Effect of sheared flow on magnetic islands

Waelbroeck, F. L.; Fitzpatrick, Richard; Grasso, D.

doi:10.1063/1.2434251

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…23,45 Here the relevant plasma flow is E ϫ B which makes the local radial electric field E r zero, i.e., E ϫ B = 0 in a frame going at this rotation; this is usually dominated by toroidal rotation and is identically the same for electrons, main ions, and any impurity ions. The island flow in the laboratory frame is thus, if viscosity dominates, ⍀ ,lab Ϸ n⍀ i + ⍀ i ‫ء‬ where ⍀ i is the toroidal plasma flow angular frequency ͑from CER of CVI for example as here on DIII-D͒ and ⍀ i ‫ء‬ is the ion diamagnetic drift frequency in the codirection for the usual profiles and directions.…”

Section: Sign Dependence or Offset In Flow Shear Effect On ⌬ј?mentioning

confidence: 99%

Islands in the stream: The effect of plasma flow on tearing stability

et al. 2010

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Reducing plasma flow clearly decreases the stability of tearing modes in multiple regimes (sawtooth, hybrid) in both high- and low-aspect-ratio tokamaks (DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus [M. Keilhacker and the JET Team, Plasma Phys. Controlled Fusion 41, 301 (1999)], National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Peng, Nucl. Fusion 40, 557 (2000)], each with distinct means of lessening rotation). Further, reducing flow makes pre-existing “saturated” islands larger at the same beta (β). Thus lower plasma flow impairs high-beta operation owing both to the destabilization and to the impact of tearing-mode islands. Experimental results suggest that flow shear (not flow) at the tearing rational surface is classically stabilizing, making the effective tearing stability index Δ′ of the total current density profile more negative (more stable). In this picture, with profiles and all else the same, the minimum metastable beta at which neoclassical tearing modes (NTMs) can destabilize is proportional to −Δ′ and hence lower flow and flow shear lead to possible destabilization (depending on seeding) at lower beta. Similarly, if destabilized, the saturated NTM island width is proportional to −β/Δ′ and thus increases as flow and flow shear are reduced. A working model gives a significant level of stabilizing shear if the plasma toroidal angular flow shear −dΩϕ/dr at a given rational surface is of order of the inverse of the product of the local values of the parallel magnetic shear length Ls and the Alfvén time τA. Experimental data are fitted for the effect of this normalization of flow shear in a simple empirical model for both onset and saturation of tearing modes. Most theoretical literature is on the consequence of flow shear on tearing stability at zero beta; tokamaks at high beta have large magnetic Prandtl number (an issue for the sign of the flow effect) and very large Lundquist number. It is in this regime that theory will be compared with experimentally based empirical models. The consequence for future tokamaks with low rotation may be lower tearing stability than now expected.

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Section: Sign Dependence or Offset In Flow Shear Effect On ⌬ј?mentioning

confidence: 99%

Islands in the stream: The effect of plasma flow on tearing stability

et al. 2010

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“…Differential rotation has generally a stabilizing effect on the growth of magnetic islands. However, it has been reported that shear flow has only limited impact on the stability of magnetic islands for a fully relaxed equilibrium (Waelbroeck, Fitzpatrick & Grasso 2007). A potentially interesting case for future considerations is the situation when the differential rotation is fast enough to match the local poloidal Alfvén speed, so that singular currents develop at those Alfvén resonances (Wang et al 1998).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Quasilinear perturbed equilibria of resistively unstable current carrying plasma

Zakharov²

2015

J. Plasma Phys.

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A formalism for consideration of island formation is presented using a model of a cylindrical resistively unstable plasma. Both current and pressure driven island formation at resonant surfaces are considered. The proposed formalism of perturbed equilibria avoids problems typical for linear analysis of resistive magneto-hydrodynamic instabilities related to extraction of the so-called small solution near the resonant surfaces. The matching technique of this paper is not sensitive to configuration parameters near the resonant surfaces. The comparison of the perturbed equilibrium method with the frequently used quasilinear mode analysis based on a perturbed averaged current density profile shows that the latter is limited in its applicability and underestimates the stability. Presented here for a cylindrical case, the perturbed equilibrium technique can be used in toroidal perturbed equilibrium codes with minor modifications.

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“…Third, the shear in the local flow profile can directly modify the plasma flow and current patterns in the immediate vicinity of the island. 18 This effect, which can only be calculated from nonlinear theory, is far less completely understood than the other two. It is predominately associated with E ϫ B flow shear, since E ϫ B flow generates an ion polarization current in the vicinity of the island, whereas parallel flow does not drive any such current.…”

Section: Introductionmentioning

confidence: 99%

Effect of local E×B flow shear on the stability of magnetic islands in tokamak plasmas

Fitzpatrick

Waelbroeck

2009

Physics of Plasmas

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The influence of local E ϫ B flow shear on a relatively wide, constant-, magnetic island embedded in a large-aspect-ratio, low-␤, circular cross-section tokamak plasma is examined, using a slab approximation to model the magnetic geometry. It is found that there are three separate solution branches characterized by low, intermediate, and high values of the shear. Flow shear is found to have a stabilizing effect on island solutions lying on the low and high shear branches, via a nonlinear modification of the ion polarization term in the Rutherford island width evolution equation, but to have a destabilizing effect on solutions lying on the intermediate shear branch. Moreover, the effect is independent of the sign of the shear. The modification of island stability by local E ϫ B flow shear is found to peak when the magnitude of the shear is approximately v i / L s , where v i is the ion thermal velocity, and L s the magnetic shear length.

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Effect of sheared flow on magnetic islands

Cited by 13 publications

References 26 publications

Islands in the stream: The effect of plasma flow on tearing stability

Islands in the stream: The effect of plasma flow on tearing stability

Quasilinear perturbed equilibria of resistively unstable current carrying plasma

Effect of local E×B flow shear on the stability of magnetic islands in tokamak plasmas

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