(Color online) The parameter space in the phase diagram is divided into four regions. (1) Hall reconnection: di > δSP . (2) Sweet–Parker reconnection: di < δSP and S < Sc . (3) Hall reconnection triggered by plasmoids: δSP (Sc /S)1/2 < di < δSP . (4) Plasmoid-dominated reconnection: S > Sc and δSP (Sc /S)1/2 > di . The dots denote the parameters for three different runs. All three runs have S = 5 × 105. The parameter L/di is 2.5 × 103 for Run A, 5 × 103 for Run B, and 104 for Run C, respectively. A fourth run, Run D, from a previous resistive MHD study,13 corresponds to L/di → ∞, therefore is not shown.
(Color online) The reconnection rate as a function of time for four different runs.
(Color online) The length (upper curve) and width (lower curve) of the main reconnection current sheet as a function of time for four different runs.
(Color online) Out-of-plane electric current density at t = 1.5 for Run A, overlaid with magnetic field lines, in the whole simulation box. Dashed lines indicate separatrices, which are the field lines that separate the two merging islands.
(Color online) Time sequence of the out-of-plane electric current density for Run B, overlaid with magnetic field lines. Dashed lines indicate separatrices. From top to bottom: (1) the Sweet–Parker current sheet breaks up into a chain of plasmoids. (2) The plasmoids grow in size; some of them are expelled to the downstream region; some of them coalesce to form larger plasmoids. (3) A new plasmoid forms at the main current sheet. (4) The formation of the new plasmoid leads to an onset of Hall reconnection that eventually expels all plasmoids. (5) The current sheet becomes extended again. (6) Subsequently, the extended current sheet breaks up into plasmoids, which lead to another onset of Hall reconnection. The bottom panel shows an expanded view of the extended current sheet at t = 1.95 (enhanced online). [URL: http://dx.doi.org/10.1063/1.3606363.1]10.1063/1.3606363.1
(Color online) The length (upper curve) and width (lower curve) of the main reconnection current sheet, normalized to the ion skin depth di , as a function of time for Run A to Run C.
(Color online) The electron and ion flows along the inflow (z) direction through the X-point for Run B at t = 1.55 and t = 1.95.
(Color online) Time sequence of the out-of-plane electric current density for the artificial test, overlaid with magnetic field lines. The initial condition is taken from Run A at t = 1.3, with the ion skin depth di artificially lowered from 4 × 10−4 to 2 × 10−4, which is the same as Run B. The opening angle between the separatrices quickly closes up, first starting from the center, then gradually propagating outward. As the current sheet becomes extended, it becomes unstable to the plasmoid instability (enhanced online). [URL: http://dx.doi.org/10.1063/1.3606363.2]10.1063/1.3606363.2
(Color online) The separatrices of the three runs when the reconnected fluxes are approximately the same . Only the region z > 0 is shown. Upper panel: the whole simulation domain. Lower panel: a close-up view around the X-point. Note that in the lower panel, the coordinates are normalized to di and shifted horizontally to account for the slight misalignment of the X-point for each run. Also the z direction is stretched for better visualization.
(Color online) Current density profiles along the inflow (upper panel) and the outflow (lower panel) directions. Here, we normalize the coordinates to di and the current density to the peak value.
(Color online) The electron and ion inflows (upper panel) and the balance of Ey = −(u e × B) y + ηJy (lower panel) in the generalized Ohm’s law, for the case L/di = 1000.
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