The invention comprises a flattened magnet coil system that reduces space between a first magnet turning section and a second magnet turning section in a synchrotron accelerator, which reduces or eliminates need for one or more quadrupole focusing elements in the accelerator. Optionally, a coil, in the flattened magnetic coil system, is wrapped about a central metal member between yoke members of a magnet. The coil has a first width and a first thickness along the length of the magnet and a second width and a second thickness along the end of the magnet where the first width is larger than the second width and the second thickness is larger than the first thickness allowing a smaller distance between the first magnet turning section and the second magnet turning section while maintaining current flow in the coil.