# Characterization of an X-ray Source Generated by a Portable Low-Current X-Pinch
## 3 Results and Discussion
### Time-Resolved Soft X-ray Emission Measurements  
A set of experiments was performed, and a variety of electrical signals were recorded on the oscilloscope at a sampling rate of 5 GS/s. Figure 3 shows typical results of four  
Figure 2: (**a**) Filtered BPX65 PIN photodiode’s spectral sensitivity as a function of the photon energy, for the Al (15 \(\upmu\)m) and Cu (10 \(\upmu\)m) filters. (**b**) X-ray spectral transmission profile of the film package: paper foil (125 \(\upmu\)m), vinyl case (175 \(\upmu\)m), and the overall transmission of the package. different X-pinch wire loads, and especially for W and Au-plated W wires crossed at 98\({}^{\circ}\) and 55\({}^{\circ}\). Each plot represents the Al-filtered PIN X-ray signal in blue, the Cu-filtered PIN X-ray signal in green, the PIN laser probe signal in red--which determines the arrival time of the laser pulse used for the optical probing diagnostics in relation to the current start--the (dI/dt) time derivative of the current I of the X-pinch load waveforms obtained from the nonintegrated Rogowski coil in purple and, finally, the corresponding waveform of the current obtained via the numerical integration of dI/dt in brown; it should be noted that the actual current is equal to the normalized I by a constant of \(\sim\)1.25 \(\times\) 10\({}^{-9}\) H, which is the mutual inductance value of the current monitor (Rogowski coil). Multiple peaks that correspond to the phases of the plasma evolution were observed at the presented X-ray burst signals. The Al-filtered PIN X-ray signal in every case, and for the time window of 40-50 ns, shows a peak after the current start. This can be attributed to the formation of the bright spot at the cross-point [26]. The peaks that follow can be attributed to an electron beam interacting with the remaining wire material and the anode [26]. However, these plasma phases--and especially the hot-spot generation--are difficult to recognize. Thus, a reconstruction procedure of the actual photocurrent I\({}_{\text{ph}}\) profile was adopted in order to overcome the limits of the slow rising and falling times due to the \"slow\" response of the diodes and the noise. Figure 4a shows the measured electrical signals of a typical shot for the two-W-wire X-pinch load crossed at an angle of 98\({}^{\circ}\). The X-ray signals determine the first peak at 50 ns which, as already mentioned, is correlated to the hot-spot generation. However, the inset interferometric image captured at 45 ns, as revealed by the first peak of the red curve, depicts the formation of a gap at the initial location of the cross-point. This observation determines that the pinching has already occurred. To overcome this inconsistency, the photocurrent I\({}_{\text{ph}}\) was reconstructed for each diode. The first step of the reconstruction process is presented in Figure 4b. The soft X-ray waveforms were filtered by a second-order low-pass Butterworth filter to eliminate the high-frequency electromagnetic noise generated by the switches [14]. Moreover, the Al-filtered and the Cu-filtered X-ray signals, as well as their ratio waveforms, are presented. The low-pass filter has a cutoff frequency  
Figure 3: Typical electrical signals as recorded on the oscilloscope for the X-pinch loads: (**a**) W wires crossed at 98\({}^{\circ}\), (**b**) W wires crossed at 55\({}^{\circ}\), (**c**) Au-plated W wires crossed at 98\({}^{\circ}\), and (**d**) Au-plated W wires crossed at 55\({}^{\circ}\). The dI/dt and I waveforms are plotted in purple- and brown-colored lines, respectively. at 1 GHz, which is 2.5 times lower than the sampling frequency. At the second step of reconstruction, a simplified equivalent operating circuit [27] was analyzed in order to be used in the calculation of the photocurrent \(\mathrm{I_{ph}}\) (Equation (2) below), for each diode. The original electrical signal on the oscilloscope \(\mathrm{V_{scope}}\) was used, with the typical values of 20 nF for the diode junction capacity \(\mathrm{C_{j}}\), and 200 \(\Omega\) for the series resistance \(\mathrm{R_{s}}\).