Magnetoacoustic Heating of Plasma Caused by Periodic Magnetosound Perturbations with Discontinuities in a Quasi-Isentropic Magnetic Gas
Abstract
The magnetoacoustic heating of a plasma by harmonic or periodic saw-tooth perturbations at a transducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wave vector may form an arbitrary angle θ with the equilibrium straight magnetic strength. In view of variable θ and plasma-β, the description of magnetosound perturbations and relative magnetosound heating is fairly difficult. The scenario of heating depends not only on plasma-β and θ, but also on a balance between nonlinear attenuation at the shock front and inflow of energy into a system. Under some conditions, the average over the magnetosound period force of heating may tend to a positive or negative limit, or may tend to zero, or may remain constant when the distance from a transducer tends to infinity. Dynamics of temperature specifying heating differs in thermally stable and unstable cases and occurs unusually in the isentropically unstable flows.Keywords:
non-linear magnetoacoustics, shock waves, adiabatical instability, acoustic activity, acoustic heatingReferences
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2. Chin R., Verwichte E., Rowlands G., Nakariakov V.M. (2010), Self-organization of magnetoacoustic waves in a thermal unstable environment, Physics of Plasmas, 17(32): 107–118.
3. Field G.B. (1965), Thermal instability, The Astrophysical Journal, 142: 531–567, https://doi.org/10.1086/148317.
4. Freidberg J.P. (1987), Ideal magnetohydrodynamics, Plenum Press, New York.
5. Geffen N. (1963), Magnetogasdynamic flows with shock waves, The Physics of Fluids, 6(4): 566–571.
6. Hamilton M., Morfey C. (1998), Model equations, [in:] Nonlinear acoustics, Hamilton M., Blackstock D. [Eds], pp. 41–63, Academic Press, New York.
7. Kelly A., Nakariakov V.M. (2004), Coronal seismology by MHD autowaves, [in:] Proceedings of SOHO 13 Waves, Oscillations and Small-Scale Transients Events in the Solar Atmosphere: a joint view from SOHO and TRACE, Lacoste H. [Ed.], Vol. 547, pp. 483–488.
8. Krall N.A., Trivelpiece A.W. (1973), Principles of plasma physics, McGraw Hill, New York.
9. Leble S., Perelomova A. (2018), The dynamical projectors method: hydro and electrodynamics, CRC Press.
10. Makaryan V.G., Molevich N.E. (2007), Stationary shock waves in nonequilibrium media, Plasma Sources Science and Technology, 16(1): 124–131, https://doi.org/10.1088/0963-0252/16/1/017.
11. Molevich N.E. (2001a), Amplification of vortex and temperature waves in the process of induced scattering of sound in thermodynamically nonequilibrium media, High Temperature, 39(6): 884–888, https://doi.org/10.1023/A:1013147207446.
12. Molevich N.E. (2001b), Sound amplification in inhomogeneous flows of nonequilibrium gas, Acoustical Physics, 47(1): 102–105, https://doi.org/10.1134/1.1340086.
13. Nakariakov V.M., Mendoza-Briceno C.A., Ibánez M.H. (2000), Magnetoacoustic waves of small amplitude in optically thin quasi-isentropic plasmas, Astrophysical Journal, 528(2): 767–775, https://doi.org/10.1086/308195.
14. Ojha S.N., Singh A. (1991), Growth and decay of sonic waves in thermally radiative magnetogasdynamics, Astrophysics and Space Science, 179(1): 45–54.
15. Osipov A.I., Uvarov A.V. (1992), Kinetic and gasdynamic processes in nonequilibrium molecular physics, Soviet Physics Uspekhi, 35(11): 903–923.
16. Parker E.N. (1953), Instability of thermal fields, The Astrophysical Journal, 117: 431–436.
17. Perelomova A. (2006), Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound, Physics Letters A, 357(1): 42–4, https://doi.org/10.1016/j.physleta.2006.04.0147.
