ABSTRACT
After incoherent space charge forces and the space-charge tune-shift are introduced, the Sacherer equations of motion are numerically solved with Matlab and the Laslett coefficients, which parameterize the coherent space-charge forces, are addressed, followed by a brief discussion of intra-beam scattering and the Touschek effect. In the next section a general overview of wake fields, impedances and loss factors is presented, followed by their inuence on coasting-beam instabilities and a derivation of the Keil-Schnell stability criterion. Longitudinal and transverse single-bunch instabilities are the subject of next section and illustrated with a model that maps the longitudinal beam matrix through a ring, taken the effect of wake fields into account. The final section briey covers multi-bunch instabilities.
