Turbulent Transport in Tokamak-plasmas: A Thermodynamic Approach

TL;DR

This paper develops nonlinear PDEs based on thermodynamic principles to model turbulent transport in tokamak plasmas, successfully predicting experimental electron losses and analytically evaluating Bohm and gyro-Bohm coefficients.

Contribution

It introduces a thermodynamic PDE framework for turbulent transport, deriving equations for transport coefficients and applying them to tokamak plasmas, including analytical evaluation of key coefficients.

Findings

The model accurately predicts electron mass and energy losses in FTU plasmas.

The approach analytically evaluates Bohm and gyro-Bohm coefficients for the first time.

The PDE framework aligns with experimental observations of turbulent transport.

Abstract

In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose them as a good candidate for describing also transport in thermodynamic systems in turbulent regimes. As a special case, we derive the nonlinear PDEs for transport coefficients when the thermodynamic system is subjected to two thermodynamic forces. In this case, the obtained PDE is, in thermodynamical field theory (TFT), analogous to Liouville's equation in Riemannian (or pseudo-Riemannian) geometry. The validity of our model is tested by analyzing a concrete example where Onsager's relations manifestly disagree with experience: transport in Tokamak-plasmas. More specifically, we compute the electron mass and energy losses in turbulent FTU (Frascati Tokamak Upgrade)-plasmas. We show the agreement between the theoretical predictions and experimental observations. This approach allows for predicting the values of the Bohm and the gyro-Bohm coefficients. To the best of our knowledge, it is the first time that such coefficients have been evaluated analytically. The aim of this series of works is to apply our approach to the Divertor Tokamak Test facility (DTT), to be built in Italy, and to ITER.