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

Version 4. Adds a screening-level plant power balance (net electric power from assumed thermal, heating and overhead efficiencies, with a Sobol study of the assumptions) and a relative cost proxy, as post-processing of the existing results (code/plant.py). Under the central assumptions the reference device at 40 MW heating is below engineering breakeven (net about -45 MW, negative for all 256 sampled assumptions; a separate heating-power scan finds positive net power for some favorable low-power assumptions); the closure adds a few megawatts at moderate thresholds. No cost is computed. Also includes the 1.1.1 wording revision (new title, well-posedness qualified as numerical, gain relation described as an empirical fit, compact-tokamak discussion). Supersedes 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, 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), a Sobol study quantifies parameter uncertainty, and a screening-level plant power balance gives the net electric power under assumed efficiencies. Code and results: https://github.com/sandlerleon/tokamak-statedependent-closure, archived at 10.5281/zenodo.23268573.