## 2 The Experimental Platform HELL: High-Energy Electrons by Laser Light
### The HELL Platform
**(bottom)** Detailed view of the HELL platform showing the auxiliary chamber with the OAP, the DM and leak mirrors; the interaction chamber with the basic driver beam for laser wake field acceleration (LWFA) and the counter-propagating beam is also shown. It is worth mentioning that the side wings that are visible on the far field of a rectangular Super Gaussian beam is the natural consequence of its shape (Figure 7). However, those wings might be diminished using different techniques usually at the cost of intensity drop. We discuss those techniques later in text. Also, in the self-injection regime, these side wings act as independent focal points and ultimately drive independent laser wake-fields, thus giving rise to wing-produced-bunches of electrons and generating, as a consequence, a mixture of electron bunches that deteriorate the main bunch parameters, as shown in Figure 8.  
Figure 5: Simulated focal distributions (**up**) for the 4.4 m off-axis parabola (OAP) and intensity plot (**down**) in the ideal case (**left**), in the artificially modulated case (center-red), with the deformable mirror (DM) compensation (**right**) and (center-blue). Figure 6: Simulated focal distributions (**up**) for the 10 m OAP and intensity plot (**down**) in the ideal case (**left**), in the artificially modulated case (center-red), with the DM compensation (**right**) and (center-blue). In the lowest intensity scenario of Figure 6, the guided regime, such wings are less capable to drive independent wake-field. On the other hand, it must be emphasized here that such regime typically makes use of specifically developed target systems. The formation of plasma by low intensity EM fields or electric discharges prior to the arrival of a high intensity pulse significantly changes the interaction of the main laser pulse with the target. Therefore, a study of the formation process is important to laser-driven electron acceleration. With the increase of available laser power the acceleration of electrons becomes increasingly sensitive to the evolution of target density profile during the interaction. A low current capillary discharge in the resistive regime may form a radial distribution of electron density that is necessary for the formation of a plasma wave guide that is capable of transporting a channeled laser beam at a distance that is much longer than its diffraction Rayleigh range [11, 28, 29, 30]. The external edges of the capillary can suffer of damages induced by the wings present in the laser focal spot. Such problem is already reported in literature [31, 32, 33, 34, 35] and two solutions to moderate the wings are discussed hereafter: (i) the laser beam apodization and (ii) the use of the deformable mirror (see Section 2.3). Figure 9 shows the simplest conceptual scheme that is considered for the apodization simulation. After a 5 m free propagation in space, the L3 square beam is apodized by a round shape clear aperture of 210 mm, then the beam propagate for other 95 m in free space and finally is focused by the 10 m focal length OAP. The apodization of the beam is shown here only as an example and can give even better results when considering non-flat cutting apertures. A second possibility, shown again as an example, will be described below in the deformable mirror subsection (see Section 2.3). Figure 10 shows the intensity focus distribution (considering 1 PW pulse) in log color scale of the 10 m OAP in  
Figure 8: 3D PIC simulation of electrons self-injection in the side wings of the far field intensity distribution for the square beam. The beam (\(\text{FWHM}=15\lambda\), 30 fs, \(\lambda=0.82\) μm ) propagates in a cylindric plasma channel with the radius of 15 μm. On axis electron number density is \(10^{19}\) cm\({}^{-3}\), outside the channel the density is four times higher. Beam intensity is \(\mathbf{10^{20}}\)\(\mathbf{W/cm^{2}}\). Figure 7: Simulated far fields of ideal intensity masks—circular (**left**) and square (**center**).