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Interplay between Kelvin–Helmholtz and lower-hybrid drift instabilities

Published online by Cambridge University Press:  08 November 2019

Jérémy Dargent*
Affiliation:
Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Pisa, Italy
Federico Lavorenti
Affiliation:
Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Pisa, Italy LPC2E, CNRS, Orléans, France
Francesco Califano
Affiliation:
Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Pisa, Italy
Pierre Henri
Affiliation:
LPC2E, CNRS, Orléans, France Laboratoire Lagrange, CNRS, Observatoire de la Cote d’Azur, Université Cote d’Azur, Nice, France
Francesco Pucci
Affiliation:
Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Belgium
Silvio S. Cerri
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
*
Email address for correspondence: jeremy.dargent@df.unipi.it

Abstract

Boundary layers in space and astrophysical plasmas are the location of complex dynamics where different mechanisms coexist and compete, eventually leading to plasma mixing. In this work, we present fully kinetic particle-in-cell simulations of different boundary layers characterized by the following main ingredients: a velocity shear, a density gradient and a magnetic gradient localized at the same position. In particular, the presence of a density gradient drives the development of the lower-hybrid drift instability (LHDI), which competes with the Kelvin–Helmholtz instability (KHI) in the development of the boundary layer. Depending on the density gradient, the LHDI can even dominate the dynamics of the layer. Because these two instabilities grow on different spatial and temporal scales, when the LHDI develops faster than the KHI an inverse cascade is generated, at least in two dimensions. This inverse cascade, starting at the LHDI kinetic scales, generates structures at scale lengths at which the KHI would typically develop. When that is the case, those structures can suppress the KHI itself because they significantly affect the underlying velocity shear gradient. We conclude that, depending on the density gradient, the velocity jump and the width of the boundary layer, the LHDI in its nonlinear phase can become the primary instability for plasma mixing. These numerical simulations show that the LHDI is likely to be a dominant process at the magnetopause of Mercury. These results are expected to be of direct impact to the interpretation of the forthcoming BepiColombo observations.

Type
Research Article
Copyright
© Cambridge University Press 2019 

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References

Bingham, R., Dawson, J. M. & Shapiro, V. D. 2002 Particle acceleration by lower-hybrid turbulence. J. Plasma Phys. 68 (3), 161172.Google Scholar
Brackbill, J. U., Forslund, D. W., Quest, K. B. & Winske, D. 1984 Nonlinear evolution of the lower-hybrid drift instability. Phys. Fluids 27 (11), 26822693.Google Scholar
Camporeale, E., Delzanno, G. L. & Colestock, P. 2012 Lower hybrid to whistler mode conversion on a density striation. J. Geophys. Res. 117, A10315.Google Scholar
Carter, T. A., Ji, H., Trintchouk, F., Yamada, M. & Kulsrud, R. M. 2001 Measurement of lower-hybrid drift turbulence in a reconnecting current sheet. Phys. Rev. Lett. 88, 015001.Google Scholar
Carter, T. A., Yamada, M., Ji, H., Kulsrud, R. M. & Trintchouk, F. 2002 Experimental study of lower-hybrid drift turbulence in a reconnecting current sheet. Phys. Plasmas 9 (8), 32723288.Google Scholar
Cerri, S. 2018 Finite-larmor-radius equilibrium and currents of the earths flank magnetopause. J. Plasma Phys. 84 (5), 555840501.Google Scholar
Cerri, S. S., Henri, P., Califano, F., Del Sarto, D., Faganello, M. & Pegoraro, F. 2013 Extended fluid models: pressure tensor effects and equilibria. Phys. Plasmas 20 (11), 112112.Google Scholar
