. Data, All data used in this study are publicly accessible . MMS data are available at the MMS Science Data Center (https, p.25, 2018.

, The OMNI data can be downloaded from the NASA Goddard Space Flight Center Coordinated Data Analysis Web (CDAWeb, p.25, 2018.

, References

L. Alm, C. J. Farrugia, K. W. Paulson, M. R. Argall, R. B. Torbert et al., Differing Properties of Two Ion-Scale Magnetopause Flux Ropes, Journal of Geophysical Research: Space Physics, vol.119, issue.5, pp.114-131, 2018.
DOI : 10.1103/PhysRevLett.119.055101

J. L. Burch, R. B. Torbert, and T. D. Phan, Electron-scale measurements of magnetic reconnection in space, Science, vol.352, issue.6290, 2016.
DOI : 10.1029/2001JA000287

T. A. Carter, M. Yamada, H. Ji, R. M. Kulsrud, and F. Trintchouk, Experimental study of lower-hybrid drift turbulence in a reconnecting current sheet, Phys. Plasmas, vol.9, issue.3272, 2002.

S. Chandrasekhar, Physics Today, vol.15, issue.3, 1961.
DOI : 10.1063/1.3058072

L. Dai, C. Wang, Y. Zhang, . Lavraud, J. Burch et al., Kinetic Alfv??n wave explanation of the Hall fields in magnetic reconnection, Geophysical Research Letters, vol.27, issue.8, pp.634-640, 2017.
DOI : 10.1029/1999GL003688

W. Daughton, Electromagnetic properties of the lower-hybrid drift instability in a thin current sheet, Physics of Plasmas, vol.8, issue.8, 2003.
DOI : 10.1029/97JA02093

A. Divin, Y. V. Khotyaintsev, A. Vaivads, A. , and M. , Lower hybrid drift instability at a dipolarization front, Journal of Geophysical Research: Space Physics, vol.36, issue.7, pp.1124-1132, 2015.
DOI : 10.1029/2009GL040663
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014JA020528

J. P. Eastwood, T. D. Phan, P. A. Cassak, D. J. Gershman, C. Haggerty et al., Ion-scale secondary flux ropes generated by magnetopause reconnection as resolved by MMS, Geophysical Research Letters, vol.117, issue.A9, pp.4716-4724, 2016.
DOI : 10.1029/2011JA017166
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016GL068747

R. C. Elphic and C. T. Russell, Magnetic flux ropes in the Venus ionosphere: Observations and models, Journal of Geophysical Research, vol.85, issue.A1, pp.58-72, 1983.
DOI : 10.1029/JA085iA13p07787

R. E. Ergun, S. Tucker, J. Westfall, K. A. Goodrich, D. M. Malaspina et al., The Axial Double Probe and Fields Signal Processing for the MMS Mission, Space Science Reviews, vol.13, issue.1/2, pp.167-188, 2014.
DOI : 10.1007/s11214-014-0109-8
URL : https://doi.org/10.1007/978-94-024-0861-4_7

S. Eriksson, H. Hasegawa, W. Teh, B. U. Sonnerup, J. P. Mc-fadden et al., Magnetic island formation between large-scale flow vortices at an undulating postnoon magnetopause for northward interplanetary magnetic field, Journal of Geophysical Research: Space Physics, vol.81, issue.A1, pp.0-17, 2009.
DOI : 10.1029/JA081i010p01636
URL : https://hal.archives-ouvertes.fr/hal-01553817

S. Eriksson, B. Lavraud, F. D. Wilder, J. E. Stawarz, B. L. Giles et al., Magnetospheric Multiscale observations of magnetic reconnection associated with Kelvin-Helmholtz waves, Geophysical Research Letters, vol.108, issue.A1, pp.5606-5615, 2016.
DOI : 10.1029/2002JA009281

