Skip to main content Accessibility help

Wave dispersion in pulsar plasma. Part 2. Pulsar frame

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


Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\mathcal{K}}$ and the pulsar frame ${\mathcal{K}}^{\prime }$ in which the plasma is streaming with speed $\unicode[STIX]{x1D6FD}_{\text{s}}$ . The effect of a Lorentz transformation on both subluminal, $|z|<1$ , and superluminal, $|z|>1$ , waves is discussed. It is argued that the preferred choice for a relativistically streaming distribution should be a Lorentz-transformed Jüttner distribution; such a distribution is compared with other choices including a relativistically streaming Gaussian distribution. A Lorentz transformation of the dielectric tensor is written down, and used to derive an explicit relation between the relativistic plasma dispersion functions in ${\mathcal{K}}$ and ${\mathcal{K}}^{\prime }$ . It is shown that the dispersion equation can be written in an invariant form, implying a one-to-one correspondence between wave modes in any two inertial frames. Although there are only three modes in the plasma rest frame, it is possible for backward-propagating or negative-frequency solutions in ${\mathcal{K}}$ to transform into additional forward-propagating, positive-frequency solutions in ${\mathcal{K}}^{\prime }$ that may be regarded as additional modes.


Corresponding author

Email address for correspondence:


Hide All
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. & Melikidze, G. I. 1998 Non-stationary pair plasma in a pulsar magnetosphere and the two-stream Instability. Mon. Not. R. Astron. Soc. 301, 5971.
Beskin, V. S., Gurevich, A. V. & Istomin, Y. N. 1993 Physics of the Pulsar Magnetosphere. Cambridge University Press.
Cairns, I. H., Li, B. & Schmidt, J. M. 2017 Chapter 14 – importance of kappa distributions to solar radio bursts. In Kappa Distributions (ed. Livadiotis, G.), pp. 549567. Elsevier.
Cordes, J. M. 1978 Observational limits on the location of pulsar emission regions. Astrophys. J. 222, 10061011.
Gedalin, M., Melrose, D. B. & Gruman, E. 1998 Long waves in a relativistic pair plasma in a strong magnetic field. Phys. Rev. E 57, 33993410.
Gupta, Y. & Gangadhara, R. T. 2003 Understanding the radio emission geometry of multiple-component radio pulsars from retardation and aberration effects. Astrophys. J. 584, 418426.
Istomin, Y. 2001 Propagation of electromagnetic waves in pulsar magnetospheres. Astrophys. Space Sci. 278, 7780.
Kaplan, S. A. & Tsytovich, V. N. 1973 Plasma Astrophysics. Pergamon Press.
Lazar, M., Stockem, A. & Schlickeiser, R. 2010 Towards a relativistically correct characterization of counterstreaming plasmas. I. Distribution functions. Open Plasma Phys. J. 3, 138147.
Lesch, H., Jessner, A., Kramer, M. & Kunzl, T. 1998 On the possibility of curvature radiation from radio pulsars. Astron. Astrophys. 332, L21L24.
Lominadze, J. G. & Pataraya, A. D. 1982 Some nonlinear mechanisms of pulsar emission. Phys. Scr. T2, 215222.
Lyne, A. G. & Graham-Smith, F. 2006 Pulsar Astronomy. Cambridge University Press.
Melrose, D. B. 1973 A covariant formulation of wave dispersion. Plasma Phys. 15, 99106.
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.
Rafat, M. Z., Melrose, D. B. & Mastrano, A. 2019a Wave dispersion in pulsar plasma. Part 1. Plasma rest frame. J. Plasma Phys. 85, 905850305.
Rafat, M. Z., Melrose, D. B. & Mastrano, A. 2019b Wave dispersion in pulsar plasma. Part 3. Beam-driven instabilities. J. Plasma Phys. (submitted).
MathJax is a JavaScript display engine for mathematics. For more information see


Wave dispersion in pulsar plasma. Part 2. Pulsar frame

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


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.