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%3A1013147207446
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
