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Abstract
The interactions between high-intensity laser and matter produce particle flux and electromagnetic radiation over a wide energy range. The generation of extremely intense transient fields in the radio frequency–microwave regime has been observed in femtosecond-to-nanosecond laser pulses with 1011–1020-W/cm2 intensity on both conductive and dielectric targets. These fields typically cause saturation and damage to electronic equipment inside and near an experimental chamber; nevertheless, they can also be effectively used as diagnostic tools. Accordingly, the characterization of electromagnetic pulses (EMPs) is extremely important and currently a popular topic for present and future laser facilities intended for laser–matter interaction. The picosecond and sub-picosecond laser pulses are considerably shorter than the characteristic electron discharge time (∼0.1 ns) and can be efficient in generating GHz EMPs. The EMP characterization study of femtosecond laser-driven solid targets is currently mainly in the order of 100 mJ laser energy, in this study, the EMP generated by intense (Joule class) femtosecond laser irradiation of solid targets has been measured as a function of laser energy, laser pulse duration, focal spot size, and target materials. And a maximum electric field of the EMP reaching up to 105 V/m was measured. Analyses of experimental results confirm a direct correlation between measured EMP energy and laser parameters in the ultrashort pulse duration regime. The EMP signals generated by femtosecond laser irradiation of solid targets mainly originate from the return current inside the target after hot electron excitation. Numerical simulations of EMP are performed according to the target charging model, which agree well with the experimental results.
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1. Introduction
The laser irradiation of a solid target at relativistic intensity is known to form plasma on the surface of the target, thus generating hot electrons. Moreover, the acceleration of electrons and ions is realized by accelerating mechanisms, such as target normal sheath acceleration [1,2], phase-locked acceleration [3,4], and radiation pressure acceleration [5]. These mechanisms can generate electromagnetic pulses (EMPs) from megahertz to terahertz [6] as well as X-rays and γ rays [7]. The resulting hot electrons also generate strong EMPs with frequencies approximating the gigahertz range. This is because of the neutralizing current flowing through the target, target holder, and ground wire [8–11]. An EMP in this frequency range can interfere with the normal measurements of certain pieces of equipment, affecting the accuracy of the experiment and causing temporary or permanent damage in severe cases [8,12].
The EMPs induced by the intense interaction between nanosecond/picosecond laser and solid targets have been widely investigated [13,14]. However, systematic experimental investigations of the dependence of EMP on laser and target parameters remain lacking, especially in the case of intense sub-picosecond or femtosecond-class lasers. The EMP characterization study of femtosecond laser-driven solid targets is currently mainly in the order of 100 mJ laser energy [11,15,16]. EMP pulse energy has been measured as a function of the laser intensity (exceeding 1020 W/cm2) and pulse duration (down to 40 fs) for a 10 μm-thickness Al target, where the electrons emission from the both, front, and rear sides of the target and the effect of ion acceleration should be considered [7]. As an indispensable supplement, in this study, the EMP generated by intense (Joule class, with laser intensity varies from 1017 to 1019 W/cm2) femtosecond laser (down to 29 fs) irradiation of a 10 mm thick solid targets has been measured as a function of laser energy, laser pulse duration, focal spot size, and target materials. In general, short-pulse lasers can produce energetic (MeV) electrons, these electrons can escape from the target more easily, hence the short duration laser can produce very large transient currents and large EMP. The picosecond and sub-picosecond laser pulses are considerably shorter than the characteristic electron discharge time (∼0.1 ns) and are beneficial for the generation of EMP [17].
In this study, the dependence of EMP on experimental parameters, such as laser energy, laser pulse duration, laser focus size, and target materials is investigated. The correlation between EMP and experimental parameters is discussed in terms of the target charging model [18]. In the experiments, strong EMP signals are obtained by irradiating a solid target with an ultra-intense ultrashort laser, a maximum electric field of the EMP reaching up to 105 V/m was measured. The EMP generated by the femtosecond laser irradiated on a solid target mainly originated from the resonance of electrons returning to the target after hot electrons escaped. Additionally, the effect of different target materials on the EMP energy are also investigated.
