Numerical Admissibility and Regularization of Shear-Suppression Closures for Reduced Tokamak Transport

Abstract

Version 3. Wording revision of 1.1.0 after review: the title is changed, the well-posedness claims are qualified as numerical (no existence-uniqueness theorem is claimed for the nonlinear heat problem), the inverse-square gain relation is described as an empirical fit over the tested range, the ITER89-P agreement is stated to be a consistency check, and a discussion subsection on compact, cost-constrained tokamak design is added. Computed results are unchanged. Supersedes 1.1.0 and 1.0.0 (the latter reported a fold at s_c = 0.047 that is an artifact of a first-order edge treatment). A computational and theoretical paper. No experimental data are used and all parameters are illustrative. Prepared for submission to IEEE Transactions on Plasma Science. A one-dimensional radial energy-transport model with fusion heating and a toroidal-rotation equation is used to study closures in which the heat diffusivity is suppressed by the local ExB shearing rate. The local closure, whose shearing rate contains the second derivative of the temperature, is numerically ill posed: the steady state depends on the edge treatment and a grid-scale instability appears at a threshold that grows as N^0.5 with the number of cells. An adaptive-field closure that smooths the shearing rate over a fixed length is stable and grid converged over the tested conditions, converges at second order, and gives a fusion gain that is fitted by an inverse-square relation in the suppression threshold (an empirical fit over the tested range, not a universal scaling). For the rotation equation, a steady flux relation F(L) L = Theta gives closed-form admissibility conditions (m ≤ 1; viscosity floors 1/9 and 0.3086) and the saturation, fold and hysteresis, reproduced by direct solutions to a relative error of 5e-11. The baseline is compared with the ITER89-P and IPB98(y,2) scalings, operating limits and neutral-beam torque (a consistency check, not a validation, because the edge temperature is imposed), and a Sobol study quantifies parameter uncertainty. Code and results: https://github.com/sandlerleon/tokamak-statedependent-closure, archived at 10.5281/zenodo.23267847.