In accordance with the technical measure of the invention in order to counteract the positive feedback between the superconducting magnet and the shim iron a pair of superconducting shunts (37, 38) is provided with a region of overlap (38a-37b) substantially matching the position of the shim iron (20) within the magnet system (40a). For the shim iron (20) being positioned below coil segments (31c, 31d) the region of overlap must include coil segments (31c, 31d). In this way a first superconducting shunt (37), having its connection points (37a, 37b), and the second superconducting shunt (38), having its connection points (38a, 38b), overlap in a region encompassing the coil segments (31c, 31d) and, thus the shim iron (20). The superconducting shunts (37, 38) are provided with operatable switches (not shown for clarity), which must be kept open during the ramp-up of the magnet. After the magnet has reached the persistent mode, the operatable switches must be kept closed for the whole operational time of the magnetic resonance imaging apparatus. Preferably, the operatable switches are implemented as per se known thermal switches connectable to a suitable heater.