Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

Abstract

The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. Topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.

Radially globalδfcomputation of neoclassical phenomena in a tokamak pedestal

“…(In ref [38] this equation is written in terms of k rather than V || , but the two versions are related by (15), noting r T ≫ ρ θ and r η ≫ ρ θ and retaining dk/dψ.) The poloidal variation of V || and k are O(ǫ) so both quantities may be treated as flux functions in (22).…”

“…To our knowledge, the only published comparison of this kind to date is in Ref. [15], in which some qualitative agreement was seen, but not precise quantitative agreement. One purpose of the work here is to demonstrate precise quantitative agreement between theory and simulation.…”

“…As such, the calculation results in one relation between the radial electric field E r and the flow (i.e. (15)). However, with only one relation between these two quantities, neither quantity is truly determined unless an additional constraint is introduced.…”

“…For improved pedestal neoclassical calculations, some researchers [3][4][5][6][7][8][9][10][11][12][13][14][15] have considered a model that may be termed "global full-f ", in contrast to the conventional approach [1,2,[16][17][18] which may be called "local δf ." In a full-f code, the entire distribution function f is solved for, whereas in a δf code, one only solves for the departure from a Maxwellian, with the Maxwellian constant on each flux surface.…”

“…Very different algorithms are used compared to previous codes such as Refs. [15,20], and in particular, a time-independent rather than time-dependent approach is used, so the solver convergence is not limited by the timescale of physical relaxation. Nested flux surface geometry of arbitrary shaping is allowed, as is arbitrary collisionality, and the full linearized Fokker-Planck collision operator is implemented with arbitrary mass ratio and charge permitted.…”