Classical thermal conductivity of a stationary toroidal plasma

The differential equation for the ion heat flux parallel to the magnetic field is solved for non-rotating, but otherwise arbitrary, MHD equilibria by using an expansion in powers of ( omega ci tau i ) -1 ( omega ci the cyclotron frequency, tau i the time between collisions of ions). A general expression for the effective thermal conductivity kappa eff i is obtained, which has the same structure as the general form of the Pfirsch-Schluter factor of classical diffusion. In the case of a Tokamak type equilibrium with an elliptic cross section of the plasma ring, kappa eff i is calculated assuming large aspect ratio R/a, but finite beta . At sufficiently high beta (of order beta approximately a/R) the average rotational transform goes to zero at the plasma boundary, but kappa eff i remains finite. The maximum temperature T max attainable with Ohmic heating in a plasma with elliptical cross section is calculated. For a current density j well below the Kruskal-Shafranov limit, T max is proportional to j 2 , but near that limit T max is only a linear function of j.