Toward integrated multi-scale pedestal simulations including edge-localized-mode dynamics, evolution of edge-localized-mode cycles, and continuous fluctuations

The high-fidelity BOUT++ two-fluid code suite has demonstrated significant recent progress toward integrated multi-scale simulations of tokamak pedestal, including Edge-Localized-Mode (ELM) dynamics, evolution of ELM cycles, and continuous fluctuations, as observed in experiments. Nonlinear ELM simulations show three stages of an ELM event: (1) a linear growing phase; (2) a fast crash phase; and (3) a slow inward turbulence spreading phase lasting until the core heating flux balances the ELM energy loss and the ELM is terminated. A new coupling/splitting model has been developed to perform simulations of multi-scale ELM dynamics. Simulation tracks five ELM cycles for 10 000 Alfvén times for small ELMs. The temporal evolution of the pedestal pressure is similar to that of experimental measurements for the pedestal pressure profile collapses and recovers to a steep gradient during ELM cycles. To validate BOUT++ simulations against experimental data and develop physics understanding of the fluctuation characteristics for different tokamak operation regimes, both quasi-coherent fluctuations (QCFs) in ELMy H-modes and Weakly Coherent Modes in I-modes have been simulated using three dimensional 6-field 2-fluid electromagnetic model. The H-mode simulation results show that (1) QCFs are localized in the pedestal region having a predominant frequency at f ≃ 300 − 400 kHz and poloidal wavenumber at k θ ≃ 0.7 cm − 1 , and propagate in the electron diamagnetic direction in the laboratory frame. The overall signatures of simulation results for QCFs show good agreement with C-Mod and DIII-D measurements. (2) The pedestal profiles giving rise to QCFs are near the marginal instability threshold for ideal peeling-ballooning modes for both C-Mod and DIII-D, while the collisional electromagnetic drift-Alfvén wave appears to be dominant for DIII-D. (3) Particle diffusivity is either smaller than the heat diffusivity for DIII-D or similar to the heat diffusivity for C-Mod. Key I-mode simulation results are that (1) a strong instability exists at n ≥ 20 for resistive ballooning mode and drift-Alfvén wave; (2) the frequency spectrum of nonlinear BOUT++ simulation features a peak around 300 kHz for the mode number n = 20, consistent with a reflectometer measurement at nearby position; (3) the calculated particle diffusivity is larger than the calculated heat diffusivity, which is consistent with a key feature of the I-mode pedestal with no particle barrier.