Wave dispersion in pulsar plasma: 1. Plasma rest frame

Abstract

Wave dispersion in a pulsar plasma (a 1D, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation these are referred to as the X, A and L modes, with the X and A modes having dispersion relation $z=z_A\approx 1-1/2{\beta }_A^2$, where $z=\omega /k_{\parallel }c$ is the phase speed and ${\beta }_{A}c$ is the Alfven speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function, $z^{2}W(z)$, which is negative for $z<z_0$ and has a sharp maximum at $z=z_m$, with $1-z_m<1-z_0\ll 1$. We give numerical estimates for the maximum of $z^{2}W(z)$ and for $z_m$ and $z_0$ for a 1D Juttner distribution. The L and A modes reconnect, for $z_A>z_0$, to form the O and Alfven modes for oblique propagation ($\theta \ne 0$). For $z_A<z_0$ the Alfven and O~mode curves reconnect forming a new mode that exists only for ${\tan }^2\theta >z_0^2-z_A^2$. The L mode is the nearest counterpart to Langmuir waves in a nonrelativistic plasma, but we argue that there are no `Langmuir-like' waves in pulsar plasma, identifying three features of the L~mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir-like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O~mode around $\theta \approx 0$. The resonance is also possible for the Alfven mode but only near a turnover frequency that has no counterpart for Alfven waves in a nonrelativistic plasma.

Accepted for publication in the Journal of Plasma Physics

References in corpus (3)

• Persistence of precursor waves in two-dimensional relativistic shocks
• Wave dispersion in pulsar plasma: 3. Beam-driven instabilities
• Wave dispersion in pulsar plasma: 2. Pulsar frame

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