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Quasi-parallel propagation of solitary waves in magnetised non-relativistic electron–positron plasmas

Published online by Cambridge University Press:  09 June 2020

Michael S. Ruderman Open the ORCID record for Michael S. Ruderman [Opens in a new window]
Michael S. Ruderman*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, SheffieldS3 7RH, UK Space Research Institute (IKI), Russian Academy of Sciences, Moscow, Russia Moscow Center for Fundamental and Applied Mathematics, Russia
*
†Email address for correspondence: m.s.ruderman@sheffield.ac.uk
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Abstract

We study the propagation of nonlinear waves in non-relativistic electron–positron plasmas. The waves are assumed to propagate at small angles with respect to the equilibrium magnetic field. We derive the equation describing the wave propagation under the assumption that the waves are weakly dispersive and also can weakly depend on spatial variables orthogonal to the equilibrium magnetic field. We obtain solutions of the derived equation describing solitons. Then we study the stability of solitons with respect to transverse perturbations.

Keywords

plasma wavesplasma nonlinear phenomenaplasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 3 , June 2020 , 905860311
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Aharonian, F. A., Bogovalov, S. V. & Khangulyan, D. 2012 Abrupt acceleration of a ‘cold’ ultrarelativistic wind from the Crab pulsar. Nature 482, 507–509.CrossRefGoogle ScholarPubMed
Arons, J. & Barnard, J. J. 1986 Wave propagation in pulsar magnetospheres: dispersion relations and normal modes of plasmas in superstrong magnetic fields. Astrophys. J. 302, 120–155.CrossRefGoogle Scholar
Bell, A. R. & Kirk, J. G. 2008 Possibility of prolific pair production with high-power lasers. Phys. Rev. Lett. 101, 200403.CrossRefGoogle ScholarPubMed
Cattaert, T., Kourakis, I. & Shukla, P. K. 2005 Envelope solitons associated with electromagnetic waves in a magnetized pair plasma. Phys. Plasmas 12, 012319.Google Scholar
Cerutti, B. & Beloborodov, A. M. 2017 Electrodynamics of pulsar magnetospheres. Space Sci. Rev. 207, 111–136.CrossRefGoogle Scholar
Chen, H., Wilks, S. C., Bonlie, J. D., Liang, E. P., Myatt, J., Price, D. F., Meyerhofer, D. D. & Beiersdorfer, P. 2009 Making relativistic positrons using ultraintense short pulse lasers. Phys. Rev. Lett. 102, 105001.CrossRefGoogle Scholar
Chew, G. F., Goldberger, M. L. & Low, F. E. 1956 The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions. Proc. R. Soc. Lond. A 236, 112–118.Google Scholar
Chian, A. C.-L. & Kennel, C. F. 1983 Self-modulational formation of pulsar microstructures. Astrophys. Space Sci. 97, 9–18.CrossRefGoogle Scholar
Cohen, R. H. & Kulsrud, R. M. 1974 Nonlinear evolution of parallel-propagating hydromagnetic waves. Phys. Fluids 17, 2215–2225.CrossRefGoogle Scholar
El-Labany, S. K., El-Shamy, E. F., Sabry, R. & Khedr, D. M. 2013 The interaction of two nonplanar solitary waves in electron-positron-ion plasmas: an application in active galactic nuclei. Phys. Plasmas 20, 012105.CrossRefGoogle Scholar
Fedun, V. M., Ruderman, M. S. & Erdélyi, R. 2008 Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing. Phys. Lett. A 372, 6107–6110.CrossRefGoogle Scholar
Gailis, R. M., Frankel, N. E. & Dettmann, C. P. 1995 Magnetohydrodynamics in the expanding Universe. Phys. Rev. D 52, 6901–6917.Google ScholarPubMed
Gahn, C., Tsakiris, G. D., Pretzler, G., Witte, K. J., Delfin, C., Wahlström, C. G. & Habs, D. 2000 Generating positrons with femtosecond-laser pulses. Appl. Phys. Lett. 77, 2662.CrossRefGoogle Scholar
Greaves, R. G., Tinkle, M. D. & Surko, C. M. 1994 Creation and uses of positron plasmas. Phys. Plasmas 1, 1439–1446.CrossRefGoogle Scholar
Ichikawa, Y.-H., Konno, K., Wadati, M. & Sanuki, H. 1980 Spiky soliton in circular polarized Alfvén wave. J. Phys. Soc. Japan 48, 279–286.CrossRefGoogle Scholar
Ikezi, H. 1973 Experiment on ion-acoustic solitary waves. Phys. Fluids 16, 1668–1675.CrossRefGoogle Scholar
