Shaping the Ion-Temperature-Gradient driven instability: a kinetic view on its localisation

In a stellarator, the toroidal magnetic field can be shaped with a high degree of freedom, significantly influencing the behaviour of the confined plasma. Different aspects of plasma dynamics respond uniquely to these geometric variations, requiring a careful understanding of the underlying physics—often in regimes far from the well-studied tokamak case. In this talk, we examine how ion-temperature-gradient (ITG) driven instabilities respond to changes in magnetic geometry. Specifically, we analyse the linear kinetic response of ions, emphasizing the crucial role of localisation along the field line. We present a simple semi-analytical formula for the mode spectrum that captures key physical effects: long-wavelength Landau damping, ion-scale Larmor radius stabilisation, the weakening of Larmor radius effects at short wavelengths, and stabilisation due to magnetic-drift resonance. This model provides a clear qualitative framework for understanding typical stellarator linear gyrokinetic spectra, including the emergence of multiple maxima or transitions to extended modes, while acknowledging its limitations for precise quantitative predictions. These insights also inform a broader discussion on the trade-offs between ITG-driven turbulence and other phenomena such as MHD stability, offering new perspectives on stellarator optimisation.