Nonlinear beam dynamics with application to space-charge-dominated beams, double-RF systems and quasi-isochronous storage rings

Profound understanding of nonlinear beam dynamics in accelerator has become critically important for successful operation of high brightness storage rings for nuclear and particle physics research. Combination of theoretical analysis, computer simulations and experimental measurements provide an effective way to understand complex problems of beam physics. This dissertation describes application of methods of nonlinear dynamics to analysis of three important problems in accelerator physics.; First, the problem of particle motion in a double RF potential is studied both theoretically and experimentally. Development of Hamiltonian formalism for double RF system allows us to conduct a theoretical analysis of effects of time dependent harmonic RF phase and voltage modulation on a single particle dynamics. Parametric resonances, created by a weak time dependent perturbation, are analyzed in terms of action-angle variables of the unperturbed Hamiltonian, studied in numerical simulations and observed experimentally.; Second, the dynamics of a test particle in a space charge dominated beam propagating through periodic focusing channel is studied. We show that a set of parametric resonances of the particle Hamiltonian call be excited by mismatched envelope oscillations in the transport channel. It is demonstrated that the onset of global chaos in the particle phase space exhibits a sharp transition when the amplitude of envelope oscillations is larger than a critical value. The relation between the critical envelope mismatch for the halo formation and the space charge perveance is obtained numerically.; Finally, theoretical analysis of a single particle dynamics in quasi-isochronous (QI) storage rings is presented. We derive analytical solution for QI system, analyze its scaling properties and study effects of phase space damping and external harmonic modulation on a particle motion. We find that the RF phase modulation is particularly important in QI storage rings; this means that for successful operation of QI storage rings one should pay special attention to control of RF phase noise. In order to analyze the effect of stochastic excitations on QI system, we investigate effects of quantum fluctuation and quantum lifetime in QI system. The effects of harmonic RF phase modulation on equilibrium distribution function, quantum lifetime reduction and the occurrence of stochastic resonance are also studied.