Effect of toroidal gradient drifts on the dissipative trapped-ion instability

Conditions for the onset of the dissipative trapped-ion instability in tokamaks with elliptic and circular cross sections are determined. Toroidal gradient drifts, ignored in earlier calculations, are included in the analysis and found to give rise to significant stabilizing effects. In particular, the results show that the ions trapped in regions of good gradient (dB/d_p > 0) contribute to the Landau damping of the unstable waves, and that ion collisional damping is also enhanced when the drifts are taken into account. Since vertical ellipticity increases the region of good gradient, these stabilizing effects are further enhanced in elliptical cross-section tokamaks. It is also shown that previously calculated restrictions on the allowable magnitude of temperature gradients for favorable damping can be relaxed. Results of the analysis are applied to expected parameters for the Princeton Large Torus experiment and growth rate estimates given for conditions violating the stability criteria.