At present, it is considered that the value of the ion fraction of the current in the welding arcs is approximately β ≈ 0.5. Assuming that the value of β does not depend on the value of the welding current (I), we determine the number of ions transferring the ion current in the cathode region (Ni) at different currents by the formula

N_{i} = I_{i}/е = βI/е,

where e — the electron charge, К_{л}, and the corresponding number of atoms evaporated from the cathode spot (N_{п}), according to the formula N_{п} = G_{п}/ m_{Fe}, where m_{Fe} — the mass of the iron atom, equal to 9,26*10^{–26} kg.

N_{i }≈ N_{п} and with increasing current, the N_{i}/N_{п} ratio increases, and the total number of evaporated N_{i }+ N_{п} atoms also increases. The mechanism of this process can be described as follows. The atoms evaporated from the cathode spot fall into the ionization part of the cathode zone, where the part of them (N_{i}) is ionized and returns to the cathode as an ion current, and the part (N_{п}) leaves the cathode zone and enters the arc column, partially displacing from the cathode zone the atoms of the protective gas.

Now consider the concentration of cathode atoms in the cathode zone, in this case iron atoms (n_{Fe}). From the surface of the cathode spot N_{i} + N_{п} of iron atoms is evaporated per unit time. In one second these atoms propagate in a volume equal to W = S_{кп} *V_{а}, where S_{кп} — the area of the cathode spot, m^{2}, and V_{а} — the velocity of the thermal motion of the atom at the cathode spot temperature equal to the boiling point of iron Т_{к} = 3160 К. The value of V_{а} is determined by the formula V_{a} = √2kT/m, where k — the Boltzmann constant, J/K; T — the temperature of the evaporating atoms, K;

m = m_{Fe}. Substituting Т = Т_{к}, we obtain V_{а} = 9,58*10^{2} m/s. The value of S_{кп} can be determined from the formula S_{кп} = I/j, where j — the current density in the cathode spot for the iron electrode, which is ∼ 2*107 А/m^{2}. According to what has been said, the concentration of iron atoms is determined by the formula

n_{Fe} = (N_{i} + N_{п})/W = (N_{i} + N_{п})j/(I √2kT /m_{Fe}).

n_{Fe} increases somewhat with increasing current and is about an order of magnitude smaller than the concentration of atoms at atmospheric pressure and the average arc temperature in СО_{2} equal to T = 7000 K, determined by the formula

n = p/(kT) = 1,04 ・ 10^{24} 1/m^{3}, где р = 10^{5} N/m^{2} — the magnitude of atmospheric pressure. However, it must be taken into account that at the boundary of the cathode zone with the arc column, the gas flow rate (iron vapor) should decrease to the gas flow rate in the arc column. This speed is determined depending on the magnitude of the current and is ((0,68…1,09)*10^{2}m/s. Therefore, the velocity of the flux of evaporated atoms decreases at the boundary of the cathode spot, i.e. In the ionization space, about 9,58 /(0,68…1,09) = 14,1…8,79 times, i.e. About the order of magnitude, which in the same way causes an increase in the concentration of iron atoms in this part of the cathode zone.