Magnetic energy per particle in constant current density

Department of Mechanics, KTH - SE-100 44 Stockholm, Sweden, EU

Corresponding author: hanno@mech.kth.se

Received: 1 August 2008
Accepted: 11 September 2008

Abstract

We assume a constant current density in a homogeneous one-component plasma of infinite extent and calculate the resulting magnetic energy per particle. 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.