Moment-Fourier approach to parallel closures and transport for a toroidally confined electron–ion plasma

A general method for solving the drift kinetic equations is developed to derive the closure and transport relations for electron–ion plasmas in an axisymmetric magnetic field with nested flux surfaces. By expanding the electron and ion distribution functions into Fourier series of general moments, the drift kinetic equations are converted to a coupled system of algebraic equations. By eliminating the fluid equations, the electron and ion systems are decoupled, allowing each system of equations to be solved separately for closures. The closure relations connect parallel heat flux density, friction force density, and viscosity to the radial and parallel gradients of density and temperature, the parallel gradient of flow velocity, and the parallel relative flow velocity of electrons and ions. When these closure relations are combined with the fluid equations, the fluid quantities are expressed in terms of the radial gradients of density and temperature, as well as the radial and parallel components of the electric field. This framework offers a robust approach to studying transport phenomena in electron–ion plasmas. The transport relations are expected to provide a foundation for investigating plasma rotation, including intrinsic rotation, in various tokamak systems and under different plasma conditions.