Research Paper:The Effect of Plasma Flow on the Longitudinal Standing Waves in Magnetic Flux Tubes with a Perturbation Approach

Document Type : Research Paper

Author

Assistant Professor, Physics department, Razi university, Kermanshah, Iran

Abstract

In this paper, the standing magnetohydrodynamic slow waves in the magnetic flux tubes are investigated under coronal conditions. The temperature and equilibrium plasma density of the tube is assumed to be homogeneous and constant and the compressive viscosity is considered as the damping mechanism. Also, the plasma flow is considered in the flux tube. Assuming that the damping rate to be much smaller than the oscillation frequency of the waves, the perturbation method is used to solve the problem. The oscillation frequency and the eigenfunctions are found from the first-order perturbation while the damping rate is determined from the second-order perturbation. To increase the flow speed makes the oscillation frequency decreases and the damping rate increases. Also, increasing  each of the flow speed and background temperature of the tube, decreases the ratio of the damping time to the oscillation period. But this ratio increases due to the increasing the length of the tube The results found here are consistent with the theoretical results obtained earlier. Also, the obtained results can justify some observational cases.

Keywords


[1] De Moortel, I., Ireland, J. and Walsh, R. W., Observation of oscillations in coronal loops. Astronomy and Astrophysics, 355,  23- 26,( 2000).
[2] Ogrodowczyk, R., Murawski, K. and Solanki, S. K., Slow magnetoacoustic standing waves in a curved solar coronal slab. Astronomy and Astrophysics, 495, 313-318, (2009).
[3] Ofman, L., Romoli, M., Poletto, G., Noci, G. and Kohl, J. L., Ultraviolet coronagraph spectrometer  observations of density fluctuations in the solar wind. ApJ, 491, 111-114, (1997).
[4] DeForest, C. E., and Gurman, J. B., Observation of quasi-periodic compressive waves in solar polar plumes. ApJ, 510, 217–220, (1998).
[5] Ofman, L., Nakariakov, V. M. and DeForest, C. E., Slow magnetosonic waves in coronal plumes. ApJ, 514, 441-447, (1999).
[6] Nakariakov, V. M., Verwichte, E., Berghmans, D. and Robbrecht, E., Slow magnetoacoustic waves in coronal loops. Astronomy and Astrophysics, 362, 1151-1157, (2000).
[7] Ofman, L. and Wang, T., Hot Coronal loop oscillations observed by SUMER: slow magnetosonic wave damping by by thermal coduction. ApJ, 580, 85–88, (2002).
[8] De Moortel, I. and Hood, A. W., The damping of slow MHD waves in solar coronal magnetic Astronomy and Astrophysics, 408, 755–765, (2003).
[9] Verwichte, E., Haynes, M., Arber, T. D. and Brady, C. S., Damping of slow MHD coronal loop oscillations by shocks. ApJ, 685, 1286-1290, (2008).
[10] Aschwanden, M. J., Physics of the Solar Corona, Springer, Berlin, (2005).
[11] Goossens, M., Terradas, J., Andries, J., Arregui and I., Ballester, J. L., On the nature of kink MHD waves in magnetic flux tubes. Astronomy and Astrophysics, 503, 213-223, (2009).
[12] Bahari, K. and Khalvandi, M. R., The effect of a twisted magnetic field on the nature of kink MHD waves. Solar Physics, 292, 192-202, (2017).
[13] Bahari, K. and Ebrahimi, Z., The nature of kink MHD waves in the solar corona: magnetic twist and phase mixing. Monthly Notices of the Royal Astronomical Society. 497, 1135–1142, (2020).
[14] Wang, T. J., Solanki, S. K., Innes, D. E., Curdt, W. and Marsch, E., Slow-mode standing waves observed by SUMER in hot coronal loops. Astronomy and Astrophysics, 402, 17–20, (2003).
[15] Wang, T. J., Solanki, S. K., Innes, D. E. and Curdt, W., Initiation of hot coronal loop oscillations: spectral features. Astronomy and Astrophysics, 435, 753–764, (2005).
[16] Krishna Prasad1, S., Banerjee, D., and Van Doorsselaere, T., Frequency-dependent damping in propagating slow magneto-acoustic waves. ApJ, 789, 118-127, (2014).
[17] Mendoza-Briceño, C. A., Erdélyi, R., and Sigalotti, L. D., The effects of stratification on oscillating coronal loops. ApJ, 605, 493–502, (2004).
[18] Sigalotti, L. D., Mendoza-Briceño, C. A. and Luna-Cardozo, M., Dissipation of standing slow magnetoacoustic waves in hot coronal loops. Solar Physics, 246, 187–212, (2007).
[19] Abedini, A., Phase speed and frequency-dependent damping of longitudinal intensity oscillations in coronal loop structures observed with AIA/SDO. Astrophys Space Sci, 361, 133-143, (2016).
[20] Abedini, A., Period dependence of physical quantities of slow magnetoacoustic waves in coronal loop structures of active regions with and without sunspots. J. Astrophys. Astr., 42, 16-33, (2021).
[21] Abedini, A., Observations of excitation and damping of transversal oscillations in coronal loops by AIA/SDO. Solar Physics, 293, 22-36, (2018).
[22] Abedini, A. and Safari, H., The effect of non-uniform magnetic field on the slow mode oscillations. New Astronomy, 16, 317–322, (2011).
[23] Abedini, A., Safari, H. and Nasiri, S., Slow-mode oscillations and damping of hot solar coronal loops. Soalr physics, 280, 137–151, (2012).
[24] Duckenfield, T. J., Kolotkov, D. Y. and Nakariakov, V. M., The effect of magnetic field on the damping of slow waves in the solar corona. Astronomy and Astrophysics, 646, A155-167, (2021).
[25] Prasad, A., Srivastava, A. K. and Wang, T. J., Role of compressive viscosity and thermal conductivity on the damping of slow waves in the coronal loops with and without heating cooling imbalance. Solar Physics 296, 20–54, (2021).
[26] Wang, T., Ofman, L., Yuan, D., Reale, F., Kolotkov, D. Y., and Srivastava, A. K., Slow-mode magnetoacoustic waves in coronal loops. Space Sci Rev, 217, 34-88, (2021).
[27] Al-Ghafri, K. S. and Erdelyi, R., Effect of variable background on an oscillating hot coronal loop. Soalr Physics, 283, 413–428, (2013).
[28] Al-Ghafri, K. S., Ruderman, M. S., Williamson, A., and Erdelyi, R., longitudinal magnetohydrodynamics oscillations in dissipative, cooling coronal loops. The Astrophysical Journal, 786, 36-43, (2014).
[29] Bahari, K. and Shahhosini, N., The effect of compressive viscosity and thermal conduction on the longitudinal MHD waves. Monthly Notices of the Royal Astronomical Society, 478, 342–350, (2018).
[30] Ruderman, M. S. and Petrukhin, N. S., Effect of siphon flow on resonant damping of kink oscillations in magneic flux tubes. Astronomy and Astrophysics, 631, 31-44, (2019).