Linear and nonlinear Analysis of Kinetic Ballooning Modes (KBM) with bootstrap current in High-beta Pedestal Plasma

We present the global 3D linear and nonlinear simulation of edge plasma instabilities based on the gyro-Landau-fluid (GLF) model with the BOUT++ framework. The geometry of the input equilibria are shift circular geometry considering the shafranov shift and bootstrap current without X-point. These initial realistic equilibria are generated by a global equilibrium solver CORSICA.

        The linear growth rate spectrum shows the stabilizing effect of the bootstrap current, both the growth rate and the unstable region of the instabilities decrease, and the spectra shift to the low toroidal mode number direction because of the kink drive of the edge current. And the Toroidal Resonance can drive the KBM unstable under the ideal peeling-ballooning threshold. Considering the global effect, we found that even though the system  becomes second stable at peak gradient position, it is still unstable at pedestal bottom and top.

      In the nonlinear simulation, we consider different  and different fraction of bootstrap current. The energy loss with bootstrap current is higher than the cases without bootstrap current. The turbulence with low  is mainly the ballooning dominant turbulence while the turbulence with high  is mainly the peeling dominant. And we have also proved the robustness of the EPED1.6 model well in nonlinear phase by fitting the relationship of pedestal width and height in the steady state.