Parallel and toroidal viscosity for nonaxisymmetric toroidal plasmas in the plateau regime

Abstract

Calculations of the viscosity expressions appearing in the fluid approach to neoclassical transport of nonaxisymmetric toroidal plasmas are presented. By assuming the Chew–Goldberger–Low form for the viscosity tensor and a large-aspect-ratio plasma, the drift kinetic equation for the plateau regime is solved and expressions for the parallel and toroidal viscosity are calculated as functions of plasma and heat fluxes. The viscosity expressions found for the plateau regime are similar to the expressions valid in the collision-dominated regime.

Entropy production and Onsager symmetry in neoclassical transport processes of toroidal plasmas

“…We should note that the ambipolarity condition 36 reduces the number of the thermodynamic forces required for determining the classical fluxes by one, and that the radial electric field does not enter the reduced set of the thermodynamic forces (X a1(a I) * ,X a2 ). Next, let us consider the entropy production ¯a due to the first-order gyroangle-averaged distribution function f a1 , which satisfies the linearized drift kinetic equation: [1][2][3][7][8][9][10][11]14,15 …”

“…Here we assume the existence of toroidal nested magnetic surfaces as in other previous works. [6][7][8][9][10][11] Balescu and Fantechi derive the full neoclassical transport coefficients for the nonaxisymmetric plasma in the plateau regime, and claim that the Onsager symmetry partly breaks down in that case. 11 Contrary to Ref.…”

“…The neoclassical transport equations for nonaxisymmetric systems [6][7][8][9][10][11] are more complicated due to the geometrical complexities, and they involve the nonambipolar parts. The absence of symmetry may also cause the breakup of magnetic surfaces into islands and ergordic regions, 12 although such problems are beyond the scope of this work.…”

How to calculate the neoclassical viscosity, diffusion, and current coefficients in general toroidal plasmas

“…In addition to these transport coefficients, our method gives a useful recipe to obtain the neoclassical viscosity coefficients, which play an important role in determining plasma rotation profiles. Since our work follows a line of the moment method, it is more transparently connected or applicable to past theoretical studies of neoclassical transport in nonaxisymmetric systems 5,[27][28][29][30][31]33 which are also based on the moment method. Furthermore, in the present study, the validity of our procedures is satisfactorily verified by numerical examples, in which our results are compared with analytical formulas on the parallel viscosity, the ripple transport coefficient, and the geometrical factor of the bootstrap current in various collision frequency regimes.…”

“…25,26 In general toroidal systems with no symmetry, we need to calculate viscosities in both poloidal and toroidal directions, and these viscosity coefficients are analytically derived for the Pfirsch-Schlüter and plateau regimes. 27,28 However, for the banana regime, analytical formulas are given only for the parallel viscosities. 5,[29][30][31] In order to accurately calculate both poloidal and toroidal viscosity coefficients in toroidal helical systems for lowcollisionality regimes, we need to make use of numerical solution of the drift kinetic solution as effectively as possible, and the present paper shows how to do that.…”