Adiabatic beam dynamics in a modified betatron

Electron beams in modified betatrons were previously analyzed by using a paraxial treatment. This treatment is valid only for a beam where particles have an axial velocity much larger than their perpendicular velocity. However, in accelerators such as the UCI Modified Betatron, the beam does not satisfy the paraxial assumption. Another treatment based on the guiding center equations is presented. In this treatment the paraxial assumption is not necessary. Corrections to the conventional ''betatron condition'' are found and compared with recent experiments. Additionally, this treatment can describe nonparaxial quasiconfined particles. The effect of these quasiconfined particles is examined, and it is shown that they provide fields that are necessary to stabilize the beam