# Experimental Study of Nanosecond Laser-Generated Plasma Channels
## 3 Experimental Setup  
As sketched in Figure 5, a 10-ns laser pulse operating at a wavelength of 1030 nm with variable energy in the range 1-5 J was focused into a gas-jet target. The laser focus was located 1 mm above the 6.8 mm \(\times\) 1.26 mm rectangular pulsed supersonic gas nozzle. The nozzle was operated with Nitrogen (N) or Argon (Ar) gas. The valve backing pressure was varied in the range of 20-64 bar, corresponding to a gas density in the range 2-6 \(\times\) 10\({}^{19}\) atoms/cm\({}^{3}\) (1 mm above the nozzle). The gas density profile was measured experimentally and simulated using the FLUENT code (details are available in [21]). The gas density profile was uniform along the 1.26-mm side (or z-axis) for the Ar case, while for the N case two peaks were present at the boundaries with density increase of 1.15 times the density at the center. Along the 6.8-mm side (or x-axis), two large peaks on the boundaries were present for the Ar case with a density increase of a factor 2 with respect the center, while for the N case a similar profile  
Figure 4: **(a)** Conceptual sketch of laser intensity distribution desired for an optimal laser wake field electron-acceleration (LWFA) in the transverse plane with respect to the nanosecond laser axis (or “z-axis”) in the focal region. The colored lines represent constant intensity zones. Red indicates maximum, orange medium and green low intensities; **(b)** y-z plane numerical simulation of the laser intensity distribution in W/cm\({}^{2}\) by the combination of a 200-mm plano-convex and a 100-mm cylindrical lens (a strong asymmetry is shown). was present with a factor of 1.4. As already mentioned, Ar and N have a specific heat ratio equivalent to helium (He) and hydrogen (H) (1.66 for Argon and Helium and 1.4 for Nitrogen and Hydrogen), thus producing very similar neutral gas density profiles. In order to characterize the generated plasma during laser irradiation, a portion of the main laser beam (a leak from one of the turning mirrors) was used as optical probe beam (45\({}^{\circ}\)-incidence angle with respect to the optical axis). A shadowgraphy technique was used, as shown in Figure 5 (CAM2). Additionally, a top-view imaging system was setup to provide complementary information on plasma generation through emission of plasma light in the optical window as sketched in Figure 5 (CAM1), integrated over 10 us, hence, also collecting the late phase of the plasma light emission. A proper delay between the main and the probe beam was chosen to optimize the plasma shadowgraphy raw images. The laser energy level was gradually reduced to determine the minimum value of energy required to generate a fully continuous plasma column along the gas-jet length, as well as a fully continuous optical emission. These results were used to estimate as the above mentioned laser significant-intensity-threshold. These values can be considered as a laser intensity upper threshold (overestimation) for local plasma formation (ionization threshold). Measurements of the elongated focus carried out in the experimental campaign demonstrated that the main laser beam was focused approximately into a 7 um \(\times\) 5.3 mm elongated structure, as shown in Figure 3. This was in good agreement with the optical simulations presented in Figure 2. In the conditions of minimum laser intensity for uniform plasma formation (the significant-intensity-threshold), the elongated plasma structure inner diameter was measured experimentally both for Ar and N targets (see Section 4) in the x-y plane. Since the hydrodynamic evolution of the plasma structure was not constant during the 10 ns laser probe duration, the inner radius measurement must be considered an average value and is presented here only for a quantitative estimation of the significant-intensity-threshold. This cannot be considered for an absolute estimation of the inner plasma structure dimensions.