Beam trapping in a modified betatron with torsatron windings

The guiding-center equations for the reference electron located at the centroid of an intense electron ring confined in a torsatron-assisted modified betatron field are derived by time averaging its fast motion. These 'slow' equations are integrated analytically to obtain the nonlinear orbits for the guiding center. In addition, from the guiding-center equations, we have obtained a nonlinear expression that predicts very accurately the ring equilibrium position, even for large displacements from the minor axis of the torus. These results have provided an invaluable insight into the development of a trapping scheme. The proposed scheme is compatible with the slow acceleration of the modified betatron and is based on a low-amplitude, rapidly varying magnetic field that shifts the ring equilibrium position from near the wall to the minor axis of the torus in a time shorter than a beam bounce period. (author)