  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.
