Skip to main content Accessibility help
×
Home

Wave dispersion in pulsar plasma. Part 1. Plasma rest frame

  • M. Z. Rafat (a1), D. B. Melrose (a1) and A. Mastrano (a1)

Abstract

Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation (wave angle $\unicode[STIX]{x1D703}=0$ ) these are referred to as the X, A and L modes, with the X and A modes having dispersion relation $|z|=z_{\text{A}}\approx 1-1/2\unicode[STIX]{x1D6FD}_{\text{A}}^{2}$ , where $z=\unicode[STIX]{x1D714}/k_{\Vert }c$ is the phase speed and $\unicode[STIX]{x1D6FD}_{\text{A}}c$ is the Alfvén speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function, $z^{2}W(z)$ , which is negative for $|z|<z_{0}$ and has a sharp maximum at $|z|=z_{\text{m}}$ , with $1-z_{\text{m}}<1-z_{0}\ll 1$ . We give numerical estimates for the maximum of $z^{2}W(z)$ and for $z_{\text{m}}$ and $z_{0}$ for a one-dimensional Jüttner distribution. The L and A modes reconnect, for $z_{\text{A}}>z_{0}$ , to form the O and Alfvén modes for oblique propagation ( $\unicode[STIX]{x1D703}\neq 0$ ). For $z_{\text{A}}<z_{0}$ the Alfvén and O mode curves reconnect forming a new mode that exists only for $\tan ^{2}\unicode[STIX]{x1D703}\gtrsim z_{0}^{2}-z_{\text{A}}^{2}$ . The L mode is the nearest counterpart to Langmuir waves in a non-relativistic plasma, but we argue that there are no ‘Langmuir-like’ waves in a pulsar plasma, identifying three features of the L mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O mode around $\unicode[STIX]{x1D703}\approx 0$ . The resonance is also possible for the Alfvén mode but only near a turnover frequency that has no counterpart for Alfvén waves in a non-relativistic plasma.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Wave dispersion in pulsar plasma. Part 1. Plasma rest frame
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Wave dispersion in pulsar plasma. Part 1. Plasma rest frame
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Wave dispersion in pulsar plasma. Part 1. Plasma rest frame
      Available formats
      ×

