Issue
EPL
Volume 84, Number 2, October 2008
Article Number 20011
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/20011
Published online 13 October 2008
EPL, 84 (2008) 20011
DOI: 10.1209/0295-5075/84/20011

Magnetic energy per particle in constant current density

H. Essén

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

hanno@mech.kth.se

received 1 August 2008; accepted in final form 11 September 2008; published October 2008
published online 13 October 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.

PACS
03.50.De - Classical electromagnetism, Maxwell equations.
52.25.Kn - Thermodynamics of plasmas.
52.25.Xz - Magnetized plasmas.

© EPLA 2008