Derivation of Reference Distribution Functions for Tokamak-plasmas by Statistical Thermodynamics

摘要

A general approach for deriving the expression of reference distributionfunctions by statistical thermodynamics is illustrated, and applied to the caseof a magnetically confined plasma. The local equilibrium is defined by imposingthe minimum entropy production, which applies only to the linear regime near astationary thermodynamically non-equilibrium state and the maximum entropyprinciple under the scale invariance restrictions. This procedure may beadopted for a system subject to an arbitrary number of thermodynamic forces,however, for concreteness, we analyze, afterwords, a magnetically confinedplasma subject to three thermodynamic forces, and three energy sources: i) thetotal Ohmic heat, supplied by the transformer coil, ii) the energy supplied byNeutral Beam Injection (NBI), and iii) the RF energy supplied by Ion CyclotronResonant Heating (ICRH) system which heats the minority population. In thislimit case, we show that the derived expression of the distribution function ismore general than that one, which is currently used for fitting the numericalsteady-state solutions obtained by simulating the plasma by gyro-kinetic codes.An application to a simple model of fully ionized plasmas submitted to anexternal source is discussed. Through kinetic theory, we fixed the values ofthe free parameters linking them with the external power supplies. Thesingularity at low energy in the proposed distribution function is related tothe intermittency in the turbulent plasma.