Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.

doi:10.1103/PhysRevLett.124.055002

Title: Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Journal Article · Tue Feb 04 00:00:00 EST 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.124.055002· OSTI ID:1616941

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Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

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 $$γ$$_TI is derived within the modified Hasegawa-Wakatani model. We show that $$γ$$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.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466; EP/M022463/1; EP/R029148/

OSTI ID:: 1616941

Alternate ID(s):: OSTI ID: 1599479

Journal Information:: Physical Review Letters, Vol. 124, Issue 5; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 22 works

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