## 2 Experimental System  
Electron acceleration using the TNSA mechanism [30; 31] was performed in the CETAL-PW laboratory using the PW laser system, which is a facility of the National Institute for Laser Plasma and Radiation Physics (NILPRP). The laser system shown in Figure 1 is a 1 PW laser with a 25 fs pulse duration working on an 800 nm central wavelength. The system is composed of a front-end laser system able to deliver 1.7 J pulses into the main amplifier with a repetition rate of 10 Hz. The main PW amplifier is pumped with three Atlas lasers (with 20 J energy, 20 ns pulse duration, and 527 nm wavelength) and delivers 35 J pulses with a 0.1 Hz maximal repetition rate. After compression, the laser system can deliver up to 1 PW laser pulse with a 35 fs pulse duration and a maximal repetition rate of 0.1 Hz. In the experiments carried out at laser peak intensity of the order of 10\({}^{21}\) W/cm\({}^{2}\), significant intensity of the pre-pulse (with 6-7 orders of magnitudes less than the main peak) may influence the target integrity prior to the arrival of the main pulse [32]. In order to avoid this, prior to the experimental campaign, the temporal intensity contrast was systematically investigated with the help of the TUNDRA (Ultrafast Innovations) device. TUNDRA is based on a third-order autocorrelator with a dynamic range of up to 10 orders of magnitude. To perform the temporal intensity contrast measurements, a small portion was collected from the main beam by hard clipping before it was focused by the off-axis parabolic mirror. The sampling beam was sent outside the interaction chamber to the TUNDRA device where a reflective periscope with 90-degree deflection was used to shift the beam polarization from P to S as required by the device. The beam energy was also attenuated below the required limit using reflective methods (Figure 2a). Figure 1: Overview of the PW laser system from CETAL-NILPRP. However, a few optical windows remained in the beam path leading to the generation of parasitic secondary peaks in the autocorrelation profile, interpreted as post-pulses at 40 ps and 20 ps delays from the main pulse. This can be seen in the measured temporal intensity presented in Figure 2b with gray empty circles. For comparison, the profiles measured when the laser was working at limited power, amplified only with the front-end but working at 10 Hz (Figure 2b--gray empty circles) is very similar to the one at PW level (black full circles) where the final amplifier is used at 0.1 Hz repetition rate. For the 0.1 Hz case, lower time resolution and range were investigated but the similarity of the two profiles allows us to estimate the temporal contrast of about 7 orders of magnitude at about 15 picoseconds before the arrival of the main peak of the pulse and up to 8 orders of magnitude at 50 picoseconds before. In the particle acceleration experiment, using an off-axis parabolic mirror (f/2.5), the laser pulse was focused on an \(\approx\)3 \(\upmu\)m spot radius on thin metallic targets reaching intensities up to 3 \(\times\) 10\({}^{21}\) W/cm\({}^{2}\). Behind the target holder, in a direction perpendicular to it, we placed the electron magnetic spectrometer. Between the target and spectrometer, we inserted two lead bricks (50 mm thickness) at a distance of 400 mm between them. They were used in order to reduce the X-rays, created by electrons farther away from the beam axis, \"flooding\" the image plates (IPs) used above the magnetic spectrometer for electron detection.