Heuristic closures for numerical simulations of neoclassical tearing modes

Gianakon, T. A.; Kruger, Scott; Hegna, C. C.

doi:10.1063/1.1424924

Cited by 30 publications

(46 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When used with extended MHD models that treat anisotropic heat flux with great accuracy, they are able to reproduce theoretically predicted thresholds for the onset of the neoclassical tearing mode. 34 Because of the extreme complexity of the underlying kinetic problem, fluid models are likely to form the basis for advanced computational modeling of magnetized plasmas for the foreseeable future. A major research thrust is to extend these models even further, for example to capture the effects of radio frequency wave deposition on global dynamics, to incorporate more accurate models for the cold plasma near the edge of a tokamak, and to provide a more accurate description of the interaction of the hot plasma with its material boundary.…”

Section: Summary and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

Self Cite

View full text Add to dashboard Cite

Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and/or temporal scales to be explored. Computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. Several ordering and closure schemes are reviewed and discussed, as are their normal modes, and algorithms that can be applied to obtain a numerical solution.

show abstract

Section: Summary and Discussionmentioning

confidence: 99%

“…34 To show how this relationship captures the dominant physics for neoclassical tearing modes, we write the electron velocity V e = V i − J / n using force balance to lowest order, Eq. ͑34a͒,…”

Section: Neoclassical Closuresmentioning

confidence: 99%

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…14 With the incorporation of these ''heuristic'' closures, NIMROD simulations of DIII-D discharge 86144 demonstrate both the NTM stability threshold associated with anisotropic thermal conduction and the stabilizing resistive curvature effect.…”

Section: B Velocity-moment Closures For Kinetic Effectsmentioning

confidence: 99%

NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics

et al. 2003

Self Cite

View full text Add to dashboard Cite

Nonlinear numerical studies of macroscopic modes in a variety of magnetic fusion experiments are made possible by the flexible high-order accurate spatial representation and semi-implicit time advance in the NIMROD simulation code ͓A. H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 ͑1999͔͒. Simulation of a resistive magnetohydrodynamics mode in a shaped toroidal tokamak equilibrium demonstrates computation with disparate time scales, simulations of discharge 87009 in the DIII-D tokamak ͓J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 ͑International Atomic Energy Agency, Vienna, 1987͒, Vol. I, p. 159͔ confirm an analytic scaling for the temporal evolution of an ideal mode subject to plasma-␤ increasing beyond marginality, and a spherical torus simulation demonstrates nonlinear free-boundary capabilities. A comparison of numerical results on magnetic relaxation finds the nϭ1 mode and flux amplification in spheromaks to be very closely related to the mϭ1 dynamo modes and magnetic reversal in reversed-field pinch configurations. Advances in local and nonlocal closure relations developed for modeling kinetic effects in fluid simulation are also described.

show abstract

“…This formulation is based on an ad-hoc closure (or a heuristic closure as in Ref. 23) for the neoclassical parallel viscosity which is strictly valid for time scale larger than an ion collisional time. 24 For simplicity, we neglect here the contribution from the radial derivative of toroidal rotation.…”

Section: Simulation Modelmentioning

confidence: 99%

Flux-driven simulations of turbulence collapse

et al. 2015

View full text Add to dashboard Cite

Using three-dimensional nonlinear simulations of tokamak turbulence, we show that an edge transport barrier (ETB) forms naturally once input power exceeds a threshold value. Profiles, turbulence-driven flows, and neoclassical coefficients are evolved self-consistently. A slow power ramp-up simulation shows that ETB transition is triggered by the turbulence-driven flows via an intermediate phase which involves coherent oscillation of turbulence intensity and E Â B flow shear. A novel observation of the evolution is that the turbulence collapses and the ETB transition begins when R T > 1 at t ¼ t R (R T : normalized Reynolds power), while the conventional transition criterion (x EÂB > c lin where x EÂB denotes mean flow shear) is satisfied only after t ¼ t C ( >t R ), when the mean flow shear grows due to positive feedback. V C 2015 AIP Publishing LLC.

show abstract

Heuristic closures for numerical simulations of neoclassical tearing modes

Cited by 30 publications

References 35 publications

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics

Flux-driven simulations of turbulence collapse

Contact Info

Product

Resources

About