Fig. 5: BOUT + + numerical modeling of the wide-pedestal QH discharge #173707.

The edge bootstrap current is increased by 20%, compared with the stationary phase (2270–2370 ms), to simulate the dynamic approaching ELM crash. a Linear growth rate as a function of toroidal mode number (n); b Mode structure of PBM (n = 10) and EDW (n = 50) in the linear (solid) and EDW nonlinear saturation stage (dashed, gray-shaded region in Fig. 5c); Time traces of c the normalized pressure perturbation \(\delta p/{p}_{0}\) and d the cross-phase between \(\delta p\) and \(\delta {v}_{r}\) for n = 10, with and without EDW, at \({\psi }_{N}\) = 0.95, outer-mid-plane; e Probability density distribution of the cross-phase for cases with and without EDW, using the same time window t = 0–400\({\tau }_{A}\). The blue curves in these plots represent quiescent edge phases without ELM crashes, while the red curves correspond to periods with ELM crashes. The profile evolution, ELM associated energy loss, and mode eddy evolution are presented in Supplementary Fig. 4b, c, Supplementary Fig. 5 and Supplementary Fig. 6 for detailed reference.