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Wave dispersion in pulsar plasma. Part 2. Pulsar frame

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  26 June 2019

M. Z. Rafat Open the ORCID record for M. Z. Rafat [Opens in a new window] ,
D. B. Melrose Open the ORCID record for D. B. Melrose [Opens in a new window]  and
A. Mastrano Open the ORCID record for A. Mastrano [Opens in a new window]
M. Z. Rafat
Affiliation:
SIfA, School of Physics, The University of Sydney, NSW 2006, Australia
D. B. Melrose*
Affiliation:
SIfA, School of Physics, The University of Sydney, NSW 2006, Australia
A. Mastrano
Affiliation:
SIfA, School of Physics, The University of Sydney, NSW 2006, Australia
*
†Email address for correspondence: [email protected]
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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.

Keywords

astrophysical plasmasplasma instabilitiesplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 3 , June 2019 , 905850311
Copyright
© Cambridge University Press 2019 

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