Iwamoto, N. 1993 Collective modes in nonrelativistic electron-positron plasmas. Phys. Rev. E 47, 604–611.Google ScholarPubMed
Kadomtsev, B. B. & Petviashvili, V. I. 1970 On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15, 539–541; [Translated from Russian: Kadomtsev, B. B. and Petviashvili, V. I. 1970 Ob ustoychivosti uedinyonnyh voln v slabo dispergiruyushchih sredah. Dokl. Akad. Nauk SSSR 192, 753–756].Google Scholar
Kakutani, T., Ono, H., Taniuti, T. & Wei, C.-C. 1968 Reductive perturbation method in nonlinear wave propagation II. Application to hydromagnetic waves in cold plasma. J. Phys. Soc. Japan 24, 1159–1166.CrossRefGoogle Scholar
Kaup, D. J. & Newell, A. C. 1978 An exact solution for a derivative nonlinear Schrödinger equation. J. Math. Phys. 19, 798–801.CrossRefGoogle Scholar
Kawakatu, N., Kino, M. & Takahara, F. 2016 Evidence for a significant mixture of electron/positron pairs in FRII jets constrained by cocoon dynamics. Mon. Not. R. Astron. Soc. 457, 1124–1136.CrossRefGoogle Scholar
Kawata, T. & Inoue, H. 1978 Exact solutions of the derivative nonlinear Schrödinger equation under the nonvanishing conditions. J. Phys. Soc. Japan 44, 1968–1976.CrossRefGoogle Scholar
Khanna, M. & Rajaram, R. 1982 Evolution of nonlinear Alfvén waves propagating along the magnetic field in a collisionless plasma. J. Plasma Phys. 28, 459–468.CrossRefGoogle Scholar
Lakhina, G. S. & Verheest, F. 1997 Alfvénic solitons in ultrarelativistic electron-positron plasmas. Astrophys. Space Sci. 253, 97–106.CrossRefGoogle Scholar
Liang, E. P., Wilks, S. C. & Tabak, M. 1998 Pair production by ultraintense lasers. Phys. Rev. Lett. 91, 4887–4890.CrossRefGoogle Scholar
Lonngren, K. E. 1983 Soliton experiments in plasma physics. Plasma Phys. Control. Fusion 25, 943–982.CrossRefGoogle Scholar
Mikhailovskii, A. B., Onishchenko, O. G. & Smolyakov, A. I. 1985a Theory of low-frequency electromagnetic solitons in a relativistic electron-positron plasma. Sov. J. Plasma Phys. 11, 215–219; [Translated from Russian: Mikhailovskii, A. B., Onishchenko, O. G., and Smolyakov, A. I. 1985a Teoriya nizkochastotnyh elektromagnitnyh solitonov v relativistskoi elektronno-positronnoy plasme. Fizika Plazmy 11, 369–375].Google Scholar
Mikhailovskii, A. B., Onishchenko, O. G. & Tatarinov, E. G. 1985b Alfvén solitons in a relativistic electron-position plasma. I. Hydrodynamic theory. Plasma Phys. Control. Fusion 27, 527–537.CrossRefGoogle Scholar
Mikhailovskii, A. B., Onishchenko, O. G. & Tatarinov, E. G. 1985c Alfvén solitons in a relativistic electron-position plasma. II. Kinetic theory. Plasma Phys. Control. Fusion 27, 539–556.CrossRefGoogle Scholar
Mio, K., Ogino, T., Minami, K. & Takeda, S. 1976a Modified nonlinear Schrödinger equation for Alfvén waves propagating along the magnetic field in cold plasmas. J. Phys. Soc. Japan 41, 265–271.CrossRefGoogle Scholar
Mio, K., Ogino, T., Minami, K. & Takeda, S. 1976b Modulational instability and envelope-solutions for nonlinear Alfvén waves propagating along magnetic-field in plasmas. J. Phys. Soc. Japan 41, 667–673.CrossRefGoogle Scholar
Mjølhus, E. 1976 On the modulational instability of hydromagnetic waves parallel to the magnetic field. J. Plasma Phys. 16, 321–334.CrossRefGoogle Scholar
Mjølhus, E. & Hada, T. 1997 Nonlinear Waves and Chaos in Space Plasmas (ed. Hada, T. & Matsumoto, H.), p. 121. Terrapub.Google Scholar
Mjølhus, E. & Wyller, J. 1986 Alfvén solitons. Phys. Scr. 33, 442–451.Google Scholar
Passot, T. & Sulem, P.-L. 1993 Multidimensional modulation of Alfvén waves. Phys. Rev. E 48, 2966–2974.Google ScholarPubMed
Rajib, T. I., Sultana, S. & Mamun, A. A. 2015 Solitary waves in rotational pulsar magnetosphere. Astrophys. Space Sci. 357, 52.CrossRefGoogle Scholar
Rogister, A. 1971 Parallel propagation of nonlinear low-frequency waves in high-$\unicode[STIX]{x1D6FD}$ plasma. Phys. Fluids 14, 2733–2739.CrossRefGoogle Scholar
Rudenko, O. V. & Soluyan, S. I. 1977 Theoretical Foundations of Nonlinear Acoustics. Plenum Publishing Corporation, Consultants Bureau.CrossRefGoogle Scholar
