# Characteristics of 2.45 GHz Surface-Wave-Sustained Argon Discharge for Bio-Medical Applications
## 3 Results
### Effects of the Dielectric Tube Inner Diameter on the Plasma Column Size  
The axial distribution of the plasma density \(n_{\text{e}}\) obtained theoretically for the three discharge tubes 8/2, 8/3 and 8/4 (see Table 1) is presented in Figure 5a--solid lines. The plasma torch where plasma is surrounded by air is presented by dashed lines. The corresponding wave power can be seen in Figure 5b. The length of the plasma torch also increases with the wave power. The torch length produced with the same wave power (100 W) is marked by dots in Figure 5a. One can see that the theoretical prediction obtains a longer plasma column with a higher plasma density at the same wave power in the discharge tube with the smaller inner radius. Respectively, the plasma column with the same length is produced in the discharge tube with a smaller inner radius by a lower wave power. The plasma torch is longer, but with a lower electron density compared to the plasma inside the dielectric tube with the same wave power. From Figure 5b, one can see also that at the end of the plasma column inside the dielectric tube, the microwave power is not completely absorbed, and the residual power is higher at a smaller internal tube radius. At the end of the plasma torch (dashed lines), the residual microwave power is much lower. The experimentally measured plasma torch length produced by using the three discharge tubes shows different behavior. In Figure 6a, the fast camera imaging of the plasma  
Figure 4: Theoretical axial distribution for the discharge tube 8 mm/2 mm at different discharge conditions of (**a**) plasma density; (**b**) wave power. Figure 5: Theoretical axial distribution for three discharge tubes with different internal radii of (**a**) plasma density; (**b**) wave power. The solid lines correspond to plasma inside dielectric tube and the dashed lines are for plasma torch (plasma surrounded by air). torches in the three tubes are presented. From such images, the plasma torch length is measured at a different wave power, and the graphs are presented in Figure 6b. At the same wave power, the longer plasma torch is obtained in the discharge tube with the bigger internal radius, which is just the opposite to the theoretical results. There are two reasons for such discrepancy: (i) in the modeling, the gas flow is neglected, while all experiments are in the gas flow regime, and the gas glow varies from 2 L/min to 15 L/min. The experimental results presented in Figure 6b are at a gas flow rate of 5 L/min. (ii) The model results are obtained under the assumptions that the discharge tube is completely filled with plasma (or the plasma torch radius is equal to the discharge tube radius), while the experiment shows that inside the tube, there exist one or more filaments. Initially, at a low wave power, the filament is only one in each tube, but does not fill the tube completely in the radial direction. With wave power, the increasing of the length of the filament is almost linear, as it is theoretically predicted, but at some power, depending on the tube inner radius, a second filament appears, and the length of the first one stops increasing. This is illustrated in Figure 6c for the 8 mm/3 mm discharge tube. Our investigation shows that the appearance of the second filament happens at a lower wave power when the inner diameter of the discharge tube is smaller. It is shown by experimental [48] and radial modeling [49] investigations that the molecular argon ions play a critical role in the radial contraction of argon microwave discharges at atmospheric pressure. Our modeling results show the axial distribution of argon atomic (Ar\({}^{+}\)) and two molecular (Ar\({}_{2}\)\({}^{+}\) and Ar\({}_{3}\)\({}^{+}\)) ions along the plasma column in the three discharge tubes (Figure 7). As it can be seen, the molecular Ar\({}_{2}\)\({}^{+}\) ion has a much higher concentration than the other two ions in all tubes, which is in good agreement with the prediction in [48; 49].