Analysis of a modified betatron with adiabatic particle dynamics

The usual analysis of a Betatron is based on the paraxial approximation. The Fermi drift in a modified Betatron treated with the paraxial approximation is a small non-linear correction to the equations of motion that can usually be neglected. For low energy injection as in the method of inductive charging, the paraxial approximation is not valid. For this case we have developed a new description based on adiabatic particle dynamics, which is more like the analysis of a tokamak than a conventional accelerator. A particle to first approximation follows the field lines. The combination of toroidal and Betatron fields would lead a particle to the wall if it were not for the Fermi drift which cancels the motion towards the wall. Orbits in which a particle does not go around the torus must also be considered which are absent in the paraxial theory. Appropriate averages over particle orbits must be defined to describe a beam. The theoretical description based on adiabatic particle dynamics will be compared with recent experimental results of the UCI Betatron.