Search

We show, for the first time, the explicit form of the nonlinear partial differential equations (PDEs) subject to the correct boundary conditions that have to be satisfied by transport coefficients having a vanishing skew-symmetric piece. We also report, for the first time, the nonlinear PDEs (with the appropriate boundary conditions) for transport coefficients when the thermodynamic system is subject to two thermodynamic forces. Since the proposed PDEs have been derived without neglecting any term present in the dynamical equations (i.e., the energy, mass, and momentum balance equations), we propose them as a good candidate for describing transport in thermodynamic systems also far from equilibrium (e.g., in the turbulent regime). The preliminary test was carried out by analyzing a concrete example where Onsager's relationships manifestly disagree with experience: magnetically confined Tokamak-plasmas. More specifically, we focus our calculations to compute mass and energy transports in Frascati Tokamak Upgrade-plasmas subject to two thermodynamic forces. We show a good agreement between the theoretical predictions and the experimental data. The aim of this study is to apply our approach to the Divertor Tokamak Test Facility, to be built in Italy, and to the International Thermonuclear Experimental Reactor.

Rotation of tokamak-plasmas, not at the mechanical equilibrium, is investigated using the Prigogine thermodynamic theorem. This theorem establishes that, for systems confined in rectangular boxes, the global motion of the system with barycentric velocity does not contribute to dissipation. This result, suitably applied to toroidally confined plasmas, suggests that the global barycentric rotations of the plasma, in the toroidal and poloidal directions, are pure reversible processes. In case of negligible viscosity and by supposing the validity of the balance equation for the internal forces, we show that the plasma, even not in the mechanical equilibrium, may freely rotate in the toroidal direction with an angular frequency, which may be higher than the neoclassical estimation. In addition, its toroidal rotation may cause the plasma to rotate globally in the poloidal direction at a speed faster than the expression found by the neoclassical theory. The eventual configuration is attained when the toroidal and poloidal angular frequencies reaches the values that minimize dissipation. The physical interpretation able to explain the reason why some layers of plasma may freely rotate in one direction while, at the same time, others may freely rotate in the opposite direction, is also provided. Invariance properties, herein studied, suggest that the dynamic phase equation might be of the second order in time. We then conclude that a deep and exhaustive study of the invariance properties of the dynamical and thermodynamic equations is the most correct and appropriate way for understanding the triggering mechanism leading to intrinsic plasma-rotation in toroidal magnetic configurations.