COUPLED MOTION IN THE SPIRAL RIDGE CYCLOTRON

The coupled dy-namics is examined analytically- and computationally, with particular reference to the proposed conversion of the Harwell synchrocyclotron, (N - 4). Effects due to the 2Q/sub v/ = Q/sub R/ resonance and higher-order coupled instabilities are observed, theory and computation being in excellent agreement. Tyv'o high-order resonances, 2Q/sub v/ 4-3Q/sub r/, and 2Q/ sub v/ = 4 (Q/sub r/-1), are significant in the proposed design, the former being the more serious. These studies provide a realistic assessment of the design, the chief conclusion being that radial betatron oscillation amplitudes must be kept within about 1/2 in., due to vertical build-up in crossing the 2Q/sub v/ - 4- -3Q/sub R/ resonance. The results do not preclude the choice of a linear spiral law, THETA = alpha /r/sub 0/, for the ridges, and indicate that alpha should be about 0. l radiands/in. (auth)