Toroid moments in electrodynamics and solid-state physics

The role is explained of toroid moments and average 2n-power radii in the structure of multipole expansions in the framework of Maxwell-Lorentz electrodynamics. A complete scheme of multipole expansions is given in terms of distribution theory. A number of particular applications of toroid moments is considered in condensed-matter physics. Special attention is paid to the microscopic symmetry of the vector order parameter in ordering orbital currents in crystals and to its description in terms of the distributed toroid moments. Conditions are discussed for the appearance of a toroid current state (orbital antiferromagnetism) in some models of solid-state theory.