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Characteristics of events with metric-to-decahectometric type II radio bursts associated with CMEs and flares in relation to SEP events

  • O. PrakashEmail author
  • Li Feng
  • G. Michalek
  • Weiqun Gan
  • Lei Lu
  • A. Shanmugaraju
  • S. Umapathy
Original Article

Abstract

A gradual solar energetic particle (SEP) event is thought to happen when particles are accelerated at a shock due to a fast coronal mass ejection (CME). To quantify what kind of solar eruptions can result in such SEP events, we have conducted detailed investigations on the characteristics of CMEs, solar flares and metric-to-decahectometric wavelength type II radio bursts (herein after m-to-DH type II bursts) for SEP-associated and non-SEP-associated events, observed during the period of 1997–2012. Interestingly, 65% of m-to-DH type II bursts associated with CMEs and flares produced SEP events. The SEP-associated CMEs have higher sky-plane mean speed, projection corrected speed, and sky-plane peak speed than those of non-SEP-associated CMEs respectively by 30%, 39%, and 25%, even though the two sets of CMEs achieved their sky-plane peak speeds at nearly similar heights within LASCO field of view. We found Pearson’s correlation coefficients between the speeds of CMEs (sky-plane speed and corrected speed) and logarithmic peak intensity of SEP events are \(\mathit{cc} = 0.62\) and \(\mathit{cc} = 0.58\), respectively. We also found that the SEP-associated CMEs are on average of three times more decelerated (\(-21.52~\mbox{m}\, \mbox{s}^{- 2}\)) than the non-SEP-associated CMEs (\(- 5.63~\mbox{m}\, \mbox{s}^{-2}\)). The SEP-associated flares have a mean peak flux (\(1.85 \times 10^{- 4}~\mbox{W}\, \mbox{m}^{- 2}\)) three times larger than that of non-SEP-associated flares, even though the flare duration (rise time) of both sets of events is similar. The SEP-associated m type II bursts have higher frequency drift rate and associated shock speed than those of the non-SEP-associated events by 70% and 25% respectively. The average formation heights of m and DH type II radio bursts for SEP-associated events (\(1.31~R_{\mathrm{o}}\) and \(3.54~R_{\mathrm{o}}\), respectively) are lower than for non-SEP-associated events (\(1.61~R_{\mathrm{o}}\) and \(3.91~R_{\mathrm{o}}\), respectively). 93% of SEP-associated events originate from the western hemisphere and 65% of SEP-associated events are associated with interacting CMEs. The obtained results indicate that, at least for the set of CMEs associated with m-to-DH type II bursts, SEP-associated CMEs are more energetic than those not associated with SEPs, thus suggesting that they are effective particle accelerators.

Keywords

Coronal mass ejections Solar flares Type II radio bursts Solar energetic particle events (SEPs) 

Notes

Acknowledgements

We thank the referee for useful constructive comments to improve the quality of this manuscript. We greatly acknowledge the data support provided by various online data centers of NOAA and NASA. We would like to thank the Wind/WAVES and Culgoora spectrograph teams for providing the type II catalogs. The SOHO/LASCO CME catalog is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. This work is fully supported by NNSFC via grants 11233008, 11427803, 11473070, 11522328, and by MSTC via 2011CB811402. O. Prakash thanks to the Chinese Academy of Sciences for providing General Financial Grant from the China Postdoctoral Science Foundation. L. Feng also acknowledges the Youth Innovation Promotion Association and the research fund from the State Key Laboratory of Space Weather for financial support. G. Michalek was supported by NCN through the grant UMO-2013/09/B/ST9/00034.

