Elasticity in drift-wave-zonal-flow turbulence.
We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉'|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉'| is the ZF shearing rate and Δωk is the turbulence decorrelation rate. For |〈v〉'|/Δωk>1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ΩZF=±γd1/2γmodu1/2, where γd is the ZF friction coefficient and γmodu is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.
WCI Center for Fusion Theory, NFRI, Daejeon 305-333, South Korea.
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Guo
WCI Center for Fusion Theory, NFRI, Daejeon 305-333, South Korea and CMTFO and CASS, University of California, San Diego, La Jolla, California 92093, USA.
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Diamond
IAS and RIAM, Kyushu University, Kasuga 816-8580, Japan.
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Kosuga
LPP, Ecole Polytechnique, CNRS, Palaiseau Cedex 91128, France.
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ÖD
Gürcan