Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry

Schnack, D. D.; Cheng, J.; Parker, S. E.; Barnes, D. C.

doi:10.1063/1.4811468

Title: Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry

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Abstract

We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k{sub ∥}/k{sub ⊥}≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length L{sub Ti0}, instability requires that either k{sub ⊥}ρ{sub i} or ρ{sub i}/L{sub Ti0} be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω=ω{sub r}+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We alsomore »« less

Authors:

Schnack, D. D. ^[1]; Cheng, J.; Parker, S. E. ^[2]; Barnes, D. C. ^[3]

Department of Engineering Physics, Center for Plasma Theory and Computation, University of Wisconsin—Madison, Madison, Wisconsin 53706 (United States)
Department of Physics, University of Colorado-Boulder, Boulder, Colorado 80303 (United States)
TriAlpha Energy, Inc., P. O. Box 7010, Rancho Santa Margarita, California 92688 (United States)

Publication Date:: Sat Jun 15 00:00:00 EDT 2013

OSTI Identifier:: 22228018

Resource Type:: Journal Article

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 20; Journal Issue: 6; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; BOLTZMANN-VLASOV EQUATION; COMPARATIVE EVALUATIONS; DISPERSION RELATIONS; EIGENFUNCTIONS; EIGENVALUES; ELECTRON TEMPERATURE; ELECTRONS; HEAT FLUX; ION TEMPERATURE; IONS; LARMOR RADIUS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; N CODES; PLASMA; PLASMA INSTABILITY; PLASMA SIMULATION; TEMPERATURE GRADIENTS

Citation Formats


                    Schnack, D. D., Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, Cheng, J., Parker, S. E., and Barnes, D. C. Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry.  United States: N. p., 2013. 
        Web.  doi:10.1063/1.4811468.

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                    Schnack, D. D., Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, Cheng, J., Parker, S. E., & Barnes, D. C. Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry.  United States.  https://doi.org/10.1063/1.4811468

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                    Schnack, D. D., Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, Cheng, J., Parker, S. E., and Barnes, D. C. 2013.  
        "Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry".  United States.  https://doi.org/10.1063/1.4811468.

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@article{osti_22228018,

  title        = {Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry},

  author       = {Schnack, D. D. and Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 and Cheng, J. and Parker, S. E. and Barnes, D. C.},

  abstractNote = {We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k{sub ∥}/k{sub ⊥}≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length L{sub Ti0}, instability requires that either k{sub ⊥}ρ{sub i} or ρ{sub i}/L{sub Ti0} be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω=ω{sub r}+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic δf code that assumes six-dimensional Vlasov ions and isothermal fluid electrons, as functions of k{sub ⊥}ρ{sub i} and ρ{sub i}/L{sub Ti0} using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as k{sub ⊥}ρ{sub i} or ρ{sub i}/L{sub Ti0} increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for L{sub Ti0}/ρ{sub i}=30 and 20. The results quantify how far fluid calculations can be extended accurately into the kinetic regime. We conclude that for the linear ITG problem in slab geometry with unsheared magnetic field when k{sub ∥}/k{sub ⊥}≪1, the extended MHD model may be a reliable physical model for this problem when ρ{sub i}/L{sub Ti0}<10{sup −2} and k{sub ⊥}ρ{sub i}<0.2.},

  doi          = {10.1063/1.4811468},

  url          = {https://www.osti.gov/biblio/22228018},
  journal      = {Physics of Plasmas},

  issn         = {1070-664X},

  number       = 6,

  volume       = 20,

  place        = {United States},

  year         = {Sat Jun 15 00:00:00 EDT 2013},

  month        = {Sat Jun 15 00:00:00 EDT 2013}

}

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