References

  1. Acuña, M.H., Ogilvie, K.W., Baker, D.N., Curtis, S.A., Fairfield, D.H., Mish, W.H.: The global geospace science program and its investigations. Space Sci. Rev. 71, 5 (1995) ADSCrossRefGoogle Scholar
  2. Anastasiadis, A.: Acceleration of solar energetic particles: the case of solar flares. J. Atmos. Sol.-Terr. Phys. 64, 481 (2002) ADSCrossRefGoogle Scholar
  3. Andrews, M.D.: A search for CMEs associated with big flares. Sol. Phys. 218, 216 (2003) CrossRefGoogle Scholar
  4. Belov, A., Garcia, H., Kurt, V., Mavromichalaki, H., Gerontidou, M.: Proton enhancements and their relation to the X-ray flares during the three last solar cycles. Sol. Phys. 229, 135 (2005) ADSCrossRefGoogle Scholar
  5. Belov, A., Abunin, A., Abunina, M., Eroshenko, E., Oleneva, V., Yanke, V., Papaioannou, A., Mavromichalaki, H., Gopalswamy, N., Yashiro, S.: Coronal mass ejections and non-recurrent Forbush decreases. Sol. Phys. 289, 3949 (2014) ADSCrossRefGoogle Scholar
  6. Bothmer, V., Daglis, I.A.: Space Weather, Physics and Effects. Springer, Berlin (2007). doi: 10.1007/978-3-540-34578-7 CrossRefGoogle Scholar
  7. Bougeret, J.-L., Kaiser, M.L., Kellogg, P.J., Manning, R., Goetz, K., Monson, S.J., Monge, N., Friel, L., Meetre, C.A., Perche, C., Sitruk, L., Hoang, S.: Waves: the radio and plasma wave investigation on the wind spacecraft. Space Sci. Rev. 71, 231 (1995) ADSCrossRefGoogle Scholar
  8. Cane, H.V., Lario, D.: An introduction to CMEs and energetic particles. Space Sci. Rev. 123, 45 (2006) ADSCrossRefGoogle Scholar
  9. Cane, H.V., Richardson, I.G., von Rosenvinge, T.T.: A study of solar energetic particle events of 1997–2006: their composition and associations. J. Geophys. Res. 115, A0810 (2010) CrossRefGoogle Scholar
  10. Cho, K.-S., Kim, K.-S., Moon, Y.-J., Dryer, M.: Initial results of the Ichon solar radio spectrograph. Sol. Phys. 212, 151 (2003) ADSCrossRefGoogle Scholar
  11. Cho, K.-S., Bong, S.-C., Kim, Y.-H., Moon, Y.-J., Dryer, M., Shanmugaraju, A., Lee, J., Park, Y.D.: Low coronal observations of metric type II associated CMEs by MLSO coronameters. Astron. Astrophys. 491, 873 (2008) ADSCrossRefGoogle Scholar
  12. Dierckxsens, M., Tziotziou, K., Dalla, S., Patsou, I., Marsh, M.S., Crosby, N.B., Malandraki, O., Tsiropoula, G.: Relationship between solar energetic particles and properties of flares and CMEs: statistical analysis of solar cycle 23 events. Sol. Phys. 291, 841 (2015) ADSCrossRefGoogle Scholar
  13. Ding, L., Jiang, Y., Zhao, L., Li, G.: The “twin-CME” scenario and large solar energetic particle events in solar cycle 23. Astrophys. J. 763, 30 (2013) ADSCrossRefGoogle Scholar
  14. Gehrels, N.: Confidence limits for small numbers of events in astrophysical data. Astrophys. J. 303, 336 (1986) ADSCrossRefGoogle Scholar
  15. Gopalswamy, N., Kaiser, M.L., Thompson, B.J., Burlaga, L., Szabo, A., Lara, A., Vourlidas, A., Yashiro, S., Bougeret, J.-L.: Radio-rich solar eruptive events. Geophys. Res. Lett. 27, 1427 (2000) ADSCrossRefGoogle Scholar
  16. Gopalswamy, N., Lara, A., Kaiser, M.L., Bougeret, J.L.: Near-Sun and near-Earth manifestations of solar eruptions. J. Geophys. Res. 106, 25261 (2001a) ADSCrossRefGoogle Scholar
  17. Gopalswamy, N., Yashiro, S., Kaiser, M.L., Howard, R.A., Bougeret, J.-L.: Characteristics of coronal mass ejections associated with long-wavelength type II radio bursts. J. Geophys. Res. 106, 29219 (2001b) ADSCrossRefGoogle Scholar
