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Stability of the trapped electron mode in steep density and temperature gradients

The stability of the trapped electron mode is studied in conditions characteristic of internal transport barriers, namely steep density and temperature gradients. An analytic model allows a unified treatment of all collisionality regimes, from the dissipative limit to the weakly collisional regime (when the velocity space boundary layer between passing and trapped populations of electrons plays a role). Furthermore, it reveals the key parametric dependences on wavelength, collisionality and ηe = d(lnTe)/d(lnne). The roles of shear damping and Landau-drift resonance are also discussed. The main outcome is that below a critical collisionality, defined by the parameter (where νthe is the thermal electron collision frequency, Ln the density scale length and vthi the ion thermal speed), there is strong stabilization of long wavelength modes, so the unstable spectrum may be restricted to shorter wavelengths as the collisionality falls and the density profile steepens. The predicted critical value of is experimentally relevant and this theory suggests a mechanism for barrier formation.