The invention comprises a charged particle beam acceleration and/or extraction 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, 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.