Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 3 2010 10.5194/npg-17-245-2010 http://www.nonlin-processes-geophys.net/17/245/2010/ http://www.nonlin-processes-geophys.net/17/245/2010/npg-17-245-2010.html http://www.nonlin-processes-geophys.net/17/245/2010/npg-17-245-2010.pdf 245 268 2010-05-07 Lower-hybrid (LH) oscillitons evolved from ion-acoustic (IA)/ion-cyclotron (IC) solitary waves: effect of electron inertia J. Z. G. Ma johnzg.ma@asc-csa.gc.ca A. Hirose Space Science Branch, Canadian Space Agency, 6767, Route De I'Aéroport, Saint-Hubert, Québec, J3Y 8Y9, Canada Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, S7N 5E2, Canada Lower-hybrid (LH) oscillitons reveal one aspect of geocomplexities. They have been observed by rockets and satellites in various regions in geospace. They are extraordinary solitary waves the envelop of which has a relatively longer period, while the amplitude is modulated violently by embedded oscillations of much shorter periods. We employ a two-fluid (electron-ion) slab model in a Cartesian geometry to expose the excitation of LH oscillitons. Relying on a set of self-similar equations, we first produce, as a reference, the well-known three shapes (sinusoidal, sawtooth, and spiky or bipolar) of parallel-propagating ion-acoustic (IA) solitary structures in the absence of electron inertia, along with their Fast Fourier Transform (FFT) power spectra. The study is then expanded to illustrate distorted structures of the IA modes by taking into account all the three components of variables. In this case, the ion-cyclotron (IC) mode comes into play. Furthermore, the electron inertia is incorporated in the equations. It is found that the inertia modulates the coupled IA/IC envelops to produce LH oscillitons. The newly excited structures are characterized by a normal low-frequency IC solitary envelop embedded by high-frequency, small-amplitude LH oscillations which are superimposed upon by higher-frequency but smaller-amplitude IA ingredients. The oscillitons are shown to be sensitive to several input parameters (e.g., the Mach number, the electron-ion mass/temperature ratios, and the electron thermal speed). Interestingly, whenever a LH oscilliton is triggered, there occurs a density cavity the depth of which can reach up to 20% of the background density, along with density humps on both sides of the cavity. Unexpectedly, a mode at much lower frequencies is also found beyond the IC band. Future studies are finally highlighted. The appendices give a general dispersion relation and specific ones of linear modes relevant to all the nonlinear modes encountered in the text. Alexeff, I., Estabrook, K., Hirose, A., Jones, W. D., Neidigh, R. V., Olsen, J. N., Scott, F. R., Stirling, W. L., Widner, M. M., and Wing, W. R.: Understanding Turbulent Ion Heating in the Oak Ridge Mirror Machine, "Burnout V", Phys. Rev. Lett., 25, 848–851, 1970. Al-Salti, N. and Shivamoggi, B. K.: Electron-inertia effects on driven magnetic field reconnection, Phys. Plasmas, 10, 4271–4277, 2003. Artsimovich, L. A.: Controlled Thermonuclear Reactions, Gordon and Breach, New York, 1964. Baumjohann, W.: The near-Earth plasma sheet: An AMPTE/IRM perspective, Space Sci. Rev., 64, 141–163, 1993. Bellan, P. M.: Fundamentals of plasma physics (paperback), Cambridge University Press, 2008. Berthomier, M., Pottelette, R., Malingre, M., and Khotyaintsev, Y.: Electron-acoustic solitons in an electron-beam