C. J. Farrugia, R. P. Rijnbeek, M. A. Saunders, D. J. Southwood, D. J. Rodgers et al., A multi-instrument study of flux transfer event structure, Journal of Geophysical Research, vol.34, issue.A12, pp.14465-14477, 1988.
DOI : 10.1016/0032-0633(86)90071-1

C. J. Farrugia, B. Lavraud, R. B. Torbert, M. Argall, I. Kacem et al., Magnetospheric Multiscale Mission observations and non-force free modeling of a flux transfer event immersed in a super-Alfv??nic flow, Geophysical Research Letters, vol.113, issue.A8, pp.6070-6077, 2016.
DOI : 10.1029/2008JA013451

S. P. Gary and J. J. Sanderson, Electrostatic temperature gradient drift instabilities, Physics of Fluids, vol.17, issue.8, pp.1500-1509, 1979.
DOI : 10.1088/0029-5515/17/1/008

D. J. Gershman, J. C. Dorelli, A. F. Vinas, L. A. Avanov, U. Gliese et al., Electron dynamics in a subproton-gyroscale magnetic hole, Geophysical Research Letters, vol.99, issue.A12, pp.4112-4118, 2016.
DOI : 10.1029/94JA01977

K. A. Goodrich, R. E. Ergun, F. D. Wilder, J. L. Burch, R. B. Torbert et al., , pp.879-889, 2018.

B. Tang, Magnetic depression of a flux rope mura MMS Multipoint electric field observations of smallscale magnetic holes, Geophys. Res. Lett, vol.43, pp.5953-5959, 2016.

D. B. Graham, Y. V. Khotyaintsev, A. Vaivads, M. Andre, and A. N. Fazakerley, Electron Dynamics in the Diffusion Region of an Asymmetric Magnetic Reconnection, Physical Review Letters, vol.112, issue.21, 2014.
DOI : 10.1103/PhysRevA.4.2094

D. B. Graham, Y. V. Khotyaintsev, C. Norgren, A. Vaivads, M. Andre et al., Lower hybrid waves in the ion diffusion and magnetospheric inflow regions, Journal of Geophysical Research: Space Physics, vol.43, issue.A5, pp.517-533, 2017.
DOI : 10.1002/2016GL069842

H. Hasegawa, B. U. Sonnerup, C. J. Owen, B. Klecker, G. Paschmann et al., The structure of flux transfer events recovered from Cluster data, Annales Geophysicae, vol.24, issue.2, pp.603-618, 2006.
DOI : 10.5194/angeo-24-603-2006
URL : https://hal.archives-ouvertes.fr/hal-00330038

H. Hasegawa, A. Retino, A. Vaivads, Y. Khotyaintsev, M. Andre et al., Kelvin-Helmholtz waves at the Earth's magnetopause: Multiscale development and associated reconnection, Journal of Geophysical Research: Space Physics, vol.113, issue.9, p.12207, 2009.
DOI : 10.1029/2007JA012850
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2009JA014042

H. Hasegawa, J. Wang, M. W. Dunlop, Z. Y. Pu, Q. Zhang et al., Evidence for a flux transfer event generated by multiple X-line reconnection at the magnetopause, Geophysical Research Letters, vol.113, issue.52, p.16101, 2010.
DOI : 10.1029/2008JA013451

J. D. Huba, N. T. Gladd, P. , and K. , Lower-hybrid-drift wave turbulence in the distant magnetotail, Journal of Geophysical Research, vol.78, issue.A11, pp.5217-5226, 1978.
DOI : 10.1029/JA078i007p01082

G. I. Korotova, D. G. Sibeck, A. Weatherwax, V. Angelopoulos, and V. Styazhkin, THEMIS observations of a transient event at the magnetopause, Journal of Geophysical Research: Space Physics, vol.93, issue.3-4, 2011.
DOI : 10.1029/JA093iA10p11341
URL : http://onlinelibrary.wiley.com/doi/10.1029/2011JA016606/pdf

L. Contel, O. Leroy, P. Roux, A. Coillot, C. Alison et al., The search-coil magnetometer for MMS, Space Sci. Rev, vol.199, pp.257-282, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01552023

