A mechanism for the formation and sustainment of the self-organized global profile andE  ×  Bstaircase in tokamak plasmas

Abstract

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.

Lévy flights on a comb and the plasma staircase

“…It is understood that in the presence of a characteristic step-size there is no asymptotic nonlocal behavior in the Lévy-Gnedenko sense, even though the entire process is not confined in the long run. These complex features have been seen in simulations [2,3,42].…”

“…In summary, we have shown that a potential function that grows steeply enough with the spatial scale may confine nonlocal transport with Lévy flights. This finding has important implications for the understanding of localization-delocalization phenomena in banded flows observed in planetary atmospheres [4,61], terrestrial oceans [62], and, more recently, in tokamak plasma [1][2][3]42]. Also it offers a simple criterion to characterize internal transport barriers that may or may not confine the nonlocal transport.…”

A new mechanism for increasing density peaking in tokamaks: improvement of the inward particle pinch with edge E × B shearing

“…The significant suppression of Ion Temperature Gradient (ITG) dominated plasma turbulence via electromagnetic fluctuations and fast ions [1,2], for instance, has opened up the scope of turbulence reduction by alternative mechanisms to the wellknown E×B shearing. Such effects have also been shown to play an important role in the so-called isotope effect [3,4] and the recently found E×B staircase phenomenon [5][6][7].…”

Scale selection and feedback loops for patterns in drift wave-zonal flow turbulence

“…Staircases were first discussed in the context of mixing in stably stratified fluids [7,8] and later in geophysical fluids [9][10][11][12]-i.e., the potential vorticity (PV) staircase, and in the context of double diffusive convection [13]. Then, they were observed in gyrokinetic simulations using GYSELA [14] and subsequently in other simulations [15][16][17]. There are hints of staircase structures in experiments [18,19] is the parallel wavenumber, ℎ is the electron thermal velocity, is the real frequency of the eigenmode, is collisional frequency), the density response of electrons is laminar, so the mean particle flux is diffusive.…”