plasma system, Phys. Plasmas, 9, 2987–2994, 2000. Berthomier, M., Pottelette, R., Muschietti, L., Roth, I., and Carlson, C.: Scaling of three dimensional electron phase space density holes observed by FAST in the auroral downward current region, Geophys. Res. Lett., 30, 2148–152, 2003. Bharuthram, R., Reddy, R. V., Lakhina, G. S., and Singh, N.: Low frequency nonlinear waves in the auroral plasma, Phys. Scripta, T98, 137–140, 2002. Boyd, T. J. M. and Sanderson J. J.: The physics of plasmas, Cambridge University Press, 2003. Briand, C.: Plasma waves above the ion cyclotron frequency in the solar wind: a review on observations, Nonlin. Processes Geophys., 16, 319–329, 2009. Burchill, J. K., Knudsen, D. J., Bock, B. J. J., Pfaff, R. F., Walis, D. D., Clemmons, J. H., Bounds, S. R., and Stenbaek-Nielsen, H.: Core ion interactions with BB~ELF, lower hybrid, and Alfvén waves in the high-latitude topside ionosphere, J. Geophys. Res., 109, A01219, doi:10.1029/2003JA010073, 2004. Cattaert, T. and Verheest, F.: Large amplitude parallel propagating electromagnetic oscillitons, Phys. Plasmas, 12, 012307, doi:10.1063/1.1824038, 2005. Cattell, C., Wygant, J., Dombeck, J., Mozer, F. S., Temerin, M., and Russell, C. T.: Observations of large amplitude parallel electric field wave packets at the plasma sheet boundary, Geophys. Res. Lett., 25, 857–860, 1998. Cattell, C., 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. Chang, T.: Lower-hybrid collapse, caviton turbulence, and charged particle energization in the topside auroral ionosphere and magnetosphere, Phys. Fluids~B-Plasma, 5, 2646–2656, 1993. Chang, T. and Coppi, B.: Lower hybrid acceleration and ion evolution in the suprauroral region, Geophys. Res. Lett., 8, 1253–1256, 1981. Chatterjee, P. and Roychoudhury, R.: Effect of finite ion temperature on ion acoustic solitary waves in a two-temperature electron-plasma system, Can. J. Phys., 75, 337–343, 1997. Chiueh, T. and Diamond, P. H.: Two-point theory of current-driven, ion-cyclotron turbulence, Phys. Fluids, 29, 76–96, 1986. Craik, A. D. D.: The origins of water wave theory, Annu. Rev. Fluid Mech., 36, 1–28, 2004. Das, G. C., Sarma, J., Gao, Y.-T., and Uberoi, C.: Dynamical behavior of the soliton formation and propagation in magnetized plasma, Phys. Plasmas, 7, 2374–2380, 2000. Davidson, R. C.: Methods in nonlinear plasma theory, Academic Press, New York, 1972. Davydov, A. S.: Solitons in Molecule Systems, McGraw-Hill, 1985. Delory, G. T.: Rocket observations of VLF waves, electron precipitation and ion heating in the auroral ionosphere, Ph.D dissertation, University of California at Berkeley, USA, 1996. Dovner, P. O., Eriksson, A. I., Boström, R., and Holback, B.: Freja multiprobe observations of electrostatic solitary structures, Geophys. Res. Lett., 21, 1827–1830, 1994. Drazin, P. G.: Solitons, Cambridge University Press, 1984. Dubinin, E., Sauer, K., and McKenzie, J. F.: Solitons and oscillitons in cold bi-ion plasmas: A parameter study, J. Plasma Phys., 68, 27–52, 2002. Dubinin, E., Sauer, K., and McKenzie, J. F.: Nonlinear stationary whistler waves and whistler solitons (oscillitons). Exact solutions, J. Plasma Phys., 69, 305–330, 2003a. Dubinin, E., Sauer, K., and McKenzie, J. F.: Solitons, oscillitons and stationary waves in a cold $p-\alpha$ plasma, J. Geophys. Res., 108, 1295, doi:10.1029/2002JA009571, 2003b. Dubinin, E., Sauer, K., and McKenzie, J. F.: Solitons, oscillitons and stationary