Capacitively coupled rf discharge with a large amount of microparticles: Spatiotemporal emission pattern and microparticle arrangement

The effect of micron-sized particles on a low-pressure capacitively coupled rf discharge is studied both experimentally and using numerical simulations. In the laboratory experiments, microparticle clouds occupying a considerable fraction of the discharge volume are supported against gravity with the help of the thermophoretic force. The spatiotemporally resolved optical emission measurements are performed with different arrangements of microparticles. The numerical simulations are carried out on the basis of a one-dimensional hybrid (fluid-kinetic) discharge model describing the interaction between plasma and microparticles in a self-consistent way. The study is focused on the role of microparticle arrangement in interpreting the spatiotemporal emission measurements. We show that it is not possible to reproduce simultaneously the observed microparticle arrangement and emission pattern in the framework of the considered one-dimensional model. This disagreement can be attributed to the two-dimensional effects (e.g., radial diffusion of the plasma components) or to the lack of the proper description of the sharp void boundary in the frame of fluid approach.

Figure 1

(a) Sketch of the experimental setup. RF argon plasma is generated between the two electrodes powered in push-pull mode. The spatiotemporal profile of the plasma emission is observed by an ICCD camera, which is synchronized with the rf voltage via a frequency divider. Microparticles are injected into the plasma, illuminated by a laser sheet and observed by a CMOS camera. Large volumetric microparticle clouds are supported against gravity by the thermophoretic force. (b) Typical appearance of a microparticle cloud with a central void. Solid, dashed, and dotted lines mark the positions of the electrodes, edges of the microparticle cloud, and axial extension of the void, respectively.

Figure 2

Depth of field investigation of the ICCD camera: Dependence of the spot area (open circles) and maximal pixel intensity (full circles) in the image of a pointlike source on the distance between the pointlike source and camera focus. Negative abscissa displacement corresponds to the displacement towards the ICCD camera. Vertical dashed lines show the typical radial void extension.

Figure 3

Typical results of a simulation run (argon pressure $27\mathrm{Pa}$, voltage $54\mathrm{V}$). (a) Spatial profiles of the microparticle number density: initial input profile (blue line) and self-consistent steady-state profile (red line). (b) Spatial profiles of the local microparticle charge: the case of the pure discharge (green line) and the discharge with microparticles (orange line). The charge distribution for the discharge with microparticles corresponds to the simulation run of Fig. 3.

Figure 4

Spatiotemporal emission patterns of an rf discharge in argon at $27\mathrm{Pa}$ and $54\mathrm{V}$ rf amplitude with increasing (from left to right) microparticle number density: (a) experiment and (b) simulations. The leftmost figures correspond to the case of pure plasma. The emission intensity is given in arbitrary units. (c) The rf-period-averaged charge density distributions for the electrons (red line), microparticles (green line) and ions (blue line) obtained from the simulations. The results correspond to the emission patterns shown in Fig. 4. The dashed lines show the boundaries of the microparticle cloud and the dotted lines show the axial void extension observed in the experiments [see Fig. 1].

Figure 5

The results of the simulation run performed for a fixed microparticle number density distribution with the void in the central region [blue line in Fig. 3]. The discharge parameters are the same as in Fig. 4. (a) Spatiotemporal emission pattern. The emission intensity is given in arbitrary units. (b) The rf-period-averaged charge density distributions for the electrons (red line), microparticles (green line), and ions (blue line). The dashed lines show the boundaries of the microparticle cloud and the dotted lines show the void extension defined in the simulation [see Fig. 3].

Figure 6

Spatiotemporal emission patterns observed in the experiments with different positions of the void. The dotted lines show the experimentally observed axial void extension [Fig. 1]. Void position was varied by changing the temperature difference between the chamber flanges: (a) $12\mathrm{K}$, (b) $13\mathrm{K}$, and (c) $15\mathrm{K}$.

Figure 7

The distribution of the total force acting on a microparticle obtained from two simulation runs. The blue line shows the force obtained from the simulation with a fixed microparticle number density distribution considered in Sec. 4c. The red line shows the force obtained from the simulation performed using a self-consistent model of the discharge. The dotted lines show the void boundaries defined for the simulation with a fixed microparticle number density distribution.

Figure 8

Distributions of the microparticle number density in the argon discharge ($L=3\mathrm{cm}$) at the gas pressure of $24\mathrm{Pa}$ and the voltage amplitudes of $30\mathrm{V}$ (blue line) and $60\mathrm{V}$ (red line). The black line shows the initial distribution of the microparticle number density used in both simulation runs.