Plasma density profile measurements for ultra-short high power laser beam guiding experiments at SPARC_LAB

External injection is a promising method to achieve high accelerating gradients and to control the beam properties. The energy gain of an electron via the wakefield is proportional to the product of the accelerating field multiplied by the effective propagation distance of the laser. Therefore, in order to bring the electron energy in the order of the GeV, a longer propagation length is required, which can be obtained by guiding the laser pulse in a wave-guide. In the case of SPARC_LAB, a 500 μm diameter hydrogen-filled capillary discharge is used; to guide the laser beam it is necessary to act on the refractive index of the plasma, depending on its density. In this work measurements of the trend over time of the longitudinal profile of the plasma density within the capillary are presented, along with openFOAM simulations of the gas profile distribution. Preliminary test of laser guiding are also shown, detecting the behaviour of the laser beam at the exit of the capillary with respect to the discharge current value.