U.S. Department of EnergyOffice of Scientific and Technical Information
Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
Abstract
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.
- Authors:
-
- PPPL
- Publication Date:
- DOE Contract Number:
- AC02-09CH11466
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Dimits shift; drift-wave turbulence; tertiary instability; zonal flows
- OSTI Identifier:
- 1608302
- DOI:
- https://doi.org/10.11578/1608302
Citation Formats
Zhu, Hongxuan, Zhou, Yao, and Dodin, I. Y. Theory of the tertiary instability and the Dimits shift from reduced drift-wave models. United States: N. p., 2019.
Web. doi:10.11578/1608302.
Zhu, Hongxuan, Zhou, Yao, & Dodin, I. Y. Theory of the tertiary instability and the Dimits shift from reduced drift-wave models. United States. doi:https://doi.org/10.11578/1608302
Zhu, Hongxuan, Zhou, Yao, and Dodin, I. Y. 2019.
"Theory of the tertiary instability and the Dimits shift from reduced drift-wave models". United States. doi:https://doi.org/10.11578/1608302. https://www.osti.gov/servlets/purl/1608302. Pub date:Tue Dec 31 23:00:00 EST 2019
@article{osti_1608302,
title = {Theory of the tertiary instability and the Dimits shift from reduced drift-wave models},
author = {Zhu, Hongxuan and Zhou, Yao and Dodin, I. Y.},
abstractNote = {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.},
doi = {10.11578/1608302},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Dec 31 23:00:00 EST 2019},
month = {Tue Dec 31 23:00:00 EST 2019}
}