Plasma Kinetics around a Dust Grain in an Ion Flow N F Cramer and S V Vladimirov, School of Physics, University of Sydney, S A Maiorov, General Physics Institute, Moscow The University of Sydney 1

The dust structures in a low-temperature weakly ionized plasma have attracted considerable recent attention associated with colloidal crystals, as well as with other self- organized formations such as dust clouds, ``drops", ``voids", etc. In a typical laboratory discharge, dust particles are negatively charged and usually levitate in the sheath or pre-sheath region under the balance of gravitational, electrostatic (due to the sheath electric field) and plasma (such as the ion drag) forces. The ion flow provides not only a direct (dragging) influence, but is also responsible for the generation of associated collective plasma processes which can strongly affect the vertical arrangement of dust grains. 2

Three-dimensional dust lattices 3

¥Micrometer sized particles embedded in a plasma acquire a charge; if the main charging mechanism is due to plasma currents then dust grains are charged negatively Dust charging 4

¥The effect of the wake behind each grain in the Mach cone (Vladimirov and Nambu, 1995; Vladimirov and Ishihara ) > ion > flow > to the > electrode > e l e c t r o d e 5

The kinetics of plasma particles around a stationary dust grain in the presence of an ion flow is studied using a 3- dimensional molecular dynamics simulation method. The model is self-consistent, involving the dynamics of plasma electrons and ions as well as charging of the dust grain. The effect of ion focusing is investigated as a function of the ion flow velocity. Distributions of electron and ion number densities, and electrostatic plasma potential are obtained. 6

The method includes consideration of the time evolution of the system consisting of N i positively charged and N e negatively charged particles confined in a region 0<x<L x, 0<y<L y, 0<z<L z. There is a macroscopic absorbing grain (“dust particle") of radius R with infinite mass and an initial (negative) charge Q=-Z d e, where -e is the electron charge. The dust grain is placed at x=x 0, y=y 0, and z=z 0. The walls bounding the simulation region are elastic for electrons. For ions, they are elastic in the y and z directions, i.e. at y=(0,L y ) and z=(0,L z ). N i 7

The ions are introduced in the system at the plane x=0 as a uniform flow with the Mach number M=V 0 /c s and the temperature T i, where c s is the ion-acoustic sound speed. At x=L x the ions are removed from the system. The paths of the ions and electrons are determined through numerical integration of the equations of motion, with all particles interacting via the Coulomb force. For the characteristic lengths we have L x /4=L y =L z =10h x, with the characteristic grid step h x =4h y =4h z =1.077  m. Other initial values are summarized in Table 1. 8

For the given values, the characteristic lengths in the plasma are: electron Debye length r De =5.256  m, ion Debye length r Di =0.831  m, and the Landau length for scattering of the ions on the dust particle by the angle  /2 is r L =0.6/M 2  m. 9

The total simulation time of the computed physical processes is 3.36 x s which is approximately half the oscillation period of plasma ions oscillating with the ion plasma frequency. 10

Fig 1: Contour plots of the ion density, for three values of the speed of the ion flow (one is subsonic with M 2 =0.6, and two supersonic, with M 2 =1.2 and M 2 =2.4). A strong ion focus is formed at the distance of a fraction of the electron Debye length behind the dust grain. 11

Fig. 2: surface plot of the ion density.The maximum value of the density at the ion focus is almost independent of the flow velocity, whereas the characteristic distance of the ion focus from the dust grain increases with increasing flow velocity. 12

This characteristic spacing corresponds to an ion focus effect in the near zone of the dust grain, which is a purely kinetic effect not associated with the collective wake field formation. The oscillating wake field which is formed in the wave zone behind the grain cannot form for the considered simulation time (half of the period of the ion oscillations). Another kinetic effect seen from Figs. 1 and 2 is the appearance of precursors in front of the dust grain, which can be attributed to those ions reflected backwards within the radius (around the x axis) of order of the Landau length. 13

Fig. 3: Surface plot of the plasma electrostatic potential (in Volts). The parts where the potential becomes positive, thus forming an attractive region for negatively charged particles, can be seen behind the grain. The potential well behind the dust grain deepens, and the characteristic distance of the potential minimum increases with the increase of the flow velocity. 14

Conclusions MD calculations show plasma kinetics around a charged macroscopic body (dust grain) in the presence of an ion flow involves a strong ion focusing behind the grain. The most important for the processes involved is the ion time- scale; the kinetics of the electrons follows a Boltzmann distribution with good agreement. To save computer time, future MD simulations can assume that the ions and the dust are immersed in an electron background which obeys a Boltzmann distribution. 15