Quasilinear flux model consistent with gyrokinetic ordering
We propose a quasilinear (QL) flux model in which the saturation amplitude is uniquely determined using multiscale gyrokinetic ordering relations. The model is fully self-contained within a linear framework and does not rely on calibration against nonlinear simulations or mixing-length estimates. The wavenumber-dependent flux is given in ion gyro-Bohm units with a weighting factor of $|k_\theta \rho_i|$, such that its area integral in the log-linear scale yields the total flux, as employed in multiscale simulations. In systems with comparable ion and electron temperature gradients, the QL ion energy flux reproduces nonlinear simulation results in both its wavenumber dependence and absolute magnitude. In contrast, the QL electron flux is predominantly generated at electron scales, indicating that the shift of electron-scale transport toward ion scales observed in nonlinear Gsimulations is not captured within the present linear framework. We argue that the relation $Q_i\sim Q_e$, obtained as a closed conclusion of the QL model, may be predictive of simulation results if the area-integrated flux is conserved in nonlinear energy cascade process.