Some Researches on Dusty Plasmas

The first and second terms on the RHS can be visualized as the tension in the lines of
force and the pressure, respectively. The Maxwell stress at the control surface can be
neglected if it is situated in the quasi-neutral region. The calculation was based on a
quasi-neutral model of the plasma, assuming Boltzmann electrons and cold ions. Such
a plasma behaves as an isothermal gas, the temperature being that of the electrons and
the density being that of the ions. The resulting force on the immersed object, was
found to be given by the (initial) flow of momentum of those ions destined to hit the
object.
The calculations to date are incomplete. An early calculation [14] based on this gas
dynamic model is shown in Figure 15. The case considered then was that of a
cylindrical probe and the drag force was irrelevant. It is interesting to note, however,
that reference was made (in 1971) to dust particles in a gas discharge. A serious
limitation to the model is that it is restricted to cold ions. In some situations the
directed velocity of the ions is more important than their random velocities, in other
cases, however, e.g. in tokamaks, this is not the case.
Collisions and other effects
I have not considered the effect of collisions in this talk. Clearly collisions will be
important under some circumstances; no plasma is entirely collision-free nor infinite
in extent. An estimate of when the OML theory will fail due to collisions can be
found in references [7] and [15]. It reads λ < r p (-V p /kT i ) ½ , where λ is the mean free
path and V p is the potential of the probe or dust particle. It is perhaps of interest to
note that this inequality does not involve the Debye distance. Other topics not covered
here include the effects associated with a flowing plasma and those due to the
presence of a magnetic field. In some cases secondary effects such as photoemission
or thermionic emission take place. Much work remains to be done.
Acknowledgements
The work described, albeit briefly, in this lecture has been carried out in collaboration
with Beatrice Annaratone, Dan Law, Bill Steel, Ed Tomme, Roderick Kennedy and a
welcome visitor from Italy, Umberto de Angelis.
References
[1] Law, D.A., Steel,W.H., Annaratone, B.M. and Allen,J.E., Probe-induced particle
circulation in a plasma crystal, 1998, Phys.Rev.Rev. Lett.,80, 4189-4192.
[2] Steel,W.H, Law,D.A, Annaratone,B.M. and Allen,J.E., Laser induced motion of
micrometre size particles in rf plasma sheaths, 1997, Proc. XXIII Int. Conf. on
Phenomena in Ionized Gases, I 194.
[3] Steel,W.H, Law,D.A,,Tomme,E.B.,Annaratone,B.M. and Allen,J.E., Effect of
Laser Light on a Plasma Crystal, 1998, Europhysics Conference Abstracts, 22H, 114.
[4] Tomme,E.B., Annaratone,B.M. and Allen,J.E., Damped dust oscillations as a
plasma sheath diagnostic, 2000, Plasma Sources Science and Technology, 9, 87.
[5] Tomme,E.B., Law,D.A., Annaratone,B.M. and Allen,J.E., Parabolic sheath
potentials and their implications for the charge on levitated dust particles, 2000,
Phys.Rev.Lett., 85, 2518.
[6] Allen,J.E., Annaratone,B.M. and de Angelis,U., On the orbital motion limited
theory for a small body at floating potential in a Maxwellian Plasma, 2000, J.Plasma
Physics,63,299.
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