Turbulence elasticity: A key concept to a unified paradigm of L→I→H transition

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_k1, 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_EB is mean E×B shear flow driven by edge radial electrostatic field), the I-mode will terminate and spiral into the H-mode.