Study of trapped electron instabilities driven by magnetic curvature drifts

The trapped electron instability in tokamaks is investigated numerically for a range of physical parameters in which the large aspect ratio expansion is not valid. The frequency and growth rate are determined as functions of ∈= r/R, ∈_t, = (R dln T_e/dr)^-1, η_e, = dln T_e/dlnn, and b = (k_lp _i)²/2. In particular, the relationship of the usual drift wave, driven by trapped electron Landau resonances or collisions, to a nonresonant mode described by Coppi and Rewoldt is studied. It is verified that the latter, on the one hand, is obtained as a continuation of the former to large b, and, on the other hand, has a qualitatively different behavior. For sufficiently small ∈_t, and for normal density gradients (η_e≥0), the mode can reverse and propagate in the ion diamagnetic direction. Explicit criteria for this to happen are derived, and the scaling of the resulting growth rates for large b is obtained. In the collisionless limit, these nonresonant growth rates can exceed those of the usual drift waves. It is therefore necessary to consider the effects of collisions, particularly those of the ions, whose effect increases as υ_ib. By means of a simple model, it is shown that the electron collisions have a small damping effect, which cannot stabilize the large b modes. The ion collisions can, however, reduce the growth rates of the large b modes below those of the drift waves. A criterion for this is derived and compared with the numerical results.