  18. Gopalswamy, N., Yashiro, S., Michałek, G., Kaiser, M.L., Howard, R.A., Reames, D.V., Leske, R., von Rosenvinge, T.: Interacting coronal mass ejections and solar energetic particles. Astrophys. J. 572, L103 (2002a) ADSCrossRefGoogle Scholar
  19. Gopalswamy, N., Yashiro, S., Michalek, G., Kaiser, M.L., Howard, R.A., Bougeret, J.-L.: In: Wang, H., Xu, R. (eds.) Solar-Terrestrial Magnetic Activity and Space Environment. COSPAR Colloquia Series, vol. 14, p. 169. Pergamon, Elmsford (2002b) Google Scholar
  20. Gopalswamy, N., Yashiro, S., Lara, A., Kaiser, M.L., Thompson, B.J., Gallagher, P.T., Howard, R.A.: Large solar energetic particle events of cycle 23: a global view. Geophys. Res. Lett. 30, SEP 3-1 (2003) CrossRefGoogle Scholar
  21. Gopalswamy, N., Aguilar-Rodriguez, E., Yashiro, S., Nunes, S., Kaiser, M.L., Howard, R.A.: Type II radio bursts and energetic solar eruptions. J. Geophys. Res. 110, 12 (2005) Google Scholar
  22. Gopalswamy, N., Mewaldt, R., Torsti, J. (eds.): Solar Eruptions and Energetic Particles. Geophysical Monograph Series, vol. 165 p. 207 (2006) Google Scholar
  23. Gopalswamy, N., Yashiro, S., Akiyama, S.: Geoeffectiveness of halo coronal mass ejections. J. Geophys. Res. 112, 6112 (2007) CrossRefGoogle Scholar
  24. Gopalswamy, N., Yashiro, S., Michalek, G., Stenborg, G., Vourlidas, A., Freeland, S., Howard, R.: The SOHO/LASCO CME catalog. Earth Moon Planets 104, 295 (2009a) ADSCrossRefGoogle Scholar
  25. Gopalswamy, N., Thompson, W.T., Davila, J.M., Kaiser, M.L., Yashiro, S., Mäkelä, P., Michalek, G., Bougeret, J.-L., Howard, R.A.: Relation between type II bursts and CMEs inferred from STEREO observations. Sol. Phys. 259, 227 (2009b) ADSCrossRefGoogle Scholar
  26. Gopalswamy, N., Mäkelä, P., Akiyama, S., Yashiro, S., Xie, H., MacDowall, R.J., Kaiser, M.L.: Radio-loud CMEs from the disk center lacking shocks at 1 AU. J. Geophys. Res. 117, A08106 (2012a) ADSCrossRefGoogle Scholar
  27. Gopalswamy, N., Xie, H., Yashiro, S., Akiyama, S., Mäkelä, P., Usoskin, I.G.: Properties of ground level enhancement events and the associated solar eruptions during solar cycle 23. Space Sci. Rev. 171, 23 (2012b) ADSCrossRefGoogle Scholar
  28. Gopalswamy, N., Xie, H., Akiyama, S., Mäkelä, P.A., Yashiro, S.: Major solar eruptions and high-energy particle events during solar cycle 24. Earth Planets Space 66, 104 (2014) ADSCrossRefGoogle Scholar
  29. Harrison, R.A.: Solar coronal mass ejections and flares. Astron. Astrophys. 162, 283 (1986) ADSGoogle Scholar
  30. Harrison, R.A.: The nature of solar flares associated with coronal mass ejection. Astron. Astrophys. 162, 304 (1995) Google Scholar
  31. Kahler, S.W.: The correlation between solar energetic particle peak intensities and speeds of coronal mass ejections: effects of ambient particle intensities and energy spectra. J. Geophys. Res. 106, 20947 (2001) ADSCrossRefGoogle Scholar
  32. Kahler, S.W., Vourlidas, A.: Do interacting coronal mass ejections play a role in solar energetic particle events? Astrophys. J. 784, 44 (2014) CrossRefGoogle Scholar
  33. Kahler, S.W., Sheeley, N.R. Jr., Howard, R.A., Koomen, M.J., Michels, D.J., McGuire, R.E., von Rosenvinge, T.T., Reames, D.V.: Associations between coronal mass ejections and solar energetic proton events. J. Geophys. Res. 89, 9683 (1984) ADSCrossRefGoogle Scholar
