The mechanism for the formation and sustainment of a self-organized global profile and the 'E × B staircase' are investigated through simulations of a flux-driven ion temperature gradient (ITG) turbulence based on GKNET, a 5D global gyrokinetic code. The staircase is found to be initiated from the radially extended ITG mode structures with nearly up–down symmetry during the saturation phase, and is established as it evolves into a quasi-steady turbulence, leading to a self-organized global temperature profile and to meso-scale isomorphic profiles of the radial electric field and the temperature gradient. It is found that the quasi-regular E × B shear flow pattern is primarily originated from an even-symmetrical zonal flow produced by the extended ITG mode, which flow pattern exhibits an in-phase relation with the mean flow variation induced by the temperature relaxation. Consequently, the staircase is initiated through the profiles of total electric field and temperature gradient with a self-organized manner. Since the sign of E × B shear flow at the central part are opposite to that at both edges, it disintegrates the ITG mode into smaller scale eddies. Meanwhile, smaller scale eddies tend to be aligned radially by spontaneous phase matching, which can provide the growth of mode amplitude and the formation of radially extended mode structures, leading to the bursty heat transport. This process is repeated quasi-periodically, sustaining self-organized structures and the E × B staircase. Moreover, the equilibrium mean field is found to be of specific importance in causing the structures and dynamics from meso- to macro scales in toroidal plasmas.
Staircase formation by resonant and non-resonant transport of potential vorticity