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The influence of collisions on the growth rate of trapped-electron modes(TEM) is assessed through both analytical linear gyrokinetics, and lineargyrokinetic simulations. Both methods are applied to the magnetic geometry ofthe DIII-D tokamak, as well as the Helically Symmetric eXperiment (HSX) andWendelstein 7-X (W7-X) stellarators. Here we analytically investigate theinfluence of collisions on the TEM eigenmode frequency by a perturbativeapproach with an energy-dependent Krook operator. A universal finding for allgeometries is a stabilisation of the growth rate at high collisionality, therate of which, however, depends on the geometry. At low collisionality, agrowth rate insensitive to the collisionality is obtained in DIII-D at allwavenumbers, and for high-wavenumber modes in HSX and W7-X. In contrast, forthe low-wavenumber modes in HSX and W7-X a destabilisation is obtained. Lineargyrokinetic simulations for the same geometries confirm these qualitativetrends. Additionally, the simulations show the destabilisation of thelow-wavenumber modes in HSX and W7-X is a result of a collision-inducedtransition of the dominant mode towards the Universal Instability (UI), a trendwhich is also continued to high-wavenumbers in W7-X.

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