Relationship between viscosity and conductivity for tokamak plasmas

Abstract

The relation between parallel viscosity and the parallel conductivity for tokamak plasma has been derived by combining Ideal MHD equilibrium equations with the concept of universal profiles. It is obtained that the parallel viscosity Π and parallel conductivity σ in a tokamak are related by Π σ −1 = γ (U −U 0 )I/R, where U is the loop voltage, U 0 is attributed to polarization, I is the toroidal current and R is the major radius of the machine. The coefficient γ depends on para-or diamagnetism and on toroidal effects and exhibits a weak dependence on the minor radius.

Relationship between normalized thermal energy and conductivity for cylindrical tokamak geometry

“…The relation [3] implies a constraint on the thermal-energy content which cannot be violated, whatever the energy transport present and the plasma heating used. It should be noted that a different relation [4,5] has been derived. Analogous to that of above models, can be obtained by following the same procedure but using Ohm's law [6].…”