Hydrodynamic equations for plasmas in strong magnetic fields - I: Collisionless approximation

Oraevskiĭ, V. N.; Chodura, R.; Feneberg, W.

doi:10.1088/0032-1028/10/9/302

Cited by 82 publications

(55 citation statements)

References 6 publications

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“…39,40,41 It may be regarded as a generalization of the bi-and tri-Maxwellian velocity distribution functions that does not require the identification of the planes of principal stress. 37,38,42,43 This approximate non-equilibrium distribution possesses a Gaussian-like distribution in each of the principal strain axes, physically, this corresponds to a non-equilibrium gas with a different temperature in each direction. Levermore 9 has shown that for nonnegative density, det Θ > 0 and Θ remain positive definite.…”

Section: B the 10-moment Gaussian Modelmentioning

confidence: 99%

Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

McDonald

Groth

2005

35th AIAA Fluid Dynamics Conference and Exhibit

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The application of the Gaussian moment closure to micron-scale flows is considered. The mathematical formulation of the closure is reviewed as well as an extension to allow for diatomic gases and treatment for solid wall boundaries. A parallel upwind finite-volume scheme with adaptive mesh refinement (AMR) using Roe and HLLE-type flux functions is described for solving the hyperbolic system of partial differential equations arising from this closure. Comparisons are made between numerical solutions of the Gaussian model and analytical solutions for several test problems, including Couette, boundary layer and cylinder flow, over a range of Knudsen numbers. Agreement between analytical and numeric solutions for these problems are very encouraging.

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Section: B the 10-moment Gaussian Modelmentioning

confidence: 99%

Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

McDonald

Groth

2005

35th AIAA Fluid Dynamics Conference and Exhibit

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“…For the description of a collisionless anisotropic plasma the 16-moments set of equations may be used which is more complete including the evolution of heat fluxes. This set of equations has been used by many authors in different theoretical approaches, especially for modeling the ionospheric plasma [45,46] and the solar wind [10,44,36,38]. A more correct and compact form of these single-fluid transport equations for the anisotropic plasma in the presence of gravity g but without magnetic diffusivity under the conditions r B ≪ V τ and r B ≪ v T τ has been derived [46]; see [45,50].…”

Section: Basic Equationsmentioning

confidence: 99%

“…In the present paper we study the linear wave instability problem on the base of more correct equationsthe 16-moments transport equations, which are derived from the Vlasov collisionless magnetized plasma kinetic equations by the fast gyromotion ordering technique [45,46,50]. These equations include additionally two dynamic evolution equations of the heat fluxes and no polytropic laws are possible.…”

Section: Introductionmentioning

confidence: 99%

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Dzhalilov

Кузнецов

Staude

2010

Contrib. Plasma Phys.

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Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approximation are studied, using the 16-moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL-MHD fluid model (single fluid equations by Chew, Goldberger, and Low [9,5]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes -strongly modified compared to the CGL model -and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL-MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities -incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes -two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models.

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“…16,[21][22][23] It may be regarded as a generalization of the bi-and tri-Maxwellian velocity distribution functions that does not require the identification of the planes of principal stress. 19,20,24,25 This approximate non-equilibrium distribution possesses a Gaussian-like distribution in each of the principal strain axes, physically, this corresponds to a non-equilibrium gas with a different temperature in each direction.…”

Section: Iic the Gaussian Closurementioning

confidence: 99%

Extended Fluid Dynamic Model for Micron-Scale Flows Based on Gaussian Moment Closure

McDonald

Groth

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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An extended fluid-dynamic model for micron-scale flows with heat transfer based on the Gaussian moment closure is presented. The standard Gaussian closue moment equations are hyperbolic and closure is achieved by assuming a form for the velocity distribution function which will, by construction, yield zero heat flux; the proposed extension leads to the addition of anisotropic thermal-diffusion terms having an elliptic nature. The extended model can be achieved by taking a Chapman-Enskog-type expansion about either the Gaussian moment equations of the kinetic equation and both methods are presented here. The elliptic nature of the additional generalized heat-flux terms lead to fully dispersed shock wave solutions, unlike the partially dispersed solutions provided by the Gaussian closure as the Mach number increases. Using a Godunov-type finite-volume scheme with block based adaptive-mesh refinement (AMR) on body-fitted multi-block meshes, the proposed equations are applied to several canonical continuum and micron-scale flow situations such as shock structure, Couette flow, and flow past a circular cylinder, as well as for transonic flow past a micro airfoil. Comparisons with analytic, experimental, and direct-simulation Monte Carlo (DSMC) results are made and demonstrate the capabilities of the proposed non-equilibrium model.

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Hydrodynamic equations for plasmas in strong magnetic fields - I: Collisionless approximation

Cited by 82 publications

References 6 publications

Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Extended Fluid Dynamic Model for Micron-Scale Flows Based on Gaussian Moment Closure

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