Wave dispersion in pulsar plasma: 2. Pulsar frame

Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${cal K}$ and the pulsar frame ${cal K}$ in which the plasma is streaming with speed $beta_{rm s}$. 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 Juttner 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 ${cal K}$ and ${cal K}$. 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 ${cal K}$ to transform into additional forward-propagating, positive-frequency solutions in ${cal K}$ that may be regarded as additional modes.