The topology of double separator reconnection during a simple zippette with positive (P1 and P2) and negative (N1 and N2) flux sources, passing from (a) the initial topology through (b) an intermediate phase to (c) the final topology. Null points lying midway between P1 and P2 and between N1 and N2 in the photospheric plane are indicated by large dots. The diagrams on the top line represent the overall topology, while those below show the detailed topology in the photospheric plane with dashed curves indicating the intersections of separatrix surfaces with the photosphere. (a) Initially, there is flux (1-1) joining P1 to N1 and flux (2-2) joining P2 to N2, separated by a vertical separatrix surface V. (b) In the intermediate stage during reconnection, there are two separatrix curves (S1 and S2) joining the null points (see above). Also, some of the fluxes 1-1 and 2-2 have been converted into overlying flux (2-1O) joining P2 to N1 but lying over separatrix S2, underlying flux (2-1U) joining P2 to N1 but lying underneath separatrix S1 and flux (1-2) that joins P1 to N2 and passes through the ring formed by separators S1 and S2. (c) In the final stage the reconnection has been completed and separator S2 has disappeared to infinity so that no flux 2-1O remains.
Twist values in each of the newly reconnected sections, and in the final flux rope, for the zipper phases as a function of shear s=s/wz for two different cases, both involving initially untwisted flux ropes (Φ0=0). Left: an arcade of length L=3wz, resolved into N=4 components. Right: an arcade of length L=5wz, resolved into N=8 components.
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Some may be tempted to object that, on the contrary, the number ofballs in the jar should be infinite when the supertask is complete.After the first stage there are 9 balls in the jar. After the secondstage there are 18. After the third stage there are 27. In the limitas the number of stages approaches infinity, the total number of ballsin the jar diverges to infinity. If the final state of the jar isdetermined by what the finite-stage states are converging to, then thesupertask should conclude with infinitely many balls in the jar.
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