An apparatus for tumor therapy using charged particles, comprising a rounded corner polygon synchrotron that accelerates the charged particles, said synchrotron comprising: a center; straight sections; turning sections; a charged particle circulation beam path running about said center, through said straight sections and through said turning sections; wherein a first of said turning sections comprises: a first bending magnet and a second bending magnet; a winding coil (1250, 1260), having a winding coil turn wherein said winding coil turn wraps around both said first bending magnet and said second bending magnet, wherein said winding coil turn does not occupy space directly between said first bending magnet and said second bending magnet; and a correction coil (1510, 1520) wrapped around both said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) comprises a correction coil turn that does not occupy space directly between said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) operates at less than three percent of the power of said winding coil (1250, 1260), wherein each of said turning sections comprises a plurality of bending magnets, wherein said circulation beam path comprises a length of less than sixty meters, and wherein a number of said straight sections equals a number of said turning sections. a center; straight sections; turning sections; a charged particle circulation beam path running about said center, through said straight sections and through said turning sections; wherein a first of said turning sections comprises: a first bending magnet and a second bending magnet; a winding coil (1250, 1260), having a winding coil turn wherein said winding coil turn wraps around both said first bending magnet and said second bending magnet, wherein said winding coil turn does not occupy space directly between said first bending magnet and said second bending magnet; and a correction coil (1510, 1520) wrapped around both said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) comprises a correction coil turn that does not occupy space directly between said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) operates at less than three percent of the power of said winding coil (1250, 1260), wherein each of said turning sections comprises a plurality of bending magnets, wherein said circulation beam path comprises a length of less than sixty meters, and wherein a number of said straight sections equals a number of said turning sections. a first bending magnet and a second bending magnet; a winding coil (1250, 1260), having a winding coil turn wherein said winding coil turn wraps around both said first bending magnet and said second bending magnet, wherein said winding coil turn does not occupy space directly between said first bending magnet and said second bending magnet; and a correction coil (1510, 1520) wrapped around both said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) comprises a correction coil turn that does not occupy space directly between said first bending magnet and said second bending magnet, wherein said correction coil (1510, 1520) operates at less than three percent of the power of said winding coil (1250, 1260), wherein each of said turning sections comprises a plurality of bending magnets, wherein said circulation beam path comprises a length of less than sixty meters, and wherein a number of said straight sections equals a number of said turning sections.