Effect of plasma shaping on critical ion-temperature-gradient in tokamaks – a comprehensive study using linear gyrokinetic simulations*

We report a first-of-its-kind systematic numerical study on the effect of plasma geometry on the critical temperature gradient for ion-temperature-gradient (ITG) instability. A 10-dimensional scan was performed with shaping parameters in the Miller formalism [1], namely: aspect ratio, elongation, triangularity, magnetic shear, pressure gradient, temperature gradient, elongation gradient, triangularity gradient, safety factor, and Shafranov shift. Using GX [2], a GPU-based gyrokinetic turbulence code, ~200,000 linear electrostatic simulations are performed with kinetic ions and adiabatic electrons. The simulations culminated in a model for the critical temperature gradient dependence on shaping parameters. The observed trends are in good agreement with theoretical expectations and experimental results [3]. Crucially, we found that the operating regimes of many existing tokamaks lie within the poorest performing parameter space, and that improvements in critical temperature gradient of up to five times might be achieved, which could result in significant enhancement of the core plasma temperature. 

[1] Miller, R. L., et al. "Noncircular, finite aspect ratio, local equilibrium model." Physics of Plasmas 5.4 (1998): 973-978.

[2] Mandell, N. R., et al. "GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design." arXiv preprint arXiv:2209.06731 (2022).

[3] Balestri, Alessandro, et al. "Physical insights from the aspect ratio dependence of turbulence in negative triangularity plasmas." Plasma Physics and Controlled Fusion (2024).