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Wave dispersion in pulsar plasma. Part 2. Pulsar frame

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

Abstract

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.

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Corresponding author

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

References

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Wave dispersion in pulsar plasma. Part 2. Pulsar frame

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

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