Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-20T07:21:06.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of plasma cylinder with current in a helical plasma flow

Published online by Cambridge University Press:  19 March 2018

Anatoly S. Leonovich ,
Daniil A. Kozlov  and
Qiugang Zong
Anatoly S. Leonovich*
Affiliation:
Institute of Solar-Terrestrial Physics SB RAS, p. o. box 291, Irkutsk, 664033, Russia
Daniil A. Kozlov
Affiliation:
Institute of Solar-Terrestrial Physics SB RAS, p. o. box 291, Irkutsk, 664033, Russia
Qiugang Zong
Affiliation:
Institute of Space Physics and Applied Technology, Peking University, Beijing, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Stability of a plasma cylinder with a current wrapped by a helical plasma flow is studied. Unstable surface modes of magnetohydrodynamic (MHD) oscillations develop at the boundary of the cylinder enwrapped by the plasma flow. Unstable eigenmodes can also develop for which the plasma cylinder is a waveguide. The growth rate of the surface modes is much higher than that for the eigenmodes. It is shown that the asymmetric MHD modes in the plasma cylinder are stable if the velocity of the plasma flow is below a certain threshold. Such a plasma flow velocity threshold is absent for the symmetric modes. They are unstable in any arbitrarily slow plasma flows. For all surface modes there is an upper threshold for the flow velocity above which they are stable. The helicity index of the flow around the plasma cylinder significantly affects both the Mach number dependence of the surface wave growth rate and the velocity threshold values. The higher the index, the lower the upper threshold of the velocity jump above which the surface waves become stable. Calculations have been carried out for the growth rates of unstable oscillations in an equilibrium plasma cylinder with current serving as a model of the low-latitude boundary layer (LLBL) of the Earth’s magnetic tail. A tangential discontinuity model is used to simulate the geomagnetic tail boundary. It is shown that the magnetopause in the geotail LLBL is unstable to a surface wave (having the highest growth rate) in low- and medium-speed solar wind flows, but becomes stable to this wave in high-speed flows. However, it can remain weakly unstable to the radiative modes of MHD oscillations.

Keywords

plasma instabilitiesplasma wavesspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 905840203
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agapitov, O., Glassmeier, K.-H., Plaschke, F., Auster, H.-U., Constantinescu, D., Angelopoulos, V., Magnes, W., Nakamura, R., Carlson, C. W., Frey, S. et al. 2009 Surface waves and field line resonances: a THEMIS case study. J. Geophys. Res. 114, A00C27.Google Scholar
Chen, L. & Hasegawa, A. 1974 A theory of long-period magnetic pulsations: 1. Steady state excitation of field line resonance. J. Geophys. Res. 79, 1024–1032.CrossRefGoogle Scholar
Dmitrienko, I. S. 2013 Evolution of FMS and Alfven waves produced by the initial disturbance in the FMS waveguide. J. Plasma Phys. 79, 7–17.CrossRefGoogle Scholar
Eastman, T. E. & Hones, E. W. Jr. 1979 Characteristics of the magnetospheric boundary layer and magnetopause layer as observed by Imp 6. J. Geophys. Res. 84, 2019–2028.Google Scholar
Forbes, T. G. & Priest, E. R. 1995 Photospheric magnetic field evolution and eruptive flares. Astrophys. J. 446, 377.Google Scholar
Gerjuoy, E. & Rosenbluth, M. N. 1961 Pinch with rotating plasma. Phys. Fluids 4, 112–122.Google Scholar