waves in a warm $p-\alpha$ plasma, J. Geophys. Res., 108, 1296, doi:10.1029/2002JA009572, 2003c. Dubinin, E. M., Maksimovic, M., Cornilleau-Wehrlin, N., Fontaine, D., Travnicek, P., Mangeney, A., Alexandrova, O., Sauer, K., Fraenz, M., Dandouras, I., Lucek, E., Fazakerley, A., Balogh, A., and Andre, M.: Coherent whistler emissions in the magnetosphere - Cluster observations, Ann. Geophys., 25, 303–315, 2007. Dubouloz, N., Treumann, R., Pottelette, R., and Malingre, M.: Turbulence generated by a gas of electron acoustic solitons, J. Geophys. Res., 98, 17415–17422, 1993. Dupree, T. H.: Theory of phase space density granulation in plasma, Phys. Fluids, 15, 334–344, 1972. 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., Moebius, E., and Kistler, L.: FAST satellite observations of large-amplitude solitary structures, Geophys. Res. Lett., 25, 2041–2044, 1998. Ergun, R. E.: Magnetic-field-aligned electric fields associated with Debye-scale plasma structures, Plasma Phys. Contr. F., 41, A61–73, 1999. Eriksson, A. I., Holback, B., Dovner, P. O., Boström, R., Holmgren, G., André, M., Eliasson, L., and Kintner, P. M.: Freja observatons of correlated small-scale density depletions and enhanced lower hybrid waves, Geophys. Res. Lett., 21, 1843–1846, 1994. Gary, S. P.: Theory of space plasma micro-instabilities, Cambridge University Press, 1993. Gradov, O. M., Stenflo, L., and Sünder, D.: Self-consistent description of solitary surface waves on a plasma cylinder, Phys. Fluids, 27, 597–599, 1984. Gradov, O. M., Stenflo, L., and Sünder, D.: Solitary surface waves on a magnetized plasma cylinder, J. Plasma Phys., 33, 53–58, 1985. Hasegawa, A. and Kodama, Y.: Solitons in Optical Communications, Clarendon Press, 1995. Hirose, A., Alexeff, I., and Jones, W. D.: Dispersion measurements of electrostatic ion waves in a uniform magnetic field, Phys. Fluids, 13, 2039–2044, 1970a. Hirose, A., Alexeff, I., and Jones, W. D.: Dispersion and damping of electrostatic ion waves in a uniform magnetic field, Phys. Fluids, 13, 1414–1416, 1970b. Hirose, A., Alexeff, I., and Jones, W. D.: Landau damping of ion acoustic waves in a uniform magnetic field, Phys. Fluids, 13, 1290–1297, 1970c. Hirose, A. and Alexeff, I.: Electrostatic instabilities driven by currents perpendicular to an external magnetic field, Nucl. Fusion, 12, 315–323, 1972. Hirose, A.: Drift Instabilities in Magnetically Confined Plasmas: A Brief Overview, Lecture Notes, Autumn College on Plasma Physics International Centre for Theoretical Physics, Trieste, Italy, 2005. Hirose, A.: Plasma waves (I), Lecture Notes, University of Saskatchewan, 2007. Høymork, S. H., Pécseli, H. L., Lybekk, B., Trusen, J., and Eriksson, A.: The shape and evolution of lower hybrid density cavities observed by FREJA, 26, 213–217, 2001. Jones, S. T. and Parker, S. E.: Including electron inertia without advancing electron flow, J. Comput. Phys., 191, 322–327, 2003. Jovanovi\'c, D. and Shukla, P. K.: Nonlinear model for coherent electric-field structures in the magnetosphere, Phys. Rev. Lett., 84, 4373–4376, 2000. 