Two-fluid magnetic island dynamics in slab geometry. I. Isolated islands

Fitzpatrick, Richard; Waelbroeck, F. L.

doi:10.1063/1.1833375

Cited by 37 publications

(38 citation statements)

References 22 publications

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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%

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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Section: Introductionmentioning

confidence: 99%

Propagation of magnetic island due to self-induced zonal flow

2010

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“…As a result of the local reduction of the diamagnetic velocity caused by the flattening, the diamagnetic velocities vary rapidly (i.e., over a scale short compared to the island width) across the separatrix of a large magnetic island. [28][29][30] In the subsonic regime (c s ) V Ã , or equivalently W ) q s L s =L n ), where the profiles are completely flattened, analytic estimates of the polarization contribution take the form …”

Section: B Role Of Propagation In Island Evolutionmentioning

confidence: 99%

“…23,25,26 In a series of papers, Fitzpatrick and collaborators subsequently showed how to solve the momentum transport equation in the island in order to determine the profiles and the propagation velocity self-consistently, considering consecutively the effects of ion viscosity, 27 electron viscosity, 28 external forces, 29 Reynolds stresses, 30 and emission of driftacoustic waves. 31 A central consideration when evaluating the velocity profile is the degree of flattening of the density profile.…”

Section: B Role Of Propagation In Island Evolutionmentioning

confidence: 99%

Magnetic island evolution in hot ion plasmas

et al. 2012

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Effects of finite ion temperature on magnetic island evolution are studied by means of numerical simulations of a reduced set of two-fluid equations which include ion as well as electron diamagnetism in slab geometry. The polarization current is found to be almost an order of magnitude larger in hot than in cold ion plasmas, due to the strong shear of ion velocity around the separatrix of the magnetic islands. As a function of the island width, the propagation speed decreases from the electron drift velocity (for islands thinner than the Larmor radius) to values close to the guiding-center velocity (for islands of order 10 times the Larmor radius). In the latter regime, the polarization current is destabilizing (i.e., it drives magnetic island growth). This is in contrast to cold ion plasmas, where the polarization current is generally found to have a healing effect on freely propagating magnetic island.

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“…Here, we are assuming that P 0 and B 0 are uniform, and P 0 ӷ B 0 ӷ 1, with and b z both O͑1͒. 7 When expressed in unnormalized quantities, our fundamental ordering takes the form…”

Section: A Reduced Equationsmentioning

confidence: 99%

“…Here, W is the full island width, is the local plasma resistivity, and ⌬Ј is the conventional tearing stability index. 5 The standard expression for the ion polarization term ͑for wide islands͒ is 6,7 ⌬ polz = 1.38…”

Section: Introductionmentioning

confidence: 99%

Effect of drift-acoustic waves on magnetic island stability in slab geometry

Fitzpatrick¹,

Waelbroeck²

2005

Physics of Plasmas

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A mathematical formalism is developed for calculating the ion polarization term in the Rutherford island width evolution equation in the presence of drift-acoustic waves. The calculation is fully nonlinear, includes both ion and electron diamagnetic effects, as well as ion compressibility, but is performed in slab geometry. Magnetic islands propagating in a certain range of phase velocities are found to emit drift-acoustic waves. Wave emission gives rise to rapid oscillations in the ion polarization term as the island phase velocity varies, and also generates a net electromagnetic force acting on the island region. Increasing ion compressibility is found to extend the range of phase velocities over which drift-acoustic wave emission occurs in the electron diamagnetic direction.

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Two-fluid magnetic island dynamics in slab geometry. I. Isolated islands

Cited by 37 publications

References 22 publications

Propagation of magnetic island due to self-induced zonal flow

Propagation of magnetic island due to self-induced zonal flow

Magnetic island evolution in hot ion plasmas

Effect of drift-acoustic waves on magnetic island stability in slab geometry

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