## 2 Materials and Method
The average time spent by the particles in the electric field was calculated as follows:  
\[t_{avg}=\frac{h}{v_{avg}} \tag{3}\]  
After calculation, for Q = 40 m\({}^{3}\)/h, tavg = 4.978 s, and for Q = 65 m\({}^{3}\)/h, 3.063 s are obtained. A lower gas flow rate ensures a longer gas passage time near the discharge electrode, which ensures better treatment of gases and dust collection. The time (approximately) to electrostatic charge of small particles (<1 \(\upmu\)m) is [7]:  
- through an electric field of 0.1 s (in 90% of the cases);  
- through diffusion 2.3 \(\div\) 5 s.  
A lower gas velocity results in better loading of dust particles and a long enough time for the plasma reactor to operate. The average electric strength in a cylindrical-type domestic electrostatic precipitator can be calculated as [32]:  
\[E_{avg}=\frac{U}{r} \tag{4}\]  
where U is the supply voltage, and r is the radius of the cylinder. For U = 10 kV, Eavg = 1.6 kV/cm, and U = 30 kV, Eavg = 4.8 kV/cm. Taking into account the distance between the electrodes, the maximum voltage is 30 kV. During many experiments (conducted over 4 years), it was found that the upper-side insulator was the most demanding (due to the high temperatures above 250 \({}^{\circ}\)C and the gas content affecting the medium-voltage electrical insulators supporting the discharge electrode) from a thermal, mechanical, and, in particular, electrical point of view (Figures 2 and 3). Figure 2: (**a**) The longitudinal cross-section from the chimney; (**b**) side view of the 90\({}^{\circ}\)-degree rotation of the chimney. In Figure 2: 1--the stainless steel tube of the chimney; 2--the upper metal cover from the top part of the chimney; 3--metal supports for attaching the metal upper cover to the tube of the chimney; 4--metal collar for fastening on the chimney tube; 5--the upper-side electrical insulator, type 1, with dimmensions of 250 \(\times\) 60 \(\times\) 20 mm, mounted in the top part to connect the discharge electrode; 6--discharge electrode; 7--metallic terminal element for supporting the discharge electrode on the upper-side electrical insulator; 8--ceramic support mounted in the lower part of the chimney for centring the discharge electrode; 9--textolite electro-insulating support (lower side electrical insulator) for supporting and centring the discharge electrode; 10--weight for stretching the discharge electrode; 11--the negative potential of the medium-voltage source mounted at the discharge electrode; 12--the positive potential of the medium-voltage source mounted on the stainless steel chimney (collecting electrode); 13--grounding the chimney (through an earth socket). The purpose of the upper and lower side electrical insulators that support the discharge electrode connected to the medium-voltage source is to ensure a high electrical resistance between the discharge electrode and the chimney (which is the collecting electrode) under conditions of dust, chemical compounds, humidity, and high temperature. Over time, two types (type 1 and type 2) of upper-side electrical insulators have been tested: a simpler rectangular porcelain insulator with a metal rain protection cover (5, type 1, Figure 2; ensures a small distance between two electrodes, equal to D/2) and a more complex one with porcelain insulators and a porcelain cover (2, 5, type 2, Figure 3; ensures a much greater distance, more than 2.5 times compared to type 1, Figure 2). The material used for the medium-voltage insulators was porcelain, which has very good properties as an electrical insulator at high temperatures, humidity, and under dirty conditions (dust deposits). Electrical insulation on the lower side is much less stressed: temperatures below 100 \({}^{\circ}\)C and it is not directly in the gas flow; instead, the dust falling on the insulator can change its properties).