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, 052305–9, 2007. Kintner, P. M., Vago, J., Chesney, S., Arnoldy, R. L., Lynch, K. A., Pollock, C. J., and Moore, T. E.: Localized lower hybrid acceleration of ionospheric plasma, Phys. Rev. Lett., 68, 2448–2451, 1992. Knudsen, D. J.: Spatial modulation of electron energy and density by nonlinear stationary inertial Alfvén waves, J. Geophys. Res., 101, 10761-10772, 1996. Knudsen, D. J., Bock, B. J. J., Bounds, S. R., Burchill, J. K., Clemmons, J. H., Curtis, J. D., Eriksson, A. I., Koepke, M. E., Pfaff, R. F., Wallis, D. D., and Whaley, N.: Lower-hybrid cavity density depletions as a result of transverse ion acceleration localized on the gyroradius scale, J. Geophys. Res., 109, A04212, doi:10.1029/2003JA010089, 2003. Kourakis, I. and Shukla, P. K.: Electron-acoustic plasma waves: oblique modulation and envelope solitons, Phys. Rev E, 69, p 036411, 2004. Kourakis, I. and Shukla, P. K.: Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas, Nonlin. Processes Geophys., 12, 407–423, 2005. Kuehl, H. H. and Zhang, C. Y.: Effects of ion drift on small-amplitude ion-acoustic solitons, Phys. Fluids~B-Plasma, 3, 26–28, 1991. LaBelle, J., Kintner, P. M., Yau, A. W., and Whalen, B. A.: Large amplitude wave packets observed in the ionosphere in association with transverse ion acceleration, J. Geophys. Res., 91, 7113–7118, 1986. Lakhina, G. S., Kakad, A. P., Singh, S. V., and Verhest, F.: Ionand electron-acoustic solitons in two temperature space plasmas, Phys. Plasmas, 15, p 062903, 2008. Lavraud, B., Borovsky, J. E., Génot, V., Schwartz, S. J., Birn, J., Fazakerley, A. N., Dunlop, M. W., Hasegawa, H., Rouillard, A. P., Berchem, J., Bogdanova, Y., Constantinescu, D., Dandouras, I., Eastwood, J. P., Escoubet, C. P., Frey, H., Jacquey, C., Panov, E., Pu, Z. Y., Shen, C., Shi, J., Sibeck, D. G., Volwerk, M., and Wild, J. A.: Tracing solar wind plasma entry into the magnetosphere using ion-to-electron temperature ratio, Geophys. Res. Lett., 36, L18109, doi:10.1029/2009GL039442, 2009. Lee, L. C. and Kan, J. R.: Nonlinear ion-acoustic waves and solitons in a magnetized plasma, Phys. Fluids, 24, 430–436, 1981. Ma, J. Z. G.: Nonlinear ion-acoustic (IA) waves driven in a cylindrically symmetric flow, Astrophys. Space Sci., 0004-640X (Print) 1572-946X (Online), 2010. Ma, J. Z. G. and Hirose, A.: Parallel propagation of ion solitons in magnetic flux tubes, Phys. Scripta, 79, p 045502, 2009a. Ma, J. Z. G. and Hirose, A.: High-frequency electrostatic lower-hybrid (LH) waves in magnetic flux tubes, Phys. Scripta, 79, p 035503, 2009b. Ma, J. Z. G., St.-Maurice, J.-P., and Hirose, A.: Non-wave mechanism of transverse ion heating in magnetic flux tubes, Phys. Scripta, 80, p 025501, 2009. Mamun, A. A. and Shukla, P. K.: Obliquely propagating electron-acoustic solitary waves, Phys. Plasmas, 9, 1474–1477, 2002. McFadden, J. P., Carlson, C. W., Ergun, R. E., Chaston, C. C., Mozer, F. S., Temerin, M., Klumpar, D. M., Shelley, E. G., Peterson, W. K., Moebius, E., Kistler, L., Elphic, R., Strangeway, R., Cattell, C., and Pfaff, R.: Electron modulation and ion cyclotron waves observed by FAST, Geophys. Res. Lett., 25, 2045–2048, 1998. McKenzie, J. F., Dubinin, E., Sauer, K., and Doyle, T. B.: The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint, J. Plasma Phys., 70, 431–462, 2004. Merlino, R. L. and D'Angelo, N.: Electron and ion inertia effects on current-driven collisional dust acoustic, dust ion acoustic, and ion acoustic instabilities, Plasma Phys., 12, p 054504, 2005. Mikhailovskii, A. B.: Theory of plasma instabilities, in: Instabilities of an Inhomogeneous Plasma, vol 2, Consultants Bureau, New York, 1974. Nakamura, Y. and Sugai, H.: Experiments on Ion-acoustic Solitons in a Plasma, Chaos Soliton Fract., 7, 1023–1031, 1996. Pécseli, H. L.: Solitons and weakly nonlinear waves in plasmas, IEEE T. Plasma Sci., 13, 53–86, 1985. Pécseli, H. L., Iranpour, K., Hotter, Ø., Lybekk, B., Holtet, J., Trulsen, J., Eriksson, A., and Holback, B.: Lower hybrid wave cavities detected by the FREJA satellite, J. Geophys. Res., 101, 5299–5316, 1996. Phan, T.