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Register a new userImpact of Temperature-dependent resistivity and thermal conduction on plasmoid Instabilities in current sheets in the solar corona
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In this paper we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection $X$-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting $X-$points and transfer the heat into the $O-$points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, $eta sim T^{-3/2}$, the decrease in plasma temperature at the $X-$points leads to: (i) increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction; (ii) increase in the reconnection rate; and, (iii) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.
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Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S^{1/4} v_A/L, where L is the length of the sheet, v_A the Alfven speed and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S^{3/8}.
A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{rm max}Lsheet sim S^{3/8}$, where $k_{rm max}$ is the wave-number of fastest growing mode, $S=Lsheet V_A/eta$ is the Lundquist number, $Lsheet$ is the length of the sheet, $V_A$ is the Alfven speed and $eta$ is the plasma resistivity), which grows super-Alfvenically fast ($gmaxtau_Asim S^{1/4}$, where $gmax$ is the maximum growth rate, and $tau_A=Lsheet/V_A$). For typical background profiles, the growth rate and the wave-number are found to {it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfven speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, $gmax tau_A sim k_{rm max} Lsheetsim S^{1/2}$. The effect of viscosity ($ u$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm= u/eta$, it is found that $gmaxsim S^{1/4}Pm^{-5/8}$ and $k_{rm max} Lsheetsim S^{3/8}Pm^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pmgg1$ regime is $Scritsim 10^4Pm^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.
We present two-dimensional resistive magnetohydrodynamic simulations of line-tied asymmetric magnetic reconnection in the context of solar flare and coronal mass ejection current sheets. The reconnection process is made asymmetric along the inflow direction by allowing the initial upstream magnetic field strengths and densities to differ, and along the outflow direction by placing the initial perturbation near a conducting wall boundary that represents the photosphere. When the upstream magnetic fields are asymmetric, the post-flare loop structure is distorted into a characteristic skewed candle flame shape. The simulations can thus be used to provide constraints on the reconnection asymmetry in post-flare loops. More hard X-ray emission is expected to occur at the footpoint on the weak magnetic field side because energetic particles are more likely to escape the magnetic mirror there than at the strong magnetic field footpoint. The footpoint on the weak magnetic field side is predicted to move more quickly because of the requirement in two dimensions that equal amounts of flux must be reconnected from each upstream region. The X-line drifts away from the conducting wall in all simulations with asymmetric outflow and into the strong magnetic field region during most of the simulations with asymmetric inflow. There is net plasma flow across the X-line for both the inflow and outflow directions. The reconnection exhaust directed away from the obstructing wall is significantly faster than the exhaust directed towards it. The asymmetric inflow condition allows net vorticity in the rising outflow plasmoid which would appear as rolling motions about the flux rope axis.
In the present work we study evolution of magnetic helicity in the solar corona. We compare the rate of change of a quantity related to the magnetic helicity in the corona to the flux of magnetic helicity through the photosphere and find that the two rates are similar. This gives observational evidence that helicity flux across the photosphere is indeed what drives helicity changes in solar corona during emergence. For the purposes of estimating coronal helicity we neither assume a strictly linear force-free field, nor attempt to construct a non-linear force-free field. For each coronal loop evident in Extreme Ultraviolet (EUV) we find a best-matching line of a linear force-free field and allow the twist parameter alpha to be different for each line. This method was introduced and its applicability was discussed in Malanushenko et. al. (2009). The object of the study is emerging and rapidly rotating AR 9004 over about 80 hours. As a proxy for coronal helicity we use the quantity <alpha_i*L_i/2> averaged over many reconstructed lines of magnetic field. We argue that it is approximately proportional to flux-normalized helicity H/Phi^2, where H is helicity and Phi is total enclosed magnetic flux of the active region. The time rate of change of such quantity in the corona is found to be about 0.021 rad/hr, which is compatible with the estimates for the same region obtained using other methods Longcope et. al. (2007), who estimated the flux of normalized helicity of about 0.016 rad/hr.
Magnetic reconnection, a fundamentally important process in many aspects of astrophysics, is believed to be initiated by the tearing instability of an electric current sheet, a region where magnetic field abruptly changes direction and electric currents build up. Recent studies have suggested that the amount of magnetic shear in these structures is a critical parameter for the switch-on nature of magnetic reconnection in the solar atmosphere, at fluid spatial scales much larger than kinetic scales. We present results of simulations of reconnection in 3D current sheets with conditions appropriate to the solar corona. Using high-fidelity simulations, we follow the evolution of the linear and non-linear 3D tearing instability, leading to reconnection. We find that, depending on the parameter space, magnetic shear can play a vital role in the onset of significant energy release and heating via non-linear tearing. Two regimes in our study exist, dependent on whether the current sheet is longer or shorter than the wavelength of the fastest growing parallel mode (in the corresponding infinite system), thus determining whether sub-harmonics are present in the actual system. In one regime, where the fastest growing parallel mode has sub-harmonics, the non-linear interaction of these sub-harmonics and the coalescence of 3D plasmoids dominates the non-linear evolution, with magnetic shear playing only a weak role in the amount of energy released. In the second regime, where the fastest growing parallel mode has no-sub-harmonics, then only strongly sheared current sheets, where oblique mode are strong enough to compete with the dominant parallel mode, show any significant energy release. We expect both regimes to exist on the Sun, and so our results have important consequences for the the question of reconnection onset in different solar physics applications.
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