Characteristics of an atmospheric-pressure line plasma excited by 2.45 GHz microwave travelling wave

As is mentioned, gas temperature is one of the essential parameters of an AP plasma because a high gas temperature sometimes makes the application of the AP plasma to non-heat-resistant materials difficult. To investigate the gas temperature of the plasma source in the present study, N₂ (C–B) rotational gas temperature is evaluated by OES^17–19) and the gas temperature is obtained supposing that the rotational temperature of the N₂ C-state is in equilibrium with the translational gas temperature. In the experiment, a trace of N₂ gas (0.5%) is admixed with He gas and the negligibly small influence of the N₂ addition on the plasma is confirmed, as shown by the absence of the variation in He emission intensity after the N₂ admixture. The solid curve in Fig. 2 shows the measured N₂ second positive band spectrum at a slot gap width of 0.5 mm and a duty cycle of 100% (cw mode) with a microwave power of 1.0 kW. The spectral resolution of the spectrometer is obtained to be 1.68 Å by mercury line width measurement using a mercury lamp. Rotational temperature is obtained by simulating the emission spectrum with the measured spectral resolution and fitting the simulated spectrum with the measured N₂ spectrum.

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Figure 3 shows the measured gas temperature as a function of the slot gap width in cw microwave power. As is mentioned, the AP microwave plasma utilizing the travelling wave indicates two types of plasma mode depending on the microwave power conditions, i.e., the pseudo line plasma mode with the fast movement of small plasmas along the slot and the real line plasma mode with a spatiotemporally uniform plasma along the slot. In this experiment, the plasma is the pseudo line plasma mode except at a slot gap of 0.1 mm; detailed results will be shown in Sect. 3.2. The gas temperature increases from 400 to 620 K with increasing gap width from 0.1 to 0.7 mm. It should also be noted that the gas temperature is lower than 620 K, which is much lower than those of other microwave plasmas (∼1,000 K),^13–15) and that a very low gas temperature of 400 K is realized at a gap of 0.1 mm. This result strongly suggests that this plasma source can be easily applied to non-heat-resistant materials such as polymer thin films or plastic materials. The reason for such a low gas temperature is probably because the present line plasma is realized using power deposition densities ranging from 1.0 to 10 kW/cm⁻³, which are much lower than those of typical microwave plasmas (∼1 MW/cm⁻³).^13–15) The lower gas temperature at the smaller gap width is presumably partly due to the shorter time for thermal diffusion to the slot metal and also partly due to the increased gas flow speed and shorter gas residence time at a fixed gas flow rate.

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To obtain an insight into the plasma movement mechanism, the movement of the plasmas is observed using the high-speed camera at a frame rate of 6.0 kHz and an exposure time of 50 µs. The average speed of the moving plasma is obtained from the transit time of small plasmas at a distance of 20 cm around the center of a 60-cm-long slot. Figure 4(a) shows average movement speed as a function of duty cycle at various slot gap widths from 0.1 to 0.7 mm. The movement speed increases almost linearly with the duty cycle of the pulsed microwave power with the fixed pulse frequency of 20 kHz. We previously reported that the movement speed always increases linearly with the duty cycle under the fixed pulse on- or off-time condition.²⁰⁾ Considering that the plasma is pulse-operated and the measured speed is the "time-averaged" speed including both the on- and off-time (the 6 kHz frame rate of the high-speed camera is lower than that at 20 kHz pulse frequency), the above results suggest that the plasma moves only during the pulse on-time, because plasma density drastically decreases in a few microseconds during the pulse off-time and it is expected that the subsequent discharge will occur in the same place. From this consideration, the real movement speed during the plasma-on condition can be estimated by extrapolating the duty cycle dependence of the speed to a duty cycle of 100% (cw mode), as shown in the fitted lines in Fig. 4(a). The result shows that the real movement speed drastically increases with decreasing slot gap width. The mechanism of the increase in movement speed with decreasing gap width will be discussed in Sect. 3.4.