-D., Paschmann, G., Baumjohann, W., Sckopke, N., and Lühr, H.: The magnetosheath region adjacent to the dayside magnetopause: AMPTE/IRM observations, J. Geophys. Res., 99, 121–141, 1994. Pickett, J. S., Chen, L.-J., Kahler, S. W., Santolík, O., Goldstein, M. L., Lavraud, B., Décréau, P. M. E., Kessel, R., Lucek, E., Lakhina, G. S., Tsurutani, B. T., Gurnett, D. A., Cornilleau-Wehrlin, N., Fazakerley, A., Rème, H., and Balogh, A.: On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath, Nonlin. Processes Geophys., 12, 181–193, 2005. Pinçn, J.-L., Kintner, P. M., Schuck, P. W., and Seyler, C. E.: Observation and analysis of lower hybrid solitary structures as rotating eigenmodes, J. Geophys. Res., 102, 17283–17296, 1997. Pottelette, R., Ergun, R. E., Treumann, R. A., Berthomier, M., Carlson, C. W., McFadden, J. P., and Roth, I.: Modulated electronacoustic waves in auroral density cavities: FAST observations, Geophys. Res. Lett., 26, 2629–2632, 1999. Pottelette, R., Treumann, R. A., Berthomier, M., and Jasperse, J.: Electrostatic shock properties inferred from AKR fine structure, Nonlin. Processes Geophys., 10, 87–92, 2003. Pottelette, R. and Berthomier, M.: Nonlinear electron acoustic structures generated on the high-potential side of a double layer, Nonlin. Processes Geophys., 16, 373–380, 2009. Reddy, R. V., Lakhina, G. S., Singh, N., and Bharuthram, R.: Spiky parallel electrostatic ion cyclotron and ion acoustic waves, Nonlin. Processes Geophys., 9, 25–29, 2002. Retterer, J., Chang, T., and Jasperse, J.: Ion acceleration by lower hybrid waves in the suprauroral region, J. Geophys. Res., 91, 1609–1618, 1986. Sauer, K., Dubinin, E., and McKenzie, J. F.: New type of soliton in Bi-ion plasmas and possible implications, Geophys. Res. Lett., 28, 3589–3592, 2001. Sauer, K., Dubinin, E., and McKenzie, J. F.: Wave emission by whistler oscillitons: Application to "coherent lion roars", Geophys. Res. Lett., 29(24), 2226, doi:10.1029/2002GL015771. Sauer, K., Dubinin, E., and McKenzie, J. F.: Solitons and oscillitons in multi-ion space plasmas, Nonlin. Processes Geophys., 10, 121–130, 2003. Schuck, P. W., Bonnell, J. W., and Kintner Jr., P. M.: A review of lower hybrid solitary structures, IEEE T. Plasma Sci., 31, 1125–1177, 2003. Sen, B., Das, B., and Chatterjee, P.: Effect of electron inertia on large amplitude solitary waves in presence of kinematic viscosity in dusty plasma, Eur. Phys. J D, 49, 211–216, 2008. Shapiro, V. D.: Modulational interaction of the Lower-hybrid waves with a kinetic-Alfvén mode, Phys. Rev. Lett., 81, 3415–3418, 1998. \item Shi, J. K., Xu, B. Y., Torkar, K., and Liu, Z. X.: Nonlinear waves in a low-β plasma with cylindrical symmetry, Phys. Plasmas, 8, p 4780, 2001. Shi, J. K., Zhang, T., Torkar, K., and Liu, Z. X.: An interpretation of electrostatic density shocks in space plasma, Phys. Plasmas, 12, p 082901, 2005. Shi, J., Qureshi, M. N. S., Torkar, K., Dunlop, M., Zhenxing Liu, and Zhang, T. L.: An interpretation for the bipolar electric field structures parallel to the magnetic field observed in the auroral ionosphere, Ann. Geophys., 26, 1431–1437, 2008. Shivamoggi, B. K.: