Using of smooth approximation for nonlinear beam dynamics investigation in RF linac
The low energy ion beam can be accelerated and focused in different types of RF focusing linac (RFQ, APF and other). In such linac the ions are accelerated by a single synchronous wave. In this paper it is investigated the influence of non-synchronous harmonics of high intensity RF field on the longitudinal and transverse ion beam dynamics in RF linac. The equation of motion in the Hamiltonian form is devised by the smooth approximation. It is shown the connection between the phase acceptance and the transverse emittance can be found by means of the effective potential function. Hamiltonian form of motion equation is used for analysis of the nonlinear ion beam dynamics in polychromic RF field. It was shown that non-synchronous harmonics of RF field can focusing and accelerate of intense ion beam. Such method of focusing and acceleration is suggested for ion beams with large transverse cross-section and low energy heavy ion beams.