Complex approach of beam dynamic investigation in SC LINAC

Beam dynamic investigation is difficult for superconducting linac consisting from periodic sequences of independently phased accelerating cavities and focusing solenoids. The matrix calculation was preferably used for previous estimate of accelerating structure parameters. The matrix calculation does not allow properly investigate the longitudinal motion. The smooth approximation can be used to investigate the nonlinear ion beam dynamics in such accelerating structure and to calculate the longitudinal and transverse acceptances. The potential function and equation of motion in the Hamiltonian form are devised by the smooth approximation. The advantages and disadvantages of each method will describe, the results of investigation will compare. Application package for ion beam dynamic analysis will create. A numerical simulation of beam dynamics in the full field will carry out for the different variants of the accelerator structure based on analytically obtained results.