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.

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.

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.

This book presents the developments in accelerator physics and technology implemented at the Tevatron proton-antiproton collider, the world’s most powerful accelerator for almost twenty years prior to the completion of the Large Hadron Collider. The book covers the history of collider operation and upgrades, novel arrangements of beam optics and methods of orbit control, antiproton production and cooling, beam instabilities and feedback systems, halo collimation, and advanced beam instrumentation. The topics discussed show the complexity and breadth of the issues associated with modern hadron accelerators, while providing a systematic approach needed in the design and construction of next generation colliders. This book is a valuable resource for researchers in high energy physics and can serve as an introduction for students studying the beam physics of colliders.

The stable region of the Fermilab Booster beam in the complex coherent-tune-shift plane appears to have been shifted far away from the origin by its intense space charge making Landau damping appear impossible. Simulations reveal a substantial buildup of electron cloud in the whole Booster ramping cycle, both inside the unshielded combined-function magnets and the beam pipes joining the magnets, whenever the secondary-emission yield (SEY) is larger than (almost equal to)1.6. The implication of the electron-cloud effects on the space charge and collective instabilities of the beam is investigated.

The Fermilab Booster is a bottleneck limiting the proton beam intensity in the accelerator complex. A study group has been formed in order to have a better understanding of this old machine and seek possible improvements. The work includes lattice modeling, numerical simulations, bench measurements and beam studies. Based on newly obtained information, it has been found that the machine acceptance is severely compromised by the orbit bump and dogleg magnets. This, accompanied by emittance dilution from space charge at injection, is a major cause of the large beam loss at the early stage of the cycle. Measures to tackle this problem are being pursued.