Nonlinear Selection Rules for Saturation Channels in Toroidal and Slab ITG Turbulence

The saturation of toroidal and slab ITG turbulence involves the transfer of energy from unstable modes to stable modes through different intermediary modes. Typically, the former occurs via the zonal flow, while the latter occurs through a marginally stable mode. The underlying physics governing the selection of these intermediary modes is not fully understood. To identify the selection rules, a three-field model with toroidal and slab branches is employed, allowing interactions between unstable and stable modes, with marginal or zonal modes as intermediaries. The investigation is conducted by examining nonlinear-coupling quantities, including triplet correlation times, spatial mode overlap, and coupling coefficients. The maximum triplet correlation times obtained from the two intermediary modes are similar for both branches. The number of mode-coupling triads whose triplet correlation time exceeds a nominal threshold value is higher in the slab limit than in the toroidal limit. Mode overlap is determined using mode structures represented by the Hermite function. The results indicate that the overlap involving marginal modes is significantly greater than that observed with zonal coupling in the slab limit, and vice versa in the toroidal limit. Consequently, correlation time and mode overlap serve as selection rules for saturation process. Additionally, we explore the potential significance of coupling coefficients in determining the selection of intermediary modes.