First step toward multi machine ELM energy scalings and extrapolations to SPARC and ITER
It is shown that the ELM energy loss normalized by the plasma stored energy ({\Delta}EELM/Wplasma) for high-density small/QCE ELM regimes scales inversely with the separatrix turbulence parameter a_t. In contrast, the neoclassical electron collisionality at the pedestal top, nu*e,neo, expected to regulate {\Delta}EELM/Wplasma according to the Loarte scaling (Plasma Phys. Control. Fusion 2003 45 1549), does not adequately capture {\Delta}EELM/Wplasma data for peeling-ballooning-limited type-I ELMs and ballooning-limited small/QCE ELMs, limiting its applicability for extrapolation to one scenario window. A multi-machine database including seven tokamaks and with {\Delta}EELM/Wplasma ranging from 0.5% to 14%, has been analyzed. A regression analysis on only type-I ELMs yields (({\Delta}E_ELM)/W_plasma )_(Type-I ) [%]=6.8*T_(e,ped)^0.03 n_(e,ped)^(-0.4) \k{appa}^(-0.4) R_major^0.4, corresponding to {\Delta}EELM/Wplasma =4.5% for nominal SPARC pedestal parameters and 12% for the ITER D-T Q=10 scenario. For the small/QCE ELM class, however, as a_t increases, the pedestal moves toward a ballooning-limited boundary, the toroidal mode number increases, the ELM frequency rises following the scaling f_ELM=46e^((2.25*a_t)), and {\Delta}EELM/Wplasma decreases via the relation ({\Delta}E_ELM)/W_plasma [%]=1.6e^(-({\alpha}_t/2)). For SPARC QCE-relevant a_t=0.86 and ITER high-fueling scenario a_t = 0.64, the scaling favorably predicts {\Delta}EELM/Wplasma of 1.0% and 1.2%, respectively, with values below 1% if the small/QCE ELM regime is pushed beyond a_t >1. The small/QCE ELM-fitted results represent an initial step toward future analysis on broader datasets, which will be necessary to improve the accuracy of projections for future reactor-relevant scenarios.