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Electron inertia effect on incompressible plasma flow in a planar channel

Part of: Complex Plasma Phenomena

Published online by Cambridge University Press:  13 July 2015

M. B. Gavrikov  and
A. A. Taiurskii
M. B. Gavrikov
Affiliation:
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya sq., 4, Moscow, 125047, Russia
A. A. Taiurskii*
Affiliation:
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya sq., 4, Moscow, 125047, Russia
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we consider a one-fluid model of electromagnetic hydrodynamics (EMHD) of quasi-neutral plasma, with ion and electron inertia fully taken into account. The EMHD and the MHD models are compared with regard to solving the classical problem of steady flow of incompressible plasma in a planar channel. In the MHD theory, the solution is given by the Hartmann flow, whereas in the EMHD model, the diagram of the longitudinal velocity is shown to be significantly different from the Hartmann profile: in particular, near-wall flows and a counterflow appear, while the flow velocity may significantly deviate from the direction of the antigradient pressure causing plasma to flow (the so-called hydrodynamic ‘Hall effect’). This study shows that the EMHD and the MHD planar channel theories are practically the same for liquid metal plasma and are very different for gas plasma.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 495810506
Copyright
© Cambridge University Press 2015 

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References

Adlam, J. H. & Allen, J. E. 1958 The structure of strong collision-free hydromagnetic waves. Phil. Mag. 3 (29), 448–455.Google Scholar
Bobrova, N. A., Lazzaro, E. & Sasorov, P. V. 2005 Magnetohydrodynamics two-temperature equations for multicomponent plasma. Phys. Plasmas 12, 022105.CrossRefGoogle Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1, p. 205. Consultants Bureau.Google Scholar
Gavrikov, M. B. 1988 Linear Waves in Non-Relativistic Magnetohydrodynamics. Keldysh Inst. Appl. Mathem. Academy of Sciences of the USSR; Preprint 199, 28 pp.Google Scholar
Gavrikov, M. B. & Savelyev, V. V. 2009 Equilibrium configurations of plasma in the approximation of two-fluid magnetohydrodynamics with electron enertia taken into account. J. Math. Sci. 163 (N1), 1–40.Google Scholar
Gavrikov, M. B., Savelyev, V. V. & Shmarovoz, G. V. 2009 Two-Fluids Plasma Acceleration in Plane Channel. Keldysh Inst. Appl. Mathem. Russian Academy of Sciences; Preprint 52, 26 pp.Google Scholar
Gavrikov, M. B., Savelyev, V. V. & Tayuskiy, A. A. 2010 Solitons in two-fluid magnetohydrodynamics with non-zero electron inertia. Izv. Vuzov ‘PND’ 18 (N4), 132–147.Google Scholar
Gavrikov, M. B. & Sorokin, R. V. 2008 Homogeneous deformation of a two-fluid plasma with allowance for electron inertia. Fluid Dyn. 43 (6), 977–989.CrossRefGoogle Scholar
Il’ichev, A. 1996 Steady waves in a cold plasma. J. Plasma Phys. 55, 181–194.Google Scholar
Imshennik, V. S. & Bobrova, N. A. 1997 Dynamics of Collision Plasma. Energoatomizdat.Google Scholar
Kingsep, A. S., Chukbar, K. V. & Yan’kov, V. V. 1990 Electron magnetohydrodynamics. In Reviews of Plasma Physics (ed. Kadomtsev, B. B.), vol. 16, pp. 243–288. Consultants Bureau.Google Scholar
Kulikovskiy, A. G. & Lyubimov, G. A. 1965 Magnetohydrodynamics. Addison-Wesley.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn, Course of Theoretical Physics, vol. 6. Butterworth-Heinemann.Google Scholar
Lüst, R. 1959 Uber die Ausbreitung von Wellen in einem Plasma. Fortsch. Phys. 7, 503–558.Google Scholar
Montgomery, D. 1959 Nonlinear Alfven waves in a cold ionized gas. Phys. Fluids 2, 585–588.Google Scholar
Morozov, A. I. 2010 Introduction to Plasma Dynamics. Cambridge International Science Publishing.Google Scholar
Saffmann, P. G. 1961 On hydromagnetic waves of finite amplitude in a cold plasma. J. Fluid Mech. 11, 552–566.Google Scholar
Sagdeev, R. Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 4, p. 23. Consultants Bureau.Google Scholar
Schlüter, A. 1950 Dynamik des plasmas – I. Grundgleichungen, plasma in gekreutzten feldern. Z. Naturforsch. 5a, 72–78.Google Scholar
Shafranov, V. D. 1966 Plasma equilibrium in magnetic field. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 2, p. 103. Consultants Bureau.Google Scholar
Spitzer, L. 1962 Physics of Fully Ionized Gases, 2nd edn. Interscience.Google Scholar