Test Charge Response For A Dusty Plasma With Size Distribution And Charging Dynamics

Michael A. Raadu and Muhammad Shafiq
Royal Institute of Technology, School of Electrical Engineering,
Department of Space and Plasma Physics, SE-100 44 Stockholm, Sweden
Abstract. The dielectric response of a dusty (complex) plasma is sensitive to the form of the grain size distribution and
can be strongly modified by dynamical charging effects. For a class of size distributions, the plasma dielectric is
equivalent to that for a Lorentzian distribution of mono-sized particles. Dynamical charging of grains enhances the
shielding of a test charge, and associated time delays lead to new physical processes. Since the charging rate depends on
the size of a dust grain the contribution of the dynamical charging to the plasma dielectric becomes a complicated
function of frequency when a grain size distribution is introduced. However an analytical form for the frequency
dependence can be found, and for low frequencies a power series gives a good approximation. The combined effects of
grain size distribution and grain charging dynamics on the response to a slowly moving test charge moving through the
dusty plasma are treated using these results.
Keywords: Dusty (complex) plasmas, Grain charging dynamics, Grain size distribution.
PACS: 52.27.Lw; 52.27.Cm; 52.25.Mq; 52.35.Fp
Dusty (complex) plasma contains relatively massive, charged dust particles (grains), along with the usual
electrons and ions. Dusty plasmas are an essential component of space, found in protostellar clouds, protoplanetary
disks, cometary tails, and in the planetary rings [1]. As a result, the physics underlying the manner in which
microscopic dust grains interact with one another and their plasma/gas environment is a field of research having
broad implications on our understanding of the development of astrophysical systems.
There has recently been a renewed interest in the grain size distribution and grain charging dynamics in dusty
plasmas due to the impact these grains have on subsequent dust and plasma dynamics.
Here, we extend our previous work on grain size distribution [2] by taking into account the effect of charging
The linear response of the dusty plasma for an electrostatic disturbance can be determined through the choice of
the plasma dielectric function. Here the dielectric will include a term for the dynamical charging of the dust grains
and the effect of a specific choice for the size distribution will be taken into account.
Grain Size Distribution
Here we choose the size distribution h (a ) used previously [3].

where the constant 0 h is defined by setting the integrated density to the dust density and β is the power law index
for small sizes. For the case of electrostatic perturbations in dusty plasmas, it turns out that the dust then responds.

The effect of a size distribution on the dielectric term for dynamical charging is complicated but in the case
studied here is found in terms of known functions. Equation (2) gives correct expression for κ , and an integration
over velocity defines the equivalent number density of the monosized grains.
The authors would like to thank their colleagues at the Alfvén laboratory for useful discussions and suggestions.
This work was partially supported by the Swedish Research Council.
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