Plasma dynamics with electron-inertia effects, J. Plasma Phys., 58, 329–344, 1997. Shukla, P. K. and Yu, M. Y.: Exact solitary ion acoustic waves in a magnetoplasma, J. Math. Phys., 19, 2506–2508, 1978. Shukla, P. K., Mamun, A., and Eliasson, B.: 3-D electron-acoustic solitary waves introduced by phase space electron vortices in magnetized space plasmas, Geophys. Res. Lett., 31, L07803, doi:10.1029/2004GL019533, 2004. Singh, S. V. and Lakhina, G. S.: Electron acoustic solitary waves with non-thermal distribution of electrons, Nonlin. Processes Geophys., 11, 275–279, 2004. Stenflo, L.: Strongly nonlinear cylindrical surface waves, Phys. Scripta, 41, 643–644, 1990. Stenflo, L. and Yu, M. Y.: Nonlinear waves in a rotating plasma cylinder, IEEE T. Plasma Sci., 20, 104–105, 1992. Stenflo, L. and Yu, M. Y.: Nonlinear waves in cylindrically bounded magnetized plasmas, Phys. Rev E, 51, 1408–1411, 1995. Sydora, R. D., Sauer, K., and Silin, I.: Coherent whistler waves and oscilliton formation: Kinetic simulations, Geophy. Res. Lett., 34, L22105, doi:10.1029/2007GL031839, 2007. Tanaca, H., Koganei, M., and Hirose, A.: Drift instability in mercury-vapor discharges, Phys. Lett., 23, 679–680, 1966a. Tanaca, H., Koganei, M., and Hirose, A.: Dispersion relation of ion waves in Mercury-vapour discharges, Phys. Rev. Lett., 16, 1079–1081, 1966b. Tanaca, H., Hirose, A., and Koganei, M.: Ion wave instabilities in Mercury-vapor plasma, Phys. Rev., 161, 94–101, 1967. Temerin, M., Woldorff, M., and Mozer, F. S.: Nonlinear Steepening of the Electrostatic Ion Cyclotron Wave, Phys. Rev. Lett., 43, 1941–1943, 1979. Tjulin, A., Eriksson, A. I., and André, M.: Lower hybrid cavities in the inner magnetosphere, Geophys. Res. Lett., 30, p 1364, 2003. Tjulin, A., André, M., Eriksson, A. I., and Maksimovic, M.: Observations of lower hybrid cavities in the inner magnetosphere by the Cluster and Viking satellites, Ann. Geophys., 22, 2961–2972, 2004. Tsurutani, B. T., Galvan, C., Arballo, J. K., Winterhalter, D., Sakurai, R., Smith, E. J., Buti, B., Lakhina, G. S., and Balogh, A.: Relationship between discontinuities, magnetic holes, magnetic decreases, and nonlinear Alfvén waves: Ulysses observations over the solar poles, Geophys. Res. Lett., 29(11), 1528, doi:10.1029/2001GL013623, 2002a. Tsurutani, B. T., Dasgupta, B., Galvan, C., Neugebauer, M., Lakhina, G. S., Arballo, J. K., Winterhalter, D., Goldstein, B. E., and Buti, B.: Phase-steepened Alfvén waves, proton perpendicular energization and the creation of magnetic holes and magnetic decreases: The ponderomotive force, Geophys. Res. Lett., 29, 24pp., 2002b. Tsurutani, B. T., Lakhina, G. S., Pickett, J. S., Guarnieri, F. L., Lin, N., and Goldstein, B. E.: Nonlinear Alfvén waves, discontinuities, proton perpendicular acceleration, and magnetic holes/decreases in interplanetary space and the magnetosphere: intermediate shocks?, Nonlin. Processes Geophys., 12, 321–336, 2005. Uberoi, C.: Electron-Inertia Effects On The Transverse Gravitational Instability, J. Plasma Fusion Res SERIES, 8, 823–825, 2009. Vladimirov, S. V., Yu, M. Y., and Stenflo, L.: Surface Wave Solitons in an Electronic Medium, Phys. Lett A, 174, 313–316, 1993. Yu, M. Y., Shukla, P. K., and Bujarbarua, S.: Fully nonlinear ion-acoustic solitary waves in a magnetized plasma, Phys. Fluids, 23, 2146–2147, 1980. Yu, M. Y. and Stenflo, L.: Nonlinear waves in a plasma cylinder, IEEE T. Plasma Sci., 19, 641–644, 1991.