A superconducting magnet structure has a number of axially aligned superconducting inner magnet coils that form an inner magnet structure (30) and a number of superconducting outer coils each having an inner diameter greater than an outer diameter of each of the inner magnet coils. The inner magnet structure is enclosed within a cryogen vessel, and the outer coils are located outside of the cryogen vessel, in thermal contact with a cooling arrangement for cooling the outer coils.