In DIII-D, temporal evolution of (a) lower divertor signal; (b) density fluctuation level; (c) frequency spectrum of E × B velocity fluctuations (including zonal flow and diamagnetic flow fluctuations), (d) magnitude of oscillating E × B velocity (all measured 0.5 cm inside the LCFS); (e) neutral beam power during a sequence of H → I(LCO), I → L, L → I, and I→ H transitions.
Spatio-temporal evolution of turbulence intensity, zonal flow energy, mean flow , and heat flux input Qa , for different heating evolutions. (a) The case for the step-like heat flux increase from the marginal power (i.e., I-phase, as shown), above the L → H power threshold, (revealing L → H transition). (b) The case for thestep-like heat flux rising above the L → H power threshold from the L-mode at . The L → H transition occurs after a single burst of zonal flow at .
Profiles of turbulence intensity, zonal flow energy, and mean flowshearing energy as a function of radius r/a, for a time interval from (a) through (d). As indicated by the arrow, the turbulence spreading advances from the core to the edge region, through the H → L back transition.
Illustration of the feedback loop during the H → L back transition. Process proceeds from (i) through (v) and then returns to (ii) and thus closes the loop.
Spatio-temporal evolution of turbulence, zonal flow energy, mean flow, and heat flux, in cases with (a) a ramp at a reference speed, (b) 4 times slower ramp-down rate, (c) 5 times faster ramp-up rate, and (d) 10 times faster ramp-up. The LCO appears for cases with a slower ramp rate (i.e., (a) and (b)), while the LCO is compressed into a single burst of zonal flow for cases with faster ramp ((c) and (d)).
The figure shows, as a function of , the area of hysteresis loops in (a) scale lengths ( ), and (b) quantities (p, n, T) for various radial locations (r/a = 0.95: in the pedestal, r/a = 0.9: on the top of pedestal, and r/a = 0.8: inside of the pedestal shoulder). Both hystereses track the scaling , as shown by the red or black bold lines.
Relative hysteresis in vs at r/a = 0.95, with different Prandtl numbers. Blue plots in indicate the evolution through the L → H transition, while red plots in indicate the evolution through the H → L back transition.
Various hysteresis loops plotted as inverse scale lengths: (a) , (b) , (c) and profile quantities: ((d) and (g)) p, ((e) and (h)) n, and ((f) and (i)) T, at r/a = 0.95 (in the pedestal), vs heat flux intensity Qa . Hystereses in gradient, (a)-(c), exhibit rectangular loops. On the other hand, those in profile quantities, (d)-(f), exhibit triangular loops. (g)-(i) Corresponds to the case with 4 times slower ramp-down (i.e., Fig. 5(b) ).
Spatio-temporal evolution of zonal flow energy in the back transition with different : (a) and (b) . Back-transition I-phase behaves differently in . Lower exhibits relatively lower limit-cycle oscillation frequency in the back transition.
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