Note: Intro -- Contents -- List of Appendices -- Preface -- Chapter 1 -- Introduction -- 1.1. Background -- 1.2. Research Issues -- 1.3. Synopsis -- 1.4. Overview of SNS Accelerator Complex -- References -- Chapter 2 -- Fundamentals of Accelerator Magnets -- 2.1. Magnetostatic Fields -- 2.2. Two-Dimensional Fields -- 2.3. Particle Motion -- 2.4. Dipole Magnets -- 2.5. Quadrupole Magnets -- 2.6. Magnet Measurements -- References -- Appendix 2.1. A Command Input File for 2D Harmonic Calculations in the Patch Rotation Method -- Chapter 3 -- Magnet Modeling -- 3.1. Overview of Simulation Codes -- 3.2. Opera/Tosca -- 3.3. A Modeling Example -- References -- Chapter 4 -- Three-Dimensional Field Multipole Expansion -- 4.1. Review of Theory -- 4.2. Expansion Techniques -- 4.3. On-Axis Gradients -- 4.4. A 5th-Order Representation -- 4.5. Higher-Order Effects -- References -- Appendix 4.1. A Command Input File to Calculate the Surface Fields and to Perform Fourier Decomposition for the 3D Multipole Expansion in OPERA3D Post-Processor -- Chapter 5 -- Particle Optics in a Magnetic Quadrupole -- 5.1. Simulation Model of 30Q58 and Field Distributions -- 5.2. Particle Trajectories and Transfer Matrices -- 5.3. Three-Dimensional Mulipole Expansion and Linear Focusing Function -- 5.4. Form Factor Theory on Magnetic Fringe Fields -- 5.5. Linear Transfer Matrices from the Trajectory Equations -- 5.6. Lens Parameters and Hard Edge Models -- 5.7. Third-Order Aberrations -- 5.8. Particle Optics in 30Q44 -- References -- Appendix 5.1. Computation of Particle Optics of a Magnetic Quadrupole -- Chapter 6 -- Magnetic Interference between Two Magnets -- 6.1. Change in Linear Focusing Function -- 6.2. Magnetic Interference as a First-Order Perturbation -- 6.3. Hard Edge Models for a Perturbed Quad -- References -- Chapter 7 -- Particle Optics in a Quad Doublet Assembly. , 7.1. Two-Dimensional Field Parameters -- 7.2. Magnetic Fringe and Interference -- 7.3. Linear Transfer Matrices and Hard Edge Models -- 7.4. Third-Order Aberrations -- 7.5. Verification of Particle Trajectories -- References -- Chapter 8 -- Beam Matching in a Quadrupole Transport Channel -- 8.1. MEBT Line in SNS Linac -- 8.2. Fringe Effect in a Single MEBT Quad -- 8.3. Magnetic Interference between Two MEBT Quads -- 8.4. Error Propagation and Accumulation in MEBT Lattice -- 8.5. A General Solution to Beam Matching -- References -- Appendix 8.1. A Mathematica Notebook File to Compute Beam Matching in the SNS MEBT Lattice -- Chapter 9 -- Field Expansion in Magnetc Dipoles with Midplane Symmetry -- 9.1. Introduction -- 9.2. Field Expansion into Taylor's Series -- 9.2.1. Review of Theory -- 9.2.2. An Expansion Example -- 9.3. 3D Multipole Field Expansion -- 9.3.1. Expansion Formalism -- 9.3.2. Numerical Verification -- 9.4. Summary -- References -- Appendix 9.1. A Command Input File for Taylor's Expansion in Magnetic Dipoles -- Appendix 9.2. A Command Input File for Surface Field Calculation in Magnetic Dipoles with a Planar, Curved Reference Trajectory -- Chapter 10 -- Particle Optics in Main Bending Dipoles of SNS Accumulator Ring -- 10.1. Introduction -- 10.2. 3D Computer Simulation and Field Distribution -- 10.2.1. 3D Simulation Model -- 10.2.2. Magnetic Field Representation -- 10.2.3. Curvature and Derivative Calculations -- 10.3. First-Order Particle Optics -- 10.3.1. Linear Transfer Matrices from the Trajectory Equations -- 10.3.2. Equivalent Hard-Edge Lens Parameters -- 10.4. Second-Order Aberrations -- 10.5. Emittance Growth due to Non-Linear Fields -- 10.6. Summary -- References -- Appendix 10.1. A Mathematica Notebook File to Compute 1st-Order and 2nd-Order Particle Optics in 17D120 -- Chapter 11. , Field Distribution and Particle Optics in SNS Ring Injection Momentum Dump Line -- 11.1. Introduction -- 11.2. 3D Simulation Model -- 11.3. Magnetic Field Distributions -- 11.4. Particle Trajectories and Optics -- 11.5. Particle Distributions on Dump Window -- 11.6. Summary -- References -- Chapter 12 -- Particle Tracking of SNS Ring Injection -- 12.1. SNS Ring Injection and Waste Beam Losses -- 12.2. Injection Constraints -- 12.2.1. Closed Orbit Bump and Good Injection -- 12.2.2. Motion and Collection of Convoy Electrons -- 12.2.3. Transport of Waste Beams through IDSM -- 12.3. Three-Dimensional Modeling of Injection Waste Beam Dump Line -- 12.3.1. Simulation Models -- 12.3.2. Magnets and Fields on Beam Line -- 12.3.3. Initial Conditions of Test Particles -- 12.4. Three-Dimensional Particle Trajectories through IDSM -- 12.5. Particle Optics Through Quadrupole Magnet to Dump -- 12.6. Remedies -- 12.6.1. H(-Proton Particle Losses in the Y-Direction in IDSM -- 12.6.2. H0-Proton Particle Losses in the X-Direction in IDSM -- 12.6.3. Modification of a Spare IDSM -- 12.6.4. Waste Beam Losses Downstream after Quadrupole Magnet -- 12.7. Experimental Verifications -- References -- Appendix 12.1. Tracking Convoy Electrons -- Chapter 13 -- SNS Ring Extraction Beam Profile Distortion -- 13.1. Beam Profile Distortion Due to Strong Skew Quad Term in ELS -- 13.2. Three-Dimensional Simulation Model -- 13.3. General Performance of ELS -- 13.4. Computation of Skew Quad Term -- 13.4.1. Patch Rotation Method -- 13.4.2. Surface Field Analysis -- 13.4.3. Dipole Fields on Grids -- 13.4.4. Comparison with Measurements -- 13.5. Origin of the Large Skew Quad Term -- 13.5.1. Effect of Longitudinal Shims on Skew Quad Term -- 13.5.2. Effect of Magnet Ends on Skew Quad Term -- 13.6. Minimization of Integrated Skew Quad Term -- 13.7. Extracted Beam Profile through ELS. , 13.8. Linear Transfer Matrices -- 13.9. ELS Interference with Adjacent Quad -- 13.9.1. Effect of the ELS on 30Q44 -- 13.9.2. Effects of 30Q44 on the ELS -- 13.10. Summary -- References -- Appendix 13.1. Computation of Beam Profile Distortion on SNS Target -- Index -- Blank Page.