## 4 Effect of Grounded Electrode Simulation Results  
The purpose of this theoretical study is to check the idea to use the grounded metal substrate under the bio-target to enhance the streamer characteristics near the target. The simulations of streamer formation in the plasma device and propagation to the target are performed in the framework of 2D fluid approach with the cylindrical symmetry. The fluid model of the discharge and streamer dynamics  
Figure 6: Intensity of OH-peak at \(\lambda\) = 309 nm in helium for different applied voltages with the grounded substrate (**a**) and the ratio of intensities of OH peaks with the grounded substrate and without it (**b**), v = 3 L/min. Figure 7: Intensity of OH-peak at \(\lambda\) = 309 nm in helium for different gas flow rates with the grounded substrate, \(U\) = 4.9 kV. includes continuity equations for electrons, ions and mean electron energy and the Poisson equation for the electric potential and electric field. The transport coefficients in the continuity equations for electrons and their mean energy are calculated from the electron energy distribution function, which is calculated with solving the Boltzmann equation for a given \(E/N\), where \(E\) is the strength of the electric field and \(N\) is the gas density, and a gas mixture. The detail model description is presented in Ref. [13]. A part of cylindrical simulation domain with the electric potential distribution is shown in Figure 8a. In simulations, as in the experiment, the streamer propagates to the target and interacts with it. The gas discharge ignition, streamer dynamics and interaction with the target were considered and compared for two positions of the (GR) substrate. In the first case, the GR substrate is placed 1 mm beneath the target and in the second case, the GR substrate is 500 mm from the target. The first and second cases refer to the experimental conditions with and without GR substrate, respectively. In simulation domain in Figure 8a, the target is at z = 36 mm. A depth of liquid layer is 5 mm. The radii of nozzle and dielectric tube are 1.15 mm and 2.4 mm, respectively. The length of dielectric tube is 25 mm. The dielectric permittivities of the quartz tube and liquid are 10 and 80, respectively. The radius of calculation domain is 60 mm. The powered electrode is embedded in the dielectric tube as in the experimental plasma device. The external ring grounded electrode with h = 3 mm and r = 4.8 mm is placed at z = 17.5 mm on the dielectric tube. The voltage amplitude \(U_{0}\) is 4.9 kV and working gas is argon. In simulations, the gradual voltage increase initiates the streamer formation near the tip of the powered electrode. The streamer propagates first inside of dielectric tube and then over the argon gas flow in the direction to the target. With approaching to the target, the streamer begins to accelerate and the ionization rate increases. The spatial potential distribution for the case without the GR substrate is shown in Figure 8a for the moment when the streamer touches the target. The potential gradually increases behind the streamer head in the direction of the powered electrode inside the dielectric tube. The position of the grounded ring electrode is seen as a potential dip. The streamer has a toroidal  
Figure 8: (**a**) Spatial distributions of electric potential at the moment when the streamer touches the target. Color palette is for 0-5000 V with the 500 V increment. (**b**) Ionization rate profile over z for the cases without the GR substrate (1) and with it (2), argon, \(U\) = 4.9 kV. shape, and the point of streamer contact with the water layer is seen in Figure 8a as the potential bump with coordinates z = 3.58 cm and r = 1.25 mm. At this point the ionization rate has a maximum value. For this moment, the profiles of the ionization rate over z at r = 1.25 mm is shown in Figure 8b. In simulations, we found that the presence of the grounded substrate beneath the target essentially affects the streamer characteristics.