Cylindrical components B_r, B_z, and B_φ of the magnetic field in our simulation from Fig. 1, shown with logarithmic color grading in code units. The total field is shown in Fig. 2. In the middle part of the disk, the magnetic field is orders of magnitude smaller than in the corona, as predicted by our analytical solution in the disk. Magnetic field is dominant outside of the disk, inside the disk it hardly influences the flow.