  34. Kallenrode, M.-B.: Current views on impulsive and gradual solar energetic particle events. J. Phys. G, Nucl. Part. Phys. 29, 965 (2003) ADSCrossRefGoogle Scholar
  35. Klein, K.-L., Posner, A.: The onset of solar energetic particle events: prompt release of deka-MeV protons and associated coronal activity. Astron. Astrophys. 438, 1029 (2005) ADSCrossRefGoogle Scholar
  36. Kocharov, L., Torsti, J.: Hybrid solar energetic particle events observed on board SOHO. Sol. Phys. 207, 149 (2002) ADSCrossRefGoogle Scholar
  37. Lara, A., Gopalswamy, N., Nunes, S., Muñoz, G., Yashiro, S.: A statistical study of CMEs associated with metric type II bursts. Geophys. Res. Lett. 30, 8016 (2003) ADSCrossRefGoogle Scholar
  38. Liu, Y., Luhmann, J.G., Bale, S.D., Lin, R.P.: Relationship between a coronal mass ejection-driven shock and a coronal metric type II bursts. Astrophys. J. 691, L151 (2009) ADSCrossRefGoogle Scholar
  39. Lugaz, N., Farrugia, C.J.: A new class of complex ejecta resulting from the interaction of two CMEs and its expected geoeffectiveness. Geophys. Res. Lett. 41, 769 (2014) ADSCrossRefGoogle Scholar
  40. MacQueen, R.M., Fisher, R.R.: The kinematics of solar inner coronaltransients. Sol. Phys. 89, 89 (1983) ADSCrossRefGoogle Scholar
  41. Magdalenić, J., Marqué, C., Krupar, V., Mierla, M., Zhukov, A.N., Rodriguez, L., Maksimović, M., Cecconi, B.: Tracking the CME-driven shock wave on 2012 March 5 and radio triangulation of associated radio emission. Astrophys. J. 791, 115 (2014) ADSCrossRefGoogle Scholar
  42. Mäkelä, P., Gopalswamy, N., Akiyama, S., Xie, H., Yashiro, S.: Estimating the height of CMEs associated with a major SEP event at the onset of the metric type II radio burst during solar cycles 23 and 24. Astrophys. J. 806, 13 (2015) ADSCrossRefGoogle Scholar
  43. Martínez Oliveros, J.C., Raftery, C.L., Bain, H.M., Liu, Y., Krupar, V., Bale, S., Krucker, S.: The 2010 August 1 type II burst: a CME-CME interaction and its radio and white-light manifestations. Astrophys. J. 748, 66 (2012) ADSCrossRefGoogle Scholar
  44. Michalek, G., Gopalswamy, N., Yashiro, S.: A new method for estimating widths, velocities, and source location of halo coronal mass ejections. Astrophys. J. 584, 472 (2003) ADSCrossRefGoogle Scholar
  45. Moon, Y.-J., Choe, G.S., Wang, H., Park, Y.-D., Gopalswamy, N., Yang, G., Yashiro, S.: A statistical study of two classes of coronal mass ejections. Astrophys. J. 581, 694 (2002) ADSCrossRefGoogle Scholar
  46. Nelson, G.J., Melrose, D.B.: Studies of emission from the Sun at metre wavelengths. In: McLean, D.J., Labrum, N.R. (eds.): vol. A87, p. 333. Cambridge University Press, Cambridge (1985) Google Scholar
  47. Neupert, W.M., Thompson, B.J., Gurman, J.B., Plunkett, S.P.: Eruption and acceleration of flare-associated coronal mass ejection loops in the low corona. J. Geophys. Res. 160, 25,215 (2001) ADSCrossRefGoogle Scholar
  48. Newkirk, G.A.: The solar corona in active regions and the thermal origin of the slowly varying component of solar radio radiation. Astrophys. J. 133, 983 (1961) ADSCrossRefGoogle Scholar
  49. Pappa Kalaivani, P., Umapathy, S., Shanmugaraju, A., Prakash, O.: Characteristics of coronal mass ejection associated with DH type II radio bursts (all and limb events). Astrophys. Space Sci. 330, 237 (2010) ADSCrossRefGoogle Scholar
