Zonal radial electric field driven by the turbulent energy flux in a tokamak plasma with multiple ion species

The zonal radial electric field (REF) driven by electrostatic turbulence in a plasma with multiple ion species is investigated theoretically and numerically. The gyrokinetic derivation reveals that the turbulence-driven REF depends on the turbulent energy flux, as well as the turbulent poloidal and toroidal Reynolds stresses of each ion species. Notably, the turbulent zonal REF is not a simple sum of individual ion species contributions, instead, it is weighted by a factor of W_j=n_jm_j/∑_jn_jm_j, where n_j and m_j denote the density and mass of j-species, respectively. The theoretical derivation is subsequently validated against nonlinear simulations under three typical parameter sets: the ITER baseline scenario, the CFETR hybrid scenario and the widely-used cyclone base case. The nonlinear simulation results demonstrate that the turbulent zonal REF is predominantly driven by the turbulent energy flux, whereas the contributions from both the turbulent poloidal and toroidal Reynolds stresses remain negligible. Furthermore, it is shown that various physical effects, including kinetic electron effects, ion composition, the temperature ratio between ion species, and the temperature and density gradients, do not affect the driving of the turbulent energy flux to the zonal REF, which is quantitatively described by the weighting factor W_j. However, the expression for W_j is strictly valid under the assumption that the equilibrium distribution of each ion species is Maxwellian distribution; for non-Maxwellian equilibrium distributions, the weighting factor W_j should be modified.