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Title: Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold

Abstract

It is shown that Ion Temperature Gradient turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows, and consequently, the numerical dissipation on these flows must be sufficiently small. Close to the nonlinear threshold for turbulence generation, a relatively small dissipation can maintain a turbulent state with a sizeable heat flux, through the damping of the zonal flow. Lowering the dissipation causes the turbulence, for temperature gradients close to the threshold, to be subdued. The heat flux then does not go smoothly to zero when the threshold is approached from above. Rather, a finite minimum heat flux is obtained below which no fully developed turbulent state exists. The threshold value of the temperature gradient length at which this finite heat flux is obtained is up to 30% larger compared with the threshold value obtained by extrapolating the heat flux to zero, and the cyclone base case is found to be nonlinearly stable. Transport is subdued when a fully developed staircase structure in the E × B shearing rate forms. Just above the threshold, an incomplete staircase develops, and transportmore » is mediated by avalanche structures which propagate through the marginally stable regions.« less

Authors:
; ; ; ; ;  [1];  [2];  [3];  [4];  [5]
  1. Physics Department, University of Bayreuth, Universitätsstrasse 30, Bayreuth (Germany)
  2. Aix Marseille Univ, CNRS, PIIM, UMR 7345, Marseille (France)
  3. General Atomics, PO Box 85608, San Diego, California 92186-5608 (United States)
  4. CCFE, Culham Science Centre, Abingdon OX14 3DB, Oxon (United Kingdom)
  5. Max Planck Institut für Plasmaphysik, Boltzmannstrasse 2 85748 Garching (Germany)
Publication Date:
OSTI Identifier:
22599892
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPARATIVE EVALUATIONS; CYCLONES; HEAT; HEAT FLUX; ION TEMPERATURE; IONS; NONLINEAR PROBLEMS; SIMULATION; TEMPERATURE GRADIENTS; TRANSPORT THEORY; TUBES; TURBULENCE; WAVELENGTHS

