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

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.

33 pages and 13 figures

References in corpus (5)

• Low frequency noise controls on-off intermittency of bifurcating systems
• Nonlinear Transport Processes in Tokamak Plasmas. Part I: The Collisional Regimes
• Family of Probability Distributions Derived from Maximal Entropy Principle with Scale Invariant Restrictions
• Relaxation of Magnetically Confined Tokamak-Plasmas to Mechanical Equilibria
• Reference Distribution Functions for Magnetically Confined Plasmas from the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to the Scale-Invariant Restrictions

Cited by in corpus (2)

• Stationary distribution functions for Tokamak-plasmas in the weak-collisional transport regime by MaxEnt principle
• Reference Distribution Functions for Magnetically Confined Plasmas from the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to the Scale-Invariant Restrictions