Guglielmi, A. V. & Potapov, A. S. 1994 Note on the dependence of Pc3-4 activity on the solar wind velocity. Ann. Geophys. 12, 1192–1196.Google Scholar
Kelvin, Lord (W. Thomson) 1871 Hydrokinetic solutions and observations. Phil. Mag. 42, 451–462.Google Scholar
Kivelson, M. G. & Pu, Z.-Y. 1984 The Kelvin–Helmholtz instability on the magnetopause. Planet. Space Sci. 32, 1335–1341.Google Scholar
Klimushkin, D. Y., Mager, P. N. & Glassmeier, K.-H. 2012 Spatio-temporal structure of Alfvén waves excited by a sudden impulse localized on an L-shell. Ann. Geophys. 30, 1099–1106.CrossRefGoogle Scholar
Kozlov, D. A. 2010 Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere. J. Atmos. Sol.-Terr. Phys. 72, 1348–1353.CrossRefGoogle Scholar
Landau, L. D. 1944 Stability of tangential discontinuities in compressible fluid. Dokl. Akad. Nauk S.S.S.R. 44, 139–142.Google Scholar
Leonovich, A. S. 2011 MHD-instability of the magnetotail: global modes. Planet. Space Sci. 59, 402–411.Google Scholar
Leonovich, A. S. 2012 Wave mechanism of the magnetospheric convection. Planet. Space Sci. 65, 67–75.Google Scholar
Leonovich, A. S. & Kozlov, D. A. 2009 Alfvenic and magnetosonic resonances in a nonisothermal plasma. Plasma Phys. Control. Fusion 51 (8), 085007.Google Scholar
Leonovich, A. S. & Mazur, V. A. 1989 Resonance excitation of standing Alfvén waves in an axisymmetric magnetosphere (nonstationary oscillations). Planet. Space Sci. 37, 1109–1116.CrossRefGoogle Scholar
Leonovich, A. S. & Mazur, V. A. 1993 A theory of transverse small-scale standing Alfven waves in an axially symmetric magnetosphere. Planet. Space Sci. 41, 697–717.CrossRefGoogle Scholar
Leonovich, A. S. & Mazur, V. A. 2001 On the spectrum of magnetosonic eigenoscillations of an axisymmetric magnetosphere. J. Geophys. Res. 106, 3919–3928.Google Scholar
Leonovich, A. S., Mazur, V. A. & Kozlov, D. A. 2016 MHD Oscillations in the Earth’s Magnetotail. In Low-Frequency Waves in Space Plasm (ed. Keiling, A., Lee, D.-H. & Nakariakov, V.), Geophysical Monograph Series, vol. 216, pp. 161–179. Wiley.Google Scholar
Leonovich, A. S. & Mishin, V. V. 2005 Stability of magnetohydrodynamic shear flows with and without bounding walls. J. Plasma Phys. 71, 645–664.Google Scholar
Mann, I. R. & Wright, A. N. 1999 Diagnosing the excitation mechanisms of Pc5 magnetospheric flank waveguide modes and FLRs. Geophys. Res. Lett. 26, 2609–2612.Google Scholar
Mann, I. R., Wright, A. N., Mills, K. J. & Nakariakov, V. M. 1999 Excitation of magnetospheric waveguide modes by magnetosheath flows. J. Geophys. Res. 104, 333–354.Google Scholar
Mazur, V. A. & Chuiko, D. A. 2011 Excitation of a magnetospheric MHD cavity by Kelvin–Helmholtz instability. Plasma Phys. Rep. 37, 913–934.Google Scholar
Mazur, V. A. & Chuiko, D. A. 2013 Influence of the outer-magnetospheric magnetohydrodynamic waveguide on the reflection of hydromagnetic waves from a shear flow at the magnetopause. Plasma Phys. Rep. 39, 959–975.Google Scholar
Mazur, V. A. & Leonovich, A. S. 2006 ULF hydromagnetic oscillations with the discrete spectrum as eigenmodes of MHD-resonator in the near-Earth part of the plasma sheet. Ann. Geophys. 24, 1639–1648.Google Scholar
McKenzie, J. F. 1970a Hydromagnetic oscillations of the geomagnetic tail and plasma sheet. J. Geophys. Res. 75, 5331–5339.Google Scholar
McKenzie, J. F. 1970b Hydromagnetic wave interaction with the magnetopause and the bow shock. Planet. Space Sci. 18, 1–23.CrossRefGoogle Scholar
Mills, K. J., Longbottom, A. W., Wright, A. N. & Ruderman, M. S. 2000 Kelvin–Helmholtz instability on the magnetospheric flanks: an absolute and convective instability approach. J. Geophys. Res. 105, 27685–27700.Google Scholar
