Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

Abstract

In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilize linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-traveling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location.

Formation of solitary zonal structures via the modulational instability of drift waves

“…In particular, the structures in Ref. [15] [ Fig. 3(b) therein] seem close to quasi-monochromatic, much similar to our Fig.…”

Solitary zonal structures in subcritical drift waves: a minimum model

“…6 (row 2) clearly show that the structures remain quasi-monochromatic in y, which in turn justifies the quasilinear approximation. In fact, the same feature is also displayed by some solitary zonal structures identified in gyrokinetic simulations [6] [ Fig. 3(b) therein].…”

“…Here, no robust solitary solution could be found, except maybe transient ones near the fine edge between the turbulent and laminar states, similar to the "edge of chaos" scenarios discussed in Refs. [6,7]. In Fig.…”

Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence

“…Note that the ferdinons that emerge in our simple ITG model bear a striking qualitative resemblance to the avalanches reported by Villard et al (2013) in global GK simulations, namely they propagate both inwards and outwards, but always with a positive heat flux, and originate from the local maxima of the ZF. Simple soliton solutions have already been proposed as a model for GK avalanches (McMillan et al 2009;McMillan, Pringle & Teaca 2018). Vortex-dipole solitons called 'modons' have been investigated in Hasegawa-Mima-like models of turbulence (Horton & Hasegawa 1994).…”