Formation of reconnection region. Current density ( ) is shown by color scale, and 5 contour values of Az , , show representative fieldlines. Note that the y-coordinate is expanded by a factor of 40.
Width and length of the current sheet as a function of time. The width is defined by the half-width half-maximum based on the current density jz . The length is defined as the distance from x = 0 to the x location of maximum ion outflow on the y = 0 line. The current sheet width monotonically decreases during the simulation after t = 800 s, and eventually becomes less than the background neutral-ion collisional mean free path , which is at the end of the simulation. Before 800 s, the tearing instability has not developed enough to give a uniquely defined current sheet width and length. As the non-linear reconnection continues, the current sheet is seen to elongate after t = 1500 s.
Profiles across the current sheet (x = 0). Panel (a) shows the ion density ( ), panel (b) shows the current density ( ), panel (c) shows the ion inflow ( ), and panel (d) shows the difference in neutral and ion inflow ( ). This figure demonstrates the sharpening in the current density and ion density as the current sheet collapses. It also indicates that the peak in is approximately 0.1 times the peak in , i.e., the inflow is decoupled.
Profiles along the current sheet (y = 0). Panel (a) shows the ion density ( ). Panel (b) shows the current density ( ). Panel (c) shows the ion outflow ( ). Panel (d) shows the difference in neutral and ion outflow ( ). The difference in ion and neutral outflow is small compared to the ion outflow, and so the neutrals and ions fluids are coupled. The x location of the peak in the ion outflow can be seen to move outward in time (panel(c)).
Illustration of the decoupling of ion and neutral inflow during reconnection. At , the current sheet width is less than the background neutral-ion collisional mean free path . Panel (a): The ion (top left quadrant) and neutral (top right quadrant) inflows ( and ). The solid lines show 5 contour values of Az , . The vectors show ion flow on the bottom left quadrant and neutral flow on the bottom right quadrant. Panel (b): The ion and neutral outflows ( and ): The contour lines and vectors are the same as in the top panel.
Contributions to the plasma and neutral momentum equations. The top left quadrant shows , where , and the top right quadrant shows . The bottom half shows . The color is on a log-scale. This shows that balances on the collisional scale , while balances on scales greater than . The solid lines are 5 contour values of Az , .
The steady state reconnection region showing contributing sources and sinks of ions in the current sheet (in units of ): Top left quadrant shows rate of loss of ions due to recombination. Bottom left quadrant shows rate of loss of ions due to outflow . Top right quadrant shows rate of gain of ions due to inflow . Bottom right quadrant shows rate of gain of ions due to ionization. The solid lines are 5 contour values of Az , . This shows that ionization is negligible, and that outflow is larger than recombination.
Temporal evolution of the reconnection rate. Panel (a): Effective resistivity . Panel (b): , the maximum value of the current density, located at , within the reconnection region. Panel (c): where Bup is evaluated at and is the half-width at half-max of the current sheet. Panel (d): , the total density inside the current sheet at . Panel (e): , the current sheet Alfvén speed. Panel (f): .
Formation of plasmoids. Current density ( ) on the right, and ion density on the left. The black line is the contour and the white line is the contour. Note that the y-coordinate is expanded by a factor of 40.
Temporal evolution of the reconnection rate during the latter stages when the plasmoid instability sets in. Left panel: , the maximum value of the out of plane current density. Right panel: , the normalized reconnection rate.
Estimates of the Sweet-Parker width ( ) and neutral ion collisional mean free path ( ) using the FALC model of the solar chromosphere. 26 The solid lines show two extremes of the calculations of the resistive length. The higher value uses an aspect ratio of and a field strength of 5 G, and the smaller uses a current sheet aspect ratio of and a field strength of 1000 G. The dot-dashed line is the neutral-ion collisional mean free path, . This figure shows that for a range of heights in the chromosphere, the Sweet-Parker width can be larger than, but comparable to, the neutral-ion collisional mean free path, .
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