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

TL;DR

This paper develops a statistical thermodynamics-based method to derive reference distribution functions for magnetically confined plasmas, incorporating multiple energy sources and thermodynamic forces, improving upon existing models for plasma behavior analysis.

Contribution

It introduces a general thermodynamic approach to derive plasma distribution functions that account for multiple energy sources and thermodynamic forces, extending current fitting models.

Findings

Derived a more general distribution function than current models.

Linked free parameters to external power supplies.

Identified low-energy singularity related to plasma intermittency.

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.