Alfvén Waves in Dusty Interstellar Clouds.

N. F. Cramer, S. V. Vladimirov, PASA, 14 (2), in press.

Next Section: The Dispersion Relation
Title/Abstract Page: Alfvén Waves in Dusty
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Model and Wave Equations

As in Pilipp et al. (1987) we consider small-amplitude waves in a static uniform molecular cloud consisting of neutral atomic and molecular species, the ionized atomic and molecular species, the electrons, neutral dust grains, and negatively charged dust grains. The cloud is assumed cold, so that the gas pressures of all the species may be neglected. A 4-fluid model of the plasma is used, which employs the linearized fluid momentum equations for plasma ions (singly charged), electrons, neutral molecules and charged dust grains: (We neglect the motion of neutral dust grains that was included by Pilipp et al. (1987))
where tex2html_wrap_inline604 is the wave electric field, tex2html_wrap_inline606 is the species mass and tex2html_wrap_inline608 is the species velocity in the wave. tex2html_wrap_inline610 is the collision frequency of a particle of species s with the particles of species t. We have neglected electron inertia and momentum exchange between ions and electrons, but have included ion and neutral molecule inertia terms because we are mainly interested in the frequency regime above the dust cyclotron frequency, where the ion and neutral molecule dynamics are important.

To complete the system of equations, Maxwell's equations ignoring the displacement current are used, with the conduction current density given by
where equilibrium charge neutrality is expressed by (1).

The background magnetic field tex2html_wrap_inline616 is assumed to be in the z-direction, and the steady electron, ion and dust densities are tex2html_wrap_inline620, tex2html_wrap_inline622 and tex2html_wrap_inline624. The parameter tex2html_wrap_inline626 measures the charge imbalance in the plasma, with the remainder of the charge residing on the dust particles, so that the total system is charge neutral. The equations are linearized, so that since we can define the transverse direction of wave field variation to be the x-axis, without loss of generality the wave fields are assumed to vary as tex2html_wrap_inline630. Thus our analysis differs from that of Pilipp et al. (1987) in that oblique propagation (i.e. non-zero tex2html_wrap_inline632) is allowed for. We assume for simplicity that the charge on the dust particles is not affected by the wave, i.e. we neglect the dust charging effects discussed by Vladimirov (1994a,b).

Define the Alfvén speed tex2html_wrap_inline634, where tex2html_wrap_inline636, the ion-cyclotron frequency tex2html_wrap_inline638 and the dust-cyclotron frequency tex2html_wrap_inline640. Eliminating tex2html_wrap_inline604 and tex2html_wrap_inline644, and using the assumed time dependence, we obtain, for tex2html_wrap_inline646,
where tex2html_wrap_inline648 is the wave magnetic field, tex2html_wrap_inline650 and tex2html_wrap_inline652. The neglect of gas pressure in all species implies that tex2html_wrap_inline654.

Next Section: The Dispersion Relation
Title/Abstract Page: Alfvén Waves in Dusty
Previous Section: Introduction
Contents Page: Volume 14, Number 2

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