From Photospheric Helicity Injection to Phase-Coherent Macro-Helicity Transport: A Unified Framework Bridging Classical MHD, the Helicity Barrier, FLR-MHD Generalised-Helicity Evolution, Electron-MHD Extensions, and Vening's Covariant Phase Field

Photospheric helicity injection injects topological charge into coronal structures. Vening(2026) provides the directional transport mechanism through the covariant scalar phase fieldΘ(x). Wenowpresent a fully elaborated unification that incorporates the rigorous derivationof generalised-helicity evolution in finite-Larmor-radius MHD (FLR-MHD), the thresholdsand physical origin of the helicity barrier (McIntyre et al. 2025), extensions to electron-MHD(EMHD) helicity barriers with inverse-cascade phenomenology, quantum-plasma helicityeffects, and detailed numerical simulation examples from hybrid-kinetic, gyrokinetic, andEMHDcodes. The revised phase-source term Ω is calibrated to encode barrier physics. Theresult is a complete, non-simplified pipeline: injection → phase-protected polar conduits→ FLR-MHD/EMHD barrier-enforced dissipation → seamless Parker-spiral export, withtopological protection explained at every scale.