Radio Emission of Pulsars. I. Slow Tearing of a Quantizing Magnetic Field. (arXiv:2111.01958v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Thompson_C/0/1/0/all/0/1">Christopher Thompson</a> (CITA, University of Toronto)
The pulsed radio emission of rotating neutron stars is connected to slow
resistive instabilities feeding off an inhomogeneous twist profile within the
open circuit. This paper considers the stability of a weakly sheared,
quantizing magnetic field in which the current is supported by a relativistic
particle flow. The electromagnetic field is almost perfectly force-free, and
the particles are confined to the lowest Landau state, experiencing no
appreciable curvature drift. In a charge-neutral plasma, we find multiple
branches of slowly growing tearing modes, relativistic analogs of the double
tearing mode, with peak growth rate $s gtrsim 4pi widetilde k_y J_z/B_z$.
Here, $B_z$ is the strong (nearly potential) guide magnetic field, $J_z$ the
field-aligned current density, and $widetilde k_y$ is the mode wavenumber
normalized by the current gradient scale. These modes are overstable when the
plasma carries net charge, with real frequency $omega sim scdot |n_0^+ –
n_0^-|/(n_0^+ + n_0^-)$ proportional to the imbalance in the densities of
positive and negative charges. An isolated current sheet thinner than the skin
depth supports localized tearing modes with growth rate scaling as (sheet
thickness/skin depth)$^{-1/2}$. In a pulsar, the peak growth rate is comparable
to the angular frequency of rotation, $s gtrsim 2widetilde k_y Omega$, slow
compared with the longitudinal oscillations of particles and fields in a polar
gap. The resistive modes experience azimuthal drift reminiscent of sub-pulse
drift and are a promising driver of pulse-to-pulse flux variations. A companion
paper demonstrates a Cerenkov-like instability of current-carrying Alfv’en
waves in thin current sheets with relativistic particle flow, and proposes
coherent curvature emission by these waves as a source of pulsar radio
emission.
The pulsed radio emission of rotating neutron stars is connected to slow
resistive instabilities feeding off an inhomogeneous twist profile within the
open circuit. This paper considers the stability of a weakly sheared,
quantizing magnetic field in which the current is supported by a relativistic
particle flow. The electromagnetic field is almost perfectly force-free, and
the particles are confined to the lowest Landau state, experiencing no
appreciable curvature drift. In a charge-neutral plasma, we find multiple
branches of slowly growing tearing modes, relativistic analogs of the double
tearing mode, with peak growth rate $s gtrsim 4pi widetilde k_y J_z/B_z$.
Here, $B_z$ is the strong (nearly potential) guide magnetic field, $J_z$ the
field-aligned current density, and $widetilde k_y$ is the mode wavenumber
normalized by the current gradient scale. These modes are overstable when the
plasma carries net charge, with real frequency $omega sim scdot |n_0^+ –
n_0^-|/(n_0^+ + n_0^-)$ proportional to the imbalance in the densities of
positive and negative charges. An isolated current sheet thinner than the skin
depth supports localized tearing modes with growth rate scaling as (sheet
thickness/skin depth)$^{-1/2}$. In a pulsar, the peak growth rate is comparable
to the angular frequency of rotation, $s gtrsim 2widetilde k_y Omega$, slow
compared with the longitudinal oscillations of particles and fields in a polar
gap. The resistive modes experience azimuthal drift reminiscent of sub-pulse
drift and are a promising driver of pulse-to-pulse flux variations. A companion
paper demonstrates a Cerenkov-like instability of current-carrying Alfv’en
waves in thin current sheets with relativistic particle flow, and proposes
coherent curvature emission by these waves as a source of pulsar radio
emission.
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