In theoretical treatments of these dusty plasma systems, it has previously been assumed
that the dust grains interact via a linear Debye-shielded interaction potential
of the form =Ze/r*exp(-r/
_d), where
_d is the Debye length.
As far as we know, this has not been analyzed when the interaction potential is small,
but not when Z=10^4. As far as we know, this has not been analyzed previously.
For example, consider the force between two dust grains. In addition to the usual linear Debye-shielded force, one grain will polarize the Debye sphere surrounding the other grain, creating an attractive force which can reduce or possibly even reverse the overall repulsive force. That is, the Debye sphere around a dust grain acts like a spherical conductor, and a charged dust grain outside this sphere will polarize it, just as a charge outside a conducting sphere produces an image charge in the sphere.
This effect arises from the nonlinear terms in the Boltzmann distribution of the plasma
shielding the grains. Such terms are neglected in the usual linear analysis of
Debye shielding, but they will be important if e*(
_d)/kT
1.
This inequality can be written as Z*
(
)³
1. In laboratory experiments in argon discharges.
the background ions are weakly correlated with
~10¯², but since Z is very large the
above inequality can be easily satisfied, so nonlinear Debye shielding can have important
consequences for the inter-grain interaction.
We propose to study these effects in order to determine the correct form for the interaction between dust grains in such discharges. Preliminary calculations show that the intergrain force is strongly reduced by the nonlinear effects, in agreement with the simple intuitive model described above. Other effects such as nonthermal distributions and depletion of background electrons by the dust grains will also be studied in the context of their effect on the intergrain interactions.