Cerri, S. S., Pegoraro, F., Califano, F., Del Sarto, D. & Jenko, F. 2014 Pressure tensor in the presence of velocity shear: stationary solutions and self-consistent equilibria. Phys. Plasmas 21 (11), 112109.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.Google Scholar
Daughton, W. 2003 Electromagnetic properties of the lower-hybrid drift instability in a thin current sheet. Phys. Plasmas 10 (8), 31033119.Google Scholar
Daughton, W., Lapenta, G. & Ricci, P. 2004 Nonlinear evolution of the lower-hybrid drift instability in a current sheet. Phys. Rev. Lett. 93, 105004.Google Scholar
Davidson, R. C. 1978 Quasilinear stabilization of lower-hybrid-drift instability. Phys. Fluids 21 (8), 13751380.Google Scholar
Davidson, R. C., Gladd, N. T., Wu, C. S. & Huba, J. D. 1977 Effects of finite plasma beta on the lower-hybrid-drift instability. Phys. Fluids 20 (2), 301310.Google Scholar
De Camillis, S., Cerri, S. S., Califano, F. & Pegoraro, F. 2016 Pressure anisotropy generation in a magnetized plasma configuration with a shear flow velocity. Plasma Phys. Control. Fusion 58 (4), 045007.Google Scholar
Delamere, P. A., Wilson, R. J., Eriksson, S. & Bagenal, F. 2013 Magnetic signatures of Kelvin–Helmholtz vortices on Saturn’s magnetopause: global survey. J. Geophys. Res. 118, 393404.Google Scholar
Derouillat, J., Beck, A., Pérez, F., Vinci, T., Chiaramello, M., Grassi, A., Flé, M., Bouchard, G., Plotnikov, I., Aunai, N. et al. 2018 Smilei: a collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation. Comput. Phys. Commun. 222, 351373.Google Scholar
Drake, J. F., Gladd, N. T. & Huba, J. D. 1981 Magnetic field diffusion and dissipation in reversedfield plasmas. Phys. Fluids 24 (1), 7887.Google Scholar
Drake, J. F., Guzdar, P. N., Hassam, A. B. & Huba, J. D. 1984 Nonlinear mode coupling theory of the lower-hybrid-drift instability. Phys. Fluids 27 (5), 11481159.Google Scholar
Fadanelli, S., Faganello, M., Califano, F., Cerri, S. S., Pegoraro, F. & Lavraud, B. 2018 North–south asymmetric Kelvin–Helmholtz instability and induced reconnection at the earth’s magnetospheric flanks. J. Geophys. Res. 123 (11), 93409356.Google Scholar
Faganello, M. & Califano, F. 2017 Magnetized Kelvin–Helmholtz instability: theory and simulations in the earths magnetosphere context. J. Plasma Phys. 83 (6), 535830601.Google Scholar
Faganello, M., Califano, F. & Pegoraro, F. 2008a Competing mechanisms of plasma transport in inhomogeneous configurations with velocity shear: the solar-wind interaction with earth’s magnetosphere. Phys. Rev. Lett. 100, 015001.Google Scholar
Faganello, M., Califano, F. & Pegoraro, F. 2008b Numerical evidence of undriven, fast reconnection in the solar-wind interaction with earth’s magnetosphere: formation of electromagnetic coherent structures. Phys. Rev. Lett. 101, 105001.Google Scholar
Faganello, M., Califano, F. & Pegoraro, F. 2009 Being on time in magnetic reconnection. New J. Phys. 11 (6), 063008.Google Scholar
Fujimoto, M., Mukai, T., Kawano, H., Nakamura, M., Nishida, A., Saito, Y., Yamamoto, T. & Kokubun, S. 1998 Structure of the low-latitude boundary layer: a case study with geotail data. J. Geophys. Res. 103 (A2), 22972308.Google Scholar
Gary, S. P. 1983 Linear density drift instabilities in very low beta plasmas: a different approach. J. Plasma Phys. 30 (1), 7594.Google Scholar
Gary, S. P. 1993 Theory of Space Plasma Microinstabilities. Cambridge University Press.Google Scholar
Gary, S. P. & Sanderson, J. J. 1978 Density gradient drift instabilities: oblique propagation at zero beta. Phys. Fluids 21 (7), 11811187.Google Scholar
Gary, S. P. & Sanderson, J. J. 1979 Electrostatic temperature gradient drift instabilities. Phys. Fluids 22 (8), 15001509.Google Scholar
