A method for magnetically shielding a cyclotron during ion acceleration, comprising: passing electrical current through first and second electrically conductive primary coils (12,14), wherein each primary coil is centered symmetrically about a central axis, one on each side of a midplane intersected perpendicularly by the central axis, wherein the electrical current is passed through the first primary coil in the same direction as the direction in which electrical current is passed through the second primary coil; releasing an ion from an ion source into the midplane proximate the central axis and accelerating the ion in an orbiting trajectory expanding outward from the central axis via a magnetic field generated at least partially by the primary coils; characterised by passing electrical current through at least a first and a second magnetic-field-shielding coil, wherein the first magnetic-field-shielding coil (31,33,35) is on the same side of the mid plane as the first primary coil and beyond the outer radius of the first primary coil, wherein the second magnetic-field-shielding coil (32,34,36) is on the same side of the midplane as the second primary coil and beyond the outer radius of the second primary coil, wherein electrical current is passed through the first and second magnetic-field-shielding coils in a direction opposite to the direction in which electrical current is passed through the primary coils, and wherein passing electrical current through the magnetic-field-shielding coils generates a canceling magnetic field that reduces the magnetic field generated at radii from the central axis beyond the magnetic-field-shielding coils. passing electrical current through first and second electrically conductive primary coils (12,14), wherein each primary coil is centered symmetrically about a central axis, one on each side of a midplane intersected perpendicularly by the central axis, wherein the electrical current is passed through the first primary coil in the same direction as the direction in which electrical current is passed through the second primary coil; releasing an ion from an ion source into the midplane proximate the central axis and accelerating the ion in an orbiting trajectory expanding outward from the central axis via a magnetic field generated at least partially by the primary coils; characterised by passing electrical current through at least a first and a second magnetic-field-shielding coil, wherein the first magnetic-field-shielding coil (31,33,35) is on the same side of the mid plane as the first primary coil and beyond the outer radius of the first primary coil, wherein the second magnetic-field-shielding coil (32,34,36) is on the same side of the midplane as the second primary coil and beyond the outer radius of the second primary coil, wherein electrical current is passed through the first and second magnetic-field-shielding coils in a direction opposite to the direction in which electrical current is passed through the primary coils, and wherein passing electrical current through the magnetic-field-shielding coils generates a canceling magnetic field that reduces the magnetic field generated at radii from the central axis beyond the magnetic-field-shielding coils.