Saturation of the kinetic ballooning instability due to the electron parallel nonlinearity

Electron parallel nonlinearity (EPN) refers to the acceleration of electrons due to the electromagnetic fluctuations in a gyrokinetic delta-f simulation. EPN is formally small in the gyrokinetic ordering, and is typically neglected in gyrokinetic turbulence simulations. Without EPN, however, simulations of micro-turbulence in tokamak plasmas above the kinetic ballooning modes (KBM) threshold have long suffered from the phenomenon of runaway. We explore runaway by implementing EPN in the gyrokinetic particle-in-cell turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. Application to the Cyclone Base Case reveals a strong effect of EPN on the saturated heat transport above the KBM threshold. The strong effect is associated with the electron radial motion due to magnetic fluttering, which turns the radial fine structures in the electron distribution function of the KBM eigenmode into fine structures in velocity and increases the magnitude of the EPN term. This understanding is consistent with the weak effect of EPN in electrostatic simulations, the sensitivity of the saturated transport level to electron mass, and the sensitivity to electron collision.