A superconducting magnet system for generating a uniform magnetic field that is uniform to within +/-0.05% in a central three-dimensional region of said superconducting magnet system, the system comprising: a first set of superconducting pucks or solenoids along a first side of the superconducting magnet system; a second set of superconducting pucks or solenoids along a second side of the superconducting magnet system; a third set of superconducting pucks or solenoids along a third side of the superconducting magnet system; a fourth set of superconducting pucks or solenoids along a fourth side of the superconducting magnet system; wherein said first, second, third and fourth sets of superconducting pucks or solenoids provide a majority of said uniform magnetic field; wherein said first, second, third and fourth sides define an area of said superconducting magnet system, and wherein said central three-dimensional region is located at a centre of said area; and characterised in that at least one of said first, second, third and fourth sets of superconducting pucks or solenoids has a magnetisation which also generates a compensating magnetic field which varies along a longitudinal direction of said superconducting magnet system to compensate for non-uniformities of said magnetic field in said central three-dimensional region of said superconducting magnet system, wherein said longitudinal direction is essentially parallel to a plane on which said first, second, third and fourth sets of superconducting pucks or solenoids are located; wherein said compensating magnetic field is varied by one or both of varying a diameter of said at least one of said first, second, third and fourth sets of superconducting pucks or solenoids and varying a current density in said at least one of said first, second, third and fourth sets of superconducting pucks or solenoids; wherein said variation has a waveshape which has an amplitude which increases towards a first end of said superconducting magnet system along said longitudinal direction, wherein said first end is located at one of said first, second, third and fourth sides of the superconducting magnet system; wherein said waveshape has the form of a ringing pulse having an amplitude which decays in a direction away from said first end towards said centre of said superconducting magnet system; and wherein said waveshape defines magnetisation values of said superconducting pucks or solenoids at discrete positions at which said superconducting pucks or solenoids are located. a first set of superconducting pucks or solenoids along a first side of the superconducting magnet system; a second set of superconducting pucks or solenoids along a second side of the superconducting magnet system; a third set of superconducting pucks or solenoids along a third side of the superconducting magnet system; a fourth set of superconducting pucks or solenoids along a fourth side of the superconducting magnet system; wherein said first, second, third and fourth sets of superconducting pucks or solenoids provide a majority of said uniform magnetic field; wherein said first, second, third and fourth sides define an area of said superconducting magnet system, and wherein said central three-dimensional region is located at a centre of said area; and characterised in that at least one of said first, second, third and fourth sets of superconducting pucks or solenoids has a magnetisation which also generates a compensating magnetic field which varies along a longitudinal direction of said superconducting magnet system to compensate for non-uniformities of said magnetic field in said central three-dimensional region of said superconducting magnet system, wherein said longitudinal direction is essentially parallel to a plane on which said first, second, third and fourth sets of superconducting pucks or solenoids are located; wherein said compensating magnetic field is varied by one or both of varying a diameter of said at least one of said first, second, third and fourth sets of superconducting pucks or solenoids and varying a current density in said at least one of said first, second, third and fourth sets of superconducting pucks or solenoids; wherein said variation has a waveshape which has an amplitude which increases towards a first end of said superconducting magnet system along said longitudinal direction, wherein said first end is located at one of said first, second, third and fourth sides of the superconducting magnet system; wherein said waveshape has the form of a ringing pulse having an amplitude which decays in a direction away from said first end towards said centre of said superconducting magnet system; and wherein said waveshape defines magnetisation values of said superconducting pucks or solenoids at discrete positions at which said superconducting pucks or solenoids are located.