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Plasma size is defined as the length along the slot of the emission region having 10% or more of the maximum emission intensity in high-speed camera photographs. Figure 4(b) shows the plasma size as a function of duty cycle at a peak input power of 1.0 kW with gap widths from 0.1 to 0.7 mm (filled plots with solid curves) and that of 2.0 kW with a gap width of 0.1 mm (open circles with a dotted curve). The plasma size increases with decreasing gap width and also with increasing microwave power or duty cycle. Plasma size increase at a smaller gap width is presumably due to the decrease in the volume of the gap space with decreasing gap width and microwave power can be used to increase the plasma size along the slot. The increase in plasma size with the peak power and duty cycle is qualitatively understood from the increase in average input power. It is notable that, at 0.1 mm gap width, the plasma size increases drastically at high duty cycles (>80% at 1.0 kW power and >60% at 2.0 kW power) and plasma becomes spatially continuous inside the slot, i.e., the plasma mode changes from pseudo line to real line. This result suggests that plasma size and the mode change strongly depend on power area density.

As reported previously, one of the important features of the plasma movement in the pseudo line plasma mode is that the direction of the plasma movement is determined by the direction of the travelling wave.¹⁶⁾ The plasma movement direction is reversed when the power flow direction is reversed. To obtain more insights into the movement mechanism of the plasma, plasma emission is observed using a high-speed gated ICCD camera at a gate time of 100 ns so that the influence of plasma movement can be ignored. Figures 5(a) and 5(b) show an image of one small plasma at a duty cycle of 100% (cw mode) with a gap width of 0.5 mm and its emission intensity distribution along the slot, respectively. The emission intensity increases toward the travelling direction of the plasma, which means the downstream region of the microwave power flow along the slot. The spatial variation in emission intensity qualitatively suggests that the plasma parameters such as excitation and ionization rates vary with the position inside the plasma along the slot direction and also suggests that the electromagnetic field varies inside the plasma along the slot direction.

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To investigate the electromagnetic field intensity in the slot, three-dimensional microwave simulation is carried out using CST MICROWAVE STUDIO^®, which is commercial software based on the finite integration technique for the analysis of high-frequency devices. As a simulation model, a 60 cm slot of 0.5 mm width and 1.0 mm thickness is cut in a waveguide. The input power is fixed at 1.0 W in the simulation software, which is one thousandth of the experimental value. To model the plasma inside the slot, a resistive conductor of 8 mm length is located at the center of the slot. The plasma conductivity σ_p is described by

$$\begin{equation} \sigma_{\text{p}} = \frac{e^{2}n_{0}}{m_{\text{e}}\nu_{\text{m}}}, \end{equation} \tag{ 1 }$$

where e, n₀, and m_e are the elementary charge, plasma density, and electron mass, respectively. The electron–neutral collision frequency ν_m is

$$\begin{equation} \nu_{\text{m}} = \frac{6.69\times 10^{5}\sqrt{T_{\text{e}}}}{\lambda_{\text{m}}}, \end{equation} \tag{ 2 }$$

where

$$\begin{equation} \lambda_{\text{m}} = \frac{k_{\text{B}}T_{\text{g}}}{pA} \end{equation} \tag{ 3 }$$

is the mean free path for electron–neutral collision and k_B is the Boltzmann constant.²¹⁾ Assuming that the plasma density, electron temperature, gas temperature, pressure, and collision cross section are n₀ ∼ 10¹⁴ cm⁻³, T_e ∼ 2 eV, T_g ∼ 620 K, p ∼ 10⁵ Pa (atmospheric pressure), and A ∼ 5 × 10⁻²⁰ m², respectively, a plasma conductivity of σ_p ∼ 5 S/m is obtained and used for the simulation. Figure 6 shows the microwave electric field intensity along the slot in the cases of (a) without and (b) with plasma. In the case of without plasma (a), the electric field is almost constant along the slot. In the case of with plasma (b), however, the electric field shows spatial variation inside the plasma, i.e., a higher electric field in the downstream region of the plasma than in the upstream region. Wave reflection occurs at an interface of different permittivity or conductivity materials, and the simulation result can be qualitatively analyzed by perturbation of the electromagnetic field by small reflection waves at the interface as follows. At the interface in the upstream region, a microwave from the left side of Fig. 6 encounters the air-plasma interface as if the slot is short-ended by the plasma conductor, resulting in the slight decrease in the microwave electric field intensity due to a small reflection wave. On the other hand, the plasma-air interface in the downstream region behaves as if it is an open-end, resulting in the slight increase in field intensity. Thus, it is supposed that the reflectivity difference between both plasma edges forms nonuniform fields inside the plasma, and that the resulting spatial variation in the electric field intensity inside the plasma causes the increase in emission intensity at the downstream side of the plasma.

