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

TL;DR

This paper challenges the common interpretation of the Bohr-van Leeuwen theorem by emphasizing the role of velocity-dependent interactions in classical diamagnetism and introduces a new repulsive force relevant to plasmas.

Contribution

It demonstrates that classical diamagnetism arises from velocity-dependent interactions and predicts a new many-body repulsive force in magnetized plasmas.

Findings

Classical diamagnetism requires velocity-dependent interactions.

A new repulsive many-body force is predicted for plasmas.

Comparison with experiments depends on the number of classically behaving electrons.

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.