Mishin, V. V. 1981 On the MHD instability of the earth’s magnetopause and its geophysical effects. Planet. Space Sci. 29, 359–363.Google Scholar
Mishin, V. V. & Morozov, A. G. 1983 On the effect of oblique disturbances on Kelvin–Helmholtz instability at magnetospheric boundary layers and in solar wind. Planet. Space Sci. 31, 821–828.Google Scholar
Miura, A. 1984 Anomalous transport by magnetohydrodynamic Kelvin–Helmholtz instabilities in the solar wind-magnetosphere interaction. J. Geophys. Res. 89, 801–818.Google Scholar
Miura, A. 1992 Kelvin–Helmholtz instability at the magnetospheric boundary – dependence on the magnetosheath sonic Mach number. J. Geophys. Res. 97, 10655–10675.CrossRefGoogle Scholar
Miura, A. & Pritchett, P. L. 1982 Nonlocal stability analysis of the MHD Kelvin–Helmholtz instability in a compressible plasma. J. Geophys. Res. 87, 7431–7444.Google Scholar
Nakariakov, V. M., Pilipenko, V., Heilig, B., Jelínek, P., Karlický, M., Klimushkin, D. Y., Kolotkov, D. Y., Lee, D.-H., Nisticò, G., Van Doorsselaere, T. et al. 2016 Magnetohydrodynamic Oscillations in the Solar Corona and Earth’s Magnetosphere: towards Consolidated Understanding. Space Sci. Rev. 200, 75–203.Google Scholar
Rajaram, R., Sibeck, D. G. & McEntire, R. W. 1991 Linear theory of the Kelvin–Helmholtz instability in the low-latitude boundary layer. J. Geophys. Res. 96, 9615–9625.Google Scholar
Sen, A. K. 1964 Effect of compressibility on Kelvin–Helmholtz instability in a plasma. Phys. Fluids 7, 1293–1298.Google Scholar
Southwood, D. J. 1968 The hydromagnetic stability of the magnetospheric boundary. Planet. Space Sci. 16, 587–605.CrossRefGoogle Scholar
Southwood, D. J. 1974 Some features of field line resonances in the magnetosphere. Planet. Space Sci. 22, 483–491.Google Scholar
Syrovatsky, S. I. 1954 Instability of tangential discontinuities in a compressible medium. Zh. Eksp. Teor. Fiz. 27, 121–123.Google Scholar
Titov, V. S. & Démoulin, P. 1999 Basic topology of twisted magnetic configurations in solar flares. Astron. Astrophys. 351, 707–720.Google Scholar
Turkakin, H., Mann, I. R. & Rankin, R. 2014 Kelvin–Helmholtz unstable magnetotail flow channels: deceleration and radiation of MHD waves. Geophys. Res. Lett. 41, 3691–3697.CrossRefGoogle Scholar
Turkakin, H., Rankin, R. & Mann, I. R. 2013 Primary and secondary compressible Kelvin–Helmholtz surface wave instabilities on the Earth’s magnetopause. J. Geophys. Res. 118, 4161–4175.CrossRefGoogle Scholar
Velikovich, A. L. & Davis, J. 1995 Implosions, equilibria, and stability of rotating, radiating Z-pinch plasmas. Phys. Plasmas 2, 4513–4520.Google Scholar
Volwerk, M., Glassmeier, K.-H., Nakamura, R., Takada, T., Baumjohann, W., Klecker, B., Rème, H., Zhang, T. L., Lucek, E. & Carr, C. M. 2007 Flow burst-induced Kelvin–Helmholtz waves in the terrestrial magnetotail. Geophys. Res. Lett. 34, 10102.Google Scholar
Walker, A. D. M. 1981 The Kelvin–Helmholtz instability in the low-latitude boundary layer. Planet. Space Sci. 29, 1119–1133.Google Scholar
Wang, C.-P., Lyons, L. R., Weygand, J. M., Nagai, T. & McEntire, R. W. 2006 Equatorial distributions of the plasma sheet ions, their electric and magnetic drifts, and magnetic fields under different interplanetary magnetic field $B_{z}$ conditions. J. Geophys. Res. 111, A04215.Google Scholar
Wright, A. N., Mills, K. J., Ruderman, M. S. & Brevdo, L. 2000 The absolute and convective instability of the magnetospheric flanks. J. Geophys. Res. 105, 385–394.Google Scholar