  50. Papaioannou, A., Sandberg, I., Anastasiadis, A., Kouloumvakos, A., Georgoulis, M.K., Tziotziou, K., Tsiropoula, G., Jiggens, P., Hilgers, A.: Solar flares, coronal mass ejections and solar energetic particle event characteristics. J. Space Weather Space Clim. 6, A42 (2016). doi: 10.1051/swsc/2016035 ADSCrossRefGoogle Scholar
  51. Payne-Scott, R., Yabsley, E.D., Bolton, J.G.: Relative times of arrival of solar noise on different radio frequencies. Nature 160, 256 (1947) ADSCrossRefGoogle Scholar
  52. Prakash, O., Umapathy, S., Shanmugaraju, A., Vršnak, B.: Type II bursts in meter and decameter – hectometer wavelength ranges and their relation to flares and CMEs. Sol. Phys. 258, 105 (2009) ADSCrossRefGoogle Scholar
  53. Prakash, O., Umapathy, S., Shanmugaraju, A., Pappa Kalaivani, P., Vršnak, B.: Type-II bursts in meter and deca – hectometer wavelengths and their relation to flares and CMEs: II. Sol. Phys. 266, 135 (2010) ADSCrossRefGoogle Scholar
  54. Prakash, O., Umapathy, S., Shanmugaraju, A., Pappa Kalaivani, P., Vršnak, B.: Characteristics of DH type II bursts, CMEs and flares with respect to the acceleration of CMEs. Astrophys. Space Sci. 337, 47 (2012a) ADSCrossRefGoogle Scholar
  55. Prakash, O., Umapathy, S., Shanmugaraju, A., Vasanth, V.: Kinematics and flare properties of radio-loud CMEs. Sol. Phys. 281, 765 (2012b) ADSCrossRefGoogle Scholar
  56. Prakash, O., Umapathy, S., Shanmugaraju, A.: Distinctions between the characteristics of before and after DH CMEs associated flares. Astrophys. Space Sci. 340, 1 (2012c) ADSCrossRefGoogle Scholar
  57. Prakash, O., Shanmugaraju, A., Michalek, G., Umapathy, S.: Geoeffectiveness and flare properties of radio-loud CMEs. Astrophys. Space Sci. 350, 33 (2014) ADSCrossRefGoogle Scholar
  58. Prasanna Subramanian, S., Shanmugaraju, A.: Study of intensive solar flares in the rise phase of solar cycle 23 and 24 and other activities. Astrophys. Space Sci. 361, 78 (2016) ADSCrossRefGoogle Scholar
  59. Ramesh, R., Lakshmi, M.A., Kathiravan, C., Gopalswamy, N., Umapathy, S.: The location of solar metric type II radio bursts with respect to the associated coronal mass ejections. Astrophys. J. 752, 107 (2012) ADSCrossRefGoogle Scholar
  60. Reames, D.V.: Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 90, 413 (1999) ADSCrossRefGoogle Scholar
  61. Reames, D.V.: The two sources of solar energetic particles. Space Sci. Rev. 175, 53 (2013) ADSCrossRefGoogle Scholar
  62. Shanmugaraju, A., Moon, Y.-J., Dryer, M., Umapathy, S.: An investigation of solar maximum metric type II radio bursts: do two kinds of coronal shock sources exist? Sol. Phys. 215, 161 (2003) ADSCrossRefGoogle Scholar
  63. Shanmugaraju, A., Prasanna Subramanian, S.: Interacting CMEs and their associated flare and SEP activities. Astrophys. Space Sci. 352, 385 (2014) ADSCrossRefGoogle Scholar
  64. Shen, C., Liao, C., Wang, Y., Ye, P., Wang, S.: Source region of the decameter-hectometric type II radio burst: shock-streamer interaction region. Sol. Phys. 282, 543 (2012) ADSCrossRefGoogle Scholar
  65. Subramanian, P., Ananthakrishnan, S., Janardhan, P., Kundu, M.R., White, S.M., Garaimov, V.I.: Giant meterwave radio telescope observations of an M2.8 flare: insights into the initiation of a flare-coronal mass ejection event. Sol. Phys. 218, 247 (2003) ADSCrossRefGoogle Scholar
  66. Suresh, K., Shanmugaraju, A.: Investigation on radio-quiet and radio-loud fast CMEs and their associated flares during solar cycles 23 and 24. Sol. Phys. 290, 875 (2015) ADSCrossRefGoogle Scholar
