Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
- PPPL
Tertiary modes in electrostatic drift-wave turbulence are localized near extrema of the zonal velocity $U(x)$ with respect to the radial coordinate $$x$$. We argue that these modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate $$\gamma_{\rm TI}$$ is derived within the modified Hasegawa--Wakatani model. We show that $$\gamma_{\rm TI}$$ equals the primary-instability growth rate plus a term that depends on the local $U''$; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This provides a generic explanation of the well-known yet elusive Dimits shift, which we find explicitly in the Terry--Horton limit. Linearly unstable tertiary modes either saturate due to the evolution of the zonal density or generate radially propagating structures when the shear $|U'|$ is sufficiently weakened by viscosity. The Dimits regime ends when such structures are generated continuously.
- Research Organization:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
- DOE Contract Number:
- AC02-09CH11466
- OSTI ID:
- 1608302
- Country of Publication:
- United States
- Language:
- English
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