tokens: al. (2011) . The percentages in Fig. 8 are therefore a minimum estimate only. Despite this, we can see in cases (ii) and (iii), a higher percentage of the flux remains at its original connection for the duration of the simulations. The change in connectivity of the field lines results in strong outflow velocities from the end of the current layers. White arrows showing the projected horizontal velocity components in the central region () in the mid-plane are displayed in Fig. 9 for case (i) at . These show large velocities from the narrow current layer along , where the maximum velocity is , where is the maximum Alfvén velocity in the mid-plane (at ), an indication of reconnection occurring. We note, that the magnetic field is 3D and reconnection is not confined to the mid-plane, but use the current contours and velocities in the mid-plane to illustrate the differences between the cases. Fig. 9 Contour of the magnitude of the current density in the mid-plane between at for case (i) with 2 sources. The arrows show the projected velocity in the plane. Fig. 10 Contours of the magnitude of the current density in the mid-plane between at a) and b) for case (ii) with 4 weak sources. The arrows show the projected velocity in the plane. Similarly, in case (ii), strong outflow velocities are seen from the current “wings” shown in Fig. 10 a at and very similar behaviour is observed for case (iii) (not shown). Later in cases (ii) and (iii), the current contours in Fig. 10 b show the “X” current formation to fragment and then (in addition to the outwards velocity towards the edge of the domain) there are inwards velocity outflows of reconnected field lines towards the centre of the mid-plane. This leads to further current being built up in the centre of the domain. The maximum velocity (in the mid-plane) for cases (ii) and (iii) are and , respectively, and occurs at , after this fragmentation of the “X” current formation. This is much smaller than in case (i) and suggests that the reconnection is weaker. The location of the sources in the case with two flux tubes appears highly idealised to produce the concentrated single current layer in the centre of the domain. In comparison, in the four-source case, as they are evenly distributed around the centre of rotation, a shear is first created between the neighbouring flux tubes, which due to the relative angles of the magnetic field lines will always be less than that induced in the two-source case and produces reduced current values and results in a smaller percentage of flux changing connectivity. 3.1.2. Energetics The energy evolution is shown by the volume integrated energy densities in Fig. 11 for the cases with two, four weak and four compact sources, displayed in pink, blue and black, respectively and can be described as follows: when the driving velocity acts on the field, the field lines are advected and the magnetic field becomes twisted, gradually increasing the magnetic energy in the domain (see
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