Comparison of gyrokinetic stability code calculated critical ion temperature gradients and growth rates to DIII-D measured gradients and diffusivities

Abstract

The gyrokinetic equations predict that various drift type waves or modes can be unstable in a tokamak. For some of these modes, such as the ion temperature gradient mode and the electron temperature gradient mode, there exists a critical gradient, above which the mode is unstable. There are also drift type modes, such as the trapped electron mode, which do not have a critical ion temperature gradient, but have a threshold which depends upon a variety of parameters. Since the existence of unstable modes can cause increased transport, plasmas which are centrally heated tend to increase in temperature gradient until the modes become unstable. Here the measured ion temperature gradients are compared to the “critical” gradients as calculated by a gyrokinetic linear stability (GKS) code [M. Kotschenreuther et al., Phys. Plasmas 2, 2381 (1995)]. Also, the maximum linear growth rate as calculated by this code is compared to experimentally derived transport coefficients. The results show that for low confinement mode (L-mode) discharges, the measured ion temperature gradient is significantly greater than the GKS calculated critical gradient over a large region of the plasma. This is the same region of the plasma where the ion thermal diffusivity is large. For high confinement mode (H-mode) discharges the ion temperature gradient is closer to the critical gradient, but often still greater than the critical gradient over some region. For the best H-mode discharges, the ion temperature is less than or equal to the critical gradient over the whole plasma. In general, the position in the plasma where the ion thermal diffusivity starts to increase rapidly is where the maximum linear growth rate is greater than the E×B shearing rate.