# Experimental Study of Nanosecond Laser-Generated Plasma Channels
## 2 Concept of Elongated Focus for Plasma-Channel Generation  
The idea of using a cylindrical lens to generate an elongated laser focus is applied to generate a high-aspect-ratio in the transverse focal plane (shown as x-y plane, see Figure 1C) with respect to the longitudinal nanosecond laser optical axis (shown as z-axis, see Figure 1C). For the use of a plasma channel in LWFA a femtosecond laser traveling on the x-axis needs to be focused into the plasma channel for guiding over the entire channel length. Figure 1C illustrates this concept. The femtosecond laser interaction is not considered here. Considering the available laser parameters of 5 J, 10 ns, 22 \(\times\) 22 mm\({}^{2}\) beam size, and a desired plasma-channel length of about 5 mm, it was necessary to use a 200-mm plano-convex lens in combination with the cylindrical lens (100-mm focal length), in order to increase the laser intensity up to 10\({}^{12}\) W/cm\({}^{2}\). The optical scheme used for the elongated focus generation (shown in Figure 1C), also called \"knife-like\" focus, was already considered and reported for an ad-hoc numerical study on plasma hydrodynamic effects [16]. The measured spatial distribution of the Bivoj nanosecond laser is shown in Figure 1A, and the simulated one in Figure 1B. The resulting simulated high-aspect-ratio shape of the laser focus is shown in Figure 2. Corresponding measurements performed at low laser power are shown in Figure 3. Numerical simulations performed by the Virtual Lab Fusion software show a peak intensity of 1.7 \(\times\) 10\({}^{12}\) W/cm\({}^{2}\) sustained over 5 mm [18]. The simulated diameter of the focus along the y-axis was 6 \(\upmu\)m full-width-half-maximum (FWHM) and the measured one 7 \(\upmu\)m FWHM, calculated by averaging it over 100 \(\upmu\)m of the x-axis, as shown in Figure 3-bottom. The measured full length of the focal distribution along the x-axis was 5.3 mm (10% variations of the intensity value). An example of the spatial profile, measured in a limited region of 2 mm due to field-of-view limit, is shown in Figure 3-top. Figure 1: (A) Measured transverse distribution of the Bivoj nanosecond laser; (**B**) simulated transverse distribution of the Bivoj laser; (**C**) 3D-axis and optical scheme used to produce a knife-like focus: a 200-mm-focal-length plano-convex lens coupled with a 100-mm-focal-length cylindrical lens. Figure 2: Simulated high-aspect ratio focal distribution (transverse plane) obtained by the combination of a 200-mm plano-convex and a 100-mm cylindrical lens. In general, an optimal guiding process requires a symmetric plasma channel in the z-y plane. This is an important feature of the intensity distribution on the z-y plane, i.e., the transverse plane with respect to the propagation direction (x-axis) of a subsequent femtosecond laser beam. Figure 4 illustrates such a geometry (Figure 4a) and the corresponding numerical simulation (Figure 4b). As clearly shown by numerical simulations, the region of high laser intensity is strongly asymmetric for the given optical configuration: the focus width is about 6 \(\upmu\)m FWHM along the y-axis and 200 \(\upmu\)m FWHM along the z-axis. A shorter focal-length of the cylindrical lens would be required if one wanted to improve the symmetry of the focus in the z-y plane. As an example, reducing by a factor of 2 the focal lengths of the two lenses would give a FWHM along the z-axis of about 120 \(\upmu\)m. Additional improvement can be reached using a telescope to increase the laser beam transverse dimensions. In this case reducing the f/number of the system would improve the symmetry without any reduction of the focal length of the cylindrical lens, thus maintaining a reasonable distance from the plasma source and preventing potential deterioration. However, in a first approximation, a certain degree of asymmetry (or unwanted optical artifacts) will remain compared to the ideal configuration of perfectly cylindrical symmetry laser fields.