Numerical admissibility and regularization of shear-suppression closures for reduced tokamak transport: model, solvers, tests, figures and manuscript

Abstract

Version 1.2.1. Wording and presentation revision of 1.2.0 after review; computed results and code are unchanged. The numerical instability of the local closure is described as observed under the tested conditions (no proof of mathematical ill-posedness is claimed), the strict-monotonicity statement of Proposition 2 and the boundary cases f = 1/9 and f = 0.3086 of Proposition 3 are stated precisely, the plant power balance separates the 256 sampled assumptions at 40 MW from the separate heating-power scan, all tables are cited in the text, the abstract is shortened, and safe punctuation edits are merged. Supersedes 1.2.0, 1.1.1, 1.1.0 and 1.0.0. 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, exhibits numerical instability and sensitivity to the edge treatment under the tested conditions: 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), a Sobol study quantifies parameter uncertainty, and a screening-level plant power balance gives the net electric power under assumed efficiencies. Contents: model and solvers (code/model.py, stability.py, arclength.py), rotation equation and coupling (momentum.py, coupled.py), closed forms (theory.py), calibration (calibration.py), uncertainty study (uncertainty.py), the script that produces every result (reproduce.py), tests (tests.py), figure scripts, the Crossref reference harvest and the manuscript builders. Manuscript preprint: 10.5281/zenodo.23282928.