Linear analysis and crossphase dynamics in the $\nabla T_e$-driven CTEM fluid model

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.