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Wave dispersion in pulsar plasma. Part 2. Pulsar frame
Published online by Cambridge University Press: 26 June 2019
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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- © Cambridge University Press 2019
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