 CME and compare the plasma properties at 1 AU with observations. The predicted CME properties agree reasonably with observational data.
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