2. Experiments
The experimental campaign was conducted with the 200-TW laser system [19] at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. As shown in Fig. 1, the 800 nm wavelength, polarized horizontally, 29 fs ∼115 fs long laser pulse was focused onto a 40 × 40 × 10 mm (thickness) flat aluminum target, by a F/1 gold coated parabolic mirror at an incident angle of 0 with respect to the target normal. The laser energy on target is varied between 0.06 J to 3.78 J. The contrast ratio at 5 ns before the main pulse is measured to be 5 × 10−9, and at 100 ps before the main pulse is measured to be 1 × 10−9. The target was supported by a 10 mm diameter and 300 mm length metal rod. The conceptual scheme of the laser target interaction is shown in Fig. 1. Among the results of laser-target interaction, EMP was measured inside the vacuum chamber (2.0 × 2.0 × 1.0m (height)) by a commercial biconical antenna (BicoLOG 20300, 20 MHz–3 GHz), which is directly behind the target 400 mm, and a log-periodic antenna (HyperLOG 30250, 380 MHz-25GHz), which is approximately 800 mm away from the target and inclined at 45° with respect to the laser axis. The two antennas were placed horizontally, parallel to the Y-axis. The experiment is performed at room temperature of 25°C. The antennas are connected to the coaxial feedthrough of the flange of the target chamber wall using RG316 double-shielded sub-miniature version A 0.5-m-long coaxial cables. Outside the chamber, two identical 2-m-long cables are used to connect the coaxial feedthrough in the flange to an oscilloscope with an analog bandwidth of 1 GHz and a sampling rate of 6.25 GS/s. The use of calibrated cables and connectors allow us to eliminate from the measurements unwanted additional errors and uncertainty. The oscilloscope and antenna bandwidth would restrict the effective operating band of our experiment to a frequency range below 2 GHz. and the attenuation from the oscilloscope and the cables are all corrected under the frequency domain. Meanwhile, attenuators were installed between the cables and the oscilloscope to protect the oscilloscope from possible overload voltage and the resulting data finally needed to be recovered by multiplying the attenuation times. The chamber vacuum remained less than 8 × 10−3 Pa.
Fig. 1. Schematic of experimental setup. The laser was focused onto a flat Al target with an F/1 offaxis parabolic mirror at an incident angle of 0 with respect to the target normal. The biconical antenna is located directly behind the target, approximately 400 mm away, whereas the log-periodic antenna is approximately 800 mm away and inclined at 45°.
3. Results and discussions
In order to characterize the EMP generated by ultrashort laser pulse, we can use its electric field energy density, which has little effect on the bandwidth of the equipment. The energy density is proportional to $\sum {V^2}/{Z_0}\; dt$, where V is the measured EMP amplitude signal given in units of V, ${Z_0}$ the impedance of free space in units of Ω. The scaling of EMP electric field energy density as a function of the laser intensities is experimentally investigated by changing the laser energy (section a), laser pulse duration (section b) and laser focus size in the target (section c), the effect of target materials (section d) are also studied. The error bars presented in this article were computed using the sample set's standard deviation. The theoretical EMP energy can be estimated by the formula [8], ${\varepsilon _{GHz}} \cong 0.1\frac{c}{{{d_t}}}{Z_0}Q_e^2$, where c is the speed of light, ${d_t}$ is the diameter of the target disk. The total charge of electrons that have escaped from the target, denoted as ${Q_e}$, can be obtained by the target charging model [18,20], which providing an accurate estimate of the charge accumulation on the surface of a metallic target irradiated by a high-intensity laser pulse of fs–ps duration, and applies to both thin and thick targets. The experimental measurements of the EMP are averaged over five laser shots under each condition.
