
Error field penetration threshold from two-fluids compressible linear drift magneto-hydrodynamics
Paolo Zanca
The linear plasma response to a resonant error field (EF) is formalized by the so-called 'delta-prime' parameter Δ', representing the amplitude and phase of the current sheet induced at the resonant surface mostly by the electron fluid rotation. In combination with momentum transport, Δ' determines the critical EF amplitude above which a wall-locked magnetic island is formed (penetration threshold). In the context of two-fluids drift linear magneto-hydrodynamic (MHD) a semi-analytical computation of Δ', carried out with a low-beta ordering assumption, and the estimated penetration threshold for the ohmic tokamak, have been recently published [P. Zanca 2025 Plasma Phys. Control. Fusion 67 105033]. Here we present a necessary completion of that work brought by the inclusion of compressible flow, density perturbation, parallel energy transport and electron viscosity. In particular, electron viscosity has been discovered to be an important term in Ohm's law in a previous study which adopted the high-poloidal beta ordering [J. C. Waybright, J.-K. Park, Phys. Plasmas 31, 022502 (2024)]. Here, we confirm the relevance of electron viscosity within the scope of a different model. On the contrary, compressible flow, density perturbation and parallel energy transport do not modify significantly the EF penetration threshold, at least within the present linear theory. After reconsidering the ohmic tokamak with the refined model, we present a new analysis of the additionally heated tokamak, showing a strong positive dependence of the EF threshold on the electron fluid perpendicular rotation frequency ωe. All the scaling laws of the EF penetration threshold here derived present a strong density dependence, in general agreement with the experiments. Moreover, the model prediction is compatible with EF penetration experiments performed in JET NBI heated discharges. Finally, we provide a sensitivity study of the model prediction from the electron viscosity strength.


