Uncoupled and Coupled Orbit Motion in a Storage Ring

Using Hamiltonformalism with action and angle variables, uncoupled and coupled orbit motion of particles in a storage ring are presented. Analytical expressions for the Twiss parameters, using Fourier components of the guide field, are deduced from the linear Hamilton-function. With these lattice functions, expressions which represent influences of non-linearities are given. The description of coupled motion is, after some canonical transformations, reduced to a one-dimensional problem. The motion is represented in a phase-plane, which has already been done for AVF cyclotrons. The theory will be applied on the Dutch proposed synchrotron radiation source PAMPUS. The results of the linear theory as given here are compared with matrixcalculations. Results for nonlinear resonances are compared with results obtained by using the theory of Guignard.