Enhanced Dα confinement mode: a theoretical model

It has been shown in a previous paper that the neoclassical theory of plasma rotation explains well the large toroidal velocity that is measured in the core of edge localized mode (ELM)-free ALCATOR C-Mod H-mode discharges. It has also been noted that the gradient of the toroidal/parallel velocity estimated at the pedestal inflexion point approaches the value required for the onset of the parallel velocity shear Kelvin–Helmholtz (PVS K–H) instability when the discharge is about to undergo an ELM-free to enhanced Dα (EDA) transition. The wavenumbers and frequencies of weakly unstable PVS K–H oscillations are consistent with those of the quasi-coherent mode that is observed in the EDA, but not in the ELM-free, regime—hence the suggestion, which is explored here further, that the transition is the consequence of PVS K–H instability onset. It is at first noted that the neoclassical expression for the toroidal velocity gradient warrants that large values of the safety factor, q, and of the triangularity parameter, δ, favour the transition, as observed. It is also shown that outward convection of toroidal momentum reduces the toroidal velocity gradient and, therefore, the instability growth rate. The anomalous particle flow and the particle confinement time in EDA discharges are then estimated on the assumption that anomalous transport maintains the velocity gradient at the threshold value. The power balance consideration shows that heat transport across the H-mode pedestal is neoclassical, at most. A simple expression of the ratio of particle and energy fluxes is then obtained; the ratio τP/τE of the respective confinement times is in the range of reported values (although it must be noted that it is difficult to quantify τP as it varies rapidly across the edge layer). The scenario assumes that the H-mode pedestal of EDA discharges (the unstable layer where anomalous transport occurs) is impermeable for neutrals since charged particles issuing from ionization would otherwise accumulate in the core; experimental parameters justify this assumption. The possibility of matching simultaneously the requirements for PVS K–H instability onset and non-permeability to neutrals in large devices is discussed.