The classical thermal conductivity in a toroidal plasma filament

In toroidal equilibrium configurations of a plasma the drift heat flux causes a change in the plasma temperature distribution over the magnetic surfaces. The compensation of the resulting temperature gradient by a longitudinal `non-magnetic' heat flux causes a certain effective heat flux across the magnetic surfaces. This additional toroidal heat flux is greater than the `magnetic' flux which determines the heat losses from the plasma in a cylindrical geometry. The paper gives a calculation of the effective toroidal thermal conductivity of the plasma for smooth toroidal systems of the Tokamak type and of the Stellarator type with a three-dimensional figure-of-eight shape. Expressions are also derived for the electrical potential distribution caused by the above-mentioned change in the temperature distribution.