On the nature of the plasma equilibrium

TL;DR

This paper analyzes the energy of a homogeneous one component plasma, showing that correlated particle motions lower the energy compared to uncorrelated motions, based on a relativistic plasma Hamiltonian derived from electromagnetic principles.

Contribution

It introduces a new calculation of plasma energy considering correlated motions using the Darwin energy and recent theoretical advances, providing insights into plasma stability.

Findings

Correlated motions reduce plasma energy compared to uncorrelated motions.

Energy lowering is due to attraction of parallel currents or inductive inertia.

Derived plasma Hamiltonian based on relativistic Darwin energy.

Abstract

We calculate the energy of a homogeneous one component plasma and find that the energy is lower for correlated motions of the particles as compared to uncorrelated motion. Our starting point is the conserved approximately relativistic (Darwin) energy for a system of electromagnetically interacting particles that arises from the neglect of radiation. For the idealized model of a homogeneous one component plasma the energy only depends on the particle canonical momenta and the vector potential. The vector potential is then calculated in terms of the canonical momenta using recent theoretical advances and the plasma Hamiltonian is obtained. The result can be understood either as due to the energy lowering caused by the attraction of parallel currents or, alternatively, as due to the inductive inertia associated with the flow of net current.