Astrophysics and Space Sciences Transactions www.astrophys-space-sci-trans.net 1810-6528 1810-6536 3 1 2007 10.5194/astra-3-15-2007 http://www.astrophys-space-sci-trans.net/3/15/2007/ http://www.astrophys-space-sci-trans.net/3/15/2007/astra-3-15-2007.html http://www.astrophys-space-sci-trans.net/3/15/2007/astra-3-15-2007.pdf 15 20 2007-09-07 Necessary conditions for the generation of acoustic solitons in magnetospheric and space plasmas with hot ions F. Verheest Frank.Verheest@UGent.be M. A. Hellberg G. S. Lakhina Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B–9000 Gent, Belgium School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410 218, India Necessary conditions are discussed for the possible generation of large solitary acoustic modes in plasmas with one or more ion species which are hotter than some or all of the electron species. The analysis is based on a fluid dynamic approach. It is found that in most of these configurations the existence ranges for the solitary wave velocities are very narrow and close to one of the thermal velocities. In the latter situation, linear Landau damping may prevent the generation of nonlinear structures. The analysis indicates that both inertial and thermal effects for the ions need to be kept in the description, thus rendering an analytical investigation much more intricate. %Ablowitz, M. J. and Clarkson, P. A.: %\textitSolitons, Nonlinear Evolution Equations and Inverse Scattering %(Cambridge University Press, Cambridge, UK, 1991). Bale, S. D., Kellogg, P. J., Larson, D. E., Lin, R. P., Goetz, K., and Lepping, R. P.: Bipolar electrostatic structures in the shock transition region: Evidence of electron phase space holes, Geophys. Res. Lett., 25, 2929-2932, 1998. % %Baumjohann, W., Treumann, R. A., Georgescu, E., Haerendel, G., % Fornacon, K.-H. and Auster, U.: %Wave form and packet structure of lion roars, %Ann. Geophys., 17, 1528–1534, 1999. Berthomier, M., Pottelette, R., Malingre, M., and Khotyaintsev, Yu.: Electron-acoustic solitons in an electron-beam plasma system, Phys. Plasmas, 7, 2987–2994, 2000. Bounds, S. R., Pfaff, R. F., Knowlton, S. F., Mozer, F. S., Temerin,~M A., and Kletzing,~C A.: Solitary potential structures associated with ion and electron beams near 1 RE altitudes, J. Geophys. Res., 104, 28709–28718, 1999. % %Buti, B.: %Non-linear electron-acoustic waves in a multi-species plasma, %J. Plasma Phys., 24, 169–180, 1980. Cattaert, T., Verheest, F., and Hellberg, M. A.: Potential hill electron-acoustic solitons and double layers in plasmas with two electron species, Phys. Plasmas, 12, 042901, 2005. % %Cattell, C. A., Dombeck, J., Wygant, J. R., Hudson, M. K., Mozer, F. S., % Temerin, M. A., Peterson, W. K., Kletzing, C. A., Russell, C. T. and % Pfaff, R. F.: %Comparisons of Polar satellite observations of solitary wave velocities in % the plasma sheet boundary and the high altitude cusp to those in the % auroral zone, %Geophys. Res. Lett., 26, 425–428, 1999. % % %Cattell, C., Neiman, C., Dombeck, J., Crumley, J., Wygant, J., % Kletzing, C. A., Peterson, W. K., Mozer, F. S. and André, M.: %Large amplitude solitary waves in and near the Earth's magnetosphere, % magnetopause and bow shock: Polar and Cluster