A cyclotron for ion acceleration is magnetically shielded during ion acceleration by passing electrical current in the same direction through both the first and second superconducting primary coils. A first magnetic-field-shielding coil is on the same side of the mid plane as the first superconducting primary coil, while a second magnetic-field-shielding coil is on the same side of the midplane as the second superconducting primary coil and beyond the outer radius of the second superconducting primary coil. Electrical current is also passed through the magnetic-field-shielding coils in a direction opposite to the direction in which electrical current is passed through the superconducting primary coils and generates a canceling magnetic field that reduces the magnetic field generated at radii from the central axis beyond the magnetic-field-shielding coils.