## 2 Methods
The possibility of their heating to a boiling point is provided:  
\[q_{s}=q_{v}-q_{T}, \tag{2}\]  
where \(q_{s}\)--the energy perceived by the surface of the protrusion from ions bombarding the cathode: \(q_{s}=SjU_{c}t\) (where \(S\)--the area of the lateral surface of the protrusion, \(U_{c}\)--the cathodic potential drop in the discharge, \(t\)--time); \(q_{v}\)--the heat content of the protrusion material at the boiling point: \(q_{v}=Vc\gamma T_{buf}\) (where \(V\)--the protrusion volume, \(c\)--the heat capacity of the metal, and \(\gamma\)--the density); and \(q_{T}\)--the energy diverted from the protrusion into the sample: \(q_{T}=2\pi\lambda RT[1-erf\left(\frac{R}{4 alt}\right)]^{-1}\), (where \(\lambda\)--the thermal conductivity of the cathode material, \(R\)--the radius of the protrusion base, and \(T\)--the cathode surface temperature). In the processes of thermal ion treatment and diffusion welding, when the temperature of the samples is much lower than the boiling point of metal, condition (2) is feasible if \(q_{T}\to 0\). In order to neglect the heat transfer to the samples, the value of t must be the same order as the glow discharge's transition time into the arc \(t=10^{-4}\)-\(10^{-6}\) sec. So, then  
\[q_{s}=q_{v}orSjU_{c}t=Vc\gamma T_{bol}, \tag{3}\]  
In this case, for the micro relief of structural steels, it is necessary that the \(S/V\) ratio is \(10^{5}\)-\(10^{7}\) cm\({}^{-1}\) (where \(S\)--the area of the lateral surface of the protrusion and \(V\)--the protrusion volume). Nevertheless, even at \(t=1\) sec, it is necessary that the value of \(S/V\geq 10^{2}\) cm\({}^{-1}\). Such ratios of the surface and volume of the micro protrusion are possible only for thin protrusions and burrs. For real surfaces machined by turning or grinding, this ratio is much less than one, which indicates a low probability of fulfilling condition (2). Hence it follows that at the cathode's current densities corresponding to a glow discharge (up to \(10^{3}\) A/m\({}^{2}\)), the probability of melting and evaporation of the roughness ridges is pretty small. This limits the possibility of thermionic emission from their vertices. At the same time, sharp protrusions on the cathode surface creates the local distortions of the electric field nearby the cathode surface. Electric field distortions near the protrusions facilitates the attraction of positive ions toward them and as a result, the active points with the increased charges concentration are formed. This, in turn, leads to dramatic increase in the electric field strength in these regions. The length of this region (\(d_{c}\)) is determined by the cathode material as well as kind and pressure (\(p\)) of the working gas, and can be found from the ratio:  
\[pd_{c}=c, \tag{4}\]  
where \(c\)--a constant value for particular gas and its pressure (for a glow discharge burning in a nitrogen, \(c=0.42\) Pa m [22]). At a nitrogen pressure of 1.33-13.3 kPa, the average electric field strength near the discharge cathode is  
\[E_{av}=\frac{U_{c}}{d_{c}}, \tag{5}\]  
where \(U_{c}\) is the cathode potential drop, which is 215 V for a glow discharge in nitrogen. In these conditions, the \(E_{av}\) reaches up to \(10^{6}\)-\(10^{7}\) V/m. A further increase in the electric field strength inevitably leads to the appearance of a current of field electron emission from the tip of the protrusion due to the ejection of electrons from the surface by a strong electric field. A noticeable field emission current, sufficient for the existence of an arc discharge, appears at the electric field strength of about \(10^{9}\) V/m. In this regard, it is advisable to assess the degree of influence of the protrusions surface roughness on a local increase in the electric field strength at the cathode of a glow discharge. Meanwhile, the magnitude of the field strength does not depend on the number of protrusions, but on their size and shape. In mechanical engineering, the surface machining of samples of the third--sixth class of cleanliness is widely used.