Numerical Methods I & II

Numerical methods is a fundamental field of research and application in accelerator physics and beam dynamics. It is widely used to study intensity effects and limitations in accelerators and becomes more important still in regimes where the simple analytical models break down and experiments can not be easily conducted. In this course we will introduce some basic concepts of numerical methods used to study collective effects in circular accelerators. The course covers macroparticle models, the implementation of the beam dynamics and applications relevant to intensity effects and limitation. This includes basic tracking in the transverse and longitudinal planes, modeling of impedance effects and finally two stream effects such as electron clouds.