Wave dispersion in pulsar plasma. Part 1. Plasma rest frame
Abstract
Wave dispersion in a pulsar plasma (a one-dimensional, 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 (wave angle ) these are referred to as the X, A and L modes, with the X and A modes having dispersion relation , where is the phase speed and is the Alfvén speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function, , which is negative for and has a sharp maximum at , with . We give numerical estimates for the maximum of and for and for a one-dimensional Jüttner distribution. The L and A modes reconnect, for , to form the O and Alfvén modes for oblique propagation ( ). For the Alfvén and O mode curves reconnect forming a new mode that exists only for . The L mode is the nearest counterpart to Langmuir waves in a non-relativistic plasma, but we argue that there are no `Langmuir-like' waves in a 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 . The resonance is also possible for the Alfvén mode but only near a turnover frequency that has no counterpart for Alfvén waves in a non-relativistic plasma.
- Publication:
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Journal of Plasma Physics
- Pub Date:
- June 2019
- DOI:
- 10.1017/S0022377819000394
- arXiv:
- arXiv:1812.07121
- Bibcode:
- 2019JPlPh..85c9005R
- Keywords:
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- astrophysical plasmas;
- plasma instabilities;
- plasma waves;
- Physics - Plasma Physics;
- Astrophysics - High Energy Astrophysical Phenomena
- E-Print:
- Accepted for publication in the Journal of Plasma Physics