Influence of collisions on trapped-electron modes in tokamaks and low-shear stellarators

The influence of collisions on the growth rate of trapped-electron modes (TEMs) in core plasmas is assessed through both analytical linear gyrokinetics and linear gyrokinetic simulations. Both methods are applied to the magnetic geometry of the DIII-D tokamak, as well as the Helically Symmetric eXperiment (HSX) and Wendelstein 7-X (W7-X) stellarators, in the absence of temperature gradients. Here we analytically investigate the influence of collisions on the TEM eigenmode frequency by a perturbative approach in the response of trapped particles to the mode, using an energy-dependent Krook operator to model collisions. Although the resulting growth rates exceed perturbative thresholds, they reveal important qualitative dependencies: a geometry-dependent stabilization rate occurs for all wavenumbers at high collisionality, while at low collisionality, a geometry-sensitive mixture of collisionless, resonantly driven, and collisionally destabilized modes is found. Additionally, linear gyrokinetic simulations have been performed with a rigorous pitch-angle scattering operator for the same geometries. In the case of DIII-D and large wavenumber modes in HSX, the trends predicted by analytical theory are reproduced. Dissimilarities are, however, obtained in W7-X geometry and for low wavenumber modes in HSX, which are shown to be due to a collision-induced transition to the Universal Instability as the dominant instability at marginal collisionality.