Ruderman, M. S. 1986 Stability of quasilongitudinally propagating narrow beams of nonlinear magnetohydrodynamic waves. Fluid Dyn. 21, 524–530; [Translated from Russian: Ruderman, M. S. 1986 Qvaziparallelnoe raspropstranenie uzkih puchkov nelineinyh magnitogidrodinamicheskikh voln. Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, 21–28].Google Scholar
Ruderman, M. S. 1987 Quasilongitudinall propagating solitons in a plasma with Hall dispersion. Fluid Dyn. 22, 299–305; [Translated from Russian: Ruderman, M. S. 1987 Ustoichivost’ kvaziprodol’no rasprostranyayushchihsya solitonov v plasme s hollovskoi dispersiey. Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 159–165].Google Scholar
Ruderman, M. S. 2002 DNLS equation for large-amplitude solitons propagating in an arbitrary direction in a high-$\unicode[STIX]{x1D6FD}$ Hall plasma. J. Plasma Phys. 67, 271–276.CrossRefGoogle Scholar
Ruderman, M. A. & Sutherland, P. G. 1975 Theory of pulsars: polar gaps, sparks, and coherent microwave radiation. Astrophys. J. 196, 51–72.CrossRefGoogle Scholar
Ruffini, R., Vereshchagin, G. & Xue, S.-S. 2010 Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes. Phys. Rep. 487, 1–140.Google Scholar
Sakai, J. & Kawata, T. 1980a Waves in an ultra-relativistic electron-positron plasma. J. Phys. Soc. Japan 49, 747–752.CrossRefGoogle Scholar
Sakai, J. & Kawata, T. 1980b Non-linear Alfvén-wave in an ultra-relativistic electron-positron plasma. J. Phys. Soc. Japan 49, 753–758.CrossRefGoogle Scholar
Sarri, G., Schumaker, W., di Piazza, A., Vargas, M., Dromey, B., Dieckmann, M. E., Chvykov, V., Maksimchuk, A., Yanovsky, V. & He, Z. H. 2013 Table-top laser-based source of femtosecond, collimated, ultrarelativistic positron beams. Phys. Rev. Lett. 110, 255002.CrossRefGoogle ScholarPubMed
Shukla, R. K. 2003 Generation of magnetic fields in the early universe. Phys. Lett. A 310, 182–186.CrossRefGoogle Scholar
Shukla, P. K., Rao, N. N., Yu, M. Y. & Tsintsadze, N. L. 1986 Relativistic nonlinear effects in plasmas. Phys. Rep. 135, 1–149.Google Scholar
Stewart, G. A. & Laing, E. W. 1992 Wave propagation in equal-mass plasmas. J. Plasma Phys. 47, 295–319.CrossRefGoogle Scholar
Sturrock, P. A. 1971 A model of pulsars. Astrophys. J. 164, 529–556.CrossRefGoogle Scholar
Surko, C. M. & Murphy, T. J. 1990 Use of the positron as a plasma particle. Phys. Fluids B 2, 1372–1375.CrossRefGoogle Scholar
Surko, C. M., Leventhal, M. & Passner, A. 1989 Positron plasma in the laboratory. Phys. Rev. Lett. 62, 901–904.CrossRefGoogle ScholarPubMed
Taniuti, T. & Wei, C.-C. 1968 Reductive perturbation method in nonlinear wave propagation. I. J. Phys. Soc. Japan 24, 941–946.CrossRefGoogle Scholar
Tatsuno, T., Berezhiani, V. I., Pekker, M. & Mahajan, S. M. 2003 Angular momenta creation in relativistic electron-positron plasma. Phys. Rev. E 68, 016409.Google ScholarPubMed
Tran, M. Q. 1979 Ion-acoustic solitons in a plasma-review of their experimental properties and related theories. Phys. Scr. 20, 317–327.Google Scholar
Verheest, F. 1996 Solitary Alfvén modes in relativistic electron-positron plasmas. Phys. Lett. A 213, 177–182.CrossRefGoogle Scholar
Verheest, F. & Lakhina, G. S. 1996 Oblique solitary Alfvén modes in relativistic electron-positron plasmas. Astrophys. Space Sci. 240, 215–224.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Willey-Interscience Publication.Google Scholar
Yajima, N. 1966 Effect of finite ion Larmor radius on propagation of magnetoacoustic waves. Prog. Theor. Phys. 36, 1–16.CrossRefGoogle Scholar
Zabolotskaya, E. A. & Khokhlov, R. V. 1969 Quasi-plane waves in the nonlinear acoustics of confined beams. Sov. Phys. Acoust. – USSR 15, 35–42; [Translated from Russian: Zabolotskaya, E. A. and Khokhlov, R. V. 1969 Kvazi-ploskie volny v nonlineinoi akustike ogranichennyh puchkov. Akoust. Zh. 15, 40–47].Google Scholar
Zank, G. P. & Greaves, R. G. 1995 Linear and nonlinear modes in nonrelativistic electron-positron plasmas. Phys. Rev. E 51, 6079–6090.Google ScholarPubMed