Dissipative Trapped-ion Instability Research Articles

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/dρ > 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.

Stability regions of dissipative trapped-ion instability

Conditions for the stability of the dissipative trapped ion mode in axisymmetric toroidal confinement systems are investigated, and the ranges of temperature and magnetic field for which the plasma is expected to be unstable are calculated numerically for several proposed Tokamaks. The collisional damping is studied as a boundary layer problem in the velocity space of the trapped ions. The Fokker-Planck equation is solved by means of a variational form with the ordering νiR/r ≪ ω ≪2π/τi, where R/r is the aspect ratio, νiR/r is the effective collision frequency, and τi is the bounce time. The relative damping rate is found to be proportional to (νiR/rω) 1/2 [In (rω/νiR)1/2]−3/2 rather than νiR/rω. This damping term is compared with the electron driving term, which is proportional to rω/Rνe, and with the Landau damping caused by resonant untrapped ions. The presence of a temperature gradient is found to be destabilizing. The Landau term provides relatively strong damping when dT/dr=0 but changes sign when d ln T/d In n > 2/3. In the latter case it is concluded that ion collisions are insufficient to stabilize the mode under typical operating conditions of the proposed machines. Finally, if d ln T/d In n > 1.75 the ion collisional damping itself changes to growth, and the mode cannot be stabilized.