Previous calculations of the amount of magnetic shear necessary to stabilize a drift wave in an inhomogeneous plasma with a linear density profile have been somewhat inconsistent in that the destabilizing influence of the resonant electrons is treated as a perturbation. By removing this inconsistency and, in fact, by including all non-resonant electron effects as well, an improved stability criterion is found analytically to agree with the previous perturbation technique result to within a multiplicative factor very nearly equal to one for 1⪆ Ln/Ls ≫ m/M, where Ln and Ls are the density and shear lengths and m and M are the electron and ion masses. Both the previous and the present treatments require ln(MLn/mLs) > 1, and the stability condition is found herein to be relaxed by approximately {ln[ln(MLn/mLs)]}1/3. Furthermore, the critical shear is shown to be relatively insensitive to the non-resonant electron corrections not retained in previous work. Consequently, when finite-β effects are included, both the neglect of non-resonant electron corrections to the fluid response and the treatment of the resonant electrons via perturbation theory are well motivated.
Role of singular layers in the plasma response to resonant magnetic perturbations