scholarly journals Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations

1998 ◽  
Author(s):  
Z. Lin ◽  
T.S. Hahm ◽  
W.W. Lee ◽  
W.M. Tang ◽  
R.B. White
Keyword(s):  
Turbulent Transport ◽  
Massively Parallel ◽  
Zonal Flows ◽  
Parallel Simulations

scholarly journals Theory of the tertiary instability and the Dimits shift within a scalar model

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
Hongxuan Zhu ◽  
Yao Zhou ◽  
I. Y. Dodin
Keyword(s):  
Turbulent Transport ◽  
Plasma Phys ◽  
Magnetized Plasma ◽  
Radial Coordinate ◽  
Flow Shear ◽  
Zonal Flows ◽  
Drift Wave ◽  
Zonal Velocity ◽  
Instability Growth ◽  
Traditional Paradigm

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge (J. Plasma Phys., vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

Massively Parallel Simulations of Motions in a Gaussian Velocity Field

1996 ◽  
pp. 47-68 ◽  
Author(s):  
René A. Carmona ◽  
Stanislav A. Grishin ◽  
Stanislav A. Molchanov
Keyword(s):  
Velocity Field ◽  
Massively Parallel ◽  
Parallel Simulations

scholarly journals Experimental Evidence of Turbulent Transport Regulation by Zonal Flows

2013 ◽  
Vol 110 (14) ◽  
Author(s):  
G. Birkenmeier ◽  
M. Ramisch ◽  
B. Schmid ◽  
U. Stroth
Keyword(s):  
Experimental Evidence ◽  
Turbulent Transport ◽  
Zonal Flows ◽  
Transport Regulation

scholarly journals Suppressing correlations in massively parallel simulations of lattice models

2017 ◽  
Vol 220 ◽  
pp. 205-211 ◽  
Author(s):  
Jeffrey Kelling ◽  
Géza Ódor ◽  
Sibylle Gemming
Keyword(s):  
Lattice Models ◽  
Massively Parallel ◽  
Parallel Simulations

scholarly journals Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
S. Toda ◽  
M. Nunami ◽  
H. Sugama
Keyword(s):  
Energy Transport ◽  
Turbulent Transport ◽  
Zonal Flow ◽  
Transport Models ◽  
Nonlinear Simulation ◽  
Ion Energy ◽  
Trapped Electrons ◽  
Zonal Flows ◽  
Reduced Models ◽  
Potential Fluctuation

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

2015 ◽  
Vol 81 (2) ◽  
Author(s):  
A. Ishizawa ◽  
S. Maeyama ◽  
T.-H. Watanabe ◽  
H. Sugama ◽  
N. Nakajima
Keyword(s):  
Temperature Gradient ◽  
Turbulent Transport ◽  
Zonal Flow ◽  
Linear Instability ◽  
Conserved Quantity ◽  
The Other ◽  
Ion Temperature ◽  
Zonal Flows ◽  
Tearing Modes ◽  
Other Hand

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

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