Neoclassical transport computations in non-isothermal tokamak plasmas

Abstract

Neoclassical transport in a non-isothermal plasma in which each plasma species has different equilibrium temperature is investigated by solving the drift kinetic equation with a Fokker–Planck (FP) collision operator in a circular tokamak model. Since it is known that a linearized FP operator does not have a self-adjoint property in a non-isothermal plasma, approximate models are developed for comparison to intend to have the self-adjoint property in the non-isothermal case. To achieve this, we set a common temperature that the system should reach after a long time, and the individual temperature of each particle species is expressed by a parameter to measure a shift of the individual temperature from the common one. Then, both the Vlasov part and the collision term of the kinetic equation are expanded around the common temperature, taking the temperature shift parameter up to the first order. It is found that the lowest order collision term of expansion preserves the self-adjointness while the first-order, nonlinear FP term does not. A large difference of the ion heat neoclassical transport is found in comparison between the developed models with and without the self-adjointness and the original FP collision term in the non-isothermal plasma, especially in a strong temperature equilibration regime, showing that a contribution of the collision term without the self-adjointness seems to be significant. Furthermore, when an impurity species is included, the result is complicated where the usual enhancement in the main ion particle transport coefficient, due to the impurity effect, is rather suppressed with the increase in the ion heat transport coefficients by the non-isothermal effects.