State-dependent shear-suppression closures for reduced tokamak transport: a controlled comparison, admissibility conditions and a fold of the steady state

A computational and theoretical paper. No experimental data are used and all parameters are illustrative. Prepared for submission to the Journal of Plasma Physics. A one-dimensional radial energy-transport model with fusion heating and a toroidal-rotation equation is used to compare a state-dependent shear-suppression closure (heat diffusivity divided by 1 + (omega_E / s_c gamma_0)^2) with a stiff critical-gradient baseline at identical inputs. The solver is verified by power balance, recovery of the baseline as s_c tends to infinity, independent time integration and grid convergence. With diamagnetic shear alone the fusion gain changes by well under one per cent at moderate coupling; the lower branch of steady states ends in a saddle-node fold at s_c* = 0.047 (extrapolated in resolution), below which no steady state exists. For the rotation equation with a shear-dependent viscosity, the steady flux relation F(L) L = Theta reduces existence, saturation, fold and hysteresis to the monotonicity of L F(L), with closed-form thresholds (m ≤ 1; floors 1/9 and 0.3086) that direct solutions reproduce. Torque-driven shear adds to the diamagnetic shear in a one-way coupling. Code and results: https://github.com/sandlerleon/tokamak-statedependent-closure, archived at 10.5281/zenodo.23229934.