### Abstract

We present a theory of turbulence elasticity, which follows from delayed response of drift waves (DWs) to zonal flow (ZF) shears. It is shown that when |V′_{ZF}|/Δω_{k}1, with |V′_{ZF}| the ZF shearing rate and Δω_{k} the local turbulence decorrelation rate, the ZF evolution equation is converted from a diffusion equation to a telegraph equation. This insight provides a natural framework for understanding temporally periodic ZF structures, e.g., propagation of the ZF/turbulence intensity fronts. Furthermore, by incorporating the elastic property of the DW-ZF turbulence, we propose a unified paradigm of low-confinement-mode to intermediate-confinement-mode to high-confinement-mode (L→I→H) transitions. In particular, we predict the onset and termination conditions of the limit cycle oscillations, i.e. the I-mode. The transition from an unstable L-mode to I-mode is predicted to occur when Δω_{k}<|V′_{ZF}|<V′_{cr}, where V′_{cr} is a critical flow shearing rate and is derived explicitly. If |V′_{E}×B|>V′_{cr} (V_{E}B is mean E×B shear flow driven by edge radial electrostatic field), the I-mode will terminate and spiral into the H-mode.

Original language | English |
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Article number | 043022 |

Journal | Nuclear Fusion |

Volume | 55 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2015 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Condensed Matter Physics

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## Cite this

*Nuclear Fusion*,

*55*(4), [043022]. https://doi.org/10.1088/0029-5515/55/4/043022