Toroidal electron and ion temperature gradient instability in stellarators

We study the properties of toroidal electron temperature gradient and toroidal ion temperature gradient modes in the plasma core of W7-X and LHD. Because stellarators typically have a large aspect ratio, the ratio of the major radius to the temperature gradient length scale can be as large as the steep gradient region in tokamak pedestals and transport barriers. This results in linear modes that have a perpendicular wavenumber that is much larger than their wavenumber in the binormal direction, and are challenging to resolve numerically. Using the gyrokinetic code \texttt{stella}, we find these toroidal modes are the fastest growing modes at a wide range of perpendicular scales.