3.1.1. Electron Densities Determination

The following expression (given by Ashkenazy et al. [28]) was used to obtain the electron number density, *Ne*, from the width of the H α-line:

$$N\_c = 8.02 \times 10^{12} \text{ (}\Delta\lambda\_{1/2}/\alpha\_{1/2}\text{)}^{3/2} \text{ cm}^{-3} \tag{1}$$

where <sup>α</sup>1/2 is half the width of the reduced Stark profiles in Å. Values of <sup>α</sup>1/2 for the Balmer series can be found in Griem [29] and also in Kepple and Griem [30].

**Figure 6.** Voigt profile fitting to experimental Hα-line emission of the plasma with a gate time of 500 ns at 4 μs delay time with a wavelength range from 6530 to 6590 Å.

In these references [29,30], it can be observed that the parameter <sup>α</sup>1/2 depends on the electron density and that it also varies slowly with the temperature, *T* (around 6% at 10,000 K). It is well known that for plasmas in air, in experimental conditions analog to those in this work, temperature will be between 10,000 and 15,000 K (El Sherbini et al. [19]; De Giacomo et al. [22]). In this work, as the profile of the Hα-line in air and in the LSP conditions were similar we used the parameter given by Griem at a temperature of 15,000 K. This assumption is justified in the next paragraph.

The values of the electron density obtained by this procedure are shown in Table 2 and were obtained using a value of <sup>α</sup>1/2 for an electron density of 10<sup>17</sup> cm<sup>−</sup>3. Subsequently, an iterative method was used until the used parameters corresponded to the electron densities obtained. The uncertainties of the central values included the deviations in the Stark broadening, shown in Table 1, plus 6% due to temperature uncertainty.


**Table 2.** Electron densities deduced from experimental values of Stark broadening of the Hα-line obtained in the LSP experiments of this work.
