  Collisionless trapped-electron mode (CTEM) turbulence is an important
contributor to heat and particle transport in fusion devices. The ITG/TEM fluid
models are rarely treated analytically, due to the large number of transport
channels involved, e.g. particle and ion/electron heat transport. The $\nabla
T_e$-driven CTEM fluid model [Anderson et al, Plasma Phys. Control. Fusion 48,
651 (2006)] provides a simplified model, in the regime where the density
gradient drive is negligeable compared to the electron temperature gradient
drive ($\nabla T_e$). This provides an interesting model to study mechanisms
associated to linear waves, such as crossphase dynamics, and its possible role
in the formation of $E\times B$ staircase. Here, the $\nabla T_e$-driven CTEM
fluid model is rigourously derived from the more general ITG/TEM model, and its
linear dynamics is first analyzed and compared with CTEM gyrokinetic
simulations with bounce-averaged kinetic electrons, while nonlinear analysis is
left for future work. Comparisons of linear ITG spectrum are also made with
other analytical models.