W. Li, M. Andre, Y. V. Khotyaintsev, A. Vaivads, D. B. Graham et al., Kinetic evidence of magnetic reconnection due to Kelvin-Helmholtz waves, Geophysical Research Letters, vol.184, issue.1-4, pp.5635-5643, 2016.
DOI : 10.1007/s11214-014-0108-9
URL : https://hal.archives-ouvertes.fr/insu-01352463

P. Lindqvist, G. Olsson, R. B. Torbert, B. King, M. Granoff et al., The Spin-Plane Double Probe Electric Field Instrument for MMS, Space Science Reviews, vol.36, issue.1-4, pp.137-165, 2014.
DOI : 10.1109/TPS.2008.2003134
URL : https://doi.org/10.1007/978-94-024-0861-4_6

S. Lundquist, Magnetohydrostatic field, Ark. Fys, pp.361-365, 1950.

T. W. Moore, K. Nykyri, and A. P. Dimmock, Cross-scale energy transport in space plasmas, Nature Physics, vol.11, issue.12, pp.1164-1169, 2016.
DOI : 10.1007/978-90-481-3499-1_1

T. K. Nakamura, W. Daughton, H. Karimabadi, and S. Eriksson, Three-dimensional dynamics of vortex-induced reconnection and comparison with THEMIS observations, Journal of Geophysical Research: Space Physics, vol.110, issue.A7, pp.5742-5757, 2013.
DOI : 10.1029/2005JA011150
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgra.50547

C. Norgren, A. Vaivads, Y. V. Khotyaintsev, A. , and M. , Lower Hybrid Drift Waves: Space Observations, Physical Review Letters, vol.109, issue.5, 2012.
DOI : 10.1029/98JA01104

M. Øieroset, T. D. Phan, J. P. Eastwood, M. Fujimoto, W. Daughton et al., Direct evidence for a threedimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause, Phys. Rev. Lett, vol.107, 2011.

T. D. Phan, G. Paschmann, J. T. Gosling, M. Oieroset, M. Fujimoto et al., and magnetic shear: Evidence from magnetopause observations, Geophysical Research Letters, vol.117, issue.1, pp.11-16, 2013.
DOI : 10.1029/2011JA016959
URL : http://onlinelibrary.wiley.com/doi/10.1029/2012GL054528/pdf

T. D. Phan, J. P. Eastwood, P. A. Cassak, M. Øieroset, J. T. Gosling et al., MMS observations of electron-scale filamentary currents in the reconnection exhaust and near the X line, Geophysical Research Letters, vol.2010, issue.1, pp.6060-6069, 2016.
DOI : 10.1007/s11214-014-0109-8

C. Pollock, T. Moore, and A. Jacques, Fast Plasma Investigation for Magnetospheric Multiscale, Space Science Reviews, vol.129, issue.1-4, pp.331-406, 2016.
DOI : 10.1007/s11214-007-9177-3
URL : https://doi.org/10.1007/978-94-024-0861-4_12

Z. Y. Pu, J. Raeder, J. Zhong, Y. V. Bogdanova, M. Dunlop et al., Magnetic topologies of an in vivo FTE observed by Double Star/TC-1 at Earth's magnetopause, Geophysical Research Letters, vol.117, issue.A11, pp.3502-3506, 2013.
DOI : 10.1029/2011JA017166
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/grl.50714

A. Roux, P. Robert, D. Fontaine, L. Contel, O. Canu et al., What is the nature of magnetosheath FTEs?, Journal of Geophysical Research: Space Physics, vol.35, issue.23, pp.4576-4595, 2015.
DOI : 10.1016/0032-0633(87)90046-8
URL : https://hal.archives-ouvertes.fr/hal-01551989

C. T. Russell and R. C. Elphic, Initial ISEE magnetometer results: Magnetopause observations, Space Sci. Rev, vol.22, pp.681-715, 1978.
DOI : 10.1007/978-94-009-9527-7_26

