## 2 Experimental Setup
From time-of-flight (TOF) measurements [17] in which the arrival signal is measured as a function of time, the particle energy can instead be calculated using the arrival time (which will be covered in greater detail later), hence there is a requirement for online, real-time diagnostics setups circumventing the Faraday cups most significant drawback. This, however, necessitates the inclusion of a discharge rate for the Faraday cup that is sufficiently high to ensure usable resolution of the data. Faraday cups often achieve a relative lower time resolution (typically on the nanosecond regime) due to the discharging rates fixed value being far lower than that which is achievable by other available detectors  
Figure 2: Schematic of laser-target collision chamber with 1030 nm central wavelength laser, 1.5 ps shot duration incident on a 2 mm Cu thickness target. The Faraday cup collector is positioned normal to back scatter. Capacitor/resistor/amplifier setup contained within the Faraday cup. (such as the sub-picosecond response time of the diamond detector), however they can be situationally preferred due to their high resistance to electromagnetic components. However, photopeak detection from Faraday cups follow a more unique generation process than the previously mentioned ion load. Incident XUV rays are absorbed by valence delocalized electrons within the metallic cups surface, causing expulsion of the electron and, therefore, a net positive charge buildup leading to a detectable photopeak signal. Due to the unique, high-energy method of signal production, Faraday cups often produce photopeaks of much lower amplitude in comparison to rival signal detection systems such as diamond detectors. Indeed, the photopeak magnitude is often a fraction of that reached by the ion load. The emission of secondary electrons remains a principal complication of Faraday cup function. As the ions kinetic energy often greatly exceeds that of the materials work function, free electrons can be emitted, causing a larger imbalance of charge. Furthermore, multiple electrons can be emitted per ion causing a potentially extravagant margin of error. Techniques have been developed to combat this process, such as optimal Faraday cup shapes or graphite shielding [16] which allow Faraday cups to maintain a reliable accuracy for TOF calculation. The energy distribution can also be derived from these data via the following equation [14]:  
\[\frac{dN_{i}}{dE_{i}}=\frac{Lm_{i}^{\frac{1}{2}}\ i(t)}{e(8E_{i})^{\frac{3}{2}}} \tag{1}\]  
where \(N_{i}\) represents the number of ions in an energy interval \(dE_{i}\), \(i(t)\) is the current produced for a time-of-flight \(t\), \(L\) is the detection distance, e is the electronic charge, \(m_{i}\) is the ion mass, and \(E_{i}\) is the ion energy. The datasets that were gathered via the Faraday cup as described above were used as testing data during code development, and the varying intensity allowed the functionality of the code to be scrutinized for a range of S/N ratios. Figure 3 shows the TOF plot for two of the provided datasets, with the largest and smallest amplitude of the datasets provided respectively. The \(x\)-axis has been adjusted to allow the photopeaks to lie on the zero-line for each shot, however due to the Faraday cups reduced photopeak signal strength, as well as the back side oriented detection setup (TNSA detection favors forward orientation), the photopeak is significantly smaller than in typical TNSA-like TOF datasets. This is arguably ideal for the development of identification software, as the codes' ability to detect the minimum possible photopeak signal can be scrutinized. Figure 3: TOF data that were obtained from PERLA 1 kHz laser at intensities of 2.2 \(\times\) 10\({}^{16}\) W/cm\({}^{2}\) with 2 mm thickness Cu target. Shots 1 and 2 gathered data using the same laser intensity and target parameter specifications under different laser focal sizes due to consecutive laser-target collisions.