Abstract
The proposed work presents a model to understand the lower hybrid turbulence in the magnetic reconnection regions of magnetopause by the energetic electron beams (generated by the magnetic reconnection process). The magnetic reconnection process has been substituted by the energetic electron beam source in this model. Due to beam energy, lower hybrid waves (LHW) evolve from very small to large amplitude (saturation) and then to LHW localization and the turbulent state. A nonlinear two-dimensional model with the help of two-fluid dynamics has been developed. The mathematical model considers the interaction between pump LHW and low frequency magnetosonic wave (MSW). The MSW, present in the background, has been contemplated as the source of density perturbations in LHW dynamics. The ponderomotive force components arise due to high-frequency LHW. With the help of the growth term associated with the electron beam, dynamical equations for LHW and MSW have been derived. The two coupled equations, thus obtained, are solved with the help of numerical simulation techniques. The results show the LHW’s temporal evolution (growth) from a very small amplitude and then the formation of localized structures and turbulence.
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References
Bale, S.D., Mozer, F.S., Phan, T.: Observation of lower hybrid drift instability in the diffusion region at a reconnecting magnetopause. Geophys. Res. Lett. 29(24), 33-1–33-4 (2002). https://doi.org/10.1029/2002GL016113
Batra, K., Sharma, R.P., Verga, A.D.: Stability analysis of nonlinear evolution patterns of modulational instability and chaos using one-dimensional Zakharov equations. J. Plasma Phys. 72, 671–686 (2006). https://doi.org/10.1017/S002237780500423X
Bingham, R., Shapiro, V.D., Shukla, P.K., Trines, R.: Lower-hybrid wave activity and reconnection at the magnetosphere. In: Physica Scripta T, vol. 2004, pp. 144–148 (2004)
Cairns, I.H., McMillan, B.F.: Electron acceleration by lower hybrid waves in magnetic reconnection regions. Phys. Plasmas 12, 1 (2005). https://doi.org/10.1063/1.2080567
Cheung, P.Y., Wong, A.Y.: Nonlinear evolution of electron-beam-plasma interactions. Phys. Fluids 28, 1538–1548 (1985). https://doi.org/10.1063/1.864988
Cozzani, G., Khotyaintsev, Y.V., Graham, D.B., Egedal, J., André, M., Vaivads, A., Alexandrova, A., le Contel, O., Nakamura, R., Fuselier, S.A., Russell, C.T., Burch, J.L.: Structure of a perturbed magnetic reconnection electron diffusion region in the Earth’s magnetotail. Phys. Rev. Lett. 127, 215101 (2021). https://doi.org/10.1103/PhysRevLett.127.215101
Daughton, W.: Electromagnetic properties of the lower-hybrid drift instability in a thin current sheet. Phys. Plasmas 10, 3103–3119 (2003). https://doi.org/10.1063/1.1594724
Davidson, R.C., Gladd, N.T.: Anomalous transport properties associated with the lower-hybrid-drift instability. Phys. Fluids 18, 1327–1335 (1975). https://doi.org/10.1063/1.861021
Davidson, R.C., Gladd, N.T., Wu, C.S., Huba, J.D.: Effects of finite plasma beta on the lower-hybrid-drift instability. Phys. Fluids 20, 301–310 (1977). https://doi.org/10.1063/1.861867
Divin, A., Khotyaintsev, Y.V., Vaivads, A., André, M., Markidis, S., Lapenta, G.: Evolution of the lower hybrid drift instability at reconnection jet front. J. Geophys. Res. Space Phys. 120, 2675–2690 (2015). https://doi.org/10.1002/2014JA020503
Gary, S.P., Sgro, A.G.: The lower hybrid drift instability at the magnetopause. Geophys. Res. Lett. 17(7), 909–912 (1990)
Graham, D.B., Khotyaintsev, Y.V., Norgren, C., Vaivads, A., André, M., Lindqvist, P.A., Marklund, G.T., Ergun, R.E., Paterson, W.R., Gershman, D.J., Giles, B.L., Pollock, C.J., Dorelli, J.C., Avanov, L.A., Lavraud, B., Saito, Y., Magnes, W., Russell, C.T., Strangeway, R.J., Torbert, R.B., Burch, J.L.: Electron currents and heating in the ion diffusion region of asymmetric reconnection. Geophys. Res. Lett. 43, 4691–4700 (2016). https://doi.org/10.1002/2016GL068613