C. T. Russell, B. J. Anderson, W. Baumjohann, K. R. Bromund, D. Dearborn et al., The Magnetospheric Multiscale Magnetometers, Space Science Reviews, vol.8, issue.10, pp.189-256, 2014.
DOI : 10.1007/BF02962520
URL : https://doi.org/10.1007/978-94-024-0861-4_8

D. G. Sibeck, M. Kuznetsova, V. Angelopoulos, K. Glaßmeier, and J. P. Mcfadden, Crater FTEs: Simulation results and THEMIS observations, Geophysical Research Letters, vol.79, issue.17, pp.17-23, 2008.
DOI : 10.1029/2008GL033568
URL : http://onlinelibrary.wiley.com/doi/10.1029/2008GL033568/pdf

B. U. Sonnerup, G. Paschmann, I. Papamastorakis, N. Sckopke, G. Haerendel et al., Evidence for magnetic field reconnection at the Earth's magnetopause, Journal of Geophysical Research, vol.82, issue.A12, pp.10049-10067, 1981.
DOI : 10.1029/JA082i004p00699

W. Teh, T. K. Nakamura, R. Nakamura, W. Baumjohann, C. T. Russell et al., Evolution of a typical ion-scale magnetic flux rope caused by thermal pressure enhancement, Journal of Geophysical Research: Space Physics, vol.43, issue.A4, pp.2040-2050, 2017.
DOI : 10.1002/2016GL071568

R. A. Treumann, J. Labelle, and R. Pottelette, Plasma diffusion at the magnetopause: The case of lower hybrid drift waves, Journal of Geophysical Research: Space Physics, vol.21, issue.20, pp.16009-16013, 1991.
DOI : 10.1063/1.862321

R. Wang, Q. Lu, R. Nakamura, W. Baumjohann, C. T. Russell et al., Interaction of Magnetic Flux Ropes Via Magnetic Reconnection Observed at the Magnetopause, Journal of Geophysical Research: Space Physics, vol.103, issue.3, pp.10436-10447, 2017.
DOI : 10.1029/97JA00076

F. D. Wilder, R. E. Ergun, S. J. Schwartz, D. L. Newman, S. Eriksson et al., Observations of large-amplitude, parallel, electrostatic waves associated with the Kelvin-Helmholtz instability by the magnetospheric multiscale mission, Geophysical Research Letters, vol.19, issue.8, pp.8859-8866, 2016.
DOI : 10.5194/angeo-19-1721-2001

H. Zhang, K. K. Khurana, M. G. Kivelson, V. Angelopoulos, Z. Y. Pu et al., Modeling a force-free flux transfer event probed by multiple Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, Journal of Geophysical Research: Space Physics, vol.51, issue.1, pp.0-05, 2008.
DOI : 10.1016/S0032-0633(03)00116-8

H. Zhang, M. G. Kivelson, K. K. Khurana, J. Mcfadden, R. J. Walker et al., Evidence that crater flux transfer events are initial stages of typical flux transfer events, Journal of Geophysical Research: Space Physics, vol.113, issue.A1, p.8229, 2010.
DOI : 10.1029/2008JA013451
URL : http://onlinelibrary.wiley.com/doi/10.1029/2009JA015013/pdf

H. Zhang, M. G. Kivelson, V. Angelopoulos, K. K. Khurana, Z. Y. Pu et al., Generation and properties of in vivo flux transfer events, Journal of Geophysical Research: Space Physics, vol.116, issue.A12, p.5224, 2012.
DOI : 10.1029/2011JA016500
URL : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011JA017166

C. Zhao, C. T. Russell, R. J. Strangeway, S. M. Petrinec, W. R. Paterson et al., Force balance at the magnetopause determined with MMS: Application to flux transfer events, Geophysical Research Letters, vol.113, issue.1-4, pp.11941-11947, 2016.
DOI : 10.1029/2008ja013451