Phase-space energy of charged particles with negligible radiation: Proof of spontaneous magnetic strutcures and new effective forces.

Authors: Essén, H.
Document Type: Article
Pubstate: Published
Journal: Phys. Rev. E.
Volume: 56   5858-5865
Year: 1997


The phase-space energy of a system of charged particles in the negligible radiation (Darwin) lonrelativistic limit is derived. The usefulness of the second-order approximation to this Hamiltonian, previously found by the present author, is discussed and given a stronger theoretical foundation. As a result a typical length scale for magnetic structures is found. The virital theorem is then applied to the second-order Hamiltonian. Together with the assumption that magnetism is a first-order perturbation it proves that magnetic interaction lowers the energy of a plasma. This proves that net currents must flow in a plasma and a simple estimate indicates that the spontaneously forming magnetic structures are resistant to thermal disruption. The effective one-particle Hamiltonian implied by the second-order Hamiltonian is calculated. It predicts a new effective many-body force that acceierates charged particles near a large plasma. It is conjectured that this effective force could give a simpler explanation for stellar wind and other large scale plasma phenomena.