Safety factor of the initial configuration, showing instability towards the kink instability.
Evolution of selected magnetic surfaces at four different times ( ). Magnetic surfaces are shown in the inner part of the column where initially . The flux rope undergoes the kink instability with a progressive displacement of the flux rope axis and unwinding of the magnetic field lines in the inner region.
Isosurface of the perpendicular electric field intensity ( ) in green and isosurfaces of the parallel electric field intensity ( ) in red and blue colours at time . The perpendicular electric field shows the Hall field regions, where electrons and ions decouple, while the bipolar structures of the parallel electric field are a typical product of kinetic streaming instability that are not present in MHD simulations.
Poincaré map on the middle of the box ( ). Two times are shown, ((a) top) and ((b) bottom). Each colour indicates a map relative to a different starting point ( ) highlight with a dark diamond. The X-Y-axes are plotted as [20, 80] instead of [0, 100] to highlight the central part of the rope.
Selected Poincaré map from Fig. 4(b) . As previously, the axes are plotted as [20, 80] to highlight the geometry in the central part of the rope.
Schematic visualisation for understanding the mapping of the field lines. From one point to another on the same layer: . Equivalently with vector functions: .
Toy model for understanding the asymmetry of QSL. In blue, we report the fan field lines, in red (respectively, in orange) a couple of field lines starting from a distance δ at the photospheric level above N1 (respectively, Nu1) surrounding a vertical (blue line) fan field line. In black, we draw the part of these couples of field lines below the photospheric level.
Isocontour (Qcut = 3000) of the Qcut -factor (calculated with the Pariat and Démoulin 63 formula) at coloured by the strength of the magnetic field.
Isocontour ( ) of the -factor (calculated with the adapted formula with periodic boundary condition) at , coloured by the strength of the magnetic field.
Slices of at different z levels ((a) , (b) , and (c) ) at plotted in logarithmic colour scale with X-Y-axis plotted in the subdomain and to highlight the central part of the rope.
Poincaré maps on different z levels ((a) , (b) , (c) ) at . As previously, the axes are plotted in the subdomain and to highlight the central part of the rope.
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