Well-Posed Shear-Suppression Closures for Reduced Tokamak Transport: Admissibility, Regularization, and Physical Calibration

Version 2. Retargeted to IEEE Transactions on Plasma Science and extended after review. The earlier version (1.0.0) reported a steady-state fold at s_c = 0.047 that is an artifact of a first-order edge treatment of the shearing rate; this version treats the edge consistently at second order, shows that the local closure is ill posed, introduces the smoothed (adaptive-field) closure, adds a physical calibration, a parameter-uncertainty study and a supplementary file, and supersedes version 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 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 well posed, converges at second order, and gives a fusion gain that follows an inverse-square law in the suppression threshold. 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 calibrated against the ITER89-P and IPB98(y,2) scalings, operating limits and neutral-beam torque, and a Sobol study quantifies parameter uncertainty. Code and results: https://github.com/sandlerleon/tokamak-statedependent-closure, archived at 10.5281/zenodo.23251965.