Cosine gradient theory in cyclotrons with general dees

This paper gives the representation of the electric field for cyclotron accelerating gap with general dee geometry. A special case of this representation is the cosine gradient theory of central region electric field developed by Kost and Mackenzie [IEEE NS-22 (3) (1975) 1922] in TRIUMF for 180° dees. A general expression of energy gain and a formula to determine the vertical electric focusing, which improves the alternating-gradient focusing proposed by Gordon and Marti [Part. Acceler. 11 (1980) 161] using a simple electric-field model, are obtained. In our theory, the velocity-variation π/2 focusing and radius-change effect have been predicted to perfect the calculation of the vertical electric focusing. We take the 100 MeV cyclotron under design and construction at China Institute of Atomic Energy, CYCIAE-100 [T. Zhang, X. Guan et al., in: Proceedings of the Third Asia Particle Accelerator Conference, Korea, 2004, p. 267], as an application of this theory in two-dee cyclotron running at push-push mode.