High precision modeling of space-charge effects is essential for designing future accelerators as well as optimizing the performance of existing machines. Synergia is a high-fidelity parallel beam dynamics simulation package with fully three dimensional space-charge capabilities and a higher-order optics implementation. We describe the Synergia framework, developed under the auspices of the DOE SciDAC program, and present Synergia simulations of the Fermilab Booster accelerator and comparisons with experiment. Our studies include investigation of coherent and incoherent tune shifts and halo formation.

We have studied space charge effects in the Fermilab Booster. Our studies include investigation of coherent and incoherent tune shifts and halo formation. We compare experimental results with simulations using the 3-D space charge package Synergia.

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.

We calculate the impedance and the wake functions for laminated structures with parallel-planes and circular geometries. We critically examine the approximations used in the literature for the coupling impedance in laminated chambers and find that most of them are not justified because the wall surface impedance is large. A comparison between the flat and the circular geometry impedance is presented. We use the wake fields calculated for the Fermilab Booster laminated magnets in realistic beam simulations using the Synergia code. We find good agreement between our calculation of the coherent tune shift at injection energy and the experimental measurements. In this paper we calculate the impedance and the wake functions for laminated structures with parallel-planes and circular geometries. First the coupling impedance is derived as a function of the wall surface impedance. Then the surface impedance is calculated by solving Maxwell's equations inside the lamination and the crack regions. We find that the commonly used resistive-wall approximations, good for metallic pipes with small surface impedance, are not valid in the laminated structures where the surface impedance is large. Realistic Synergia simulations of the Booster machine with wake fields predict transverse coherent tune shifts in good agreement with the experiment.

High precision modeling of space-charge effects is essential for designing future accelerators as well as optimizing the performance of existing machines. Synergia is a high-fidelity parallel beam dynamics simulation package with fully three dimensional space-charge capabilities and a higher-order optics implementation. We describe the Synergia framework and model benchmarks we obtained by comparing to semi-analytic results and other codes. We also present Synergia simulations of the Fermilab Booster accelerator and comparisons with experiment.

A progress report on efforts to understand and improve adiabatic capture in the Fermilab Booster by experiment and simulation is presented. In particular, a new RF voltage program for capture which ameliorates transverse space-charge effects is described and simulated. 7 refs., 4 figs.