A betatron includes a betatron magnet with a first guide magnet having a first pole face and a second guide magnet having a second pole face. Both the first and the second guide magnet have a centrally disposed aperture and the first pole face is separated from the second pole face by a guide magnet gap. A core is disposed within the centrally disposed apertures in an abutting relationship with both guide magnets. The core has at least one core gap. A drive coil is wound around both guide magnet pole faces. An orbit control coil has a contraction coil portion wound around the core gap and a bias control portion wound around the guide magnet pole faces. The contraction coil portion and the bias control portion are connected but in opposite polarity. Magnet fluxes in the core and guide magnets return through peripheral portions of the betatron magnet.