Plasma Dielectric for a Warm Dusty Plasma with Grain Size Distribution and Charging

Michael A. Raadu

Royal Institute of Technology, Alfvén Laboratory, Division of Plasma Physics, SE-100 44 Stockholm, Sweden

Abstract : Dust grains in a dusty plasma introduce new physical processes. The dynamical charging of grains leads to wave damping and an enhanced shielding of charges that is physically different to ordinary Debye shielding. A distribution of grain sizes is generally expected in actual dusty plasmas, and the contribution of a thermalised dust to the plasma dielectric may in special cases be equivalent to that for a kappa (generalised Lorentzian) distribution of mono-sized particles. The combined effects are studied here. The plasma dielectric charging term is derived and is given by a double integration over the size and velocity distribution. A modified form of Landaušs rule is required to deal with the pole in the integrand. Known results are recovered in the limiting case of a cold dust component with unique grain size. A series approximation is found for the warm dust response in the long wavelength limit. In the cold case the shielding due to dynamical charging and the wave damping can be expressed in forms resembling previous results but now with parameters given by weighted means over the mass distribution.

Key Words : dusty plasma, dynamical charging, size distribution, kappa distribution

Information : Published as an Alfvén Laboratory report (December 2002)
TRITA-ALP-2002-04 (ISRN KTH/ALP/R-02/4-SE)