observations, %Nonlin. Proc. Geophys., 10, 13–26, 2003. % % %Chen, F. F., %\textitIntroduction to Plasma Physics %(Plenum Press, New York, 1974), pp. 65–66. Dubouloz, N., Pottelette, R., Malingre, M., and Treumann, R. A.: Generation of broadband electrostatic noise by electron acoustic solitons, Geophys. Res. Lett., 18, 155–158, 1991. % %Ergun, R. E., Carlson, C. W., McFadden, J. P., Mozer, F. S., % Delory, G. T., Peria, W., Chaston, C. C., Temerin, M., Roth, I., % Muschietti, L., Elphic, R., Strangeway, R., Pfaff, R., Cattell, C. A., % Klumpar, D., Shelley, E., Peterson, W., Möbius, E. and Kistler, L.: %FAST satellite observations of large-amplitude solitary structures, %Geophys. Res. Lett., 25, 2041–2044, 1998. Franz, J. R., Kintner, P. M., and Pickett, J.S.: POLAR observations of coherent electric field structures, Geophys. Res. Lett., 25, 1277–1280, 1998. % %Hackenberg, P., Mann, G. and Marsch, E.: %Solitons in multi-ion plasmas, %J. Plasma Phys., 60, 845–859, 1998. % % %Hellberg, M. A., Baboolal, S., Mace, R. L. and Bharuthram, R.: %The role of self-consistency in double-layer calculations, %IEEE Trans. Plasma Sci., 20, 695–700, 1992. Hellberg, M. A., Verheest, F., and Cattaert, T.: Existence domains for nonlinear structures in complex two-ion-temperature plasmas, J. Phys. A: Math. Gen., 39, 3137–3146, 2006. Kakad, A. P., Singh, S. V., Reddy, R. V., Lakhina, G. S., Tagare,~S G., and Verheest, F.: Generation mechanism for electron acoustic solitary waves, Phys. Plasmas, 14, 052305 (2007). Mace, R. L. and Hellberg, M. A.: Dust-acoustic double layers: Ion inertial effects, Planet. Space Sci., 41, 235–244, 1993. Mace, R. L. and Hellberg, M. A.: The Korteweg-de Vries-Zakharov-Kuznetsov equation for electron-acoustic waves, Phys. Plasmas, 8, 2649–2656, 2001. Mace, R. L., Baboolal, S., Bharuthram, R., and Hellberg, M. A.: Arbitrary-amplitude electron-acoustic solitons in a two-electron-component plasma, J. Plasma Phys., 45, 323–338, 1991. % %Mace, R. L., McKenzie, J. F. and Webb, G. M.: %Conservation laws for steady flow and solitons in a multi-fluid %plasma revisited, %Phys. Plasmas, 14, 012310, 2007. Matsumoto, H., Kojima, H., Miyatake, T., Omura, Y., Okada, M., Nagano, I., and Tsutsui M.: Electrostatic Solitary Waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL, Geophys. Res. Lett., 21, 2915–2918, 1994. McKenzie, J.F., Dubinin, E., Sauer, K., and Doyle, T.B.: The application of the constants of the motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic point of view, J. Plasma Phys., 70, 431–462 (2004). Onsager, T. G., Thomsen, M. F., Elphic, R. C., Gosling, J. T., Anderson, R. R., and Kettmann, G.: Electron generation of electrostatic waves in the plasma sheet boundary layer, J. Geophys. Res., 98, 15509–15520, 1993. Parks, G. K., McCarthy, M., Fitzenreiter, R. J., Etcheto, J., Anderson, K. A., Anderson, R. R., Eastman, T. E., Frank, L. A., Gurnett, D. A., Huang, C., Lin, R. P., Lui, A. T. Y., Ogilvie, K. W., Pedersen, A., Rème, H., and Williams, D. J.: Particle and field characteristics of the high latitude plasma sheet boundary layer, J. Geophys. Res., 89, 8885–8906, 1984. % %Paschmann, G., Haerendel, G., Sckopke, N., Möbius, E., Luhr, H. and % Carlson, C. W.: %Three-dimensional plasma structures with anomalous flow directions near % the Earth's bow shock, %J. Geophys. Res., 93, 11279–11294, 1988. % % %Petkaki, P. and Dougherty, M.: %Waves close to the crossover frequency in the Jovian middle magnetosphere, %Geophys. Res. Lett., 28, 211–214, 2001. Pickett, J. S., Menietti, J. D., Gurnett, D. A., Tsurutani, B., Kintner,~P M., Klatt,~E., and Balogh,~A.: Solitary potential structures observed in the magnetosheath by the Cluster spacecraft, Nonlin.