18. Perelomova A. (2010), Interaction of acoustic and thermal modes in the gas with nonequilibrium chemical reactions. Possibilities of acoustic cooling, Acta Acustica united with Acustica, 96(1): 43–48, https://doi.org/10.3813/AAA.918254.
19. Perelomova A. (2012), Nonlinear influence of sound on vibrational energy of molecules in relaxing gas, Archives of Acoustics, 37(1): 89–96.
20. Perelomova A. (2014), Thermal self-action effects of acoustic beam in a vibrationally relaxing gas, Applied Mathematical Modelling, 38(23): 5684–5691, https://doi.org/10.1016/j.apm.2014.04.055.
21. Perelomova A. (2016a), On the nonlinear effects of magnetoacoustic perturbations in a perfectly conducting viscous and thermo-conducting gas, Acta Physica Polonica A, 130(3): 727–733, https://doi.org/10.12693/APhysPolA.130.727.
22. Perelomova A. (2016b), On the nonlinear distortions of sound and its coupling with other modes in a gaseous plasma with finite electric conductivity in a magnetic field, Archives of Acoustics, 41(4): 691–699, https://doi.org/10.1515/aoa-2016-0066.
23. Perelomova A. (2018a), Magnetoacoustic heating in a quasi-isentropic magnetic gas, Physics of Plasmas, 25: 042116, https://doi.org/10.1063/1.5025030.
24. Perelomova A. (2018b) Magnetoacoustic heating in nonisentropic plasma caused by different kinds of heating-cooling function, Advances in Mathematical Physics, 2018: Article ID 8253210, 12 pages, https://doi.org/10.1155/2018/8253210.
25. Perelomova A. (2019), Propagation of initially sawtooth periodic and impulsive signals in a quasiisentropic magnetic gas, Physics of Plasmas, 26(5): 052304, https://doi.org/10.1063/1.5093390.
26. Rosner R., Tucker W.H., Vaiana G.S. (1978), Dynamics of the quiescent solar corona, Astrophysical Journal, 220: 643–665, https://doi.org/10.1086/155949.
27. Rudenko O.V., Soluyan S.I. (1977), Theoretical foundations of nonlinear acoustics, Plenum, New York.
28. Sharma V.D., Singh L.P., Ram R. (1987), The progressive wave approach analyzing the decay of a saw tooth profile in magnetogasdynamics, Physics of Fluids, 30(5): 1572–1574, https://doi.org/10.1063/1.866222.
29. Singh L.P., Singh R., Ram S.D. (2012), Evolution and decay of acceleration waves in perfectly conducting inviscid radiative magnetogasdynamics, Astrophysics and Space Science, 342(2): 371–376, https://doi.org/10.1007/s10509-012-1189-0.
30. Van Doorsselaere T.,Wardle N., Del Zanna G., Jansari K., Verwichte E., Nakariakov V.M. (2011), The first measurement of of the adiabatic index in the solar corona using time-dependent spectroscopy of HINODE/EIS observations, The Astrophysical Journal Letters, 727(2): L32, https://doi.org/10.1088/2041-8205/727/2/l32.
31. Vesecky J.F., Antiochos S.K., Underwood J.H. (1979), Numerical modeling of quasi-static coronal loops. I – Uniform energy input, Astrophysical Journal, 233(3): 987–997.
32. Zavershinsky D.I., Molevich N.E. (2014), Alfvén wave amplification as a result of nonlinear interaction with a magnetoacoustic wave in an acoustically active conducting medium, Technical Physics Letters, 40(8): 701–703, https://doi.org/10.1134/S1063785014080288.
33. Zavershinsky D.I., Molevich N.E., Ryashchikov D.S. (2015), Structure of acoustic perturbations in heatreleasing medium, Procedia Engineering, 106: 363–367, https://doi.org/10.1016/j.proeng.2015.06.046.
