THE ELECTROSTATICS OF A DUSTY PLASMA. E. C. Whi^pple and D. A.
Mendis, University of California, San Diego, T. G. Northrop,
Goddard Space Flight Center. We have derived the potential
distribution in a plasma containing dust grains where the Debye
length can be larger or smaller than the average intergrain
spacing. We treat three models for the grain-plasma system, with
the assumption that the system of dust and plasma is
charge-neutral: a permeable graih model, an impermeable grain
model, and a capacitor model that does not require the nearest
neighbor approximation of the other two models. We use a
gauge- invariant form of Poisson's equation which is linearized
about the average potential in the system. The charging currents
to a grain are f\mctions of the difference between the grain
potential and this average potential. We obtain expressions for
the equilibrium potential of the grain and for the gauge-
invariant capacitance between the grain and the plasma. The
charge on a grain is determined by the product of this
capacitance and the grain-plasma potential difference.
The three models give similar but not identical results.
The results depend primarily on the parameter Z = 4irX NC, where X
is the Debye length, N is the grain concentration, and C is the
grain to plasma capacitance. When Z >> 1, the number of charges
on a grain that is only charged by plasma currents is given by
C-Q/e) = [(u-l)/(y+l)] [ (ii .+n ) /N] where p is the square-root of
the Ion to electron mass ratio, and n and n are the average ion
and electron densities. The charge on a grain in such regions is
severely decreased from its free space value. The charge
reduction occurs because the plasma electrons are depleted so
that the grain does not need to be as negatively charged to
equalize the ion and electron fluxes to its surface, despite the
increased grain to plasma capacitance.