“…The QN axisymmetric model includes the following equations from above: Equation for the ions and the excited species, as well as Equation , , and , using again the expressions 2, 3, 6, 8, and 12. There are two differences compared to the QN Cartesian model, namely, (i) the gas flow is not described (i.e., we do not solve Equation and ) and (ii) the convection terms in Equation , , and , i.e., , , and , are replaced with an effective convection term, , , and , respectively, representing effectively the influence of elongation and/or relative velocity between the arc and the background gas flow with a parameter , called the convection frequency (see details in). In general we write the variation of a conserved variable (i.e., species density, electron energy density, etc.)…”