Copyright

Corresponding author

Email address for correspondence: donald.melrose@sydney.edu.au

References

Hide All
Arendt, P. N. Jr & Eilek, J. A. 2002 Pair creation in the pulsar magnetosphere. Astrophys. J. 581, 451469.
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, 120137.
Asseo, E. 1993 Microtexture in the pulsar radio emission zone. Mon. Not. R. Astron. Soc. 264, 940.
Asseo, E. 1995 The importance of boundary effects in the emission region of the pulsar magnetosphere. Mon. Not. R. Astron. Soc. 276, 74102.
Asseo, E. & Melikidze, G. I. 1998 Non-stationary pair plasma in a pulsar magnetosphere and the two-stream instability. Mon. Not. R. Astron. Soc. 301, 5971.
Asseo, E., Pellat, R. & Sol, H. 1983 Radiative or two-stream instability as a source for pulsar radio emission. Astrophys. J. 266, 201214.
Asseo, E. & Riazuelo, A. 2000 Relativistic anisotropic pair plasmas. Mon. Not. R. Astron. Soc. 318, 9831004.
Benford, G. & Buschauer, R. 1977 Coherent pulsar radio radiation by antenna mechanisms - general theory. Mon. Not. R. Astron. Soc. 179, 189207.
Beskin, V. S. & Philippov, A. A. 2012 On the mean profiles of radio pulsars – I. Theory of propagation effects. Mon. Not. R. Astron. Soc. 425, 814840.
Egorenkov, V. D., Lominadze, D. G. & Mamradze, P. G. 1983 Beam instability of the plasma in pulsar magnetospheres. Astrophysics 19, 426431.
Eilek, J. A. & Hankins, T. H. 2016 Radio emission physics in the Crab pulsar. J. Plasma Phys. 82 (3), 635820302.
Gallant, Y. A., Hoshino, M., Langdon, A. B., Arons, J. & Max, C. E. 1992 Relativistic, perpendicular shocks in electron-positron plasmas. Astrophys. J. 391, 73101.
Gedalin, M., Gruman, E. & Melrose, D. B. 2002 New mechanism of pulsar radio emission. Phys. Rev. Lett. 88 (12), 121101.
Godfrey, B. B., Newberger, B. S. & Taggart, K. A. 1975 A relativistic plasma dispersion function. IEEE Trans. Plasma Sci. 3, 6067.
Hardee, P. E. & Rose, W. K. 1976 A mechanism for the production of pulsar radio radiation. Astrophys. J. 210, 533538.
Hardee, P. E. & Rose, W. K. 1978 Wave production in an ultrarelativistic electron-positron plasma. Astrophys. J. 219, 274287.
Hibschman, J. A. & Arons, J. 2001 Pair production multiplicities in rotation-powered pulsars. Astrophys. J. 560, 871884.
Hinata, S. 1976a Level of electrostatic excitation associated with relativistic beam-plasma system and pulsar radiation. Astrophys. Space Sci. 44, 389395.
Hinata, S. 1976b Relativistic plasma turbulence and its application to pulsar phenomena. Astrophys. J. 206, 282294.
Iwamoto, M., Amano, T., Hoshino, M. & Matsumoto, Y. 2017 Persistence of precursor waves in two-dimensional relativistic shocks. Astrophys. J. 840, 52.
Jüttner, F. 1911 Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Annalen der Physik 339, 856882.
Kaplan, S. A. & Tsytovich, V. N. 1973 Plasma Astrophysics. Pergamon Press.
Lominadze, D. G. & Mikhailovskiǐ, A. B. 1979 Longitudinal waves and two-stream instability in a relativistic plasma. Sov. Phys. JETP 49, 483.
Lominadze, D. G., Mikhaǐlovskiǐ, A. B. & Sagdeev, R. Z. 1979 Langmuir turbulence of a relativistic plasma in a strong magnetic field. Sov. Phys. JETP 50, 927.
Lominadze, J. G. & Pataraya, A. D. 1982 Some nonlinear mechanisms of pulsar emission. Phys. Scr. T2, 215222.
Lominadze, J. G., Stenflo, L., Tsytovich, V. N. & Wilhelmsson, H. 1982 A new explanation of the high effective temperatures in pulsar radioemissions. Phys. Scr. 26, 455458.
Luo, Q. & Melrose, D. B. 2004 Orthogonal mode polarization of pulsar radio emission. In Young Neutron Stars and their Environments (ed. Camilo, F. & Gaensler, B. M.), IAU Symposium, vol. 218, p. 381.
Luo, Q., Melrose, D. B. & Fussell, D. 2002 Wave dispersion in gyrotropic relativistic pulsar plasmas. Phys. Rev. E 66 (2), 026405.
Lyubarskii, Y. E. 1992 Possible mechanism of pulsar radio emission. Astron. Astrophys. 265, L33L36.
Lyutikov, M. 1999 Beam instabilities in a magnetized pair plasma. J. Plasma Phys. 62, 6586.
Lyutikov, M. 2000 Excitation of Alfvén waves and pulsar radio emission. Mon. Not. R. Astron. Soc. 315, 3136.
Medin, Z. & Lai, D. 2010 Pair cascades in the magnetospheres of strongly magnetized neutron stars. Mon. Not. R. Astron. Soc. 406, 13791404.
Melrose, D. B. 1986 Instabilities in Space and Laboratory Plasmas. Cambridge University Press.
Melrose, D. B. 2008 Quantum Plasmadynamics: Unmagnetized Plasmas. Springer.
Melrose, D. B. 2013 Quantum Plasmadynamics: Magnetized Plasmas. Springer.
Melrose, D. B. & Gedalin, M. E. 1999 Relativistic Plasma Emission and Pulsar Radio Emission: A Critique. Astrophys. J. 521, 351361.
Melrose, D. B., Gedalin, M. E., Kennett, M. P. & Fletcher, C. S. 1999 Dispersion in an intrinsically relativistic, one-dimensional, strongly magnetized pair plasma. J. Plasma Phys. 62, 233248.
Melrose, D. B. & McPhedran, R. C. 1991 Electromagnetic Processes in Dispersive Media. Cambridge University Press.
Rafat, M. Z., Melrose, D. B. & Mastrano, A.2019a Wave dispersion in pulsar plasma. Part 2. Pulsar frame. J. Plasma Phys. (accepted for publication). arXiv:1812.07120.
Rafat, M. Z., Melrose, D. B. & Mastrano, A.2019b Wave dispersion in pulsar plasma. Part 3. Beam-driven instabilities. J. Plasma Phys. (submitted). arXiv:1906.01822.
Sironi, L. & Spitkovsky, A. 2009 Particle acceleration in relativistic magnetized collisionless pair shocks: dependence of shock acceleration on magnetic obliquity. Astrophys. J. 698, 15231549.
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.
Suvorov, E. V. & Chugunov, Y. V. 1973 Distribution function of relativistic electrons in a strong magnetic field. Astrophys. Space Sci. 23, 189199.
Suvorov, E. V. & Chugunov, Y. V. 1975 Electromagnetic waves in a relativistic plasma with a strong magnetic field. Astrophysics 11, 203222.
Synge, J. L. 1957 The Relativistic Gas. North-Holland Pub.
Timokhin, A. N. & Arons, J. 2013 Current flow and pair creation at low altitude in rotation-powered pulsars’ force-free magnetospheres: space charge limited flow. Mon. Not. R. Astron. Soc. 429, 2054.
Tsytovich, V. N. & Kaplan, S. A. 1972 Relativistic turbulent plasma in pulsars. Astrofizika 8, 441460.
Ursov, V. N. & Usov, V. V. 1988 Plasma flow nonstationarity in pulsar magnetospheres and two-stream instability. Astrophys. Space Sci. 140, 325336.
Usov, V. V. 1987 On two-stream instability in pulsar magnetospheres. Astrophys. J. 320, 333335.
Usov, V. V. 2000 Radiating regions in pulsar magnetospheres: from theory to observations and back. In IAU Colloq. 177: Pulsar Astronomy – 2000 and Beyond (ed. Kramer, M., Wex, N. & Wielebinski, R.), Astronomical Society of the Pacific Conference Series, vol. 202, p. 417. ASP.
Weatherall, J. C. 1994 Streaming instability in relativistically hot pulsar magnetospheres. Astrophys. J. 428, 261266.
Weatherall, J. C. 1997 Modulational instability, mode conversion, and radio emission in the magnetized pair plasma of pulsars. Astrophys. J. 483, 402413.
Weatherall, J. C. 1998 Pulsar radio emission by conversion of plasma wave turbulence: nanosecond time structure. Astrophys. J. 506, 341346.
Wright, T. P. & Hadley, G. R. 1975 Relativistic distribution functions and applications to electron beams. Phys. Rev. A 12, 686697.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Wave dispersion in pulsar plasma. Part 1. Plasma rest frame

  • M. Z. Rafat (a1), D. B. Melrose (a1) and A. Mastrano (a1)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed