Algebraic and numerical studies on the roles of momentum conservation and self-adjointness in moment-based neoclassical particle fluxes

Abstract

Linearized collision operators are model operators that approximate the nonlinear Landau collision operator, but cannot capture all the features of the Landau operator. Various linearized collision operators have been proposed, including the one that ensures the self-adjointness of the operator and another that maintains the friction–flow relations derived from the exact linearized collision operator. To elucidate the basis for choosing an appropriate model operator that derives the matrix elements used to express the friction forces, the roles of momentum conservation and the self-adjointness of the collision operator in the neoclassical particle flux are investigated theoretically, algebraically, and numerically within the framework of the moment method. Linear algebraic calculations confirm that ambipolarity only requires the property of momentum conservation, while the self-adjointness is additionally necessary to ensure the independence of poloidal flow and particle flux from the radial electric field, which must be established in an axisymmetric system. This fact is also numerically validated by the one-dimensional fluid-based transport code TASK/TX, extended to handle impurity species, and the moment-method-based neoclassical transport code Matrix Inversion. In tokamak experiments, where a parallel electric field is typically present, it induces the inward Ware flux, where even electrons can have the same or larger particle flux as main ions and impurities. The Ware flux can significantly contribute to the total neoclassical particle flux, highlighting the importance of considering the electron flux when modeling neoclassical impurity fluxes.