## 2 The Experimental Platform HELL: High-Energy Electrons by Laser Light
### Diagnostics for Plasma Interaction and Electron Beams  
To optimize the laser-plasma interaction, thus the acceleration of electrons, it is important to consider the gas target neutral density profile that determines the generated longitudinal and transverse plasma profile. Moreover, its evolution is important both before and after the main driver pulse. For this, a probe beam is usually used in the direction perpendicular to the driver pulse. In addition to such active probing of the plasma, Thomson scattering emission provides useful information during the interaction by means of optical imaging [40; 41]. Such diagnostics can be realized by directly detecting the laser light scattered by the relativistic electron bunch with a CCD or CMOS camera, and also setting up an optical system to resolve the fine details of the laser propagation in the acceleration area around the laser waist position. Since the Thomson scattering pattern is polarization dependent, typically it is observed from a top window in the interaction chamber, i.e., in the direction perpendicular to the p-polarized laser beam plane of incidence. Figure 18 shows an example of top-view Thomson scattering image from which it is possible to infer the laser beam propagation direction inside the supersonic gas target by identifying the position corresponding to the maximum scattered light intensity. This diagnostics is very useful both in the first stage of a LWFA experiment (or during the warm-up of an electron acceleration beamline as HELL) and in the fine tuning optimization of the electron beam parameters. Indeed, in the first phase, it is used to optimize the plasma interaction by monitoring the laser propagation into the plasma (Thomson scattering) and moving the gas target and/or changing the gas density profile. Since such light scattering is also density dependent, a proper gas-jet density profile measure is very important. This is obtained with simultaneous interferometric measurements. Figure 19 shows the optical setup used for interferometry (left), the longitudinal phase-shift profile (center), the transversal phase-shift  
Figure 17: **(left)** logarithmic cross section of the Point Spread Function of the diffraction limited beam (red) and with the beam shaping (green) with the wavefront reported in the diagram on the (**right**). profile of a 4 mm by 1 mm gas-jet profile in the case of Argon at 40 bar (right). Figure 20 shows the gas density distribution at three different heights \(z\) above the nozzle exit obtained by the multiplicative algebraic reconstruction technique. The neutral density profile measurement in combination with the Thomson scattering diagnostics are of key importance for the optimization of the propagation of the driver pulse, hence to efficiently accelerate the electron beam. The effect of different gas-density profile on LFWA can be beneficial in particular conditions [42]. Electron beams accelerated in the HELL platform will be characterized in terms of their geometrical properties (charge, divergence, and pointing stability) and energy spectrum (pC MeV\({}^{-1}\) msr\({}^{-1}\)). In order to retrieve this information, a combination of fluorescent screens and magnetic dipoles has been designed and tested. The design of the spectrometer is not trivial, since the expected range of energies at the HELL platform spans over more than three orders of magnitude (MeV-GeV), and a single magnetic dipole cannot cover with sufficient resolution such a wide range of energies. Figure 19: **(left)** optical setup used for interferometry, (**center**) the measured longitudinal phase-shift profile, (**right**) the measured transversal phase-shift profile. Figure 20: **(left)** neutral density reconstruction in Argon at 40 bar backing pressure at 0.1 mm from the nozzle, (**center**) at 1 mm, (**right**) at 2 mm. Figure 18: **(left)** Example of an experimental top-view image showing the Thomson scattered light within a gas target with near-uniform neutral density in the case of a 300 m\(\mid\)—40 fs laser beam propagation in Nitrogen.