Abstract of a talk to be presented by Martin Lampe, Code 6709,
at the Graduate Summer Institute on Complex Plasmas,
Stevens Institute of Technology, Hoboken, NJ, August 4, 2008
Dynamics of Dust Grains in Flowing Plasma *
Martin Lampe and Gurudas Ganguli,
Naval Research Laboratory, Washington, DC 20375-5346,
and Glenn Joyce, University of Maryland
lampe@nrl.navy.mil
In discharges, dust resides at the sheath edge above the lower electrode, where it is subject to
ion streaming at velocity ~ cs. The grains therefore interact via a dynamically shielded
potential (r) that takes the form of a downstream wakefield, which can be accurately
approximated by linear response theory. Once this is done, the plasma is eliminated from the
problem, and the dust cloud can be treated simply as a set of N grains interacting via (r).
However, the potential is not symmetric upstream/downstream, and therefore Newton’s third
law fails and neither energy nor momentum is conserved. We use both analytic theory and
simulation in a systematic exploration of this N-body system, beginning with N=2. In the
absence of any confining potential, the dust self-organizes into stable molecules that can have
two, three or four grains, vertically aligned. The molecules propel themselves upstream
against the ion flow, due to the non-reciprocal repulsive/attractive forces between grains.
Longer strings can exist only if there is a vertical confining force V(z). By increasing the
strength of V(z), the grains can be squeezed together as close as z ~ 0.4De. If the spacing is
closer, the string breaks up. Even if z > 0.4De, a string of > 2 grains is subject to a hose
instability, driven by the ion streaming. This instability is stabilized by friction for neutral
pressure P above some critical value P2. For P less than a smaller critical value P1, the
instability breaks up the string. If P1<P<P2, the string survives but goes to a limit cycle of
large-amplitude hose oscillations, which are self-excited and persist in spite of frictional
dissipation. If the grains are in an axisymmetric 2-D potential well V(r,z) that provides both
horizontal and vertical confinement, there are usually multiple equilibria. As the strength of
the vertical confining force is varied, the equilibrium cycles through a hysteresis loop, with
jumps that resemble phase transitions. If V(r,z) is bi-harmonic, the two-grain problem is
integrable and can be solved for ground and excited states. For this case, it is found that the
two grains are either aligned vertically on axis, or symmetrically in the mid-plane. However,
for two or more grains in an anharmonic well, there are no constants of the motion, and if
there are multiple equilibria it is not possible to distinguish a ground state. Equilibria are
found that are not symmetric with respect to the axis or the midplane, and in certain
parameter ranges the grains go into self-excited oscillations about the mid-plane, which
persist in spite of friction. We find analytic solutions for two grains in a quadratic/quartic
well, and we show simulation results for a variety of cases. The results provide at least
qualitative explanation for many of the experimental results. Most of this work is published
in IEEE Trans. Plasma Sci. 33, 57 (2005).
*Supported by ONR