EMP distribution in target chamber

Fig. 2 shows the variations in the distributions of the EMP peak amplitudes obtained by calculating the maximum absolute value of the signal amplitude in the time domain. These EMPs were generated by the interaction between the PW laser and different targets, including the Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH), and CDNWA (PH) targets. The result indicate that the EMP distributions were affected significantly by the spatial position: (1) For the Al target, the peak value was significantly higher and the distribution was more uniform at diverse angles compared with those of the other targets. (2) The EMP intensities of the CD and CDNWA targets using PHs were significantly lower than those using MHs. This is expected as the MH has a higher conductivity than the PH, which implies that it can generate a larger return current under similar shooting conditions^[24]. (3) In front of the target, the overall distributions from the CD and CDNWA were uneven and stronger along the laser reflection direction a1. (4) At the back of the target, the CD and Al targets exhibited the strongest signal along the a4 position, whereas for the CDNWA targets with improved EMP performance compared with regular planar targets, the strongest signal was observed along a5, which was the closest to the transmission direction of the laser. Several studies showed that NWA targets can improve laser absorption and plasma-conversion efficiency compared with ordinary solid targets^[34-37]. For the NWA targets, approximately 50% of the energy can be converted into electrons^[38], which subsequently enhances the radiated EMPs^{[27, 39]}. (5) Additionally, we observed that the peak values of the five targets were higher at the back of the target than in front of the target, which is consistent with the emission direction of the high-energy-density electrons.

Fig. 2Full-screen View

(Color online) Distribution of peak of EMPs generated by PW laser collision with different targets, including Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH) and CDNWA (PH) targets; measurement was performed at a1 to a6 from different angles with respect to normal direction of target. Red arrow indicates incident direction of laser, which is 25° relative to the normal direction of the target; and all laser focal spots measure 22 μm

Results in time and frequency domains

To investigate the variations in the time and frequency domains as well as the energy of EMPs generated by the interaction of the PW laser with the Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH), and CDNWA (PH) targets, five EMP signals from the a5 antenna were compared. Here, “0 ns” refers to the time at which the laser interacts with the target. Fig. 3 shows the peak intensities of the EMPs based on the Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH), and CDNWA (PH) targets, whose intensities were 738.4, 238.7, 100.7, 388.8, and 140.3 V, respectively. The results indicate that the EMPs generated by the laser–target interactions depended on the material properties of the target (the greatest for metal, followed by the CDNWA and CD) and the target holder (metal larger than plastic). Notably, the EMP magnitude increased at 34 ns for both the CDNWA (MH) and CD flat (MH) targets. The CDNWA (MH), CD flat (MH), CDNWA (PH), CD flat (PH), and AL flat (MH) targets differ in terms of the material combinations used for the target rod and body. Specifically, the first two incorporate a combination of insulators and conductors, whereas the last three involve combinations of similar materials, i.e., insulators with insulators or conductors with conductors.

Fig. 3Full-screen View

(Color online) Time domains of five EMPs generated by PW laser interacting with Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH) and CDNWA (PH) targets at position a5

For the insulator–conductor combinations, once the threshold voltage (known as the insulator breakdown voltage) is surpassed, the resistance to electron movement decreases significantly. During the interaction between the laser and target, significant electron emission from the target increases the potential difference. Electrons from the target rod, which are connected to the ground, compensate for the missing electrons. In the initial phase, the potential difference is amplified because the electron supply is not compensated timely. Once the breakdown voltage is breached, the electrons rush in swiftly, thus significantly increasing the return current. Because this current is one of the primary sources of EMPs, the observed signal is diminished significantly.

The observed trends of the curve suggest that the EMP attenuation is slower and persists for a longer duration when an Al target or plastic target rod is used. In particular, the curve exhibits a gradual decay over an extended period when compared with other target materials, thus indicating that the EMP attenuation properties of these materials differ significantly.

To gain a more comprehensive understanding of the temporal and spectral properties of EMPs, we employed wavelet transform to analyze the signals depicted in Fig. 3; the resulting time–frequency diagram is presented in Fig. 4. For the Al flat (MH) target, when the laser reached the target, the EMP energy was primarily released within 0–120 ns, with the spectral concentration primarily in the higher frequency range between 14 and 16 GHz, along with higher harmonic oscillations at 7 and 14 GHz. The high-order harmonics were generated owing to nonlinear effects. For example, during the interaction between the laser and target, the generated EMPs were generated via multiple mechanisms, thus resulting in a rich frequency spectrum. Throughout the propagation of the EMPs, these frequencies underwent superposition, mixing, reflection, and other effects, thus resulting in nonlinear responses. Meanwhile, the free-electron density of the target material changed significantly, which induced thermal effects in the target and resulted in plasmas with varied density distributions. When an EMP propagates and encounters these media or interfaces, the nonlinear effects result in new frequency components with high-order harmonics. Additionally, a few EMPs continued to radiate between 120 and 260 ns. The EMPs generated by the CD flat (PH) and CDNWA (PH) targets exhibited similar durations and frequencies as the Al (MH) target, albeit with different intensities.

