Sketch of a glow-discharge plasma. (a) The main plasma region is bounded by sheaths, which have a deficit of electrons and a strong electric field. (b) The time-averaged (dc) electric potential has positive peak. In the main plasma, from the sheath edge to the center, the height of this peak is a multiple of one or two times . The dc electric field points away from the main plasma, expelling ions.
(a) Dependence of ion drag force on ion flow velocity . Due to acceleration by , generally increases with distance from the plasma center. An equilibrium occurs when , as indicated for example by the dot. This depends on parameters such as ion density and microparticle charge, which may vary with position. (b) Dependence of ion mobility coefficient on . Data shown here are calculated for typical experimental parameters: microparticle radius , a 0.12 torr neon gas, and plasma parameters , , and .
(a) Demonstration of the final step of our resonance method of estimating and simultaneously. The downward and upward-sloping curves are the solutions from steps 3 and 4, respectively, as functions of the unknown parameter . Their intersection yields for the values of both and . (b) Demonstration of our force-balance method of estimating . The horizontal line represents a constant value for , while the upward-sloping line represents ion drag force variation with ion density. The intersection yields the result for the value of ion density.
Side-view image of the microparticle suspension in our demonstration experiment. In this still image from a video recording, microparticles appear as white spots, due to illumination by a vertical sheet of laser light. An analysis of the video yields the small-amplitude motion and equilibrium positions of microparticles in the single layer (at the bottom of the void), which are used as the inputs for our two methods. Distances are measured from the plasma center, halfway between the electrodes.
Results for and (from the resonance method), and (from the force-balance method, using and as inputs). Results for are computed using Eq. (1). Data shown are from our demonstration experiment. There are two unknown parameters for the resonance method: relates and in a gas discharge and quantifies the fractional contribution of to the force constant , where the remaining contribution arises from . For the force-balance method, is an unknown parameter. These results demonstrate the methods and their sensitivity to the unknown parameters. An iteration process is also demonstrated to determine the unknown parameters and . The final results appear in the last line of this table.
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