Effect of ellipticity on the collisional trapped-particle instability

Stability criteria for the collisional trapped-particle instability in an axisymmetric, large-aspect-ratio tokamak with an elliptic cross-section are derived. Comparison with the circular configuration indicates that an increase in the vertical ellipticity can lead to a factor-of-two reduction in the critical density below which the mode is unstable. The improvement is a result of an enhancement of both ion Landau damping and ion collisional damping in the boundary layer of the trapped ions. Collisions are treated via the Fokker-Planck operator and the resulting problem is solved, as in earlier work, by a variational method. Unlike previous treatments of resonant effects, Landau damping by trapped rather than untrapped ions is considered, and the damping rate is found to be approximately the same in magnitude as the untrapped rate derived in earlier work. Results are applied to design parameters for Princeton’s PLT (Princeton Large Torus) device and for a reactor, and stability conditions for several tokamaks presently in operation are also determined.