Causes of plasma column contraction in surface-wave-driven discharges in argon at atmospheric pressure

In this work we compute the main features of a surface-wave-driven plasma in argon at atmospheric pressure in view of a better understanding of the contraction phenomenon. We include the detailed chemical kinetics dynamics of Ar and solve the mass conservation equations of the relevant neutral excited and charged species. The gas temperature radial profile is calculated by means of the thermal diffusion equation. The electric field radial profile is calculated directly from the numerical solution of the Maxwell equations assuming the surface wave to be propagating in the ${\mathrm{TM}}_{00}$ mode. The problem is considered to be radially symmetrical, the axial variations are neglected, and the equations are solved in a self-consistent fashion. We probe the model results considering three scenarios: (i) the electron energy distribution function (EEDF) is calculated by means of the Boltzmann equation; (ii) the EEDF is considered to be Maxwellian; (iii) the dissociative recombination is excluded from the chemical kinetics dynamics, but the nonequilibrium EEDF is preserved. From this analysis, the dissociative recombination is shown to be the leading mechanism in the constriction of surface-wave plasmas. The results are compared with mass spectrometry measurements of the radial density profile of the ions ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}_2^{+}$. An explanation is proposed for the trends seen by Thomson scattering diagnostics that shows a substantial increase of electron temperature towards the plasma borders where the electron density is small.

Figure 1

Scheme of a typical experimental setup. The problem is solved for a given cross section in the axial direction for which the electron density at the axis is known. The cross section is specified by its distance $\mathrm{\Delta }z=3.7\mathrm{mm}$ from the launcher gap.

Figure 2

Flow chart representing the self-consistent routine. Some of the symbols were not introduced in the text, namely, $D_e$, the electron free diffusion coefficient; $N_j$, the density of the heavy species $j$; and $k_a$, the rate coefficient of the electronic collisional processes.

Figure 3

Electron density profile. Three different scenarios are shown, namely, full model, with no restrictions (black solid line), Maxwellian EEDF (blue dashed line), no dissociative recombination (green dot-dashed line), and the Bessel profile (red dotted line).

Figure 4

Reaction rates of charge creation as a function of the normalized radial coordinate. The creation processes are shown in blue, where the solid line is the ionization from the $4s$ states, the long-dashed line is the ionization from the molecular argon excimer, and the dotted line is the ionization from the $4p$ states. The destruction processes, here shown as negative creation processes, are given by the red lines, where the solid line is the dissociative recombination and the short-dashed line is the atomic three-body recombination. These results were generated using the full model.

Figure 5

Diffusion rate of charges as a function of the relative radial coordinate. These results were generated using the full model.

Figure 6

Radial profile of the densities of the excited species considered in the model [$\mathrm{Ar}\left({}^{3}P_2\right)$, $\mathrm{Ar}\left({}^{1}P_1\right)$, $\mathrm{Ar}\left({}^{3}P_0\right)$, $\mathrm{Ar}\left({}^{3}P_1\right)$, Ar($4p)$, and ${\mathrm{Ar}}_2^{*}$]. These results were generated using the full model.

Figure 7

Normalized number densities of ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}_2^{+}$. The blue and red solid lines are the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}_2^{+}$ densities, respectively, calculated by means of the full model. The dashed blue and red curves are the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}_2^{+}$ densities, respectively, obtained when the EEDF was assumed to be Maxwellian. The experimental values for ${\mathrm{Ar}}^{+}$ (blue symbols) and ${\mathrm{Ar}}_2^{+}$ (red symbols) are also shown [20].

Figure 8

Radial profile of the gas temperature (solid sloping curve), generated using the full model. The horizontal lines are used to display graphically the values of the calculated mean (dashed) and the measured (dot-dashed) temperatures, $\langle T_g\rangle$ and $T_{g,\mathrm{OH}}$, where $\langle T_g\rangle =542$ K and $T_{g,\mathrm{OH}}=659\left(8\right)$ K.

Figure 9

Radial profiles of the reduced electric field $E/N$ (blue solid line), electron temperature $T_e=2/3\langle \epsilon \rangle$ (red solid line), and Thomson temperature $T_{e,th}$ (red dashed line). These quantities were derived from the full model results.

Figure 10

Radial profile of the magnitude of the axial component of the electric field, $E_z$, obtained in the full model simulation.

Figure 11

Comparison between the radial profiles of the electron density, $n_e$, and the Thomson electron temperature, $T_{e,th}$. These quantities were derived from the full model results.

Figure 12

Electron energy distribution functions at different radial coordinates: $r/R=0$ mm (blue solid line), $r/R=0.25$ mm (red solid line), and $r/R=0.5$ mm (green solid line). The Maxwellian distribution which was fitted in the low energy electron interval is also shown: $r/R=0$ mm (blue dashed line), $r/R=0.25$ mm (red dotted line), and $r/R=0.5$ mm (green dot-dashed line). The EEDFs were obtained using the full model simulation.