An Effective-Geometry Framework for Plasma Sustainability in Tokamaks: Critical-Gradient Transport Barriers from a Unified Field Invariant

Long-duration tokamak operation (EAST: 1066 s H-mode, 2025; WEST: 1337 s, 2025) is ultimately bounded by plasma disruption driven by magnetohydrodynamic (MHD) instabil- ities and critical-gradient transport barrier dynamics. We formulate a geometric framework in which the electromagnetic field invariant F2 = Fµν Fµν and the four-potential Aσ define a dimensionless curvature density Θpl on an effective metric geff µν that governs MHD-wave propagation. The Planck-scale motivation of the original ansatz is retained only as theoret- ical inspiration; all physics operates at plasma energy scales (∼10 keV). We derive a master sustainability criterion Θpl ≤Θcrit(s,q,α), identify Θcrit with transport-barrier (ITB) thresh- olds, and show how the criterion interlocks with the standard tokamak operating limits. The framework yields one falsifiable numerical prediction per discharge