Linear and nonlinear studies at RHIC interaction regions and optical design of the rapid cycling medical synchrotron

Development and application of the action and phase technique used to evaluate and correct local errors, linear and non linear (skew quadrupole errors, gradient errors and sextupole errors), at RHIC interaction regions is presented in the first part of this thesis.; The skew quadrupole errors have their origin on the roll angles of the quadrupoles. It is then possible to estimate the skew quadrupole error present in a RHIC triplet if all the roll angles of the quadrupoles of a particular triplet are known. These values were estimated with the measured roll angles during the 2002 RHIC shutdown period and compared to the measured skew quadrupole errors obtained with the action and phase technique. The agreement is fairly good validating the action and phase technique for at least skew quadrupole errors.; Another way of validating the action and phase technique is by intentionally introducing known values of errors while attempting to measure the values with the technique. This was done for skew quadrupole errors and gradient errors with excellent results. Analysis of some of the experiments shows that the set errors can be reproduced by the technique with accuracies below 5 percent. Same experiments were repeated for sextupole errors an a clear correlation between the measured and the set error was found but the precision in this case is not as good as for the linear errors case.; The optical design of the Rapid Cycling Medical Synchrotron and related efforts to optimize the design are presented in the second part of this thesis. An interesting outcome of this work is the development of the so called IBEFUMFO technique which allow a better understanding of the optical parameters involved in a lattice design and hence facilitate the task of the designer.; The rapid repetition frequency of the RCMS has raised concerns about the sextupole components induced in the beam due to strong Eddy currents. Tracking simulations with Marylie have been done in order to evaluate the effect of these sextupoles in quantities like the dynamic aperture and the footprint of the accelerator.