Prospects of analytical models for accelerator technology in industry (past, present, future)

In the past particle accelerators were invented and developed to a large extent for scientific purposes. As time proceeded the relatively small machines became dedicated to applications while the fundamntal research required higher and higher energies and improved ion optical beam quality. In many university laboratories machines originally used for fundamental physics are now applied for analyzing techniques and technological developments. Furthermore a very large number of accelerators is installed in industrial sites and hospitals. To a certain extent the fundamental theory of acceleration was developed separately for each type of accelerator. In this paper we will try to give a general theoretical treatment for the smaller accelerators as well as some indroductory historical remarks and a rough extrapolation to the future.