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In tokamak plasmas, sheared flows perpendicular to the driving temperaturegradients can strongly stabilize linear modes. While the system is linearlystable, regimes with persistent nonlinear turbulence may develop, i.e. thesystem is subcritical. A perturbation with small but finite amplitude may besufficient to push the plasma into a regime where nonlinear effects aredominant and thus allow sustained turbulence. The minimum threshold fornonlinear instability to be triggered provides a criterion for assessingwhether a tokamak is likely to stay in the quiescent (laminar) regime. At thecritical amplitude, instead of transitioning to the turbulent regime ordecaying 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 thisedge manifold. This simple advecting solution is qualitatively similar to, butsimpler than, the avalanche-like bursts seen in earlier turbulent simulationsand provides an insight into how turbulence is sustained in subcritical plasmasystems. For large flow shearing rate, the system is only convectivelyunstable, and given a localised initial perturbation, will eventually return toa laminar state at a fixed spatial location.

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