For a low frequency drift wave helical structure to be embedded in a strongly inhomogeneous plasma edge, a self-consistent radial electric field must have built up such that δ(ωE + ω*e)/δx ≡ 0 (ω ≡ ωE + ω*E is the drift mode angular frequency, where ωE is the E × B Doppler shift and ω*e is the electron diamagnetic frequency). Further, at marginal stability, the destabilizing action of the wave through neutrals ionization must be balanced by electron Landau damping (rather than collisional damping, as the latter would lead to a thermally unstable equilibrium constraint). These two conditions imply certain relationships between the profiles which are shown to be apparently satisfied in DIII-D (this experiment affording a high spatial resolution). The marginal stability condition, in which Landau damping is proportional to the toroidal mode number (l), suggests that only the l=1 mode may persist in the equilibrium: this is the case with the Toi mode observed in the low confinement regime of the ASDEX tokamak. The marginal stability condition closes the system of quasi-linear cross-field transport equations, in which the square of the modulus of the eigenfunction is-by comparison with neoclassical transport theory - an extra unknown entering the expressions of the anomalous particle and heat fluxes. The quasi-linear particle flux, however, is directed inward: quasi-linear theory, therefore, is not compatible with a stationary equilibrium edge model in which ionization of the neutrals produced by recycling would trigger the anomalous return flow of ionized particles to the material structure. In the plasma edge, quasi-linear cross-field transport theory is inappropriate if 'open' field lines-impinging on the target plates - penetrate the plasma to a depth of a few centimetres, as will be the case if the mode develops a sufficiently broad magnetic island