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.

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• Dimits shift, avalanche-like bursts, and Solitary propagating structures in the two-field Flux-Balanced Hasegawa-Wakatani model for plasma edge turbulence
• Sub-grid-scale effects in magnetised plasma turbulence
• Solitary zonal structures in subcritical drift waves: a minimum model
• Bistable turbulence in strongly magnetised plasmas with a sheared mean flow
• Predicting the Z-pinch Dimits shift through gyrokinetic tertiary instability analysis of the entropy mode
• Suppression of temperature-gradient-driven turbulence by sheared flows in fusion plasmas
• Optimizing the control of transition to turbulence using a Bayesian method