The Fermilab Booster is a nearly 40-year-old proton synchrotron, designed to accelerate injected protons from a kinetic energy of 400 MeV to 8 GeV for extraction into the Main Injector and ultimately the Tevatron. Currently the Booster is operated with a typical intensity of 4.5 x 1012 particles per beam, roughly twice the value of its design, because of the requirement for high particle flux in various experiments. Its relatively low injection energy provides certain challenges in maintaining beam quality and stability under these increasing intensity demands. An understanding of the effects limiting this intensity could provide enhanced beam stability and reduced downtime due to particle losses and subsequent damage to the accelerator elements. Design of future accelerators can also benefit from a better understanding of intensity effects limiting injection dynamics. Chapter 1 provides a summary of accelerator research during the 20th century leading to the development of the modern synchrotron. Chapter 2 puts forth a working knowledge of the terminology and basic theory used in accelerator physics, and provides a brief description of the Fermilab Booster synchrotron. Synergia, a 3d space-charge modeling framework, is presented, along with some simulation benchmarks relevant to topics herein. Emittance, a commonly used quantity characterizing beam size and quality in a particular plane, is discussed in Chapter 3. Space-charge fields tend to couple the motion among the planes, leading to emittance exchange, and necessitating a simultaneous measurement to obtain a complete emittance description at higher intensities. A measurement is described and results are given. RMS beam emittances are shown to be in keeping with known Booster values at nominal intensities and emittance exchange is observed and accounted for. Unmeasurable correlation terms between the planes are quantified using Synergia, and shown to be at most an 8% effect. Results of studies on the coherent and incoherent shifts of transverse (betatron) frequencies with beam intensity at injection energies are presented. In Chapter 4 the coherent frequency shifts are shown to be due to dipole- and quadrupole-wakefield effects. The asymmetry of the Booster beam chamber through the magnets, as well as the presence of magnet laminations, are responsible for the magnitudes and for the opposing signs of the horizontal and vertical tune shifts caused by these wakefields. Chapter 5 details the procedures for obtaining a linear coherent-tune-shift intensity dependence, yielding -0.009/1012 in the vertical plane and +0.001/1012 in the horizontal plane. Data demonstrate a requirement of several hundred turns to accumulate to its maximal value. Two independent studies are compared, corroborating these results. In Chapter 6, a measure of the incoherent tune shift with intensity puts an upper limit on the magnitude of the direct space-charge effect in the Fermilab Booster. A prediction is made for the representative incoherent particle tune shift using a realistic Gaussian distribution, allowing for growth of the beam envelope with intensity, and found to be 0.004/1012. The tune-spread dependence obtained by quantification of the resonant stopband width from beam-extinction measurements was measured at 0.005/1012, similar to the predicted value. These will be shown to be one order of magnitude smaller than the space-charge term from the Laslett tune shift for a fixed-size, uniform beam.

A realistic lattice model is a fundamental basis for the operation of a synchrotron. In this study various beam-based measurements, including orbit response matrix (ORM) and BPM turn-by-turn data are used to verify and calibrate the lattice model of the Fermilab Booster. In the ORM study, despite the strong correlation between the gradient parameters of adjacent magnets which prevents a full determination of the model parameters, an equivalent lattice model is obtained by imposing appropriate constraints. The fitted gradient errors of the focusing magnets are within the design tolerance and the results point to the orbit offsets in the sextupole field as the source of gradient errors. A new method, the independent component analysis (ICA) is introduced to analyze multiple BPM turn-by-turn data taken simultaneously around a synchrotron. This method makes use of the redundancy of the data and the time correlation of the source signals to isolate various components, such as betatron motion and synchrotron motion, from raw BPM data. By extracting clean coherent betatron motion from noisy data and separates out the betatron normal modes when there is linear coupling, the ICA method provides a convenient means to measure the beta functions and betatron phase advances. It also separates synchrotron motion from the BPM samples for dispersion function measurement. The ICA method has the capability to separate other perturbation signals and is robust over the contamination of bad BPMs. The application of the ICA method to the Booster has enabled the measurement of the linear lattice functions which are used to verify the existing lattice model. The transverse impedance and chromaticity are measured from turn-by-turn data using high precision tune measurements. Synchrotron motion is also observed in the BPM data. The emittance growth of the Booster is also studied by data taken with ion profile monitor (IPM). Sources of emittance growth are examined and an approach to cure the

The Fermilab Booster is a nearly 40-year-old proton synchrotron, designed to accelerate injected protons from a kinetic energy of 400 MeV to 8 GeV for extraction into the Main Injector and ultimately the Tevatron. Currently the Booster is operated with a typical intensity of 4.5 x 10¹² particles per beam, roughly twice the value of its design, because of the requirement for high particle flux in various experiments. Its relatively low injection energy provides certain challenges in maintaining beam quality and stability under these increasing intensity demands. An understanding of the effects limiting this intensity could provide enhanced beam stability and reduced downtime due to particle losses and subsequent damage to the accelerator elements. Design of future accelerators can also benefit from a better understanding of intensity effects limiting injection dynamics. Chapter 1 provides a summary of accelerator research during the 20th century leading to the development of the modern synchrotron. Chapter 2 puts forth a working knowledge of the terminology and basic theory used in accelerator physics, and provides a brief description of the Fermilab Booster synchrotron. Synergia, a 3d space-charge modeling framework, is presented, along with some simulation benchmarks relevant to topics herein. Emittance, a commonly used quantity characterizing beam size and quality in a particular plane, is discussed in Chapter 3. Space-charge fields tend to couple the motion among the planes, leading to emittance exchange, and necessitating a simultaneous measurement to obtain a complete emittance description at higher intensities. A measurement is described and results are given. RMS beam emittances are shown to be in keeping with known Booster values at nominal intensities and emittance exchange is observed and accounted for. Unmeasurable correlation terms between the planes are quantified using Synergia, and shown to be at most an 8% effect. Results of studies on the coherent and incoherent shifts of transverse (betatron) frequencies with beam intensity at injection energies are presented. In Chapter 4 the coherent frequency shifts are shown to be due to dipole- and quadrupole-wakefield effects. The asymmetry of the Booster beam chamber through the magnets, as well as the presence of magnet laminations, are responsible for the magnitudes and for the opposing signs of the horizontal and vertical tune shifts caused by these wakefields. Chapter 5 details the procedures for obtaining a linear coherent-tune-shift intensity dependence, yielding -0.009/10¹² in the vertical plane and +0.001/10¹² in the horizontal plane. Data demonstrate a requirement of several hundred turns to accumulate to its maximal value. Two independent studies are compared, corroborating these results. In Chapter 6, a measure of the incoherent tune shift with intensity puts an upper limit on the magnitude of the direct space-charge effect in the Fermilab Booster. A prediction is made for the representative incoherent particle tune shift using a realistic Gaussian distribution, allowing for growth of the beam envelope with intensity, and found to be 0.004/10¹². The tune-spread dependence obtained by quantification of the resonant stopband width from beam-extinction measurements was measured at 0.005/10¹², similar to the predicted value. These will be shown to be one order of magnitude smaller than the space-charge term from the Laslett tune shift for a fixed-size, uniform beam.