The invention comprises a charged particle beam acceleration, extraction, and/or targeting method and apparatus used in conjunction with charged particle beam radiation therapy of cancerous tumors. Novel design features of a synchrotron are described. Particularly, turning magnets, edge focusing magnets, concentrating magnetic field magnets, winding and control coils, and extraction elements are described that minimize the overall size of the synchrotron, provide a tightly controlled proton beam, directly reduce the size of required magnetic fields, directly reduces required operating power, and allow continual acceleration of protons in a synchrotron even during a process of extracting protons from the synchrotron.