Poloidal magnetic field lines around the BH (solid black lines), with the event horizon (black disk) and the ergosphere (black dashed line), for a fiducial snapshot from a simulation with a = 0.8 and a thin disk (in chartreuse yellow in the equatorial plane). The thicker field lines delimit the region between the ISCO and the separatrix coupling the BH to the disk, visible in the zoomed-in view in the bottom panel. The color maps represent the total plasma density, n, in units of n_GJ (top left), the mean Lorentz factor of the particles (top right), the toroidal component of the H field (bottom left), and the radial component of the current, J (bottom right). To compensate for spatial dilution, plasma density and current were multiplied by r². A smoothing Gaussian kernel a few cells wide was applied to the current map. In the plasma density map, the red circle locates the Y point. Distances to the BH on the x and y axes are given in units of r_g. The white line in the top-right corner stands for the outer light surface.