Wave dispersion in pulsar plasma: 1. Plasma rest frame. (arXiv:1812.07121v1 [physics.plasm-ph])
<a href="http://arxiv.org/find/physics/1/au:+Rafat_M/0/1/0/all/0/1">M. Z. Rafat</a>, <a href="http://arxiv.org/find/physics/1/au:+Melrose_D/0/1/0/all/0/1">D. B. Melrose</a>, <a href="http://arxiv.org/find/physics/1/au:+Mastrano_A/0/1/0/all/0/1">A. Mastrano</a>
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 $z=z_Aapprox1-1/2beta_A^2$,
where $z=omega/k_parallel c$ is the phase speed and $beta_Ac$ is the Alfven
speed. The L mode dispersion relation is determined by a relativistic plasma
dispersion function, $z^2W(z)$, which is negative for $ z < z_0 $ and has a
sharp maximum at $z=z_m$, with $1-z_m<1-z_0ll1$. We give numerical estimates
for the maximum of $z^2W(z)$ 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 ($thetaneq0$). For $z_A
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 $thetaapprox0$. 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.
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 $z=z_Aapprox1-1/2beta_A^2$,
where $z=omega/k_parallel c$ is the phase speed and $beta_Ac$ is the Alfven
speed. The L mode dispersion relation is determined by a relativistic plasma
dispersion function, $z^2W(z)$, which is negative for $ z < z_0 $ and has a
sharp maximum at $z=z_m$, with $1-z_m<1-z_0ll1$. We give numerical estimates
for the maximum of $z^2W(z)$ 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 ($thetaneq0$). For $z_A<z_0$ the Alfven
and O~mode curves reconnect forming a new mode that exists only for
$tan^2theta>z_0^2-z_A^2$.
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 $thetaapprox0$. 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.
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