Staircase formation by resonant and non-resonant transport of potential vorticity

Abstract

The E×B staircase is a quasi-periodic pattern of pressure profile corrugations. In this work, we present a new mechanism for E×B staircase formation, that involves resonant transport verses non-resonant transport. We start from a potential vorticity evolution system and use quasi-linear theory, a model dispersion relation, and a bi-Lorentzian spectrum approximation, to construct the relation between the fluxes and the profiles. With these fluxes, we close the profile evolution equations and the extended turbulence intensity evolution equation, which together constitute a turbulence-profile evolution system. In this system, the Doppler effect from the E×B mean flow can cause resonance between trapped ion precession motion and the trapped ion mode, which drives a resonant transport contribution to the fluxes. The profiles will be flattened where the resonant transport is switched on. In contrast, for the regions of non-resonant transport, profiles are steeper. A quasi-periodic pattern of profile corrugation (the E×B staircase) spontaneously emerges in this system, which is the two states mentioned above, arranged as alternating layers in space. The feedback processes during the staircase pattern formation are identified. An estimate of the critical value of the boundary heat flux is obtained, above which staircase formation will be triggered. An estimate scaling of the step size in the staircase pattern is obtained. The resonant turbulent transport is also a mechanism for collisionless saturation of zonal flow. This work is related to internal transport barrier(ITB) formation and suggests some new scenarios, such as an enhanced confined L mode.

Zonal profile corrugations and staircase formation: Role of the transport crossphase

“…Contrary to models based on waves in random media, zonal flows are not random spatially, but instead form well-defined patterns, similar to those found in other non-equilibrium systems [5]. The most common radial pattern first observed in gyrokinetic simulations of ion-temperature gradient driven (ITG) turbulence has been dubbed 'E × B staircase' [6,7,8,9], due to its quasiperiodic nature, for which the leading explanation is that zonal flows are responsible for the pattern, and that the density and temperature profile corrugations and hence transport modulation are a consequence of the zonal flow pattern directly suppressing the turbulence intensity [10,11]. Similar patterns were observed in the KSTAR tokamak and reproduced by global δf gyrokinetic simulations of collisionless trapped-electron modes (CTEM) [12,13,14].…”

Staircase resiliency in a fluctuating cellular array

“…For an extensive study on the two-scale mixing process, see Refs. [15][16][17][18]. The other approach is the jams model [19][20][21].…”

Summary of the 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS)

“…Different transport states can lead to different temperature profiles, which in turn modulates the profile of E×B mean flow. Finally, the system forms a quasi-periodic staircase through a feedback loop [18].…”