Further progress in nonlinear acceleration theory for cyclotrons

Sato, Kenji*; Ninomiya, Shiro*; Miyawaki, Nobumasa; Fukuda, Mitsuhiro; Obata, Shuji*

It is possible to transform three equations of motion into a convenient form which is expressed by terms up to 2nd differential of variables of the Lorentz factor and angular velocity by the use of a field index of magnetic field distribution. The expression plays a vital role in a two-step nonlinear acceleration theory of spiral orbital motions in cyclotrons because this single equation of motion refers to both longitudinal motion and transverse motion.