Abstract: Global tearing modes (TMs) can interact among themselves or with small-scale instabilities, exerting profound influence on fusion plasma performance. Experiments in reversed-field pinches (RFPs) demonstrate that TMs couple, cascade, and cause robust transport, while partial suppression of their activity can result in enhanced confinement. The presence of unstable drift waves during the TM cascade in the RFP allows interactions with microinstabilities. Local gyrokinetic simulations with externally imposed magnetic perturbations modeling TMs have demonstrated that the magnetic perturbations erode zonal flows that are nonlinearly generated by the microinstabilities, resulting in higher turbulence levels. Similarly, when resonant magnetic perturbations (RMPs) are applied to mitigate edge-localized modes in tokamaks, the RMPs suppress the zonal flows, which in turn can increase the heat flux. These phenomena highlight the importance of multi-scale interactions between large-scale magnetic fluctuations and zonal-flow-regulated microturbulence, an incompletely understood topic.
For a comprehensive understanding of these interactions, self-consistent computations simultaneously evolving TMs and small-scale fluctuations are needed. Here, calculations are performed with the global gyrokinetic code GENE, which was modified to include a background current density. This provides the TM drive, and it is verified that the modified GENE code properly models global TMs. Working towards multi-scale simulations, a non-reversed RFP discharge is studied; linear simulations show that the non-reversed equilibrium is unstable to large-scale TMs, which dominate in the core region, while small-scale density-gradient-driven-TEMs dominate near the plasma edge. Nonlinear simulations with only TMs show that large-scale TMs in the core are coupled and excite smaller-scale stable TMs. The latter resonates at rational surfaces closer to the edge, where density-gradient-driven-TEMs are active, indicating that multi-scale interactions are possible. In nonlinear global density-gradient-driven-TEM simulations, zonal flows dominate the saturated state, leading to negligible transport in the absence of TMs, consistent with local simulations. When TMs and TEMs are simultaneously included in nonlinear simulations, TMs partially erode zonal flows. This erosion of zonal flows disrupts energy mediation by zonal flows, leading to a significant increase in heat flux. However, the zonal flows remain a dominant characteristic of fluctuations, causing the transport fluxes to remain much smaller than in experiments. To quantitatively reproduce experiments in future work, higher density gradients are required to weaken the zonal flows, or a stronger TM drive is needed to intensify the magnetic perturbations. These multi-scale simulations offer valuable insights for understanding RFP experiments and studying potential interactions of MHD phenomena and microturbulence in tokamaks.
In contrast to TEM behavior, static magnetic perturbations do not strongly affect the ITG-driven turbulence of RFPs. This is because the ITG in RFPs is characterized by a slab limit and does not rely as strongly on zonal flows for saturation; instead, it depends on marginal modes. Zonal flows, on the other hand, play a crucial role in toroidal-ITG saturation. This prompts the exploration of saturation-channel selection rules that capture the preference of the toroidal limit for zonal flows and of the slab limit for marginal modes. Nonlinear coupling quantities are determined, and the triplet correlation time and mode overlap results are presented. Combining these metrics allows for predicting the dominant saturation channel for a given physical-parameter scenario, providing a powerful new tool that will aid a deeper understanding of nonlinear interactions and may also be used to enhance reduced models of anomalous transport.