## 2 Methods
Such values of the local electric field strength provide for a current density of field emission from the peak of the protrusions of \(\mathrm{j_{fe}}\geq 10^{7}\) A/m\({}^{2}\), sufficient for an arc breakdowns exciting in the interelectrode gap [26]. The latter is in many orders higher than the current density in the cathode spot of the glow discharge. It is suggested that in these conditions the Joule's heating and evaporation of the vertices of the protrusions entail the arc breakdowns [27]. In this case, condition (2) can already be fulfilled, i.e., the probability of melting and evaporation of protrusions increases dramatically. In turn, the latter contributes to the development of thermionic emission from these areas with the arc formation on the surface of the cathode spot of an arc discharge. As was mentioned above the long-term action of a stable arc discharge on a surface of the samples can lead to their melting and destruction. Hence, for the prevention of a glow discharge transition into an electric arc, the length of the cathodic potential drop must exceed the maximum height of the roughness protrusions. The cleanliness class of the samples surface treatment determines this. The adequacy of this assumption has been checked under conditions of ion treatment in a glow discharge in a nitrogen. The cylindrical c with dimensions of 20 \(\times\) 60 mm made of steel A 659 CS Type 1020 (cathode of discharge simultaneously) were used. The glow discharge was powered from a controlled full-wave rectifier with an output voltage of 0-1000 V through a ballast resistor of 80 Ohm. The discharge current was of 4 A. A flat  
Figure 3:4 The dependence of the field enhancement on the cathode surface on the ratio of the protrusion’s height and the length of the cathodic potential drop region: 1—ratio a/b = 4; 2—ratio a/b = 2.  
annular anode located at a distance of 0.008 m from the cathode surface was used as the second discharge electrode (Figure 7). The steel samples obtained by rough, semi-finishing and finishing had the height of the surface roughness protrusions of 60-80, 30-40, and 10-15 \(\upmu\)m accordingly. During treatment, a gradual increase in gas pressure in the working chamber was performed. As the criteria of glow discharge stability, the limiting pressure at which the short-term arcs at the interelectrode gap emerge developing, apparently from the tops of the highest or most sharp protrusions was chosen. A further rising of a gas pressure is accompanied by an increase in the frequency of microarc discharges formation until a stable electric arc is established in the discharge gap. The cathode (products) temperature while treatment was 700-1000 K. The cathode's temperature was measured with the chromel-alumel thermocouple at three different points in the axial direction and then the results was averaged. The view of treatment by stable glow discharge and in the moments of arcing breakdowns (blurred by flare and multitude of micro-arcs) are shown in Figure 3:5  
Figure 3:6 The visualized scheme of treatment in a stable (**a**) and disturbed (**b**) by a multiple micro-arcs breakdown glow discharge. Figure 3:7 The schematic view of experiments: 1—treated samples (cathode); 2—anode ring; 3—plasma of glow discharge; \(\mathrm{d_{c}}\)—the length of the cathode potential drop. The experimental results are shown in Figure 9 in the form of a curve corresponding to the averaged over the results of a number of measurements, the limiting values of gas pressure depending on the parameters of the surface relief. Here along with the dimensions of the roughness protrusions, the values of the extent of the cathodic potential drop region corresponding to the gas pressures are given. The obtained results indicate that the glow discharge's instabilities really begin to appear when the boundary of the cathodic potential drop region (\(d_{c}\)) approaches the vertices of the micro protrusions. A glow discharge remains stable at gas pressures below the obtained experimental curve.