Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

Li, Ping-Yu; Terry, Paul W.

doi:10.1063/5.0080511

Title: Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

Journal Article · 01 April 2022 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0080511 · OSTI ID:1864711

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Univ. of Wisconsin, Madison, WI (United States); Univ. of Texas, Austin, TX (United States)
Univ. of Wisconsin, Madison, WI (United States)

In this work, the saturation physics of ion temperature gradient (ITG) turbulence is probed by studying how amplitudes and scalings with key parameters vary across a hierarchy of reduced models. The models derive from nonlinear fluid equations for toroidal ITG turbulence under approximations to the mode coupling interactions in wavenumber space and the representation of turbulent decorrelation. Mode coupling approximations include local-in-wavenumber treatments like the spectral density of flux in quasilinear theory, a truncation to three nonlinearly interacting waves, and the interactions in a cascade to high radial wavenumber mediated by a single zonal flow. Turbulent decorrelation treatments are based on the triplet correlation time with and without eddy damping. Model fidelity is assessed by the scalings and magnitudes of the squared amplitudes of unstable mode, stable mode, and zonal flow with respect to the flow-damping rate and temperature gradient. It is shown that all models reproduce fundamental scalings, provided they incorporate the coupling of unstable mode, stable mode, and zonal flow. Accurate amplitude prediction requires eddy damping in the triplet correlation time and proper representation of the zonal-flow drive by interactions associated with the radial wavenumber cascade.

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Research Organization:: Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-89ER53291

OSTI ID:: 1864711

Alternate ID(s):: OSTI ID: 1860521

Journal Information:: Physics of Plasmas, Vol. 29, Issue 4; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Figures / Tables (12)

Figure 1(p. 6)

Figure 2(p. 16)

Figure 3(p. 18)

2, and |β$$^{"}_{2}$$|² as a function of ν for three interacting waves from inversion of the energy balance equations of statistical closure theory. The triplet correlation time is given by Eq. (14) with no eddy-damping contribution." data-ostiid="1864711">

Figure 4(p. 20)

2, and |β$$^{"}_{2}$$|² from the primitive three-wave equations, Eqs. (3) - (5). Timescales for both the mode energies and the zonal kinetic energy are much shorter than linear wave periods." data-ostiid="1864711">

Figure 5(p. 21)

2, and |β$$^{"}_{2}$$|² as a function of ν for three interacting waves from inversion of the energy balance equations of statistical closure theory. The triplet correlation time includes nonlinear corrections from Eqs. (17) - (19)." data-ostiid="1864711">

Figure 6(p. 22)

Figure 7(p. 25)

2, and |β$$^{"}_{2}$$|² as functions of ν, showing comparison between solutions of full fluid model (points) and the cascade closure model (solid traces). For this result $$k^{′}_{x}$$ = 0.2, k_x = 0.2, and k_y = 0.2." data-ostiid="1864711">

Figure 8(p. 26)

2, and |β$$^{"}_{2}$$|² as functions of η, showing comparison between solutions of full fluid model (points) and the cascade closure model (solid traces). For this result $$k^{′}_{x}$$ = 0.2, k_x = 0.2, and k_y = 0.2." data-ostiid="1864711">

Figure 9(p. 27)

Table 1(p. 28)

2, and |β$$^{"}_{2}$$|² as functions of η, showing comparison between solutions of full fluid model (points) and the cascade closure model (solid traces). For this result $$k^{′}_{x}$$ = 0.15, k_x = 0.15, and k_y = 0.2." data-ostiid="1864711">

Figure 10(p. 29)

Table 2(p. 30)

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70 PLASMA PHYSICS AND FUSION TECHNOLOGY
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Title: Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

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