Integral eigenmode analysis of shear flow effects on the ion temperature gradient mode

Artun, M.; Reynders, John; Tang, W. M.

doi:10.1063/1.860575

Cited by 10 publications

(14 citation statements)

References 14 publications

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“…This situation differs somewhat from the case with finite magnetic shearŝ 10,37 , where there are linearly growing modes for a finite range of γ E . At finite magnetic shear, growing eigenmodes are possible because while γ E leads to an effective dependence of the radial wavenumbers on time,ŝ makes them dependent also on the position along the field line.…”

Section: Subcritical Turbulencementioning

confidence: 73%

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

et al. 2011

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First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in this reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical PVG turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.

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Section: Subcritical Turbulencementioning

confidence: 73%

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

et al. 2011

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“…finite maximum and then decreases towards zero, which it reaches at t = t 0 , whereupon growth turns to decay. 5 Thus, there is a period of strong transient amplification, which lasts for a finite fraction of time t 0 . The amplification exponent is…”

Section: Case Of Weak Shearmentioning

confidence: 99%

Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas

Schekochihin¹,

Highcock²,

Cowley³

2012

Plasma Phys. Control. Fusion

109

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Differential rotation is known to suppress linear instabilities in fusion plasmas. However, numerical experiments show that even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence, limiting the ability of the velocity shear to suppress anomalous transport. Here transient growth of electrostatic fluctuations driven by the parallel velocity gradient (PVG) and the ion temperature gradient (ITG) in the presence of a perpendicular (E × B) velocity shear is considered. The maximally simplified (but most promising for transport reduction) case of zero magnetic shear is treated in the framework of a local shearing box approximation. In this case there are no linearly growing eigenmodes, so all excitations are transient. In the PVG-dominated regime, the maximum amplification factor is found to be e N with N ∝ q/ǫ (safety factor/aspect ratio), the maximally amplified wavenumbers perpendicular and parallel to the magnetic field are related by k y ρ i ≈ (ǫ/q) 1/3 k v thi /S, where ρ i is the ion Larmor radius, v thi the ion thermal speed and S the E × B shear. In the ITGdominated regime, N is independent of wavenumber and N ∝ v thi /(L T S), where L T is the ion-temperature scale length. Intermediate ITG-PVG regimes are also analysed and N is calculated as a function of q/ǫ, L T and S. Analytical results are corroborated and supplemented by linear gyrokinetic numerical tests. Regimes with N 1 for all wavenumbers are possible for sufficiently low values of q/ǫ ( 7 in our model); ion-scale turbulence is expected to be fully suppressed in such regimes. For cases when it is not suppressed, an elementary heuristic theory of subcritical PVG turbulence leading to a scaling of the associated ion heat flux with q, ǫ, S and L T is proposed; it is argued that the transport is much less "stiff" than in the ITG regime.

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“…Stimulated by the experimental observations, the ion temperature gradient ͑ITG͒ driven instability has been studied intensively and significant progress has been made in the last decade. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Currently, it is widely accepted that linear and nonlinear ITG instability theories and simulations are enough to explain the ion transport anomaly qualitatively. It has been shown that the ion thermal diffusivity reduces to the neoclassical level in advanced tokamak plasmas with internal transport barriers ͑ITB's͒.…”

Section: Introductionmentioning

confidence: 99%

Gyrokinetic study of the electron temperature gradient instability in plasmas with slightly hollow density profiles

2001

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The electron temperature gradient driven instabilities in plasmas with slightly hollow density profiles are studied. The gyrokinetic integral eigenvalue equation valid for a sheared slab configuration is employed. The Debye shielding effect on the modes is investigated. The effects of a sheared E×B flow on the modes are considered. Six modes with even or odd parities are found to be simultaneously unstable. The mixing length estimate for the transport is calculated. The flow shear suppression on the modes, as well as on the transport, is demonstrated. The correlations of the results with helical system Heliotron/Torsotron and tokamak experiments are discussed.

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Integral eigenmode analysis of shear flow effects on the ion temperature gradient mode

Cited by 10 publications

References 14 publications

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas

Gyrokinetic study of the electron temperature gradient instability in plasmas with slightly hollow density profiles

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