Abstract
We perform a set of two dimensional resistive magnetohydrodynamic simulations to study the reconnection process occurring in current sheets that develop during solar eruptions. Reconnection commences gradually and produces smallscale structures inside the current sheet, which has one end anchored to the bottom boundary and the other end open. The main features we study include plasmoids (or plasma blobs) flowing in the sheet, and Xpoints between pairs of adjacent islands. The statistical properties of the fine structure and the dependence of the spectral energy on these properties are examined. The flux and size distribution functions of plasmoids roughly follow inverse square power laws at large scales. The mass distribution function is steep at large scales and shallow at small scales. The size distribution also shows that plasmoids are highly asymmetric soon after being formed, while older plasmoids tend to be more circular. The spectral profiles of magnetic and kinetic energy inside the current sheet are both consistent with a power law. The corresponding spectral indices γ are found to vary with the magnetic Reynolds number of the system, but tend to approach a constant for large . The motion and growth of blobs change the spectral index. The growth of new islands causes the power spectrum to steepen, but it becomes shallower when old and large plasmoids leave the computational domain.
We think the anonymous referee for very useful comments. This research is supported by NASA Grant NNX11AB61G, NASA Contract NNM0FAB0FC, and NSF SHINE Grant AGS1156076 to the Smithsonian Astrophysical Observatory. This work was also supported by Program 973 Grants 2011CB811403 and 2013CBA01503, NSFC Grant 11273055, and CAS Grant KJCX2EWT07.
I. INTRODUCTION
II. NUMERICAL METHOD
III. CRITICAL MAGNETIC REYNOLDS NUMBER
IV. PLASMOID FLUX, WIDTH, AND MASS DISTRIBUTION FUNCTIONS
V. SPECTRAL ANALYSIS OF THE CURRENT SHEET
VI. VARIATION OF THE ENERGY SPECTRUM VERSUS TIME
VII. VARIATIONS OF THE ENERGY SPECTRUM VERSUS
VIII. PHYSICAL MECHANISMS RESPONSIBLE FOR CHANGES IN MAGNETIC ENERGY SPECTRA
IX. CONCLUSION
Figures
Density ρ (color scales) and magnetic flux (solid lines) contours as reconnection progresses in different Rm environments: (a) , (b) , and (c) .
Density ρ (color scales) and magnetic flux (solid lines) contours as reconnection progresses in different Rm environments: (a) , (b) , and (c) .
Plasmoid flux distribution function for different Rm . The dashed straight line represents .
Plasmoid flux distribution function for different Rm . The dashed straight line represents .
Plasmoid width distribution function for different Rm . Here, wx is the full width of each plasmoid measured in the xdirection across the current sheet. The dashed straight line corresponds to .
Plasmoid width distribution function for different Rm . Here, wx is the full width of each plasmoid measured in the xdirection across the current sheet. The dashed straight line corresponds to .
Plasmoid mass distribution function f(m) for different Rm . Here, m is the amount mass contained inside each plasmoid. The dashed straight line shows an m −2 power law for reference.
Plasmoid mass distribution function f(m) for different Rm . Here, m is the amount mass contained inside each plasmoid. The dashed straight line shows an m −2 power law for reference.
Plasmoid width distribution in two directions for the case of . Here, wz and wx are the widths of each plasmoid along the zand xdirections, respectively. Colorbar indicates the mass contained in each plasmoid.
Plasmoid width distribution in two directions for the case of . Here, wz and wx are the widths of each plasmoid along the zand xdirections, respectively. Colorbar indicates the mass contained in each plasmoid.
Distributions of magnetic energy density Em along the zaxis (a), and the corresponding Fourier power spectrum (b). The straight line in (b) is the fitting of a power law function to the experimental data with index of 2.92.
Distributions of magnetic energy density Em along the zaxis (a), and the corresponding Fourier power spectrum (b). The straight line in (b) is the fitting of a power law function to the experimental data with index of 2.92.
Same as Fig. 6 , but for the kinetic energy.
(a) Variations of and versus time for . The solid line is for and the dashed line is for . (b) Variations of and of simulation box versus time. The solid line is for and the dashed line is for . The arrows in both panels specify the time when the nonlinear stage begins.
(a) Variations of and versus time for . The solid line is for and the dashed line is for . (b) Variations of and of simulation box versus time. The solid line is for and the dashed line is for . The arrows in both panels specify the time when the nonlinear stage begins.
Dependence of the Fourier power spectrum indices on Rm : (a) versus Rm , and (b) versus Rm . The solid lines are for the spectral index averaged over a given time interval when the total electric current density is close to its maximum, and the dashed lines are for the index at maximum.
Dependence of the Fourier power spectrum indices on Rm : (a) versus Rm , and (b) versus Rm . The solid lines are for the spectral index averaged over a given time interval when the total electric current density is close to its maximum, and the dashed lines are for the index at maximum.
Magnetic energy spectrum becomes steeper with the growth of magnetic islands. (a) The distributions of density ρ along the center of the current at different times, which shows that the new magnetic islands form and grow rapidly during this period; (b) The distribution of magnetic energy at t = 32.5 and t = 33.0; (c) and (d) are for magnetic energy spectrum at initial and final time.
Magnetic energy spectrum becomes steeper with the growth of magnetic islands. (a) The distributions of density ρ along the center of the current at different times, which shows that the new magnetic islands form and grow rapidly during this period; (b) The distribution of magnetic energy at t = 32.5 and t = 33.0; (c) and (d) are for magnetic energy spectrum at initial and final time.
Magnetic energy spectrum becomes steeper with the merging process of magnetic islands. (a)–(d) are same as Fig. 10 .
Magnetic energy spectrum becomes steeper with the merging process of magnetic islands. (a)–(d) are same as Fig. 10 .
Magnetic energy spectrum becomes shallower when the large scale magnetic islands move out the system. (a)–(d) are same as Fig. 10 .
Magnetic energy spectrum becomes shallower when the large scale magnetic islands move out the system. (a)–(d) are same as Fig. 10 .
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