**4. Validity of the model**

**Figure 4** demonstrates the comparison amidst in our results and those given by Becker et al. [30] (**Figure 4(a)**) ion and electron concentrations, (**Figure 4(b)**) electric field and electric potential, (**Figure 4(c)**) metastable atom concentration and (**Figure 4(d)**) mean electron energy. This figure substantiates the validity of our 1D code. The main dissimilarity amidst in those given by Becker et al. and our results are pointing up in the **Table 2**.

We find that the similar discharge has been studied by Fiala et al. [45], where the hybrid model has been employed in two dimensional configurations. We find that the results got by Fiala et al., it was approximately indistinguishable to our results. In exacting, the maximum of particle concentrations is 1.1 <sup>10</sup><sup>9</sup> cm<sup>3</sup> and the electric field at the cathode is 675 V/cm for applying voltage that is equal to 126.3 V. Consequently, the hybrid model is equivalent to our fluid model in the presence of the metastable atom concentrations of these discharge circumstances. Besides our model identifier both properties of the discharge, the mean electron energy and the metastable atom concentrations.
