Hostname: page-component-5c6d5d7d68-ckgrl Total loading time: 0 Render date: 2024-08-09T00:21:54.105Z Has data issue: false hasContentIssue false
  • English
  • Français

On nonlinear waves in Hall–MHD plasma

Published online by Cambridge University Press:  01 October 2008

R. MITEVA  and
G. MANN
R. MITEVA
Affiliation:
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, Potsdam, D-14482, Germany (rmiteva@aip.de, gmann@aip.de)
G. MANN
Affiliation:
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, Potsdam, D-14482, Germany (rmiteva@aip.de, gmann@aip.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

Low-frequency magnetic field fluctuations are observed in space plasmas, e.g. as upstream waves at the Earth's bow shock. Such upstream waves can steepen into very large amplitude wave phenomena, e.g. short large-amplitude magnetic structures (or SLAMS for short), shocklets or discrete wave packets. Such observations motivated us to study the nonlinear behavior of low-frequency and large-amplitude plasma waves in terms of the full nonlinear Hall–MHD framework. In the case of stationary (nonlinear) waves, the Hall–MHD equations can be rewritten in the so-called Sakai–Sonnerup system of equations that describe this plasma state and provide oscillatory and solitary types of solutions. An overall parameter study on the polarization characteristics, together with the magnetic field components and density variations of the different ranges of solutions, is presented here. These results can be further on applied to the theoretical treatment of particle interaction with such waves, e.g. at shocks in space plasmas, possibly leading to particle acceleration.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 5 , October 2008 , pp. 607 - 628
Copyright
Copyright © Cambridge University Press 2008

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

Akimoto, K., Winske, D., Onsager, T. G., Thomsen, M. F. and Gary, S. P. 1991 Steepening of parallel propagating hydromagnetic waves into magnetic pulsations – a simulation study. J. Geophys. Res. 96, 17 599–17 607.CrossRefGoogle Scholar
Baumgärtel, K. 1999 Soliton approach to magnetic holes. J. Geophys. Res. 104, 28 295–28 308.CrossRefGoogle Scholar
Fairfield, D. H. and Behannon, K. W. 1976 Bow shock and magnetosheath waves at Mercury. J. Geophys. Res. 81, 3897–3906.CrossRefGoogle Scholar
Goldstein, M. L., Smith, C. W. and Matthaeus, W. H. 1983 Large amplitude MHD waves upstream of the Jovian bow shock. J. Geophys. Res. 88, 9989–9999.CrossRefGoogle Scholar
Gurnett, D. A. 1985 Plasma Waves and Instabilities (Geophysical Monograph Series, 35). Washington DC: American Geophysical Union, pp. 207–224.Google Scholar
Hoppe, M. and Russell, C. T. 1981 On the nature of ULF waves upstream of planetary bow shocks. Adv. Space Res. 1, 327–332.CrossRefGoogle Scholar
Hoppe, M. and Russell, C. T. 1983 Plasma rest frame frequencies and polarizations of the low-frequency upstream waves—ISEE 1 and 2 observations. J. Geophys. Res. 88, 2021–2027.CrossRefGoogle Scholar
Hoppe, M. M., Russell, C. T., Frank, L. A., Eastman, T. E. and Greenstadt, E. W. 1981 Upstream hydromagnetic waves and their association with backstreaming ion populations—ISEE 1 and 2 observations. J. Geophys. Res. 86, 4471–4492.CrossRefGoogle Scholar
Huba, J. D. 1995 Hall magnetohydrodynamics in space and laboratory plasmas. Phys. Plasmas 2, 2504–2513.CrossRefGoogle Scholar
Mann, G. and Lühr, H. 1991 Comparison of low frequency magnetic field fluctuations upstream of earth's bow shock with a strong Alfvénic turbulence model. Ann. Geophys. 9, 681–689.Google Scholar
Mann, G., Lühr, H. and Baumjohann, W. 1994 Statistical analysis of short large-amplitude magnetic field structures in the vicinity of the quasi-parallel bow shock. J. Geophys. Res. 99, 13315–13323.CrossRefGoogle Scholar
McKenzie, J. F. and Doyle, T. B. 2002 The properties of fast and slow oblique solitons in a magnetized plasma. Phys. Plasmas 9, 55–63.CrossRefGoogle Scholar
Mjølhus, E. 2006 Velocity–amplitude relationships and polarizations in families of MHD solitary waves. Phys. Scr. T 122, 135–153.CrossRefGoogle Scholar
Miteva, R. and Mann, G. 2007 On the electron acceleration at shock waves in the solar corona. Astron. Astrophys. 474, 617–625.CrossRefGoogle Scholar
Paschmann, G., Sckopke, N., Bame, S. J., Asbridge, J. R., Gosling, J. T., Russell, C. T. and Greenstadt, E. W. 1979 Association of low-frequency waves with suprathermal ions in the upstream solar wind. J. Geophys. Res. 6, 209–212.Google Scholar
Riedler, W., Schwingenschuh, K., Yeroshenko, Y. G., Styashkin, V. A. and Russell, C. T. 1986 Magnetic field observations in Comet Halley's coma. Nature 321, 288–289.CrossRefGoogle Scholar
Sakai, J.-I. and Sonnerup, U. O. 1983 Modulational instability of finite amplitude dispersive Alfvén waves. J. Geophys. Res. 88, 9069–9079.CrossRefGoogle Scholar
Scholer, M. 1993 Upstream waves, shocklets, short large-amplitude magnetic structures and the cyclic behavior of oblique quasi-parallel collisionless shocks. J. Geophys. Res. 98, 47–57.CrossRefGoogle Scholar
Scholer, M., Trattner, K. J. and Kucharek, H. 1992 Ion injection and Fermi acceleration at earth's bow shock—the 1984 September 12 event revisited. Astrophys. J. 395, 675–681.CrossRefGoogle Scholar
Schwartz, S. J. and Burgess, D. 1991 Quasi-parallel shocks—a patchwork of three-dimensional structures. Geophys. Res. Lett. 18, 373–376.CrossRefGoogle Scholar
Stasiewicz, K. 2004 Theory and observations of slow-mode solitons in space plasmas. Phys. Rev. Lett. 93, 125 004(1–4).CrossRefGoogle ScholarPubMed
Tsurutani, B. T., Brinca, A. L., Smith, E. J., Thorne, R. M., Scarfe, F. L., Gosling, J. T. and Ipavich, F. M. 1987a Magnetohydrodynamic waves detected by ice at distances equal-to 280,000,000-kilometers from comet p/Halley—cometary or solar wind origin. Astron. Astrophys. 187, 97–102.Google Scholar
Tsurutani, B. T., Smith, E. J., Thorne, R. M., Gosling, J. T. and Matsumoto, H. 1987b Steepened magnetosonic waves at Comet Giacobini-Zinner. J. Geophys. Res. 92, 11074–11082.CrossRefGoogle Scholar
Tsurutani, B. T., Ho, C. M., Arballo, J. K., Goldstein, B. E. and Balogh, A. 1995 Large amplitude IMF fluctuations in corotating interaction regions: Ulysses at midlatitudes. Geophys. Res. Lett. 22, 3397–3400.CrossRefGoogle Scholar