\vadjust Proc. Geophys., 10, 3–11, 2003. % %Pickett, J. S., Kahler, S. W., Chen, L.-J., Huff, R. L., Santolik, O., % Khotyaintsev, Y., Décréau, P. M. E., Winningham, D., Frahm, R., % Goldstein, M. L., Lakhina, G. S., Tsurutani, B. T., Lavraud, B., % Gurnett, D. A., André, M., Fazakerley, A., Balogh, A. and Rème, H.: %Solitary waves observed in the auroral zone: the Cluster multi-spacecraft % perspective, %Nonlin. Proc. Geophys., 11, 183–196, 2004. % % %Pottelette, R., Ergun, R. E., Treumann, R. A., Berthomier, M., % Carlson, C. W., McFadden, J. P. and Roth, I.: %Modulated electron-acoustic waves in auroral density cavities: FAST % observations, %Geophys. Res. Lett., 26, 2629–2632, 1999. Rice, W. K. M., Hellberg, M. A., Mace, R. L., and Baboolal, S.: Finite electron mass effects on the existence of ion-acoustic solitons in a two electron temperature plasma, Phys. Lett. A, 174, 416–420, 1993. % %Sagdeev, R.Z.: %Cooperative phenomena and shock waves in collisionless plasmas, %in: \textitReviews of Plasma Physics, vol. 4 %(Ed. M.A. Leontovich, Consultants Bureau, New York, 1966) pp. 23–91. % % %Schwartz, S. J., Kessel, R. L., Brown, C. C., Woolliscroft, L. J. C., % Dunlop, M. W., Farrugia, C. J. and Hall, D. S.: %Active current sheets near the Earth's bow shock, %J. Geophys. Res., 93, 11295–11310, 1988. % % %Singh, S. V. and Lakhina, G. S.: %Electron acoustic solitary waves with non-thermal distribution of %electrons, %Nonlin. Proc. Geophys., 11, 275–279, 2004. % % %Stasiewicz, K., Shukla, P. K., Gustafsson, G., Buchert, S., Lavraud, B., % Thidé, B. and Klos, Z.: %Slow magnetosonic solitons detected by the Cluster spacecraft, %Phys. Rev. Lett., 90, 085002, 2003a. % % %Stasiewicz, K., Longmore, M., Buchert, S., Shukla, P. K., Lavraud, B. and % Pickett, J.: %Properties of fast magnetosonic shocklets at the bow shock, %Geophys. Res. Lett., 30, 2241, 2003b. % % %Stix, T. H.: %\textitWaves in Plasmas %(American Institute of Physics, New York, 1992). Tagare, S. G., Singh, S. V., Reddy, R. V., and Lakhina, G. S.: Electron acoustic solitons in the Earth's magnetotail, Nonlin. Proc. Geophys., 11, 215–218, 2004. % %Thomsen, M. F., Gosling, J. T., Bame, S. J., Quest, K. B., Russell, C. T. % and Fuselier, S. A.: %On the origin of hot diamagnetic cavities near the Earth's bow shock, %J. Geophys. Res., 93, 11311–11325, 1988. Verheest, F., Cattaert, T., Lakhina, G. S., and Singh, S. V.: Gas-dynamic description of electrostatic solitons, J. Plasma Phys., 70, 237–250, 2004. Verheest, F., Cattaert, T., and Hellberg, M. A.: Compressive and rarefactive electron-acoustic solitons and double layers in space plasmas, Space Sci. Rev., 121, 299–311, 2005. Yu, M. Y. and Shukla, P. K.: Linear and non-linear modified electron-acoustic waves, J. Plasma Phys., 29, 409–413, 1983.