Shear flows at the tokamak edge and their interaction with edge-localized modes

Aydemir, A. Y.

doi:10.1063/1.2727330

Cited by 23 publications

(33 citation statements)

References 34 publications

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“…The radial electric field, which determines the toroidal rotation, is naturally similarly difficult to calculate analytically, but may be easily extracted from simulation results. It is found that strong, up-down asymmetric toroidal edge flows may exist in highly resistive SOLs, in accordance with previous simulation results [3]. Parallel viscosity has been demonstrated to damp poloidal flows significantly, as previously anticipated [36].…”

Section: Discussionsupporting

confidence: 85%

“…It was previously found in simulations using a resistive one-fluid model [3] that the toroidal flows in the resistive scrapeoff layer (SOL)-the region immediately outside the LCFS-are dominantly up-down antisymmetric. Furthermore, these flows were found to be quite strong-of order 100 km/s-when the Lundquist number of the SOL is of order 10.…”

Section: Toroidal Flowsmentioning

confidence: 98%

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Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states

Ferraro

Jardin

2009

Journal of Computational Physics

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Section: Discussionsupporting

confidence: 85%

Section: Toroidal Flowsmentioning

confidence: 98%

Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states

Ferraro

Jardin

2009

Journal of Computational Physics

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“…Unlike the poloidal flows, however, the toroidal flow changes sign with the toroidal field (which reverses E v ), and the toroidal current (which reverses B θ ), but not when both are reversed simultaneously, as in figure 1. A more complete discussion of the symmetries of these flows can be found in [5,6]. The direction of the flows outside the separatrix are determined by a global mass conservation requirement.…”

Section: Introductionmentioning

confidence: 99%

An intrinsic source of radial electric field and edge flows in tokamaks

Aydemir¹

2009

Nucl. Fusion

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We propose a new mechanism for radial electric fields and edge flows in tokamaks that will also serve as an intrinsic momentum source in systems without an up-down symmetry. An essential feature of toroidal plasmas is that charge-dependent ∇B and curvature drifts would lead to a vertical polarization of the discharge if it were not for the Pfirsch-Schlüter currents that neutralize the resulting charge separation. However, in the presence of collisions, there is a residual vertical electric field that drives an E×B flow in the direction of increasing major radius, regardless of the orientation of the fields and currents. This flow is excluded from the hot core and is localized to the more collisional edge plasma. It has many features in common with the edge flows observed in tokamaks such as C-Mod. In an up-down symmetric geometry it carries no net toroidal angular momentum; however, its viscous interaction with asymmetric boundaries leads to a net momentum input to the plasma. Both this momentum input, and the residual vertical electric field, the source of these flows, may play an important role in the ∇B direction-dependence of the power threshold for the L-H transition.

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“…(This contrasts with the single-fluid resistive symmetry group, which possesses the element vbÃ, in accordance with prior findings. 12 ) Under bz, the magnetic geometry is flipped, B u is reversed and V u is unchanged. If V R and V Z are, respectively, odd and even functions of Z (up-down symmetric rotation), as is the case for rotation about the magnetic axis, then bz will reverse the poloidal velocity in a fixed frame of reference.…”

Section: Field Transmentioning

confidence: 98%

Symmetries of resistive two-fluid magnetohydrodynamics under reversals of toroidal field, current, and rotation

Ferraro

2012

Physics of Plasmas

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The discrete symmetries of time-dependent, non-axisymmetric, two-fluid magnetohydrodynamics (MHD) equations are considered. Solutions of the time-independent, axisymmetric, ideal-MHD equations remain solutions under reversals of the toroidal field, current density, or rotation. Introducing non-axisymmetry, resistivity, and two-fluid effects into the equations each break different symmetries. Symmetry groups for solutions possessing up-down spatial symmetry, and the effect of flipping the magnetic geometry across the horizontal midplane, are also considered. It is shown that poloidal velocity may or may not be reversed under a simultaneous reversal of the toroidal field and a vertical reflection of the magnetic geometry, depending on the symmetry of the velocity. Because the symmetry groups of ideal, resistive, and two-fluid MHD are distinct, it may be possible to ascertain the dominant physical mechanism of various phenomena through empirical observations of symmetry-breaking. These results, which hold for nonlinear solutions in arbitrary geometry, should also be of use in testing numerical codes.The magnetic geometry of a solution to the GradShafranov equation is unaffected by reversing the direction of the toroidal field, the toroidal current, or the toroidal rotation. However, it is known from experiment that the relative directions of these quantities do impact both the stability and transport properties of tokamaks. 1-4 For example, it is found that tearing-mode excitation thresholds are sensitive to the direction of toroidal rotation relative to the plasma current, 3,4 and H-mode power thresholds are found to depend on the direction of the toroidal field. 2 The physical basis for these observed asymmetries is generally not well understood. In order to gain a better understanding, we consider here how various physical effects impact the symmetry properties of fluid models.The continuous Lie symmetries of the ideal and resistive single-fluid magnetohydrodynamics (MHD) equations have been obtained by Fuchs. 5 These symmetries include spatial translations and rotations, as well as dilations and Galilean transformations. Using these symmetries, it is possible to obtain special exact solutions of the MHD equations; 6 however, these solutions are not easily applicable to tokamak phenomenology. Similar analysis has also recently been performed on the Grad-Shafranov equation. [7][8][9] Perhaps more directly applicable to the interpretation of tokamak experiments is the separate issue of the discrete symmetries of model equations under reversal of equilibrium quantities. This issue has been considered by Cohen and Ryutov 10 who found symmetry properties of a general kinetic model, and of a resistive single-fluid model. Additional symmetries were found in the special case of up-down symmetric solutions. Catto and Simakov have extended Cohen and Ryutov's analysis to include the effect of flipping the magnetic geometry across the horizontal midplane. 11 Furthermore, Aydemir has described symmetries of axisymmetric solut...

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Shear flows at the tokamak edge and their interaction with edge-localized modes

Cited by 23 publications

References 34 publications

Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states

Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states

An intrinsic source of radial electric field and edge flows in tokamaks

Symmetries of resistive two-fluid magnetohydrodynamics under reversals of toroidal field, current, and rotation

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