Elsevier S & T

Nonlinear Diffusion of Electromagnetic Fields: With Applications to Eddy Currents and Superconductivity

Mayergoyz, Isaak D.

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Table of contents
  • Cover
  • Contentsvii
  • Prefacexi
  • Chapter 1. Diffusion of Electromagnetic Fields in Magnetically Nonlinear Conducting Media (Linear Po1
  • 1.1 Statement of the Problem1
  • 1.2 Nonlinear Diffusion in the Case of Abrupt (Sharp) Magnetic Transitions5
  • 1.3 Model Problem for Gradual Magnetic Transitions20
  • 1.4 Solution of the Model Problem (Self-Similar Solutions)27
  • 1.5 Generalization of Self-Similar Solutions37
  • 1.6 Standing Mode of Nonlinear Diffusion51
  • 1.7 Nonlinear Diffusion in a Cylinder58
  • 1.8 Applications to Circuit Analysis70
  • 1.9 Eddy Current Hysteresis and the Preisach Model80
  • References94
  • Chapter 2. Diffusion of Electromagnetic Fields in Magnetically Nonlinear Conducting Media (Vector Po96
  • 2.1 Nonlinear Diffusion of Circularly Polarized Electromagnetic Fields in Isotropic Media96
  • 2.2 Perturbation Technique113
  • 2.3 Nonlinear Diffusion of Elliptically Polarized Electromagnetic Fields in Isotropic Media124
  • 2.4 Nonlinear Diffusion of Circularly Polarized Electromagnetic Fields in Anisotropic Media137
  • 2.5 Nonlinear Diffusion of Elliptically Polarized Electromagnetic Fields in Anisotropic Media154
  • 2.6 Eddy Current Losses in Thin Laminations166
  • References180
  • Chapter 3. Nonlinear Diffusion of Weak Magnetic Fields182
  • 3.1 Nonlinear Diffusion of Linearly Polarized Electromagnetic Fields182
  • 3.2 Nonlinear Diffusion of Circularly Polarized Electromagnetic Fields in Isotropic Media199
  • 3.3 Nonlinear Diffusion of Elliptically Polarized M~gnetic Fields in Isotropic Media208
  • 3.4 Nonlinear Diffusion in Anisotropic Media218
  • References224
  • Chapter 4. Nonlinear Diffusion in Superconductors225
  • 4.1 Superconductors with Sharp Resistive Transitions (The Bean Model for Superconducting Hysteresis225
  • 4.2 Preisach Model with Stochastic Input as a Model for Creep (Aftereffect)242
  • 4.3 Nonlinear Diffusion in Superconductors with Gradual Resistive Transitions (Linear Polarization)258
  • 4.4 Nonlinear Diffusion in Isotropic Superconductors with Gradual Resistive Transitions (Circular Po275
  • 4.5 Nonlinear Diffusion in the Case of Elliptical Polarizations and Anisotropic Media286
  • References302
  • Chapter 5. Nonlinear Impedance Boundary Conditions and Their Application to the Solution of Eddy Cur304
  • 5.1 Mathematical Structure of Maxwell's Equations for Eddy Current Problems304
  • 5.2 Calculation of the Source Field H0311
  • 5.3 Inipedance Boundary Conditions321
  • 5.4 Finite Element Implenientation of Impedance Boundary Conditions330
  • 5.5 Impedance Boundary Conditions for Thin Magnetic Conducting Shells and Their Finite Element Imple342
  • 5.6 Calculation of Eddy Currents in Thin Nonmagnetic Conducting Shells351
  • 5.7 Analysis of Thin Magnetic Shells Subject to Static Magnetic Fields367
  • References383
  • Appendix A. The Preisach Model of Hysteresis385
  • Index409
Book details
  • Vendor Elsevier S & T
  • SKU 9780124808706
  • ISBN-13 9780080537696
  • Author Mayergoyz, Isaak D.
  • Category Technology & Engineering
  • Subject Optics

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Nonlinear Diffusion of Electromagnetic Fields covers applications of the phenomena of non-linear diffusion of electromagnetic fields, such as magnetic recording, electromagnetic shielding and non-destructive testing, development of CAD software, and the design of magnetic components in electrical machinery. The material presented has direct applications to the analysis of eddy currents in magnetically nonlinear and hysteretic conductors and to the study of magnetization processes in electrically nonlinear superconductors. This book will provide very valuable technical and scientific information to a broad audience of engineers and researchers who are involved in these diverse areas.

Key Features
* Contains extensive use of analytical techniques for the solution of nonlinear problems of electromagnetic field diffusion
* Simple analytical formulas for surface impedances of nonlinear and hysteretic media
* Analysis of nonlinear diffusion for linear, circular and elliptical polarizations of electromagnetic fields
* Novel and extensive analysis of eddy current
losses in steel laminations for unidirectional and rotating magnetic fields
* Preisach approach to the modeling of eddy current hysteresis and superconducting hysteresis
* Extensive study of nonlinear diffusion in
superconductors with gradual resistive transitions (scalar and vertorial problems)