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El. knyga: Advanced Multipoles for Accelerator Magnets: Theoretical Analysis and Their Measurement

  • Formatas: EPUB+DRM
  • Serija: Springer Tracts in Modern Physics 277
  • Išleidimo metai: 25-Sep-2017
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319656663
Kitos knygos pagal šią temą:
Advanced Multipoles for Accelerator Magnets: Theoretical Analysis and Their MeasurementDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Serija: Springer Tracts in Modern Physics 277
  • Išleidimo metai: 25-Sep-2017
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319656663
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This monograph presents research on the transversal beam dynamics of accelerators and evaluates and describes the respective magnetic field homogeneity.

The widely used cylindrical circular multipoles have disadvantages for elliptical apertures or curved trajectories, and the book also introduces new types of advanced multipole magnets, detailing their application, as well as the numerical data and measurements obtained. The research presented here provides more precise descriptions of the field and better estimates of the beam dynamics. Moreover, the effects of field inhomogeneity can be estimated with higher precision than before. These findings are further elaborated to demonstrate their usefulness for real magnets and accelerator set ups, showing their advantages over cylindrical circular multipoles. The research findings are complemented with data obtained from the new superconducting beam guiding magnet models (SIS100) for the FAIR (Facility for Antiproton and Ion Research) project.

Lastly, the book offers a comprehensive survey of error propagation in multipole measurements and an appendix with Mathematica scripts to calculate advanced magnetic coil designs.

1 Introduction
1(10)
1.1 Motivation
1(2)
1.2 The Laboratory and Its New Project
3(1)
1.3 The Magnets
4(3)
1.4 Scope of this Treatise
7(4)
References
9(2)
2 Electromagnetic Fields and Particle Motion
11(10)
2.1 Maxwell's Equations
11(6)
2.1.1 Magnetic Quasistatic Approximation
12(1)
2.1.2 Magnetic Field in Linear Material
13(4)
2.2 Particle Motion in Magnetic Fields
17(4)
2.2.1 Particle Motion in a Cyclotron
18(1)
2.2.2 Paraxial Approximations
18(1)
2.2.3 Summary
19(1)
References
19(2)
3 Coordinate Systems
21(14)
3.1 Orthogonal Curvilinear Systems
21(2)
3.2 Cylindrical Coordinate Systems
23(4)
3.2.1 Cylindrical Circular Systems
23(1)
3.2.2 Cylindrical Elliptical Systems
24(3)
3.3 Toroidal Coordinate Systems
27(4)
3.3.1 Global Toroidal Coordinates
27(1)
3.3.2 Local Toroidal Coordinates
27(2)
3.3.3 Local Toroidal Elliptical Coordinates
29(2)
3.4 Frenet-Serret Coordinates
31(1)
3.5 Summary
32(3)
References
32(3)
4 Field Descriptions
35(40)
4.1 Basis: Cylindrical Circular Multipoles
36(5)
4.1.1 Conventions
37(3)
4.1.2 Effect of Transformations
40(1)
4.1.3 Circular Multipoles Using Real Variables
40(1)
4.2 Cylindrical Elliptical Multipoles
41(14)
4.2.1 Complex Elliptical Multipoles
43(4)
4.2.2 Relations Between Circular and Elliptical Multipoles
47(4)
4.2.3 Elliptical Multipole Field Expansions for Elliptical Components
51(2)
4.2.4 Complex Potential for Normal and Skew Elliptical Multipoles
53(2)
4.3 Toroidal Circular Multipoles
55(14)
4.3.1 Approximate R-Separation
56(1)
4.3.2 The Potential
57(1)
4.3.3 Real Basis Vector Field in Local Toroidal Coordinates
58(11)
4.3.4 Approximation Error of the Differential Equation
69(1)
4.4 Toroidal Elliptical Multipoles
69(2)
4.5 Summary
71(4)
References
72(3)
5 Rotating Coils
75(10)
5.1 Derivation of Coil Probe Geometry Factors
75(4)
5.1.1 Complex Potential
76(1)
5.1.2 Magnetic Flux Through a Surface
76(2)
5.1.3 Magnetic Flux Picked Up by a Rotating Coil
78(1)
5.2 Radial Rotating Coil Layout
79(1)
5.3 Voltage Induced in a Rotating Pick Up Coil
80(1)
5.4 Compensated Systems
81(4)
References
84(1)
6 Experimental Setup
85(16)
6.1 Test Facility
85(2)
6.2 The Anticryostat
87(2)
6.3 Magnetic Measurement Equipment
89(9)
6.3.1 History: Choice of Method
89(2)
6.3.2 A Modular Mole
91(7)
6.4 Summary
98(3)
References
99(2)
7 Applications
101(6)
7.1 Appropriate Handling of Calculation Data
101(1)
7.2 Calculating Cylindrical Elliptical Multipoles
102(3)
7.3 Summary
105(2)
References
106(1)
8 Measuring Advanced Multipoles
107(26)
8.1 Measuring Straight Elliptical Multipoles
108(8)
8.1.1 Calculation Procedure
108(8)
8.1.2 Measurement Results
116(1)
8.2 Measuring Toroidal Multipoles
116(14)
8.2.1 The Magnetic Flux
120(2)
8.2.2 Conversion Matrices
122(2)
8.2.3 Choosing a Coil Probe Length
124(2)
8.2.4 Magnitude of the Terms
126(3)
8.2.5 Measurement Results on the SIS 100 Curved Dipole Magnet
129(1)
8.3 Summary
130(3)
References
130(3)
9 Error Propagation
133(16)
9.1 Error Propagation of Elliptic Multipoles Measurement
133(11)
9.1.1 Description of Calculation Procedure
133(2)
9.1.2 Combining the Coefficients
135(3)
9.1.3 Error Propagation of the Measured Coefficients
138(3)
9.1.4 Error Propagation to Coefficients of the Circular Multipoles
141(3)
9.1.5 Influence of Coil Probe Displacement
144(1)
9.2 Toroidal Multipole Measurement
144(1)
9.3 Measurement Accuracy Estimate for the CSLD
145(1)
9.4 Summary
146(3)
References
146(3)
10 Conclusions
149(4)
10.1 Outlook
151(2)
Appendix A Changes to Previous Publications 153(2)
Appendix B Mathematica Scripts 155(10)
Appendix C Approximate Inversion of a Perturbed Matrix 165
Dr. Pierre Schnizer has studied accelerator physics at the University of Graz and at the Large Hadron Collider at CERN. He has been research associate at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, analyzing and evaluating accelerator magnets for FAIR (Facility for Antiproton and Ion Research). He has been deputy director in the CERN-GSI collaboration for testing superconducting magnets. Today, he is technical project director at the Helmholtz Center for Energy and Materials in Berlin, responsible for BESSY VSR (variable pulse-length storage ring).
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