Tanabe J.T. Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements

SLAC-R-754 — Stanford Linear Accelerator Center, Stanford Synchrotron Radiation Laboratory, Stanford, CA 94025 Work supported in part by Department of Energy contract DE-AC02-76SF00515, 2005. — 354 p.Basic ConceptsMagnetTypes
Pictures
Conventions
The Field from a Line Current (Biot-Savart law)
Magnetic Forceona Line Current
MKSUnits
Force Directions
Dipole Magnet
Quadrupole Magnet
Sextupole Magnet
Corrector Magnets
Specialized Magnets
More Polarity
Alternate Polarity Convention
Closure
Problems
TheoryMaxwell’s Magnet Equations
Continuity
Units
The Functionofa Complex Variable
The Two-Dimensional Fields
Fields from the Two-Dimensional Function of a Complex Variable
Two Dimensional Fieldsina Vacuum
Multipoles
Laplace’s Equation
Solutionsto Laplace’s Equation
Two-Dimensional Vector and Scalar Potentials
Magnetic Fieldsfrom the Two-Dimensional Potentials
A Particular Function of the Complex Variable, F = Cnzn
Ideal Two-Dimensional Multipole Magnets
Two-Dimensional Flux Linesand Poles
Pole Contours
Complex Extrapolation
Magnetic Fields Using the Functionof the Complex Variable
n=1, the Dipole Magnet
n=2, the Quadrupole Magnet
n=3, the Sextupole Magnet
Multipole Errors
The Error Spectrum
Allowedor Systematic Multipole Errors
Multipole Field Errors
Simple Conformal Maps
Mapping Functions
Quadrupoleto Dipole Map
Dipoleto Quadrupole Map
Sextupoleto Dipole Map
Dipoleto Sextupole Map
Gradient Magnetto Dipole Map
Dipoleto Gradient Magnet Map
Closure
Problems
Pole Tip Design
Understanding the Dipole Magnet
The Orthogonal Analog Model
The Orthogonal Analog Modelandthe Quadrupole
The HDipole Geometry
H-Magnet Uniformity
Understandingthe Quadrupole Magnet
Quadrupole Uniformity
Understandingthe Gradient Magnet
Gradient Magnet Uniformity
Mappingan Existing Gradient Magnet Design
Baseline Optimized Pole
New Unoptimized Pole
BaselineMapped Pole
New Mapped Unoptimized Pole
Scaling and Shifting
Center Expansion
Mapping Backinto the Quadrupole Space
Closure
Problems
PerturbationsAlgorithms and Tables
Quadrupole Pole Error Coefficients, N=2
Sextupole Pole Error Pole Error Coefficients, N=3
Computing Error Multipoles
Two Piece Quadrupole
Magnet Assymetry
Differencesin Lengthsof the Upperand Lower Halves
Sorting
Two Piece Quadrupole Errors
Tolerances (Examplesof Computations)
Alignment Error
Excitation Error
Random Multipole Error
Sextupole Trim Windings
Orthogonality
Horizontal Steering Trim
Vertical Steering and Skew Quadrupole Trim
Trim Excitations
Closure
Problems
Magnetic Excitation and Coil DesignMaxwell’s Inhomogeneous Equation
Continuity
Magnet Excitations
Magnet Efficiency
Dipole Magnets
Quadrupole Magnet
Sextupole Magnet
Coil Design
Coil Power
Coil Cooling
Pressure Drop
Flow Velocity
Units
Coil Cooling
Calculations
Sensitivities
Closure
Problems
Poisson
Elements of the Family of Codes
Documentation
Problem Flow
Auto Mesh
Boundary Conditions and Constraints
Geometry
Setting Up and Testing the Geometry
Symmetries
Example - Collins or Figure Eight Quadrupole
Coil Geometry
Yoke Geometry
The Vector Potential Boundary Condition
Simple Dipole
The Simple Dipole with Vector Potential Boundary Conditions
The Vector Potential Boundary Condition for Optimizing the QuadrupolePole
Other Applications of the Vector Potential Boundary Conditions
Closure
Problems
Stored Energy, Magnetic Forces and Dynamic Effects
Force on Coils
Forceona Pole
Units
A Reference Point
Magnet Stored Energy
Inductance
Eddy Currents
Field Attenuation due to Eddy Currents in a Semi-infinite Conductive Horizontal Plate
Field Attenuation due to Eddy Currents in a Pair of Semi infinite Conductive Vertical Plates
Field Attenuation due to Eddy Currents in a Closed RectangularChamber
Field Amplification
Closure
Problems
Magnetic Measurements
The VectorPotential
Fourier Analysis
Output Voltage
The Compensated Coil
The Quadrupole Coil
The Dipole Coil
The Sextupole Coil
Spilldown and Magnetic Center
Quadrupole Magnetic Center
Sextupole Magnetic Center
Rotating Coil Magnetic Measurements
The Measurement System
Fourier Analysis
Uncompensated Signal
Compensated Signal
Expressionsfor the Integrated Multipole Fields
Excitation and Transfer Function
Relative Phases
Units
Measurements and Output
Measurement Plan
Raw Data Output
Bucking Ratio
Normalized Multipole Errors
Error Spectrum Normalized to the Required Good Field Radius
Magnetic Center
Measurement Output
Tabular Output
Analog Output (Iso-Error Plots)
Closure
Problems
Magnet Yoke Design and FabricationSaturation
Two Dimensional Design
Three Dimensional Design
Dipole Fringe Field
Quadrupole Fringe Field
SolidIronor Steel Laminations
Reprocucibility and Symmetry
Solid Iron Cores
Laminated Steel Cores
Economics
Laminated Yoke Fabrication
Yoke Assembly/Fabrication Techniques
Gluing
Welded Laminated Yokes
Mechanically Assembled Laminated Yokes
Core Grounding
Closure
Appendix
Magnet Coil FabricationConductor Size and Turnto Turn Insulation
Coil Winding
Coil Potting (Encapsulation)
Coil Failures
Specifications
Measurements and Tests
Closure
Magnet AssemblyCoil Supports and Bussing
Bussing
Magnet Tests
Closure
Magnet Installation and AlignmentMagnet Support
Predetermined Alignment
Generic Fiducialization
Adjusted Alignment
Adjustable Struts
Adjustable Support Blocks
Pedigreed Fiducialization
Closure
Solutions