# 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
The load resistance \(\mathrm{R_{L}}\) was set to be equal to the input resistance of the oscilloscope, at 50 \(\Omega\). \[\mathrm{I_{ph}}=\mathrm{C_{j}}\left(\frac{\mathrm{R_{s}}}{\mathrm{R_{L}}}+1 \right)\frac{\mathrm{dV_{scope}}}{\mathrm{dt}}+\frac{\mathrm{V_{scope}}}{ \mathrm{R_{L}}} \tag{2}\]  
In Figure 4c, the reconstructed current waveforms for the two diode signals and their corresponding ratio are demonstrated. The first peak of the Al-filtered PIN signal waveform occurs at 38 ns, which is also when the hot spot is generated, 7 ns before the interferometric image capture, with an FWHM pulse duration of \(\sim\)3 ns. A flat and very small Cu-filtered PIN signal was also recorded. Therefore, the soft X-ray emission spectrum is less than the lower limit of 3.4 keV (see Figure 2a), and corresponds to the thermal processes within the X-pinch cross-point region. A soft X-ray burst was observed within the time interval of 45-50 ns, and was recorded by both diodes. This X-ray emission occurred after the pinching time, corresponding to bremsstrahlung radiation emitted by a cascade of electrons, accelerated across the anode-cathode gap [12; 13]. Considering the X-ray emission to be isotropic, the energy-filtered X-ray emission yield \(\mathrm{Y_{X-ray}}\) of the source can be related to the reconstructed current of the diodes in the region of their sensitivity:  
\[\mathrm{Y_{X-ray}}=\frac{4\pi\,\mathrm{r}^{2}}{\mathrm{A}}\frac{\int_{\mathrm{ t}1}^{\mathrm{t}2}\mathrm{I_{ph}}\mathrm{dt}}{\overline{\mathrm{S}(\mathrm{E})_{ f}}} \tag{3}\]  
where r is the distance of the diode from the X-ray source, A is the active surface of the diode, and \(\overline{\mathrm{S}(\mathrm{E})_{f}}\) is the energy average of the spectral sensitivity in the presence of a filter. The sensitive area of the BPX65 PIN detector is 1 mm\({}^{2}\), while the distance between the cross-point of the X-pinch load and the diodes is 150 mm. For the aforementioned range of energy, the average spectral sensitivity of Al- and Cu-filtered PIN diodes is 0.015 A/W and 0.02 A/W, respectively. Figure 4d shows the time integral of the reconstructed photocurrent. For the time interval of 38-50 ns, where the Al-filtered diode was conductive, the electrical charge was calculated to be 2.8 nC, while for the Cu-filtered diode the corresponding time interval was 45-50 ns, and the electrical charge was 0.4 nC. The pure and Au-plated W have an average X-ray yield with the Al-filtered PIN (1-20 keV), depending on the angle of the wire configuration--estimated to be \(\sim\)50 mJ and \(\sim\)70 mJ for the X-pinch load angles of 98\({}^{\circ}\)and 55\({}^{\circ}\), respectively. Moreover, the X-ray energies from 3.4 to 9.0 keV contribute to the total X-ray yield at a percentage of less than 15%, as shown by the analysis of the Cu-filtered PIN data. For a series of shots, Figure 5a,b demonstrate the PIN diodes' current values as a function of time for all of the X-pinch configurations, for the first and the second peaks, respectively. The vertical and horizontal error bars correspond to a 20% variation in the average peak current and average peak time, respectively. In Figure 5a, at 44.5 ns, it is evident that the W wire and the Au-plated W wire configurations loaded at a crossed angle of 98\({}^{\circ}\) have the same average value of 0.4 A, confirming that in this case the results are independent of the Au coating. The greater X-ray average power was obtained by the Au-plated W wire configuration load crossed at 55\({}^{\circ}\), compared to the other configurations, resulting in an average peak current of 0.84 A at 48.5 ns. Moreover, all of the results of the PIN diodes' peak current values corresponding to the maximum X-ray intensity presented in Figure 5a have a smaller amplitude when the first X-ray burst is delayed. Figure 5b shows that the Au-plated W wires crossed at 55\({}^{\circ}\) and 98\({}^{\circ}\) have the same average current value of 0.3 A at 58 ns, suggesting that the load's crossed angle does not affect the results.