Gary, S. P. & Sgro, A. G. 1990 The lower hybrid drift instability at the magnetopause. Geophys. Res. Lett. 17 (7), 909912.Google Scholar
Gershman, D. J., Raines, J. M., Slavin, J. A., Zurbuchen, T. H., Sundberg, T., Boardsen, S. A., Anderson, B. J., Korth, H. & Solomon, S. C. 2015 MESSENGER observations of multiscale Kelvin–Helmholtz vortices at Mercury. J. Geophys. Res. 120, 43544368.Google Scholar
Gingell, P. W., Sundberg, T. & Burgess, D. 2015 The impact of a hot sodium ion population on the growth of the Kelvin–Helmholtz instability in mercury’s magnetotail. J. Geophys. Res. 120 (7), 54325442.Google Scholar
Graham, D. B., Khotyaintsev, Y. V., Vaivads, A., André, M. & Fazakerley, A. N. 2014 Electron dynamics in the diffusion region of an asymmetric magnetic reconnection. Phys. Rev. Lett. 112, 215004.Google Scholar
Graham, D. B., Khotyaintsev, Y. V., Vaivads, A., Norgren, C., André, M., Webster, J. M., Burch, J. L., Lindqvist, P.-A., Ergun, R. E., Torbert, R. B. et al. 2017 Instability of agyrotropic electron beams near the electron diffusion region. Phys. Rev. Lett. 119, 025101.Google Scholar
Guglielmi, A. V., Potapov, A. S. & Klain, B. I. 2010 Rayleigh–Taylor–Kelvin–Helmholtz combined instability at the magnetopause. Geomagn. Aeron. 50 (8), 958962.Google Scholar
Haaland, S., Reistad, J., Tenfjord, P., Gjerloev, J., Maes, L., DeKeyser, J., Maggiolo, R., Anekallu, C. & Dorville, N. 2014 Characteristics of the flank magnetopause: cluster observations. J. Geophys. Res. 119 (11), 90199037.Google Scholar
Hasegawa, H., Fujimoto, M., Maezawa, K., Saito, Y. & Mukai, T. 2003 Geotail observations of the dayside outer boundary region: interplanetary magnetic field control and dawn–dusk asymmetry. J. Geophys. Res. 108 (A4), 1163.Google Scholar
Hasegawa, H., Fujimoto, M., Phan, T. D., Rème, H., Balogh, A., Dunlop, M. W., Hashimoto, C. & TanDokoro, R. 2004 Transport of solar wind into Earth’s magnetosphere through rolled-up Kelvin–Helmholtz vortices. Nature 430 (7001), 755758.Google Scholar
Henri, P., Cerri, S. S., Califano, F., Pegoraro, F., Rossi, C., Faganello, M., Šebek, O., Trávníček, P. M., Hellinger, P. & Frederiksen, J. T. 2013 Nonlinear evolution of the magnetized Kelvin–Helmholtz instability: from fluid to kinetic modeling. Phys. Plasmas 20 (10), 102118.Google Scholar
Huba, J. D., Drake, J. F. & Gladd, N. T. 1980 Lower-hybrid-drift instability in field reversed plasmas. Phys. Fluids 23 (3), 552561.Google Scholar
Huba, J. D., Gladd, N. T. & Papadopoulos, K. 1978 Lower-hybrid-drift wave turbulence in the distant magnetotail. J. Geophys. Res. 83 (A11), 52175226.Google Scholar
Huba, J. D. & Ossakow, S. L. 1980 Influence of magnetic shear on the current convective instability in the diffuse aurora. J. Geophys. Res. 85 (A12), 68746876.Google Scholar
Kasaba, Y., Bougeret, J.-L., Blomberg, L., Kojima, H., Yagitani, S., Moncuquet, M., Trotignon, J.-G., Chanteur, G., Kumamoto, A., Kasahara, Y. et al. 2010 The plasma wave investigation (pwi) onboard the bepicolombo/mmo: first measurement of electric fields, electromagnetic waves, and radio waves around mercury. Planet. Space Sci. 58 (1), 238278; comprehensive Science Investigations of Mercury: the scientific goals of the joint ESA/JAXA mission BepiColombo.Google Scholar
Lapenta, G. & Brackbill, J. U. 2002 Nonlinear evolution of the lower hybrid drift instability: current sheet thinning and kinking. Phys. Plasmas 9 (5), 15441554.Google Scholar
Le, A., Daughton, W., Chen, L.-J. & Egedal, J. 2017 Enhanced electron mixing and heating in 3-d asymmetric reconnection at the earth’s magnetopause. Geophys. Res. Lett. 44 (5), 20962104.Google Scholar
