Spatial Nonlinear Alfven Wave Absorption by Dissipative Plasma

The mathematical model of AlfVen wave absorption makes it possible, in particular, to explain the anomalous heating of the solar corona by Alfven waves generated in the lower, much colder layers of the sun. According to calculations, Alfven wave absorption occurs over distances of the skin order, on which classical magnetohydrodynamics (MHD) equations are obviously inapplicable. Therefore, the research is based on equations of the two-fluid MHD with a full account of the electron inertia. The study revealed a number of important regularities, in particular, the depth finitness of the layer heating, where Alfven waves penetrate into plasma. In our research we evaluated the penetration depth and established the parameters of Alfven waves absorbed, and their convergence to the quasi-stationary mode.

References

[1] Alfven H. Cosmical electrodynamics. Clarendon Press, 1963. 228 p.

[2] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 8. Elektrodinamika sploshnykh sred [Theoretical physics. Vol. 8. Electrodynamics of continuous media]. Moscow, Nauka Publ., 1982. 652 p.

[3] McIntosh S.W., Pe Pontien B., Carlsson M., Hansteen V., Boerner P., Goossens M. Alfvenic waves with sufficient energy to power the quiet solar corona and fast solar wind. Nature, 2011, vol. 475, pp. 478-480. DOI: 10.1038/nature10235 Available at: http://www.nature.com/nature/journal/v475/n7357/full/nature10235.html

[4] Braginskiy S.I. Yavleniya perenosa v plazme [Transport phenomenon in plasma]. Voprosy teorii plazmy. Vyp. 1 [Plasma theory questions. Iss. 1]. Moscow, Gosatomizdat Publ., 1963, pp. 183-272 (in Russ.).

[5] Dnestrovskiy Yu.N., Kostomarov D.P. Matematicheskoe modelirovanie plazmy [Plasma mathematic simulation]. Moscow, Nauka Publ., 1993. 336 p.

[6] Gavrikov M.B. Osnovnye uravneniya dvukhzhidkostnoy magnitnoy gidrodinamiki. Ch. I. Preprint № 59 [The basic equations for two-fluid electromagnetic hydrodynamics. Part I. Preprint no. 59]. Moscow, Inst. Appl. Math. Publ., 2006. 28 p. (in Russ.). Available at: http://www.keldysh.ru/papers/2006/prep59/prep2006_59.html (accessed 15.06.2016).

[7] Gavrikov M.B., Taiurskii A.A. Electron inertia effect on incompressible plasma flow in a planar channel. J. Plasma Phys, 2015, vol. 81, no. 5, pp. 495810506. DOI: 10.1017/S0022377815000720 Available at: https://www.cambridge.org/core/journals/journal-of-plasma-physics/article/div-classtitleelectron-inertia-effect-on-incompressible-plasma-flow-in-a-planar-channeldiv/D2675017840F927236881A2CDF592F10

[8] Gavrikov M.B., Tayurskiy A.A. The influence of electron inertia on the incompressible plasma flow in a planar channel. Matematicheskoe modelirovanie, 2013, vol. 25, no. 8, pp. 65-79.

[9] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 6. Gidrodinamika [Theoretical physics. Vol. 6. Hydrodynamics]. Moscow, Nauka Publ., 1986. 736 p.

[10] Spitzer L. Physics of fully ionized gases. New York-London, John Wiley and Sons, 1962.

[11] Chapman S., Cowling T.G. The mathematical theory of non-uniform gases. Cambridge, Univ. Press, 1939.

[12] Landau L.D. Kinetic equation in case of Coulomb interaction. ZhБTF, 1937, vol. 7, p. 203 (in Russ.).

[13] Grim G. Protsessy izlucheniya v plazme. Sbornik: Osnovy fiziki plazmy. T. 1 [Emission processes in plasma. In: Fundamentals of plasma physics. Vol. 1]. Moscow, Energoatomizdat Publ., 1983. 641 p. (in Russ.).

[14] Chukbar K.V. Lektsii po yavleniyam perenosa v plazme [Lectures on transport phenomenon in plasma]. Dolgoprudnyy, Intellekt Publ. House, 2008. 256 p.

[15] Kulikovskiy A.G., Lyubimov G.A. Magnitnaya gidrodinamika [Magnetic hydrodynamics]. Moscow, Logos Publ., 2005. 328 p.

[16] Allen C.W. Astrophysical quantities. The Athlone Press, 1973.

[17] Gray D.F. The observation and analysis of stellar photospheres. New York, Wiley, 1976.