Ion-temperature-gradient modes in noncircular tokamak geometry

The work of Xu and Rosenbluth [Phys. Fluids B 3, 627 (1991)] on ion-temperature-gradient modes in toroidal geometry is extended to noncircular cross sections to examine the scaling with the elongation κ. The growth rate, wave numbers, and stability thresholds are calculated for a flat density profile characteristic of H-mode operation, and a mixing-length estimate of the ion thermal diffusivity χi is calculated. It is found that in the plasma core, growth rates decrease as the central elongation κ increases, due to finite-Larmor-radius effects. The calculated χi is approximately of the form χi=DTi3/2[(LTi)c−LTi] where D and (LTi)c depend on τ=(Te/Ti) and geometry, and LTi=‖Ti/∇Ti‖. Preliminary evidence indicates fair agreement with experimental data near the plasma edge, where LTi≪ (LTi)c, but the fit is poorer in the core where LTi∼(LTi)c and the theoretical χi is very sensitive to the accuracy in calculating (LTi)c.