Le, A., Daughton, W., Ohia, O., Chen, L.-J., Liu, Y.-H., Wang, S., Nystrom, W. D. & Bird, R. 2018 Drift turbulence, particle transport, and anomalous dissipation at the reconnecting magnetopause. Phys. Plasmas 25 (6), 062103.Google Scholar
Leroy, M. H. J. & Keppens, R. 2017 On the influence of environmental parameters on mixing and reconnection caused by the Kelvin–Helmholtz instability at the magnetopause. Phys. Plasmas 24 (1), 012906.Google Scholar
Liljeblad, E., Karlsson, T., Raines, J. M., Slavin, J. A., Kullen, A., Sundberg, T. & Zurbuchen, T. H. 2015 MESSENGER observations of the dayside low-latitude boundary layer in Mercury’s magnetosphere. J. Geophys. Res. 120 (10), 83878400.Google Scholar
Liljeblad, E., Sundberg, T., Karlsson, T. & Kullen, A. 2014 Statistical investigation of Kelvin–Helmholtz waves at the magnetopause of Mercury. J. Geophys. Res. 119, 96709683.Google Scholar
Malara, F., Pezzi, O. & Valentini, F. 2018 Exact hybrid vlasov equilibria for sheared plasmas with in-plane and out-of-plane magnetic field. Phys. Rev. E 97, 053212.Google Scholar
Masters, A., Achilleos, N., Cutler, J. C., Coates, A. J., Dougherty, M. K. & Jones, G. H. 2012 Surface waves on Saturn’s magnetopause. Planet. Space Sci. 65, 109121.Google Scholar
Matsumoto, Y. & Hoshino, M. 2004 Onset of turbulence induced by a Kelvin–Helmholtz vortex. Geophys. Res. Lett. 31, L02807.Google Scholar
Matsumoto, Y. & Hoshino, M. 2006 Turbulent mixing and transport of collisionless plasmas across a stratified velocity shear layer. J. Geophys. Res. 111, A05213.Google Scholar
Matsumoto, Y. & Seki, K. 2010 Formation of a broad plasma turbulent layer by forward and inverse energy cascades of the Kelvin–Helmholtz instability. J. Geophys. Res. 115, A10231.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolictangent velocity profile. J. Fluid Mech. 19 (4), 543556.Google Scholar
Miura, A. & Pritchett, P. L. 1982 Nonlocal stability analysis of the mhd Kelvin–Helmholtz instability in a compressible plasma. J. Geophys. Res. 87 (A9), 74317444.Google Scholar
Mozer, F. S. & Pritchett, P. L. 2011 Electron physics of asymmetric magnetic field reconnection. Space Sci. Rev. 158 (1), 119143.Google Scholar
Nakamura, T., Hasegawa, H., Daughton, W., Eriksson, S., Li, W. Y. & Nakamura, R. 2017 Turbulent mass transfer caused by vortex induced reconnection in collisionless magnetospheric plasmas. Nature Commun. 8 (1), 1582.Google Scholar
Nakamura, T. K. M. & Daughton, W. 2014 Turbulent plasma transport across the earth’s low-latitude boundary layer. Geophys. Res. Lett. 41 (24), 87048712.Google Scholar
Nakamura, T. K. M., Daughton, W., Karimabadi, H. & Eriksson, S. 2013 Three-dimensional dynamics of vortex-induced reconnection and comparison with THEMIS observations. J. Geophys. Res. 118 (9), 57425757.Google Scholar
Nakamura, T. K. M. & Fujimoto, M. 2005 Magnetic reconnection within rolled-up mhd-scale Kelvin–Helmholtz vortices: two-fluid simulations including finite electron inertial effects. Geophys. Res. Lett. 32, L21102.Google Scholar
Nakamura, T. K. M. & Fujimoto, M. 2008 Magnetic effects on the coalescence of Kelvin–Helmholtz vortices. Phys. Rev. Lett. 101, 165002.Google Scholar
Nakamura, T. K. M., Hasegawa, H. & Shinohara, I. 2010 Kinetic effects on the Kelvin–Helmholtz instability in ion-to-magnetohydrodynamic scale transverse velocity shear layers: particle simulations. Phys. Plasmas 17 (4), 042119.Google Scholar
Norgren, C., Vaivads, A., Khotyaintsev, Y. V. & André, M. 2012 Lower hybrid drift waves: space observations. Phys. Rev. Lett. 109, 055001.Google Scholar
Paral, J. & Rankin, R. 2013 Dawn–dusk asymmetry in the Kelvin–Helmholtz instability at Mercury. Nature Commun. 4, 1645.Google Scholar
