Nature of Transport across Sheared Zonal Flows in Electrostatic Ion-Temperature-Gradient Gyrokinetic Plasma Turbulence

It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.

Figure 1

Above: geometry of simulations discussed in text. Below: Safety factor [right, blue (or dark gray)] and ${\eta }_i$ [left, red (or gray)] profiles.

Figure 2

Electrostatic energies for: no flow (black), self-consistent flow (red or gray), and externally driven flow [blue (or dark gray)]. $t_0$ (see text) marked with arrow. Inset: snapshot of toroidal cross sections of temperature fluctuations [$\mathrm{\text{positive}}\to \mathrm{\text{red}}(\mathrm{\text{or gray}})$, $\mathrm{\text{negative}}\to \mathrm{\text{blue}}(\mathrm{\text{or dark gray}})$] and poloidal flow pattern [$\mathrm{\text{red}}(\mathrm{\text{or gray}})\to \mathrm{\text{strong}}$, $\mathrm{\text{green}}(\mathrm{\text{or light}}\mathrm{\text{gray}})\to \mathrm{\text{weak}}$].

Figure 3

Ion propagators for: no flow (black), self-consistent flow (red or gray) and externally driven flow [green (or light gray)]. Best fits shown in (same color or shading) dashed lines: Lévy fit in [red (or gray)] gives $\alpha =1.43$; other fits are Gaussian. Inset: ion propagator snapshots for self-consistent flow. Dashed line is not a fit.

Figure 4

Variance of ion propagators for: no flow (black), self-consistent flow [red (or gray)] and externally driven flow [green (or light gray)]. Vertical lines signal selected times for propagators in Fig. 3.