Graham, D.B., Khotyaintsev, Y.V., Norgren, C., Vaivads, A., André, M., Toledo-Redondo, S., Lindqvist, P.A., Marklund, G.T., Ergun, R.E., Paterson, W.R., Gershman, D.J., Giles, B.L., Pollock, C.J., Dorelli, J.C., Avanov, L.A., Lavraud, B., Saito, Y., Magnes, W., Russell, C.T., Strangeway, R.J., Torbert, R.B., Burch, J.L.: Lower hybrid waves in the ion diffusion and magnetospheric inflow regions. J. Geophys. Res. Space Phys. 122, 517–533 (2017). https://doi.org/10.1002/2016JA023572
Graham, D.B., Khotyaintsev, Yu.V., Norgren, C., Vaivads, A., Andre, M., Drake, J.F., Egedal, J., Zhou, M., Le Contel, O., Webster, J.M., Lavraud, B., Kacem, I., Genot, V., Jacquey, C., Rager, A.C., Gershman, D.J., Burch, J.L., Ergun, R.E.: Universality of Lower Hybrid Waves at Earth’s Magnetopause (2019). https://doi.org/10.1029/2019JA027155
Ji, H., Kulsrud, R., Fox, W., Yamada, M.: An obliquely propagating electromagnetic drift instability in the lower hybrid frequency range. J. Geophys. Res. Space Phys. 110, A08212 (2005). https://doi.org/10.1029/2005JA011188
Karimabadi, H., Roytershteyn, V., Wan, M., Matthaeus, W.H., Daughton, W., Wu, P., Shay, M., Loring, B., Borovsky, J., Leonardis, E., Chapman, S.C., Nakamura, T.K.M.: Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20, 012303 (2013). https://doi.org/10.1063/1.4773205
Lu, Q., Wang, S., Dou, X.: Electrostatic waves in an electron-beam plasma system. Phys. Plasmas 12, 1 (2005). https://doi.org/10.1063/1.1951367
Matthaeus, W.H.: Turbulence in space plasmas: who needs it? Phys. Plasmas 28, 032306 (2021). https://doi.org/10.1063/5.0041540
Nicholson, D.: Introduction to Plasma Theory. Wiley, New York (1983)
Norgren, C., Vaivads, A., Khotyaintsev, Y.V., André, M: Lower hybrid drift waves: space observations. Phys. Rev. Lett. 109, 055001 (2012). https://doi.org/10.1103/PhysRevLett.109.055001
Omidi, N., O’Farrell, A., Krauss-Varban, D.: Sources of magnetosheath waves and turbulence. Adv. Space Res. 14(7), 45–54 (1994)
Plaschke, F., Angelopoulos, V., Glassmeier, K.H.: Magnetopause surface waves: THEMIS observations compared to MHD theory. J. Geophys. Res. Space Phys. 118, 1483–1499 (2013). https://doi.org/10.1002/jgra.50147
Shapiro, V.D.: Modulational Interaction of the Lower-Hybrid Waves with a Kinetic-Alfvén Mode (1998)
Shapiro, V.D., Shevchenko, V.I., Solov’ev, G.I., Kalinin, V.P., Bingham, R., Sagdeev, R.Z., Ashour-Abdalla, M., Dawson, J., Su, J.J.: Wave collapse at the lower-hybrid resonance. Phys. Fluids B 5, 3148 (1993). https://doi.org/10.1063/1.860652
Silin, I., Büchner, J., Vaivads, A.: Anomalous resistivity due to nonlinear lower-hybrid drift waves. Phys. Plasmas 12, 1 (2005). https://doi.org/10.1063/1.1927096
Tjulin, A., André, M., Eriksson, A.I., Maksimovic, M.: Observations of Lower Hybrid Cavities in the Inner Magnetosphere by the Cluster and Viking Satellites (2004)
Vaivads, A., André, M., Buchert, S.C., Wahlund, J.E., Fazakerley, A.N., Cornilleau-Wehrlin, N.: Cluster observations of lower hybrid turbulence within thin layers at the magnetopause. Geophys. Res. Lett. 31, L03804 (2004). https://doi.org/10.1029/2003GL018142
Walker, S.N., Balikhin, M.A., Alleyne, H.S.C.K., Hobara, Y., André, M., Dunlop, M.W.: Lower hybrid waves at the shock front: a reassessment. Ann. Geophys. 26, 699–707 (2008). https://doi.org/10.5194/angeo-26-699-2008
Zhou, M., Li, H., Deng, X., Huang, S., Pang, Y., Yuan, Z., Xu, X., Tang, R.: Characteristic distribution and possible roles of waves around the lower hybrid frequency in the magnetotail reconnection region. J. Geophys. Res. Space Phys. 119, 8228–8242 (2014). https://doi.org/10.1002/2014JA019978
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Manoj Kumar Upadhyay wrote and prepared the main manuscript text. Others supervised the work. All authors reviewed the manuscript.
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Upadhyay, M.K., Pathak, N., Uma, R. et al. Lower hybrid wave nonlinear saturation and turbulence in the magnetopause. Astrophys Space Sci 368, 30 (2023). https://doi.org/10.1007/s10509-023-04186-2
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DOI: https://doi.org/10.1007/s10509-023-04186-2