A superconductor magnet system, comprising - a cryostat having a room temperature bore, - a superconductor bulk magnet, contained in the cryostat and arranged coaxially with the room temperature bore, and - a cryogenic cooling system adapted for cooling the superconductor bulk magnet, wherein the superconductor bulk magnet comprises at least N axially stacked bulk sub-magnets (6a-6c), with N≥3, wherein the bulk sub-magnets (6a-6c) are substantially ring shaped and arranged coaxially with the room temperature bore, wherein between each two axially neighboring bulk sub-magnets (6a-6c), an intermediate body (7a-7b) is arranged, wherein the intermediate bodies (7a-7b) are substantially ring-shaped and arranged coaxially with the room temperature bore, and the bulk sub-magnets (6a-6c) are supported on the intermediate bodies (7a-7b), characterized in that the intermediate bodies (7a-7b) are made from a non-metallic thermal insulator material, having a specific thermal conductivity smaller than a specific thermal conductivity of the material of the bulk sub-magnets (6a-6c), and that the cryogenic cooling system is adapted for independently controlling the temperature of each bulk sub-magnet (6a-6c), wherein for each bulk sub-magnet (6a-6c), there is comprised - a temperature sensor (16a-16c) for sensing the temperature of the respective bulk sub-magnet (6a-6c), and - an adjustment unit (13a-13c) for adjusting a heating power and/or a cooling power at the respective bulk sub-magnet (6a-6c). - a cryostat having a room temperature bore, - a superconductor bulk magnet, contained in the cryostat and arranged coaxially with the room temperature bore, and - a cryogenic cooling system adapted for cooling the superconductor bulk magnet, wherein the superconductor bulk magnet comprises at least N axially stacked bulk sub-magnets (6a-6c), with N≥3, wherein the bulk sub-magnets (6a-6c) are substantially ring shaped and arranged coaxially with the room temperature bore, wherein between each two axially neighboring bulk sub-magnets (6a-6c), an intermediate body (7a-7b) is arranged, wherein the intermediate bodies (7a-7b) are substantially ring-shaped and arranged coaxially with the room temperature bore, and the bulk sub-magnets (6a-6c) are supported on the intermediate bodies (7a-7b), characterized in that the intermediate bodies (7a-7b) are made from a non-metallic thermal insulator material, having a specific thermal conductivity smaller than a specific thermal conductivity of the material of the bulk sub-magnets (6a-6c), and that the cryogenic cooling system is adapted for independently controlling the temperature of each bulk sub-magnet (6a-6c), wherein for each bulk sub-magnet (6a-6c), there is comprised - a temperature sensor (16a-16c) for sensing the temperature of the respective bulk sub-magnet (6a-6c), and - an adjustment unit (13a-13c) for adjusting a heating power and/or a cooling power at the respective bulk sub-magnet (6a-6c). - a temperature sensor (16a-16c) for sensing the temperature of the respective bulk sub-magnet (6a-6c), and - an adjustment unit (13a-13c) for adjusting a heating power and/or a cooling power at the respective bulk sub-magnet (6a-6c).