In Part I, three independent models of Fermilab's Booster synchrotron are presented. All three models are constructed to investigate and explore the effects of unavoidable machine errors on a proton beam under the influence of space-charge effects. The first is a stochastic noise model. Electric current fluctuations arising from power supplies are ubiquitous and unavoidable and are a source of instabilities in accelerators of all types. A new noise module for generating the Ornstein-Uhlenbeck (O-U) stochastic noise is first created and incorporated into the existing Object-oriented Ring Beam Injection and Tracking (ORBIT-FNAL) package. After being convinced with a preliminary model that the noise, particularly non-white noise, does matter to beam quality, we proceeded to measure directly current ripples and common-mode voltages from all four Gradient Magnet Power Supplies (GMPS). Then, the current signals are Fourier-analyzed. Based upon the power spectra of current signals, we tune up the Ornstein-Uhlnbeck noise model. As a result, we are able to closely match the frequency spectra between current measurements and the modeled O-U stochastic noise. The stochastic noise modeled upon measurements is applied to the Booster beam in the presence of the full space-charge effects. This noise model, accompanied by a suite of beam diagnostic calculations, manifests that the stochastic noise, impinging upon the beam and coupled to the space-charge effects, can substantially enhance the beam degradation process throughout the injection period. The second model is a magnet misalignment model. It is the first time to utilize the latest beamline survey data for building a magnet-by-magnet misalignment model. Given as-found survey fiducial coordinates, we calculate all types of magnet alignment errors (station error, pitch, yaw, roll, twists, etc.) are implemented in the model. We then follow up with statistical analysis to understand how each type of alignment errors are currently distributed around the Booster ring. The ORBIT-FNAL simulations with space charge included show that rolled magnets, in particular, have substantial effects on the Booster beam. This survey-data-based misalignment model can predict how much improvement in machine performance can be achieved if prioritized or selected realignment work is done. In other words, this model can help us investigate different realignment scenarios for the Booster. In addition, by calculating average angular kicks from all misaligned magnets, we expect this misalignment model to serve as guidelines for resetting the strengths of corrector magnets. The third model for the Booster is a time-structured multi-turn injection model. Microbunch-injection scenarios with different time structures are explored in the presence of longitudinal space-charge force. Due to the radio-frequency (RF) bucket mismatch between the Booster and the 400-MeV transferline, RF-phase offsets can be parasitically introduced during the injection process. Using the microbunch multiturn injection, we carry out ESME-ORBIT-combined simulations. This combined simulation allows us to investigate realistic charge-density distribution under full space-charge effects. The growth rates of transverse emittances turned out to be 20 % in both planes. This microbunch-injection scenarios is also applicable to the future 8-GeV Superconducting Linac Proton Driver and the upgraded Main Injector at Fermilab. In Part II, the feasibility of momentum-stacking method of proton beams is investigated. When the Run2 collider program at Fermilab comes to an end around year 2009, the present antiproton source can be available for other purposes. One possible application is to convert the antiproton accumulator to a proton accumulator, so that the beam power from the Main Injector could be enhanced by a factor of four. Through adiabatic processes and optimized parameters of synchrotron motion, we demonstrate with an aid of the ESME code that up to four proton batches can be stacked in the momentum acceptance available for the Accumulator ring. This momentum-stacking method is expected to be a part of Fermilab's SuperNuMI (SNuMI) project.
