Skip to main content
SpringerLink
Log in

Characteristics of the Energy Transfer by Alfvén Waves in the Solar Atmosphere

  • Published:
Geomagnetism and Aeronomy Aims and scope Submit manuscript

Abstract

The propagation of linear Alfvén waves with periods of 10–200 s from the photosphere to the solar chromosphere under the conditions of an isothermal atmosphere taking into account the amplitude-phase relationships are considered. It was found that the amplitude of the wave velocity perturbation increases and the magnetic field perturbation decreases with increasing height, while the phase difference between the perturbations tends to π/2. The so-called turning points cannot adequately characterize the energy flux of Alfvén waves. This conclusion indicates that results based on the analysis of oscillation theorems must be revised. It is shown that the efficiency of wave-energy transfer increases with increasing frequency of Alfvén modes (when dissipative processes are disregarded).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Aschwanden, M.J., Gošic, M., Hurlburt, N.E., et al., Convection-driven generation of ubiquitous coronal waves, Astrophys. J., 2018, vol. 866, no. 1, id 73. https://doi.org/10.3847/1538-4357/aae08b

  2. Chae, J. and Litvinenko, Y.E., Linear acoustic waves in a nonisothermal atmosphere. I. Simple nonisothermal layer solution and acoustic cutoff frequency, Astrophys. J., 2018, vol. 869, no. 1, id 36. https://doi.org/10.3847/1538-4357/aaec05

  3. Hollweg, J.V., Resonances of coronal loops, Astrophys. J., 1984, vol. 277, no. 1, pp. 392–403.

    Article  Google Scholar 

  4. Klimchuk, J.A., Key aspects of coronal heating, Phil. Trans. R. Soc. A, 2015, vol. 373, no. 2042, pp. 20140256–20140256. https://doi.org/10.1098/rsta.2014.0256

    Article  Google Scholar 

  5. Murawski, K. and Musielak, Z.E., Linear Alfvén waves in the solar atmosphere, Astron. Astrophys., 2010, vol. 518, idA37. https://doi.org/10.1051/0004-6361/201014394

    Article  Google Scholar 

  6. Musielak, Z.E., Musielak, D.E., and Mobashi, H., Method to determine cutoff frequencies for acoustic waves propagating in nonisothermal media, Phys. Rev. E, 2006, vol. 73, id 036612. https://doi.org/10.1103/PhysRevE.73.036612

  7. Myshkis, A.D., Matematika dlya VTUZov: Spetsial’nye kursy (Mathematics for Engineering Universities: Special Courses), Moscow: Nauka, 1971.

  8. Perera, H.K., Musielak, Z.E., and Murawski, K., Theoretical evidence for cutoff frequencies for Alfvén waves propagating in the solar atmosphere, Mon. Not. R. Astron. Soc., 2015, vol. 450, no. 3, pp. 3169–3180.

    Article  Google Scholar 

  9. Pushkar’, E.A., Differentsial’nye uravneniya: Uchebnoe posobie (Differential Equations: A Teaching Guide), Moscow: Mosk. gos. ind. univ., 2007.

  10. Rabinovich, M.I. and Trubetskov, D.I., Vvedenie v teoriyu kolebanii i voln (Introduction to the Theory of Oscillations and Waves), Moscow: Nauka, 1984.

  11. Routh, S., Musielak, Z.E., and Hammer, R., Conditions for propagation of torsional waves in solar magnetic flux tubes, Sol. Phys., 2007, vol. 246, no. 1, pp. 133–143.

    Article  Google Scholar 

  12. Sakurai, T., Heating mechanisms of the solar corona, Proc. Jpn. Acad.,Ser. B, 2017, vol. 93, pp. 87–97.

    Google Scholar 

  13. Schmitz, F. and Fleck, B., On wave equations and cut-off frequencies of plane atmospheres, Astron. Astrophys., 1998, vol. 337, pp. 487–494.

    Google Scholar 

  14. Soler, R., Terradas, J., Oliver, R., et al., Energy transport and heating by torsional Alfvén waves propagating from the photosphere to the corona in the quiet Sun, Astrophys. J., 2019, vol. 871, no. 1, id 3. https://doi.org/10.3847/1538-4357/aaf64c

  15. Srivastava, A.K., Shetye, J., Murawski, K., et al., High-frequency torsional Alfvén waves as an energy source for coronal heating, Sci. Rep., 2017, vol. 7, id 43147. https://doi.org/10.1038/srep43147

  16. Tsap, Y.T., On the penetration of Alfvén waves from the chromosphere into the corona, in Proc.IAU Symp no. 233: Solar Activity and its Magnetic Origin, Bothmer, V. and Hady, A.A., Eds., Cambridge: Cambridge Univ. Press, 2006, pp. 253–254. https://doi.org/10.1017/S1743921306001967

  17. Tsap, Y.T., Reflection of Alfvén waves and plasma turbulization in solar corona, Bull. Crim. Astrophys. Obs., 2012, vol. 108, no. 1, pp. 46–51. https://doi.org/10.3103/S0190271712010226

    Article  Google Scholar 

  18. Tsap, Yu.T. and Kopylova, Yu.G., Acoustic damping of fast kink oscillations of coronal loops, Astron. Lett., 2001, vol. 27, no. 11, pp. 737–744.

    Article  Google Scholar 

  19. Tsap, Yu.T., Kopylova, Yu.G., and Stepanov, A.V., On the penetration of acoustic–gravity and Alfvén waves from the chromosphere into the corona of the Sun, Izv. Krym. Astrofiz. Obs., 2007, vol. 103, no. 3, pp. 71–78.

    Google Scholar 

  20. Wójcik, D., Murawski, K., Musielak, Z.E., et al., Numerical simulations of torsional Alfvén waves in axisymmetric solar magnetic flux tubes, Sol. Phys., 2017, vol. 292, no. 2, id 31. https://doi.org/10.1007/s11207-017-1058-7

Download references

Funding

The study was partially supported by the Russian Foundation for Basic Research, project no. 18-02-00856 and the Ministry of Education and Science, project no. 0831-2019-0006.

Author information

Authors and Affiliations

  1. Crimean Astrophysical Observatory, Russian Academy of Sciences, 298409, Nauchnyi, Russia

    Yu. T. Tsap

  2. Central Astronomical Observatory at Pulkovo, Russian Academy of Sciences, 196140, St. Petersburg, Russia

    A. V. Stepanov & Yu. G. Kopylova

  3. Moscow State University, Faculty of Physics, 119234, Moscow, Russia

    O. V. Khaneichuk

Authors
  1. Yu. T. Tsap
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Stepanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. G. Kopylova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. V. Khaneichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu. T. Tsap, A. V. Stepanov or Yu. G. Kopylova.

Ethics declarations

The authors declare they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsap, Y.T., Stepanov, A.V., Kopylova, Y.G. et al. Characteristics of the Energy Transfer by Alfvén Waves in the Solar Atmosphere. Geomagn. Aeron. 60, 446–451 (2020). https://doi.org/10.1134/S0016793220040143

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0016793220040143

Search

Navigation