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dc.contributor.authorZhu, Hongxuan-
dc.contributor.authorZhou Yao-
dc.contributor.authorDodin, I.Y.-
dc.description.abstractThe Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry--Horton system has been proposed by St-Onge [J. Plasma Phys. {\bf 83}, 905830504 (2017)] as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$, where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U''$. Then, depending on $U''$, the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $U'$. Our analytic predictions are in agreement with direct numerical simulations of the modified Terry--Horton system.en_US
dc.description.tableofcontentsreadme and digital data filesen_US
dc.publisherPrinceton Plasma Physics Laboratory, Princeton Universityen_US
dc.relationJournal of Plasma Physicsen_US
dc.subjectfusion plasmasen_US
dc.subjectplasma instabilitiesen_US
dc.subjectplasma wavesen_US
dc.titleTheory of the tertiary instability and the Dimits shift within a scalar modelen_US
dc.contributor.funderU. S. Department of Energyen_US
Appears in Collections:Theory and Computation

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