## 3 Experimental Results and Discussion
### Dependence of the Power of EMPs on the Laser Pulse Energy  
In this study, the effect of the EMPs amplitudes versus different laser energies of 240, 300, 600, and 850 mJ were measured while keeping the other experimental parameters constant: \(t=30\) fs, \(\theta=0^{\circ}\), and \(d=40\) cm (Figure 6). From 240 mJ to 850 mJ, the amplitude of EMPs increased with the laser pulse energy at a given pulse width (Figure 6a). In other words, a significant increase in the amplitude of EMPs occurred in the laser energy interval of 240-600 mJ, while the growth trend of this amplitude slowed down in the laser energy interval of 600-850 mJ. This was mainly because under the experimental conditions of \(t=30\) fs, \(\theta=0^{\circ}\), and \(d=30\) cm, the EMPs generated by the interaction between femtosecond laser filament 3 mm-thick aluminum target gradually saturated around the laser energy of 600 mJ, and the increase in laser energy was no longer a decisive factor for EMP enhancement. The corresponding spectrum is shown in Figure 6b, which shows that the frequency domain near 0.19 GHz was still the most dominant contribution. In addition, a significant EMP signal also appeared near 0.31 GHz, and a more significant EMP signal appeared near 0.45 GHz for the low laser energy. The power of the EMPs produced by interaction between the femtosecond laser filamentation and a 3 mm-thick aluminum target was tens of times stronger than the EMP produced by the femtosecond laser interacting with air under the same laser parameters, using the EMP laser-guided filamentation energy conversion efficiency mode [18]:  
\[\eta_{power}=\frac{P_{EMP}}{P_{L}}\,\sim\,\frac{\pi^{2}}{8}\bigg{(}\frac{a_{L }\lambda_{0}}{c\tau_{L}}\bigg{)}^{2}\bigg{(}\frac{2N_{p}r_{p}c\tau_{L}+r_{p}^{ 2}}{R^{2}}\bigg{)}\]  
Figure 5: (**a**) The total power of EMPs as a function of \(t\). (**b**) Fourier spectra of the EMP signals for various values of \(t\). The corresponding experimental parameters are: \(E=485\) mJ, \(\theta=0^{\circ}\), \(d=65\) cm, and the different values of t are 39, 156, 195, 231, 300 fs. Figure 6: (**a**) The amplitude of EMPs as a function of laser energy. (**b**) Comparison of EMP spectra for four laser energies. The corresponding parameters are: \(t=30\) fs, \(d=40\) cm, \(\theta=0^{\circ}\), and different values of \(E\) are 240, 300, 600, 850 mJ. where, \(a_{L}\) is the laser strength parameter, \(\lambda_{0}\) is the laser wavelength, and \(\tau_{L}\) is laser pulse duration. In our experiment, the laser wavelength was \(\lambda_{0}=0.8\) um, the laser strength parameter was \(a_{L}=\frac{q|E_{L}|}{mc\omega_{0}}\sim 5.7\times 10^{-3}\), the number of plasma wavelengths behind the pulse was \((N_{p})\sim 1\), the plasma filament spot size was \((r_{p})\sim 100\) um, the laser focus spot was \((R)\sim 200\) um, and the laser pulse duration was \(\tau_{L}=30\) fs. It could be estimated that the EMP energy efficiency of laser filament formation in this experiment could reach \(\eta_{EMP\_air}=7.5\times 10^{-8}\), and it was thus estimated that the EMP energy efficiency generated by the laser filamentation and the action of the 3 mm-thick aluminum target could reach \(\eta_{EMP\_air+,Al}\sim 10^{-6}\). Furthermore, the EMP intensity was proportional to the laser pulse intensity and energy, which was consistent with the results of other studies on short laser pulses [10] and those on high power ps lasers [11]. For interaction between femtosecond laser filament and a metal target, the EMP generated by the plasma channel, owing to the femtosecond laser air filamentation effect, was only a tiny fraction of the overall EMP. A vast majority of the EMP came from the contribution of hot electron excitation and electron reflux generated by the interaction of the femtosecond laser air filamentation with the metal target. The hot electrons radiated part of the energy in the form of bremsstrahlung radiation, covering a wide range of spectra.