1. An accelerator comprising:an annular main coil;
a plurality of magnetic poles configured to form isochronous magnetic fields;
an ion injection port configured to inject ions into an ion injection portion disposed at a position that is different from a position of a center of gravity of the main coil in a radial direction;
an acceleration electrode configured to accelerate the ions; and
an extraction port through which an accelerated ion beam is extracted,
wherein the ion injection portion, a tip of an inner circumferential end portion of the acceleration electrode, or a tip of one of the magnetic poles extends closer to the extraction port than the center of gravity of the main coil in the radial direction.