Non-Coulomb perturbations influence on beam dynamics in extended accelerating/focusing channels

It is generally taken that the main source of particle losses in extended linac channel is the Coulomb field of space charge dominated beam. However, there are the non-Coulomb effects concerned with external field perturbations (external perturbations) and their influence on beam dynamic is comparable with the action of space charge. The calculation of the accelerating/focusing channel always based on the specific mathematical model involving description of external accelerating and focusing forces. In this model as a rule, the focusing field linear dependence on transverse coordinates and accelerating field axis distribution is used. The channel based on such models will be called ideal. Of course, there are no unprojected losses in the ideal channel.