Nonlinear magnetohydrodynamics simulation using high-order finite elements

Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A.; Barnes, D. C.; Nebel, Richard; Kruger, Scott; Schnack, D. D.; Plimpton, Steven J.; Tarditi, Alfonso G.; Chu, M. S.

doi:10.1016/j.jcp.2003.10.004

Cited by 500 publications

(487 citation statements)

References 44 publications

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“…Similar voltage spikes ͑or oscillations͒ were seen in the Compact Torus Experiment, CTX, when it was driven by a high impedance power source, 7 but their cause was not understood. The results presented in the present paper show that voltage spikes accompany magnetic reconnection in a resistive magnetohydrodynamic ͑MHD͒ simulation using the three-dimensional NIMROD code 8,9 which provides a description of the reconnection physics within the resistive MHD approximation.…”

Section: Introductionmentioning

confidence: 74%

Magnetic reconnection during flux conversion in a driven spheromak

et al. 2005

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Section: Introductionmentioning

confidence: 74%

Magnetic reconnection during flux conversion in a driven spheromak

et al. 2005

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“…The goal is to form the plasma suitable for initiating the full tokamak discharge. 9,10 Two-dimensional simulations of this formation using the NIMROD code 11 found that the reconnection agreed well with the Sweet-Parker model. 12,13 Whole-device, three-dimensional resistive MHD simulations of the NSTX helicity injection experiments 14 not only reached a similar conclusion about reconnection but also found a low-level, non-axisymmetric mode (n ¼ 1, high m) during the driven phase.…”

Section: Introductionmentioning

confidence: 69%

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

Hooper

Sovinec

2016

Physics of Plasmas

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An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (∼10–20 eV), the mode is benign, but at high temperatures (∼100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode.

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“…12͒ simulation of classical, resistive tearing modes in shaped toroidal geometry. 12 Figure 1 shows a Poincaré plot of saturated 2/1 and 3/1 magnetic islands resulting from this simulation. While traveling along magnetic field lines in this geometry, particles experience Coulomb collisional effects while seeing varying fluid quantities and magnetic field modulus, B.…”

Section: ͑2͒mentioning

confidence: 99%

“…͑15͒ in plasma fluid studies using the NIMROD code. 12 Two major issues arise in such an implementation. The first involves the formal calculation of the nonlocal closure throughout the domain.…”

Section: Numerical Implementation Of Nonlocal Closuresmentioning

confidence: 99%

Nonlocal closures for plasma fluid simulations

et al. 2004

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The application of fluid models in studies of transport and macroscopic stability of magnetized, nearly collisionless plasmas requires closure relations that are inherently nonlocal. Such closures address the fact that particles are capable of carrying information over macroscopic parallel scale lengths. In this work, generalized closures that embody Landau, collisional and particle-trapping physics are derived and discussed. A gyro/bounce-averaged drift kinetic equation is solved via an expansion in eigenfunctions of the pitch-angle scattering operator and the resulting system of algebraic equations is solved by integrating along characteristics. The desired closure moments take the form of integral equations involving perturbations in the flow and temperature along magnetic field lines. Implementation of the closures in massively parallel plasma fluid simulation codes is also discussed. This implementation includes the use of a semi-implicit time advance of the fluid equations to stabilize the dominant closure terms which are introduced explicitly. Application of the nonlocal, parallel heat flow closure, q ʈ , in studies of temperature flattening across helical magnetic islands in toroidal geometry reveal a scaling of temperature versus critical island width for flattening of Tϳw d Ϫ1.5 . This result predicts more robust flattening at small island widths when compared to the diffusive scaling, Tϳw d Ϫ1.7 , which assumes a Braginskii-type parallel heat conductivity. Preliminary application of q ʈ to tokamak disruption simulations shows qualitative agreement of wall heat loads with experimental observations, smooth distribution in toroidal angle, and striation in the poloidal direction along the wall.

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Nonlinear magnetohydrodynamics simulation using high-order finite elements

Cited by 500 publications

References 44 publications

Magnetic reconnection during flux conversion in a driven spheromak

Magnetic reconnection during flux conversion in a driven spheromak

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

Nonlocal closures for plasma fluid simulations

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