# Experimental Study of Nanosecond Laser-Generated Plasma Channels
## 4 Experimental Results and Discussion
In fact, the plasma ionization threshold can occur in localized region where local laser intensity or local gas density levels are favorable for plasma formation, but this does not occur along the entire elongated plasma structure. For a quantitative estimation of the significant-intensity-threshold upper and lower bound, we studied the optical plasma emission dependence on the laser energy. The optical plasma emission is measured by calculating the blue-channel value integrated over the gas-jet area in the plasma top-view images. The minimum energy value allowing an optical plasma emission is recorded when a small localized plasma is generated. Increasing the laser energy, the optical plasma emission signal increases, until it reaches a saturation level. Such saturation value resulted to be higher than the energy level corresponding to the generation of an entirely elongated plasma structure in the shadowgraphy images. Consequently, one can deduce that the significant-intensity-threshold, in a first approximation not considering density profile modulations, is confined within such an optical emission dynamic range. A simple threshold model was used to fit the experimental data in the following form:  
\[a\cdot(\mathrm{atan}(k(\mathit{Elaser}-\mathit{Es.i.t.}))-\mathit{cost}) \tag{1}\]  
where _Elaser_ is the laser energy, _Es.i.t._ is the energy corresponding to the upper boundary of the significant-intensity-threshold range, \(a\), \(k\) and \(\mathit{cost}\) are the other free parameters of the fit. Figure 10 shows the dependence of the plasma optical emission (blue-channel) on the laser energy for both Ar (52.1 bar pressure) and N(64 bar) gas targets. Figure 9: Experimental measurements obtained with N at 64 bar for different laser energies. **(a)** Shadowgraphy profiles of the elongated plasma structures in the y-axis, averaged over 1 mm in the x-axis; **(b)** top-view profiles of the optical plasma emission along the x-axis, averaged along the entire z-axis. The laser energy range for plasma generation is 3.5-5 J in the case of N gas target and 0.9-2.5 J in the Ar case. The lower boundary corresponds to a local plasma formation (plasma ionization threshold). The upper boundary corresponds to the formation of an entirely elongated plasma structure, both in the optical and in the shadowgraphy images, thus independently from the gas-jet density profile variations. It is worth mentioning that to avoid an excessive radial plasma extension from the cylindrical axis, beyond the radial extension required to have a symmetric hydrodynamic expansion, such density variations will be important in future, thus a lower boundary level is preferable for our considerations. For this reason, we rely on the _Es.i.t._ value obtained from the data fit, i.e., 1.7 J for Ar and 4.2 J for N. Moreover, to determine the significant-intensity-threshold, it is important to take into account the variations of plasma generation coming from laser energy fluctuations (total energy fluctuations or longitudinally local variations) or from gas density fluctuations. Such variations can be mitigated more easily if one operates in a laser/energy intensity range where the curves shown in Fig.10 present a smaller slope. Based on these considerations, we can conclude that the laser significant-intensity-threshold falls in the energy range of 3-4 J (corresponding to a peak intensity 5-6.7 \(\times\) 10\({}^{11}\) W/cm\({}^{2}\)) for a N-gas at the backing pressure of 64 bar (\(6\times 10^{19}\) atoms/cm\({}^{3}\) neutral density) and 0.9-1.5 J (corresponding to 1.4-2.7 \(\times\) 10\({}^{11}\) W/cm\({}^{2}\)) for an Ar-gas at the backing pressure of 51.2 bar (\(5\times 10^{19}\) cm\({}^{3}\) atomic density). Such estimations are in agreement with similar estimations present in literature [22; 23].