Collision-dominated dust sheaths andvoids - observations in micro-gravity experiments and numericalinvestigation of the force balance relations

Abstract

Numerical solutions of stationary force balance equations areused to investigate the possible dust configurations (duststructures) in complex plasmas between two floating potentialplane electrodes. The distance between electrodes is assumed tobe larger than the ion-neutral mean free path and thehydrodynamic description is used. It includes the known forcesoperating in this limit, the ionization source and the dustcharge variations. The stationary balance equations are solvedboth in the case of the presence of one-size dust grains and for thecase of a mixture of grains with two different sizes. Recentmicro-gravity experiments with single-size dust grains and two-different-size dust grains show the formation of a system ofdust sheaths and dust voids between the two plane electrodes. The observed configurations of dust structures depend strongly onthe gas pressure and the degree of ionization used. Thenumerical investigations are able to show the necessaryconditions for the types of structure to be created and givetheir size. The size of the structures observed is larger thanthe ion-neutral mean free path and is of the order of magnitudeof that obtained numerically. The numerical investigations givedetails of the spatial distributions, the dust particles,the electron/ion densities, the ion drift velocity and dustcharges inside and outside different dust structures. Thesedetails have not yet been investigated experimentally and can indicatedirections for further experimental work to be performed.The single-dust-sheath structure with single-size dust particlessurrounded by dust free regions (dust wall-voids) and floatingpotential electrodes is computed. Such a structure was observedrecently and the computational results are in agreement withobservations. It is shown that more often a dust void in thecentre is observed. It is found that a dust void in the centreregion between two electrodes is formed if the ionization rateis larger than the critical ionization rate and that in the presence ofthe floating potential walls the central void should besurrounded by two dust sheaths. The necessary condition forthis dust structure to be formed is found to be that betweenthe sheaths and the walls there are formed two other wall-voidregions. The size of the central void and the distributions of thestructure parameters in the two sheaths and in the three voidsare computed. The qualitative features of the structure obtainedin the numerical computations correspond to those observed. Thedistributions of the structure parameters in the case of the twodust sheaths are quite different from that for the case of asingle central sheath. The possible structures between theelectrodes for the case of the presence of dust particles of twodifferent sizes are analysed numerically. It is shown that dust particles with different sizes cannot coexist inequilibrium at the same position and that the regions withdifferent size dust particles must be separated in space. Thisconclusion is in agreement with most observations performed sofar. It is illustrated numerically that for the case where thecentral void is present the dust particles of larger size form aseparate dust sheath which should be located at larger distancesfrom the centre than that for the smaller dust particles. Thisresult also coincides qualitatively with the observations.Computations for the distributions of the parameters in thelarger size dust sheath were performed both in the case wherethe central part is occupied by a dust sheath with smaller sizedust particles and for the case where in the central part there existsa dust void surrounded by dust sheaths with smaller size dustparticles. The size of the dust void between the sheaths withdifferent size dust particles is calculated and shown to besmall as compared to the sheath thickness. In the sheath withlarger size dust particles the distribution of dust and plasmaparameters differs qualitatively from that of the first dustsheath with smaller size dust particles. The stability of thestationary structures both with respect to excitation of dustconvection cells and with respect to oscillations of dust voidsize is discussed.