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<img src='content_image/334307.jpg'>

this works in a fluid model see Ref. [43]). This situation is shown in Fig. 3 (left frame, dashed line), where the total pedestal energy is reduced by a quarter of its initial content before the peak flux phase. Therefore we test sensitivity against sources. Maintenance of the ion temperature profile by a fixed ion heat source localised to the inner boundary (following the method for driven cases in Ref. [45]) ensures nearly unchanged gradients during the linear growth phase. At the end of the simulation time ( t = 90) after the ELM burst, the energy content is reduced to around 10% of the initial content when the source is absent or is switched off at the peak flux time ( t = 40), and to around 20% when the source is maintained for the whole simulation time. 

The influence of either switching off the source or maintaining the zonal profiles on the nonlinear ion heat flux Q$_{i}$ ( t ) is shown in Fig. 3 (right): the linear growth phase and the peak flux is not significantly changed by the source. As expected, the heat flux saturates for late times with maintained core boundary inflow and is otherwise decaying. 

Consistency checks on the perpendicular resolution are made by varying n$_{y}$ between 64, 128, 256 and 512. The evolution of Q$_{i}$ ( t ) for these cases is shown in Fig. 4. The n$_{y}$ = 64 case is clearly under-resolved and overestimates the total energy decay by a factor 2. For n$_{y}$ = 128 the initial part of the post-peak decay phase disagrees with the n$_{y}$ = 512 case. Convergence is found for n$_{y}$ = 256 and higher. The nonlinear saturation phase thus requires resolving the ion gyroradius scale. This is the clearest indication that turbulence for toroidal mode numbers beyond about 30 extending down to the k$_{y}$ρ$_{i}$ ∼ 1 range is involved in the 

