Beam dynamics of the alternating phase focusing linac and frequency dependence of the penetration of electromagnetic fields through a small coupling hole in a thick wall

In the first part of this dissertation, we study the beam dynamics of alternating phase focusing (APF), in which simultaneous longitudinal and transverse focusing are obtained in a drift tube linac by alternating the sign of the synchronous phase. We explore the parameter space of APF by comparing various approximate theories without space charge and obtain analytical forms for the kinetic properties of an APF channel. Nonlinear analysis is then carried out by using canonical perturbation theory. We also use Poincare maps to study chaotic motion and the resonance behavior.; It is found that, in the APF linac with a symmetric synchronous phase sequence, the lowest order resonance due to the synchrobetatron coupling occurs naturally, causing significant emittance transfer between the longitudinal and transverse motions. A model for the coupled motion is proposed. Two approximate invariants are derived. The acceleration effect is also taken into account. Results from simulations of a bunched beam yield good agreement with formulas derived from the theory. The description for the emittance growth given by the model is also confirmed qualitatively by the simulations. We provide, moreover, a way to move the parameters away from the lowest order resonance.; The space charge effect is studied via the three dimensional uniform ellipsoid model. Simulation results for the effects of space charge and synchrobetatron coupling are briefly discussed.; In the second part of this dissertation, we consider two identical cylindrical cavities connected by a circular hole in a common metallic wall. We then derive an integral equation for the transverse electric field at the junction of the cavity and the iris and construct a variational form for the computation of the resonant frequencies. By relating the frequency shifts from those of a closed cavity to the polarizability of the hole, we obtain these quantities for the case of finite wavelength. Numerical results are then obtained as a function of various parameters. We particularly explore the limit of large cavity dimensions in order to isolate the dependence on the hole radius, the hole thickness, and the wavelength.