The relationship between EMP emission and laser energy was examined using an Aluminum target. In this section, the laser energy on target was varied between 0.06 and 3.78 J, the laser pulse duration was fixed at 29 fs, and the laser focus size (full width at half maximum) was 19.5 μm. As shown in Fig. 2(a), the electric field energy density of EMP increases with the laser energy, and the growth trend when laser energy is larger than 1 J is consistent with the calculated EMP energy (Fig. 2(b)) with the target charging model. In the low-energy region (laser energy ≤ 0.6 J), the EMP energy slightly increases with the laser energy. In the high-energy region (laser energy ≥ 1.56 J), as the laser energy increases, the increase trend of the experimentally measured EMP energy is fundamentally consistent with that of the calculated EMP energy, which tends to increase linearly. When the laser energy is relatively high (≥ 1.56 J) and the femtosecond laser interacts with the aluminum target, the generated and calculated EMP energies using the target charging model are more compatible. However, when the laser energy is low (< 0.6 J), the actual EMP energy generated does not increase as fast as the calculated EMP energy. This is probably because the laser absorption efficiency used in the simulation is 40%, but in the actual experiments, at low laser energy, the absorption efficiency is low due to the different heating mechanisms of the laser on the target (the main mechanism is not J × B). Additionally, for high laser energies, when the target heating mechanism is J × B-dominated, the energy absorption tends to saturate as the laser energy increases because of the limitations of the laser interaction area. As shown in Fig. 2(a), this results in a gradual EMP energy (3.78 J) increase; the figure also shows the standard deviation of the EMP energy. The measured time-domain signals of the voltage could be converted to an electromagnetic field value. The electric field strength could be deduced according to the method given in Ref. [21]. In this experiment, with the laser energy of 3.78 J, the pulse width of 29 fs, and the focal spot of 19.5 $\mu $m, the peak magnitude of the resulting electric field value of the EMP came to 105 V/m, about the same order of magnitude when compared with the EMP intensity acquired with several hundred Joule sub-ns laser irradiate solid target [22].
Fig. 2. (a) Dependence of the electric field energy of EMP on the laser energy. (b) Dependence of the calculated total EMP energy on the laser energy. (c)Waveforms of the voltages detected by bicoantenna for the laser pulses of 3.78 J, 29 fs, focus size 19.5$\mu $m and 1.56 J, 29 fs, focus size 19.5$\mu $m and (d) their corresponding frequency spectra. The error bars are the standard deviation observed over 5 shots for each laser energy. The frequency spectra in Fig. 2(d) are plotted up to 2 GHz. No higher frequency components are observed. The oscilloscope and antenna bandwidth restrict the effective operating band of our experiment to a frequency range below 2 GHz.
The shown time domain (Fig. 2(c)) and frequency domain (Fig. 2(d)) signals with laser energies of 1.56 and 3.78 J indicate that the spectra of EMP signals obtained from the experiments are similar at different laser energies. Moreover, the EMP frequencies are all mainly concentrated at approximately 0.25 GHz. Using the target charging model frequency calculation formula [8,23], fs = c/(4 × (ls + ds/2)) (where c is the speed of light, ls is the length of the ground line (30 cm), and ds is the side dimension of the aluminum target (4 cm)), the EMP frequency can be calculated (fs = 0.234 GHz). This calculated value is fundamentally the same as the actual measured value (0.25 GHz). The EMP spectra confirm that when the femtosecond laser irradiates the solid target, numerous electrons are emitted from the target, resulting in a positively charged target. The return current in the target results in a strong EMP signal; this agrees well with the target charging model.
The dependence of EMP on laser pulse duration is shown in Fig. 3. The laser pulse duration is gradually increased from 29 to 115 fs. The laser focus size (full width at half maximum) and energy are 19.5 $\mu $m, and 0.06 J, respectively. The target material is aluminum. Results indicate that as the laser pulse duration increases, the electric field energy of EMP exhibits a decreasing trend as represented in Fig. 3(a). The theoretical total EMP energy estimated by the target charging model in Fig. 3(b) also show a slight decrease. This is probably because the laser power intensity decreases with increasing laser pulse duration, consequently decreasing the EMP amplitude and energy. In contrast, the increase in the laser pulse duration prolongs the duration of EMP emission, slightly enhancing the EMP energy. Overall, the combination of these two factors gradually decreases the EMP energy as the laser pulse duration increases. Note that in this round of experiments, the low laser energy generates low EMP energy; moreover, a high standard deviation is observed. The time domain EMP signals measured at two different laser pulse durations (29 and 115 fs) and the corresponding frequency domain signals are shown in Fig. 3(c) and Fig. 3(d), respectively. The figure also shows that the spectra of EMP signals obtained from the experiments are similar at different laser pulse durations.
