The magnetic field in an acceleration chamber defined by a magnet structure is shaped by shaping the poles of a magnetic yoke and/or by providing additional magnetic coils to produce a magnetic field in the median acceleration plane that decreases with increasing radial distance from a central axis. The magnet structure is thereby rendered suitable for the acceleration of charged particles in a synchrocyclotron. The magnetic field in the median acceleration plane is "coil-dominated," meaning that a strong majority of the magnetic field in the median acceleration plane is directly generated by a pair of primary magnetic coils (e.g., superconducting coils) positioned about the acceleration chamber, and the magnet structure is structured to provide both weak focusing and phase stability in the acceleration chamber. The magnet structure can be very compact and can produce particularly high magnetic fields.