Phase-resolved optical emission of dusty rf discharges: Experiment and simulation

The spectral emission of atoms in a dusty radio frequence (rf) discharge plasma in argon and helium has been measured with a gated ICCD camera. The spatially and temporally resolved emission/excitation of the argon and helium atoms during the rf cycle in the dusty discharge was compared to the dust-free case. In the bulk plasma above the dust cloud, the emission is clearly enhanced in the dusty discharge with respect to the pure discharge, whereas in the sheath the emission is reduced. In addition, the emission of a dusty argon plasma is studied via particle-particle particle-mesh (P${}^3\mathrm{M}$) simulations. The rf dynamics with a single dust particle trapped in the sheath was calculated. Like in the experiment the dust modifies the atomic emission. The spatiotemporal excitation pattern of the experiment is reproduced and a detailed understanding of the difference in excitation of the discharge with and without dust is presented.

Figure 1

Scheme of the setup. See text for details.

Figure 2

Spectral intensities of (a) the argon and (b) the helium discharge. The investigated lines are indicated.

Figure 3

Measured spatiotemporally resolved emission at 750 nm of the argon discharge (a) without and (b) with 10 $\mu$m dust trapped in the sheath. The temporal axis covers 200 ns corresponding to nearly 3 rf cycles.

Figure 4

Spatiotemporal excitation of the 750 nm spectral line with 10 $\mu$m dust trapped in the sheath derived from the deconvolution of the emission [see Fig. 3b]. The upper panel shows the rf voltage applied to the lower electrode.

Figure 5

Difference of the excitation of the argon 750 nm lines with dust and without dust. The dust trapped in the sheath has a diameter of (a) 3.5 $\mu$m and (b) 10 $\mu$m. The difference has been normalized to the maximum value of the excitation in the dust-free case. The height where the dust is trapped is indicated by the horizontal dashed lines.

Figure 6

Difference of the excitation of the helium 667.8 nm lines with dust and without dust. The dust trapped in the sheath has a diameter of (a) 3.5 $\mu$m and (b) 10 $\mu$m. The difference has been normalized to the maximum value of the excitation in the dust-free case. The height where the dust is trapped is indicated by the horizontal dashed lines.

Figure 7

Time-averaged relative excitation ${\mathrm{X̄}}_{\mathrm{exc}}(z)$ in (a) an argon discharge and (b) a helium discharge versus height above the electrode using dust of 3.5 (dotted line) and 10 $\mu$m (solid line) diameter. The shaded areas indicate the height where the dust is trapped.

Figure 8

Spatially averaged emission difference $\Delta I(t)$ as a function of time for the different argon lines at 750 nm, 810 nm, and 840 nm.

Figure 9

(a) The plot shows the rf voltage at the lower electrode and (b) the simulated phase-resolved, normalized changes in the dust charge according to electron and ion fluxes over rf period to the dust after the transient charging phase. In (c) changes in the dust charge under same conditions as in (b) are shown, except that an artificially decreased collision rate was used.

Figure 10

(a) Spatiotemporally resolved excitation difference determined from experimental data of the $750.4\hspace{0.5em}\mathrm{nm}$ spectral line of argon [compare Fig. (5)] and (b) from the simulation. The difference in excitation was calculated by subtracting from the pattern with dust the excitation without dust normalized to the reference without dust. The horizontal solid black line indicates the position of the dust grain; parameters of the experiment $U=250\hspace{0.5em}\mathrm{V}$, $p=30\hspace{0.5em}\mathrm{Pa}$ and of the simulation $p=50\hspace{0.5em}\mathrm{Pa}$, $U_{\mathrm{rf}}=50\hspace{0.5em}\mathrm{V}$.

Figure 11

Phase-resolved difference in electron density. Only particles with a higher energy than the indicated energy threshold are counted for the density. The horizontal solid black line indicates dust particle position.

Figure 12

Normalized differences of the time-averaged integral EEDF $\delta n(E)=n_{e,\mathrm{dust}}(E)-n_{e,\mathrm{ref}}(E)$. The top plot shows the phase and the middle plot the difference in excitation. The vertical solid black line in these plots indicates the phase of the rf cycle. At the bottom the EEDF is plotted. For convenience, the EEDF is summed up over the whole axial extent of the difference in excitation. Indicated by the vertical dashed black line is the energy threshold for excitation from ground state to $2p_1$ at $13.47\hspace{0.5em}\mathrm{eV}$. From this energy on the density difference is magnified five times.