Nanz S. Toroidal Multipole Moments in Classical Electrodynamics: An Analysis of their Emergence and Physical Significance

Springer, Fachmedien, Wiesbaden, 2016. – 100 p. – ISBN: 3658125489Stefan Nanz investigates the necessity for three multipole families in classical electrodynamics. He shows that by imposing symmetry and parity constraints, it is sufficient to deal with only two multipole families. This implies that the toroidal multipole moments do not represent an independent multipole family, and they only emerge in the long-wavelength limit.Introduction and Overview
Why another Multipole Family?
A Brief History of Toroidal Moments
Characterization of General Charge and Current Distributions
Necessity for Three Multipole Families
Distinction between Toroidal Moment and Anapole
Basic Equations and Notations
Maxwell’s Equations
Wave Equation and Helmholtz Equation
Potentials
Multipole Expansion of the Potentials
Multipole Expansion in Cartesian Coordinates
Cartesian Traceless Expansion including Toroidal Moments
Multipole Expansion in Spherical Coordinates
Direct Multipole Expansion of Electromagnetic Fields
Decomposition of the Fields
Expansion Coefficients for given Electric Field
Expansion Coefficients for given Sources
Physical Relevance of the Longitudinal Part
Connection and Comparison of the Different Approaches
Conversion of Spherical into Cartesian Moments and Vice Versa
Properties of the Fields including Toroidal Moments
Summary and Outlook