  67. Trottet, G., Samwel, S., Klein, K.-L., Dudok de Wit, T., Miteva, R.: Statistical evidence for contributions of flares and coronal mass ejections to major solar energetic particle events. Sol. Phys. 290, 819 (2015) ADSCrossRefGoogle Scholar
  68. Vainio, R., Agueda, N., Aran, A., Lario, D.: Modeling of solar energetic particles in interplanetary space. In: Lilensten, J. (ed.) Space Weather: Research Towards Applications in Europe, pp. 27–37. Springer, Dordrecht (2007). ISBN 978-1-4020-5445-7. doi: 10.1007/1-4020-5446-7_4 CrossRefGoogle Scholar
  69. Vasanth, V., Umapathy, S., Vršnak, B., Lakshmi, M.A.: Characteristics of type-II radio bursts associated with flares and CMEs. Sol. Phys. 273, 143 (2011) ADSCrossRefGoogle Scholar
  70. Vasanth, V., Chen, Y., Kong, X.L., Wang, B.: Sol. Phys. 290, 1815 (2015) ADSCrossRefGoogle Scholar
  71. Vršnak, B.: Processes and mechanisms governing the initiation and propagation of CMEs. Ann. Geophys. 26, 3089 (2008) ADSCrossRefGoogle Scholar
  72. Vršnak, B., Maričić, D., Stanger, A.L., Veronig, A.M.: Coronal mass ejection of 15 May 2001: II. Coupling of the CME acceleration and the flare energy release. Sol. Phys. 225, 355 (2004) ADSCrossRefGoogle Scholar
  73. Wang, Y.M., Ye, P.Z., Wang, S., Zhou, G.P., Wang, J.X.: A statistical study on the geoeffectiveness of Earth-directed coronal mass ejections from March 1997 to December 2000. J. Geophys. Res. 107, 1340 (2002) CrossRefGoogle Scholar
  74. Wild, J.P., McCready, L.L.: Observations of the spectrum of high-intensity solar radiation at metre wavelengths. I. The apparatus and spectral types of solar burst observed. Aust. J. Sci. Res., Ser. A 3, 387 (1950) ADSGoogle Scholar
  75. Xie, H., Ofman, L., Lawrence, G.: Cone model for halo CMEs: application to space weather forecasting. J. Geophys. Res. 109, A03109 (2004) ADSGoogle Scholar
  76. Yashiro, S., Gopalswamy, N., Michalek, G., St. Cyr, O.C., Plunkett, S.P., Rich, N.B., Howard, R.A.: A catalog of white light coronal mass ejections observed by the SOHO spacecraft. J. Geophys. Res. 109, A07105 (2004) ADSCrossRefGoogle Scholar
  77. Zhang, J., Dere, K.P., Howard, R.A., Kundu, M.R., White, S.M.: On the temporal relationship between coronal mass ejections and flares. Astrophys. J. 559, 452 (2001) ADSCrossRefGoogle Scholar
  78. Zhang, M., Golub, L., Deluca, E., Berkepile, J.: The timing of flares associated with the two dynamical types of solar coronal mass ejections. Astrophys. J. 574, L97 (2002) ADSCrossRefGoogle Scholar
  79. Zhang, J., Dere, K.P., Howard, R.A., Vourlidas, A.: A study of the kinematic evolution of coronal mass ejections. Astrophys. J. 604, 420 (2004) ADSCrossRefGoogle Scholar
  80. Zhang, J., Richardson, I.G., Webb, D.F., Gopalswamy, N., Huttunen, B., Kasper, J., Nitta, N., Poomvises, W., Thompson, B.J., Wu, C.-C., Yashiro, S., Zhukov, A.: Correction to “Solar and interplanetary sources of major geomagnetic storms (\(\mathrm{Dst}\leq -100~\mbox{nT}\)) during 1996–2005”. J. Geophys. Res. 112, A12105 (2007) ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  2. 2.Astronomical Observatory of Jagiellonian UniversityKrakowPoland
  3. 3.University of Chinese Academy of SciencesBeijingChina
  4. 4.Department of PhysicsArul Anandar CollegeMaduraiIndia
  5. 5.School of PhysicsMadurai Kamaraj UniversityMaduraiIndia

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