Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

Abstract

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.

added references, revised

References in corpus (5)

• Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
• From least action in electrodynamics to magnetomechanical energy -- a review
• The exact Darwin Lagrangian
• On the nature of the plasma equilibrium
• A first principles explanation for the density limit in magnetized plasmas

Cited by in corpus (3)

• Meissner effect, diamagnetism, and classical physics - a review
• A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit
• Magnetic Field Expulsion from an Infinite Cylindrical Superconductor