Wave dispersion in pulsar plasma: 2. Pulsar frame

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 ${\beta }_{\mathrm{s}}$. 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.

Accepted for publication in Journal of Plasma Physics

References in corpus (1)

• Wave dispersion in pulsar plasma: 1. Plasma rest frame

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