Eur. Phys. J. D (2014) 68: 44
https://doi.org/10.1140/epjd/e2013-40287-x

Regular Article

Derivation of reference distribution functions for Tokamak-plasmas by statistical thermodynamics

¹ Université Libre de Bruxelles (U.L.B.), Department of Theoretical Physics and Mathematics, Campus de la Plaine C.P. 231, Bvd du Triomphe, 1050 Brussels, Belgium
² EURATOM-ENEA Fusion Association, Via E. Fermi 45, C.P. 65, 00044 Frascati ( Rome), Italy
³ EURATOM-MEdC Fusion Association, University of Craiova, Faculty of Exact Sciences, Str.A.I.Cuza Street 13, Craiova - 200585, Romania
⁴ Université Catholique de Louvain (UCL), École Polytechnique de Louvain (EPL), Rue Archimède, 1 bte L6.11.01, 1348 Louvain-la-Neuve, Belgium

^a e-mail: cardinali@frascati.enea.it

Received: 6 May 2013
Received in final form: 10 October 2013
Published online: 11 March 2014

Abstract

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: (i) the total Ohmic heat, supplied by the transformer coil; (ii) the energy supplied by neutral beam injection (NBI); and (iii) the RF energy supplied by ion cyclotron resonant heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.