Numerical studies of neoclassical transport, beginning with the fundamental drift-kinetic equation (DKE), have been extended to include the self-consistent coupling of electrons and multiple ion species. The code, NEO, provides a firstprinciples based calculation of the neoclassical transport coefficients directly from solution of the distribution function by solving a hierarchy of equations derived by expanding the DKE in powers of ρ * i , the ratio of the ion gyroradius to system size. This includes the calculation of the first-order electrostatic potential via the Poisson equation, although this potential has exactly no effect on the steady-state transport. Systematic calculations of the second-order particle and energy fluxes and first-order plasma flows and bootstrap current and comparisons with existing theories are given for multi-species plasmas. The ambipolar relation a z a a = 0, which can only be maintained with complete cross-species collisional coupling, is confirmed, and finite mass-ratio corrections due to the collisional coupling are identified. The effects of plasma shaping are also explored, including a discussion of how analytic formulae obtained for circular plasmas (i.e. Chang-Hinton) should be applied to shaped cases. Finite-orbit-width effects are studied via solution of the higher-order DKEs and the implications of non-local transport on the validity of the δf formulation are discussed.
The complete linearized Fokker-Planck collision operator has been implemented in the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010) for the calculation of neoclassical transport coefficients and flows. A key aspect of this work is the development of a fast numerical algorithm for treatment of the field particle operator. This Eulerian algorithm can accurately treat the disparate velocity scales that arise in the case of multi-species plasmas. Specifically, a Legendre series expansion in ξ (the cosine of the pitch angle) is combined with a novel Laguerre spectral method in energy to ameliorate the rapid numerical precision loss that occurs for traditional Laguerre spectral methods. We demonstrate the superiority of this approach to alternative spectral and finite-element schemes. The physical accuracy and limitations of more commonly used model collision operators, such as the Connor and Hirshman-Sigmar operators, are studied, and the effects on neoclassical impurity poloidal flows and neoclassical transport for experimental parameters are explored.
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