Fig. 3. (a) Plots of electric field energy of EMP evaluated from measured amplitude signal and (b) calculated total EMP energy versus laser pulse duration (laser energy is 0.06 J, and laser focus size (full width at half maximum) is 19.5 $\mu $m). (c)Waveforms of the voltages detected by bicoantenna for the laser pulses of 0.06 J, 29 fs, focus size 19.5 $\mu $m and 0.06 J, 115 fs, focus size 19.5 $\mu $m and (d) their corresponding frequency spectra.
The effect of laser focus on EMP is presented in Fig. 4. The on-target laser energy and laser pulse duration are consistent at 3.78 J and 29 fs, respectively. In the experiment where the femtosecond laser irradiates an aluminum target, a sharp decrease in the generated electric field energy of EMP is observed as the laser focus size increases from 45 to 64 $\mu $m (Fig. 4(a)). This is mainly because at an energy of 3.78 J, when the laser focus size is 45 $\mu $m, the laser intensity (≈1.69 × 1018 W/cm2) is still relativistic. In contrast, when the laser focus size is 64 $\mu $m, the laser intensity (≈0.88 × 1018 W/cm2) is non-relativistic. An increase in the laser focal spot for a given absorbed pulse energy and pulse duration decreases the laser intensity, consequently reducing the number of ejected electrons. From the results of total EMP energy we calculated at Fig. 2(b) and Fig. 4(b), we can find that the energy of EMP for laser focus size 40 $\mu $m is larger than the energy of EMP for laser focus size 19.5 $\mu $m (other parameters are same, the laser energy is 3.78 J, laser pulse width is 29 fs), this counter-intuitive result may be due to the following reasons, the EMP is intricately linked to the charge of the outgoing electrons. Usually, increase of the laser focal spot and of the pulse duration for a given absorbed pulse energy results in a decrease of laser intensity and, consequently, of the number of ejected electrons. But if the the laser is intense enough, a nearly complete ejection of hot electrons occurred [17], in this case, increase of the laser focal spot, more electrons would be involved in the interaction, resulting the stronger EMP emission. The dependence on the number of ejected electrons can be more complicated in experiments where laser defocusing is accompanied by a variation in absorption owing to nonlinear laser–plasma interactions. The EMP energy generated in relativistic intensity is significantly higher than that generated in non-relativistic intensity under the same conditions. Also, the trend of the electric field energy of EMP is consistent with the theoretical total EMP in the area of 35-112 $\mu $m. The EMP signals measured at two different laser focus sizes (19.5 $\mu $m and 56 $\mu $m) in the time and frequency domains are shown in Fig. 4(c) and Fig. 4(d), respectively. The frequency domain signals also show that the spectra of EMP signals obtained from the experiments are similar at different laser focus sizes.
Fig. 4. (a) Plots of electric field energy of EMP evaluated from measured amplitude signal and (b) calculated total EMP energy versus laser focus size (laser energy is 3.78 J, and laser pulse width is 29 fs). (c)Waveforms of the voltages detected by biconical antenna for the laser pulses of 3.78 J, 29 fs, focus size 19.5 $\mu $m and 3.78 J, 29 fs, focus size 56 $\mu $m and (d) their corresponding frequency spectra.
