| This work can be broken down into two main parts, the first an analytic derivation for the averaged dynamics of a space-charge dominated beam, which is matched into a non-linear FODO lattice utilizing higher order magnetic poles and the second focused on model independent accelerator control and component tuning. Because real, non- idealized particle beams experience nonlinear space charge forces, it is impossible to match them to a lattice of linear magnetic components such as a pure quadruple FODO setup. As was calculated by Batygin, the introduction of nonlinear focusing elements allows one to match a nonlinear space-charge dominated beam to a lattice, which may be adiabatically changed into a standard quadrupole FODO lattice, in such a way so that the beam itself becomes well matched to the linear lattice. The first part of this thesis calculates the averaged dynamics of a beam in such a nonlinear focusing lattice. Because particle accelerators are complex and beam dynamics are nonlinear, with time-varying dynamics of and coupling between many components, an adaptive, model-independent control or tuning scheme may be useful to replace or greatly shorten the duration of typical lengthy hand-tuning of components, tuning which must be re-done many times due to un-modeled behavior such as thermal cycling, arbitrary phase drift of RF systems, and beam source fluctuations. |
