3D view of the magnetic field line mapping between an unperturbed dipole and simulations with (a) no IMF and P_d = 2 nPa, (b) Sun-Earth IMF |B|_IMF = 10 nT and P_d = 105 nPa, and (c) Sun-Earth IMF |B|_IMF = 100 nT and P_d = 2 nPa. The dashed white line indicates the inner boundary of the simulation domain (R∕R_E = 2), and the dotted white line shows the upper boundary of the ionosphere model (R∕R_E = 2.5). The red lines show the magnetic field lines in the simulation with only the dipole magnetic field and the blue lines the magnetic field lines in the simulation with dipole + IMF magnetic fields.