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As described previously, the plasma movement direction is determined by the microwave power flow direction, and the speed increases with decreasing slot gap width. Although the plasma movement is determined by the microwave power flow direction, this cannot be explained simply by the one-way travelling microwave because the microwave propagation speed inside the waveguide (10⁸ m/s) is much higher than the plasma movement speed (∼10 m/s). To understand the mechanism of the plasma movement in the pseudo line plasma mode, a plasma diffusion model including the spatially asymmetric ionization property in a moving plasma is numerically simulated and compared with the experimental observation.

Figure 7 shows a schematic of the simulation model geometry, which provides a coordinate system: the positive x- and y-axes pointing in the vertical and normal directions to the slot, respectively. The positive z-axis extends along the slot from the plasma center at t = 0 s. In the model, the microwave power propagation inside the waveguide is parallel to the positive z-axis. Plasma movement is analyzed on the basis of the diffusion equation of the plasma:

$$\begin{equation} \frac{\partial n}{\partial t} = D_{\text{a}}\nabla^{2}n + S, \end{equation} \tag{ 4 }$$

where n, D_a, and S are the plasma density, ambipolar diffusion coefficient, and reaction rate in the gas phase, respectively.²²⁾ To simplify the model, the following assumptions are made:

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• 1)   
  The ambipolar diffusion coefficient D_a can be described simply.²³⁾

  $$\begin{equation} D_{\text{a}}\approx\mu_{\text{i}}\frac{k_{\text{B}}T_{\text{e}}}{e} \end{equation} \tag{ 5 }$$

  The ion mobility μ_i is obtained from Chanin and Biondi²⁴⁾ and the electron temperature T_e is estimated to be 2 eV.
• 2)   
  Only the He₂⁺ positive ion is considered because He⁺ rapidly forms the molecular ion He₂⁺ under atmospheric pressure.^25,26)
• 3)   
  Regarding the gas phase reaction, the following two reactions are considered: the ionization of electron neutral (He+e → He⁺ → He₂⁺) and recombination of electron ion (He₂⁺+e+He → 2He).
• 4)   
  The gas temperature T_g is constant along the slot and varies with slot width as is obtained from Fig. 4. Gas number density is obtained by the ideal gas law n_g = p/k_BT_g, assuming a pressure p of 100 kPa.

On the basis of the above assumptions, Eq. (4) is converted to a one-dimensional form of the z-axis (along the slot direction)

$$\begin{align} \frac{\partial n(z,t)}{\partial t} &= D_{\text{a}}\left(\frac{\partial^{2}}{\partial z^{2}} - \frac{1}{d_{x}^{2}} - \frac{1}{d_{y}^{2}}\right)n(z,t)\\ &\quad + g_{0}G(z,t) - k_{\text{re}}n_{\text{g}}n(z,t)^{2}, \end{align} \tag{ 6 }$$

where g₀, k_re, d_x, and d_y are the ionization rate, recombination rate, slot width, and thickness (1.0 mm), respectively. The ionization rate is approximately determined to be g₀ = 1.23n_g cm⁻³ s⁻¹ from the cross-sectional data²⁷⁾ and electron energy distribution function. The normalized spatial distribution of the ionization rate $G(z,t)$ is estimated from the spatial profile of the emission intensity shown in Fig. 5(b). The recombination rate k_re = 2.16 × 10⁻³¹T_g is estimated from Ref. 27. The model equation is solved numerically by the finite-difference method²⁸⁾ (time step, δt = 10⁻⁸ s; mesh size, δz = 0.02 mm).

Figure 8 shows the simulation result of the temporal variation in plasma movement in the case of a 0.3 mm gap. It is observed that the plasma moves toward the +z-axis at a constant velocity. Figure 9 shows the simulated and experimental results of movement speed as a function of gap width indicated by circle and square plots, respectively. A similar tendency of decreasing movement speed with decreasing gap width is observed both in the experiment and simulation. A slight difference in the slope of the curves between the simulation and the experiment is probably due to the simulation being oversimplified compared with real experimental conditions such as electron temperature, spatial distribution of ionization rate, and gas temperature. Nevertheless, the simulation roughly reproduces the experimental result and suggests that the mechanism of the moving plasma is a balance between the generation and diffusion of the plasma under asymmetric ionization in a moving plasma.

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