Citation Formats

Peeters, A. G., Rath, F., Buchholz, R., Grosshauser, S. R., Strintzi, D., Weikl, A., Camenen, Y., Candy, J., Casson, F. J., and Hornsby, W. A. Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold. United States: N. p., 2016. Web. doi:10.1063/1.4961231.
Peeters, A. G., Rath, F., Buchholz, R., Grosshauser, S. R., Strintzi, D., Weikl, A., Camenen, Y., Candy, J., Casson, F. J., & Hornsby, W. A. Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold. United States. doi:10.1063/1.4961231.
Peeters, A. G., Rath, F., Buchholz, R., Grosshauser, S. R., Strintzi, D., Weikl, A., Camenen, Y., Candy, J., Casson, F. J., and Hornsby, W. A. 2016. "Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold". United States. doi:10.1063/1.4961231.
@article{osti_22599892,
title = {Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold},
author = {Peeters, A. G. and Rath, F. and Buchholz, R. and Grosshauser, S. R. and Strintzi, D. and Weikl, A. and Camenen, Y. and Candy, J. and Casson, F. J. and Hornsby, W. A.},
abstractNote = {It is shown that Ion Temperature Gradient turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows, and consequently, the numerical dissipation on these flows must be sufficiently small. Close to the nonlinear threshold for turbulence generation, a relatively small dissipation can maintain a turbulent state with a sizeable heat flux, through the damping of the zonal flow. Lowering the dissipation causes the turbulence, for temperature gradients close to the threshold, to be subdued. The heat flux then does not go smoothly to zero when the threshold is approached from above. Rather, a finite minimum heat flux is obtained below which no fully developed turbulent state exists. The threshold value of the temperature gradient length at which this finite heat flux is obtained is up to 30% larger compared with the threshold value obtained by extrapolating the heat flux to zero, and the cyclone base case is found to be nonlinearly stable. Transport is subdued when a fully developed staircase structure in the E × B shearing rate forms. Just above the threshold, an incomplete staircase develops, and transport is mediated by avalanche structures which propagate through the marginally stable regions.},
doi = {10.1063/1.4961231},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = 2016,
month = 8
}
  • This paper presents effects of finite ballooning angles on linear ion temperature gradient (ITG) driven mode and associated heat and momentum flux in Gyrokinetic flux tube simulation GENE. It is found that zero ballooning angle is not always the one at which the linear growth rate is maximum. The ITG mode acquires a short wavelength (SW) branch (k{sub ⊥}ρ{sub i} > 1) when growth rates maximized over all ballooning angles are considered. However, the SW branch disappears on reducing temperature gradient showing characteristics of zero ballooning angle SWITG in case of extremely high temperature gradient. Associated heat flux is even with respectmore » to ballooning angle and maximizes at nonzero ballooning angle while the parallel momentum flux is odd with respect to the ballooning angle.« less
  • In this paper a theory of weak ion temperature gradient-driven turbulence near the threshold of instability is presented. The model considers kinetic ions and adiabatic electrons in a sheared slab geometry. Linear theory shows that for {eta}{sub th}{lt}{eta}{sub {ital i}}{approx lt}{eta}{sub th}+(1+{ital T}{sub {ital i}}/{ital T}{sub {ital e}}) {ital L}{sub {ital n}}/{ital L}{sub {ital s}} (where {eta}{sub th}=0.95 is the instability threshold and {ital L}{sub {ital n}}/{ital L}{sub {ital s}}{much lt}1) then {gamma}{much lt}{omega} and a weak turbulence theory applies. The nonlinear wave kinetic equation indicates that ion Compton scattering is the dominant nonlinear saturation process, and it is shownmore » that the energy scatters to the linearly stable low {ital k}{sub {ital y}} modes. The resulting fluctuation spectrum (peaked about {ital k}{sub {perpendicular}}{rho}{sub {ital i}}{congruent}1) is much lower than that suggested by naive extrapolation from the strong turbulence regime. The resulting ion thermal conductivity is also extremely low, so that strong ion heating can be expected to drive the ion temperature gradient to a level where this weakly turbulent threshold regime is surpassed. Thus the critical {eta}{sub {ital i}} relevant to magnetic confinement experiments is not the linear instability threshold but the point where the diminutions of the weak turbulence regime vanish, and the transport increases to the strong fluid turbulence level.« less
  • The ion gyroradius scaling of ion thermal transport caused by ion-temperature-gradient-driven turbulence is studied with a global fluid simulation code in three-dimensional toroidal geometry. It is found that the effective conductivity scales like the ion gyroradius (gyro-Bohm scaling). {copyright} {ital 1997} {ital The American Physical Society}
  • A drift wave transport model, recently developed by Ottaviani, Horton and Erba (OHE) [Ottaviani {ital et al.}, Plasma Phys. Controlled Fusion {bold 39}, 1461 (1997)], has been implemented and tested in a time-dependent predictive transport code. This OHE model assumes that anomalous transport is due to turbulence driven by ion temperature gradients and that the fully developed turbulence will extend into linearly stable regions, as described in the reference cited above. A multiplicative elongation factor is introduced in the OHE model and simulations are carried out for 12 discharges from major tokamak experiments, including both L- and H-modes (low- andmore » high-confinement modes) and both circular and elongated discharges. Good agreement is found between the OHE model predictions and experiment. This OHE model is also used to describe the performance of the International Thermonuclear Experimental Reactor (ITER) [Putvinski {ital et al.}, in {ital Proceedings of the 16th IAEA Fusion Energy Conference}, Montr{acute e}al, Canada, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 2, p. 737.] A second version of the OHE model, in which the turbulent transport is not allowed to penetrate into linearly stable regions, has also been implemented and tested. In simulations utilizing this version of the model, the linear stability of the plasma core eliminates the anomalous thermal transport near the magnetic axis, resulting in an increase in the core temperatures to well above the experimental values. {copyright} {ital 1998 American Institute of Physics.}« less
  • High resolution numerical simulations of plasma turbulence driven by ion temperature gradients in the presence of magnetic field inhomogeneities have been performed with special attention to the behavior of the anomalous ion energy flux. The pressure gradient evolution is treated consistently with energy transport, allowing for the study of the saturated state in situations of relevance to tokamak plasmas. It is found that the presence of large-scale coherent structures significantly affects the turbulent losses, leading to a reduction of the flux with respect to mixing length estimates.