Some Aspects on Linear and Non-Linear Orbit Motion in Storage Rings

Our purpose is the development of a general analytical theory which describes the orbit motion of particles in a storage ring, including the effect of the acceleration, analogous as done for cyclotrons. We only present here the start, neglecting the effect of the RF system. We will use a Hamilton formalism with action and angle variables and show that this leads, after several correct transformations, to expressions for the off-energy function , tunes and chromaticities. This theory can be extended to the influence of non-linear elements as sextupoles and octupoles and long straight sections on the orbit motion. Our treatment only needs direct field quantities in the form of Fourier components of the guide field elements. No a priori information about the lattice functions (¿,ß etc.) is required, whereas normally one uses the behaviour of these functions as provided by lattice designing matrix codes. The results of the analytical theory as given here will be compared with numerical results applied on the lattice of the proposed Dutch dedicated synchrotron radiation storage ring PAMPUS.