Comparing the line broadened quasilinear model to Vlasov code

The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.