Price, L., Swisdak, M., Drake, J. F., Cassak, P. A., Dahlin, J. T. & Ergun, R. E. 2016 The effects of turbulence on threedimensional magnetic reconnection at the magnetopause. Geophys. Res. Lett. 43 (12), 60206027.Google Scholar
Pritchett, P. L. & Coroniti, F. V. 1984 The collisionless macroscopic Kelvin–Helmholtz instability: 1. Transverse electrostatic mode. J. Geophys. Res. 89 (A1), 168178.Google Scholar
Pritchett, P. L., Mozer, F. S. & Wilber, M. 2012 Intense perpendicular electric fields associated with three-dimensional magnetic reconnection at the subsolar magnetopause. J. Geophys. Res. 117, A06212.Google Scholar
Roytershteyn, V., Daughton, W., Karimabadi, H. & Mozer, F. S. 2012 Influence of the lower-hybrid drift instability on magnetic reconnection in asymmetric configurations. Phys. Rev. Lett. 108, 185001.Google Scholar
Roytershteyn, V., Dorfman, S., Daughton, W., Ji, H., Yamada, M. & Karimabadi, H. 2013 Electromagnetic instability of thin reconnection layers: comparison of three-dimensional simulations with MRX observations. Phys. Plasmas 20 (6), 061212.Google Scholar
Sgro, A. G., Peter Gary, S. & Lemons, D. S. 1989 Expanding plasma structure and its evolution toward long wavelengths. Phys. Fluids B 1 (9), 18901899.Google Scholar
Shapiro, V. D., Shevchenko, V. I., Cargill, P. J. & Papadopoulos, K. 1994 Modulational instability of lower hybrid waves at the magnetopause. J. Geophys. Res. 99 (A12), 2373523740.Google Scholar
Singh, N. & Leung, W. C. 1998 Numerical simulation of plasma processes occurring in the ram region of the tethered satellite. Geophys. Res. Lett. 25 (5), 741744.Google Scholar
Slavin, J. A., Acuña, M. H., Anderson, B. J., Baker, D. N., Benna, M., Gloeckler, G., Gold, R. E., Ho, G. C., Killen, R. M., Korth, H. et al. 2008 Mercury’s magnetosphere after messenger’s first flyby. Science 321 (5885), 8589.Google Scholar
Sundberg, T., Boardsen, S. A., Slavin, J. A., Anderson, B. J., Korth, H., Zurbuchen, T. H., Raines, J. M. & Solomon, S. C. 2012 MESSENGER orbital observations of large-amplitude Kelvin–Helmholtz waves at Mercury’s magnetopause. J. Geophys. Res. 117, A04216.Google Scholar
Takagi, K., Hashimoto, C., Hasegawa, H., Fujimoto, M. & TanDokoro, R. 2006 Kelvin–Helmholtz instability in a magnetotail flank-like geometry: three-dimensional mhd simulations. J. Geophys. Res. 111, A08202.Google Scholar
Umeda, T., Miwa, J.-i, Matsumoto, Y., Nakamura, T. K. M., Togano, K., Fukazawa, K. & Shinohara, I. 2010 Full electromagnetic vlasov code simulation of the Kelvin–Helmholtz instability. Phys. Plasmas 17 (5), 052311.Google Scholar
Umeda, T., Ueno, S. & Nakamura, T. K. M. 2014 Ion kinetic effects on nonlinear processes of the Kelvin–Helmholtz instability. Plasma Phys. Control. Fusion 56 (7), 075006.Google Scholar
Yoo, J., Jara-Almonte, J., Yerger, E., Wang, S., Qian, T., Le, A., Ji, H., Yamada, M., Fox, W., Kim, E.-H. et al. 2018 Whistler wave generation by anisotropic tail electrons during asymmetric magnetic reconnection in space and laboratory. Geophys. Res. Lett. 45 (16), 80548061.Google Scholar
Yoo, J., Na, B., Jara-Almonte, J., Yamada, M., Ji, H., Roytershteyn, V., Argall, M. R., Fox, W. & Chen, L.-J. 2017 Electron heating and energy inventory during asymmetric reconnection in a laboratory plasma. J. Geophys. Res. 122 (9), 92649281.Google Scholar
Yoo, J., Wang, S., Yerger, E., Jara-Almonte, J., Ji, H., Yamada, M., Chen, L.-J., Fox, W., Goodman, A. & Alt, A. 2019 Whistler wave generation by electron temperature anisotropy during magnetic reconnection at the magnetopause. Phys. Plasmas 26 (5), 052902.Google Scholar
Yoo, J., Yamada, M., Ji, H., Jara-Almonte, J., Myers, C. E. & Chen, L.-J. 2014 Laboratory study of magnetic reconnection with a density asymmetry across the current sheet. Phys. Rev. Lett. 113, 095002.Google Scholar
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