Natural Velocity of Magnetic Islands

Waelbroeck, F. L.

doi:10.1103/physrevlett.95.035002

Cited by 18 publications

(17 citation statements)

References 18 publications

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“…In this frame it is straightforward to show that the velocity of the island depends on the degree of profile flattening inside the separatrix. [55] This follows from the frozen-in and the no-slip conditions. The frozen-in condition expresses the fact that the separatrix traps the electron fluid whenever W > ρ s √ C where…”

Section: Transport In Magnetic Islandsmentioning

confidence: 99%

Theory and observations of magnetic islands

2009

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Abstract. Islands are a ubiquitous feature of magnetically confined plasmas. They arise as the result of plasma instabilities as well as imperfections in the coils. Effective techniques have been developed for keeping their width small. Even thin islands, however, are observed to have nonlocal effects on the profiles of rotation and current. This has stimulated interest in using magnetic islands to control plasma transport. They are also of interest as a tool to improve our understanding of microscopic plasma dynamics.

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Section: Transport In Magnetic Islandsmentioning

confidence: 99%

Theory and observations of magnetic islands

2009

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“…We determine the phase velocity by solving a system of coupled equilibrium and transport equations derived previously by Connor et al [28] and use the results to determine the effect of the polarization current. A condensed account of some of the results of the present work can be found in [50].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear tearing mode in inhomogeneous plasma: I. Unmagnetized islands

Waelbroeck¹

2007

Plasma Phys. Control. Fusion

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A theory of the nonlinear growth and propagation of magnetic islands in the semi-collisional regime is presented. The theory includes the effects of finite electron temperature gradients and uses a fluid model with cold ions in slab geometry to describe islands that are unmagnetized in the sense that their width is less than ρ s , the ion Larmor radius calculated with the electron temperature. The polarization integral and the natural phase velocity are both calculated. It is found that increasing the electron temperature gradient reduces the natural phase velocity below the electron diamagnetic frequency and thus causes the polarization current to become stabilizing.

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“…4,5 Since there is no degree of freedom determining the island propagation in conventional MHD models, much efforts have been devoted to determine the island propagation direction based on the drifttearing model, combined with effects of electron density and temperature gradients causing finite frequency related to the linear electron diamagnetic drift frequency. 6,7 Analytical and numerical studies in nonlinear effects on magnetic island propagation imply the importance of the following factors: the ratio of viscosities of ion fluid and electron fluid, 8 the degree of flattening of density profile, 9 the role of the ion polarization current, 10,11 and zonal flow generation by drifttearing mode. [12][13][14] In this paper, we elucidate the role of the ion parallel velocity and ion diamagnetic effects in the propagation of the magnetic island.…”

Section: Introductionmentioning

confidence: 99%

“…9. ͑Color online͒ Contributions of each stress to zonal flow generation in saturation regime as a function of the viscosity.…”

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confidence: 99%

Propagation of magnetic island due to self-induced zonal flow

2010

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We have investigated the propagation of magnetic island caused by the drift-tearing mode by numerically solving a reduced set of two-fluid equations 1) . It is found that the island propagates into the ion diamagnetic direction when the island growth is saturated, and the propagation velocity becomes small as the viscosity increases. We have found that the island phase velocity is approximately same as the E × B flow averaged inside the island at the saturation state. In Figure 1 the total E × B flow velocity and each Fourier component �v (m) E � = �∂ x φ m e i2πmy � from m = 0 to m = 2 at saturation state are shown as a function of the viscosity. When the viscosity is around 5 × 10 −5 , excitation of m = 1 mode is comparable to that of the m = 0 mode, and both modes affect the direction of the averaged E × B flow. Since the signs of zonal flow and other modes are opposite, the propagation directinon of the island is determined by the competition between them. The zonal flow component is slightly larger than other modes, and thus the total E × B flow directs toward the ion diamagnetic direction. It is observed that the averaged E × B flow velocity monotonically decreases as the viscosity reduces. The contribution of the zonal flow to the averaged E × B flow becomes dominant to those of other modes when the viscosity is smaller than 10 −5 . This indicates that the self-induced zonal flow plays an important role in determining the propagation direction when the viscosity is small. We have examined the generation mechanism of the zonal flow and found that the contribution of each stress depends on the viscosity. Figure 2 plots contributions of each stress to zonal flow generation at saturation state as a function of the viscosity. The sum of contributions from the Reynolds stress �v (R) 0 �, the Maxwell stress �v (M ) 0 � and the viscous stress �v (V ) 0 � is also plotted as a reference. Note that all contributions are averaged inside the island. The Reynolds stress is positive so that it forces the zonal flow into the equilibrium electron diamagnetic direction in all viscoisty regimes. On the contrary, the direction of the flow due to the Maxwell stress shows monotonically decreasing function with respect to the viscosity. When the viscosity is small, the Reynolds stress generates the zonal flow in the electron diamagnetic direction and the Maxwell stress almost cancels out the flow generation by the Reynolds stress. The small difference between them drives the flow in the electron diamagnetic direction. The flow velocity driven by the ion diamagnetic stress is negative so that it directs in ion diamagnetic direction. The direction of the flow due to the Maxwell stress is negative for small viscosity cases and is positive for large viscosity cases. The flow velocity driven by viscous stress is negative and is very small when the viscosity is small. The balance of these stresses depends on the viscosity. When the viscosity is small, the Reynolds stress and the Maxwell stress almost cancel out each other, and ...

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Natural Velocity of Magnetic Islands

Cited by 18 publications

References 18 publications

Theory and observations of magnetic islands

Theory and observations of magnetic islands

Nonlinear tearing mode in inhomogeneous plasma: I. Unmagnetized islands

Propagation of magnetic island due to self-induced zonal flow

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