On the transition to large fluxes and access to second stability in gyrokinetic simulations of electromagnetic turbulence in STEP

Abstract

This work investigates the nonlinear transition to large heat fluxes observed in local gyrokinetic simulations of electromagnetic turbulence in STEP. Using the stress-balance framework of Zhang et al. (arXiv:2606.04616, arXiv:2607.11789), we confirm that the onset of extreme transport correlates with a critical value of $q^{2}β_{e}$, where $q$ is the safety factor and $β_{e}$ is the ratio of electron thermal pressure to magnetic pressure, and relate this to a limit on the poloidal beta $β_{\mathrm{pol}}$. Crucially, this critical value lies below any relevant linear stability limit in the ($q$, $β_{e}$) space (e.g., the onset of ideal or kinetic ballooning modes). Using an extensive set of nonlinear gyrokinetic simulations, we demonstrate that the transition to large fluxes in STEP is governed by a balance between the electrostatic and magnetic-flutter stresses. We argue, and also show numerically, that larger-major-radius tokamaks reach the electromagnetic non-zonal regime at lower $β_{e}$, making this MHD-controlled saturation limit more accessible in reactor-scale devices than in small spherical tokamaks. We also demonstrate that access to a second-stable regime enables re-saturation at larger values of $β^{\prime}$. We further show that the ideal ballooning mode (IBM) threshold serves as a useful proxy for delineating this second-stable region and also as a qualitative guide for the onset of large fluxes. These results provide a predictive framework for identifying no-go zone predictions from local gyrokinetics and offer new insight into the electromagnetic saturation physics relevant to STEP and other high-$β_{e}$ devices.