Several publications have reported that the target material can considerably impact electron and EMP emissions. The emitted EMP can be significantly modified when the inductance, impedance, or capacitance of the target changes. The difference between an aluminum target (metallic target) and a plastic target using the same laser energy (0.6 J) and laser pulse duration (29 fs) is also investigated. In the experiments, note that the two types of targets are bonded together and fixed on a holder. As shown in Fig. 5(a), the maximum amplitude of the EMP generated when the laser irradiates the metal target is approximately six times higher than that of the EMP generated with the plastic target. This is mainly because the increase in the conductivity of the target and laser absorptivity intensifies the movement of hot electrons, considerably increasing the number of escaping electrons. In contrast, the drop in EMP with the plastic target is caused by a corresponding reduction in the return current through the target. Compared with the electrons in the plastic target, the electrons in the metal target are more rapidly compensated for the loss of electrons in the region; this provides a suitable condition for the excitation of more hot electrons. The number of electrons generated by the laser irradiating the metal target is considerably greater than that generated by the laser irradiating the plastic target; this factor determines the strength of EMP emission. The frequency domain results shown in Fig. 5(b) indicate that the frequencies of the EMP generated by the two types of targets are concentrated at 0.25 and 0.64 GHz. This is mainly because the metal and plastic targets share the same target disc, target support, ground wire, and vacuum target chamber.
Fig. 5. (a) Time domain EMP signals generated by laser irradiation of metal and plastic targets at 1 J, 29 fs and 19.5$\mu $m. (b) Corresponding frequency domain signals obtained from fast Fourier transform of time domain EMP signals in (a). (c) Time domain EMP signals measured with biconical antenna (magenta line) and log-periodic antenna (green line) (plastic target, laser energy is 1 J, and laser pulse duration is 29 fs, and focus size is 19.5 $\mu $m); and (d) frequency domain signal obtained from fast Fourier transform of EMP signals in (c).
The EMPs are simultaneously measured using the biconical and log-periodic antennas (Fig. 5(c) and Fig. 5(d)). The biconical antenna is located directly behind the target, approximately 400 mm away, whereas the log-periodic antenna is approximately 800 mm away and inclined at 45°. The measurement results of the two antennas show that the EMP of the log-periodic antenna arrives approximately 3 ns later than that of the biconical antenna (Fig. 5(c)); this is probably due to the different locations of the two antennas. However, the signals measured by the antennas fundamentally have the same frequency range (e.g., the frequency domain signals shown in Fig. 5(d)), confirming the reliability of the experimental measurements. This further indicates that the generated EMPs fill the entire vacuum target chamber, and the EMPs from different positions have different intensities. However, the EMP frequency does not change significantly for the different locations of antennas. Evidently, slight variations in the frequency components can result when the antennas have different antenna factors.
4. Conclusion
In this study, the characteristics of the EMP generated by the interaction between a femtosecond laser and solid target are systematically investigated by varying the laser and target parameters. The dependence of the EMP energy on laser energy, laser pulse duration, and focus size is consistent with the results calculated using the target charging model. Moreover, the EMPs have broad frequency bands and are mainly concentrated at 0.25 GHz; this is considerably consistent with the values calculated using the target charging model. This analysis shows that EMP emissions mainly originate from the oscillation of neutralizing current between the laser target and nearest ground. Additionally, metal and plastic targets are irradiated separately using a femtosecond laser. The intensity of the EMP generated by the metal target is found to be six times higher than that of the EMP generated by the plastic target. In summary, this study clarifies and validates the mechanism of EMP emission driven by short-pulsed (sub-picosecond and femtosecond) lasers. The experimental results are in good agreement with the target charging model. This study is anticipated to aid in gaining a better understanding of the sensitivity of EMP to laser and target parameters, providing a solid background for designing mitigation techniques.
Funding
National Natural Science Foundation of China (12204502, 12325409, 12388102, U226720057); Chinese Academy of Sciences, Shanghai Branch (Shanghai Pilot Program for Basic Research); CAS Project for Young Scientists in Basic Research (YSBR-060); China Association for Science and Technology (Young Elite Scientist Sponsorship Program); China Postdoctoral Science Foundation (2021M703329); Shanghai Rising-Star Program (Shanghai Sailing Program 22YF1455000); Key Research Program of Frontier Science, Chinese Academy of Sciences.
Acknowledgments
We would like to thank for the help from Xinjun Guo and Tiejun Wang.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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