Fig. 4Full-screen View

(Color online) Relationship between time and frequency obtained via wavelet transformation of signals presented in Fig. 3

An analysis of the CD flat (MH) and CDNWA (MH) targets revealed that, compared with the case of other targets, the EMPs generated by these targets were primarily dispersed in a lower frequency range and had a relatively short duration of approximately 100 ns following the arrival of the primary laser pulse at the target. The specific energy distribution and frequency characteristics of the EMPs are shown in Fig. 5.

Fig. 5Full-screen View

(Color online) (a) Power spectra of signals from Fig. 3; (b) total integrated energy of Al target from (a); (c) total integrated energy of other four targets. Spectra complexity is attributable to various factors, including multiple possible sources of EMPs and internal arrangement of target chamber, as discussed in prior publications^{[30, 40, 41]}

To analyze the frequency components of the signals depicted in Fig. 3, we performed the fast Fourier transform to convert the time-domain signals into frequency-domain amplitudes. Subsequently, we squared and divided the spectra by 2 to obtain the power spectra. The resulting power spectra are illustrated in Fig. 5 (a), which show the spectral properties of the EMPs generated by the interaction of the PW laser with the Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH), and CDNWA (PH) targets.

As shown in Fig. 2, the distribution of EMPs is non-uniform, thus rendering the formula for uniform distribution^[27] inadequate for evaluating the power radiated by the EMPs. Hence, we incorporated a distribution coefficient β into the original formula, which yielded a more precise evaluation of the radiated power. β considers the non-uniform distribution of EMPs and is derived by averaging the ratio of EMP peak values between a1–a6 to a5. The total integrated energy of the EMPs (E_EMP) can be evaluated using Equation (1). $E=\frac{\text{β}\times \left(2\text{π}{d}^{2}P\right)\times {\tau }_{\text{EMP}}}{\pi r^2\times R},$ (1) where P is the radiant power obtained by integrating the power spectra shown in Fig. 5 (a). The distance from the antenna to the target is d = 20 cm and the effective radius of B-dot is r = 0.5 cm. The EMP duration τ_EMP is 260 ns for the Al flat (MH), CD flat (PH), and CDNWA (PH) targets, and 100 ns for the CD flat (MH) and CDNWA (MH) targets. The load resistance R is 50 Ω. The distribution coefficients β for the targets above are 0.86, 0.88, 0.65, 0.71, and 0.49, respectively. The E_EMP, as shown in Figs. 5 (b) and (c), indicates that the total integrated energy of the Al flat (MH), CD flat (MH), CD flat (PH), CDNWA (MH), and CDNWA (PH) targets are 285.77, 4.61, 2.36, 6.77, and 4.24 μJ, respectively. An early study^[24] showed that using PHs reduced the energy of EMPs by 1/3 compared with using MHs. Our test results indicated a similar trend: The EMP energy based on CD flat (PH) was 0.52 times that of CD flat (MH), whereas the EMP energy of CDNWA (PH) was 0.79 times that of CDNWA (MH).

The power spectral distribution can be observed more clearly from the increasing trend of the integrated energy. First, the Al flat (MH) target demonstrated the widest and strongest energy distribution, which primarily dispersed within the range of 0–16 GHz. Second, the EMPs generated from the CDNWA (MH) target were primarily distributed below 2 GHz, with a narrow power range between 2 and 11 GHz and a shorter power range from 11 to 16 GHz. Third, the CD flat (PH) and CDNWA (PH) targets primarily appeared in the range of 6 to 11 GHz, and the CD flat (MH) target was distributed below 3.2 GHz.

The results of the power spectra and integral energy indicated strong dependence on the type of target and target holder used. Specifically, (1) the EMP radiation energy from the NWA target was, on average, 1.6 times higher than that from a typical plastic target. However, this increase in energy was only evident in the amplitude of the spectrum, whereas no clear changes were observed in the spectral range. (2) The EMP generated by the metal target rod was, on average, 1.8 times larger than that generated by the plastic target rod. Nevertheless, the energy values in the frequency ranges of 0–2 GHz and 2–16 GHz indicated that the low-frequency region of the EMP spectrum was suppressed, whereas the high-frequency region was enhanced when the plastic target rod was used. (3) The EMPs generated by the metal targets exhibited a significantly higher energy, i.e., approximately 62 times greater than that generated by the plastic targets. Furthermore, the spectra of these EMPs were the widest and strongest, thus resulting in to severe interference with electronic equipment. This phenomenon is due to the metal targets generating more energetic hot electrons and the low resistivity of the metal, thus promoting the lateral transport of the electrons. If these energetic electrons exhibit higher acceleration rates, escape velocities, and quantities, then EMPs with higher frequencies and greater power can be generated^[27]. In addition, the neutralization current predominantly radiated strong EMPs at low frequencies, which is similar to the result presented in a previous study^[42].

EMPs and hot electrons in different focal spots

Fig. 6 shows the EMP radiation energy and thermal electron energy spectra measured by the ES, as shown in Fig. 1, for four different focal spots. The total EMP energies yielded by the interaction between the PW laser and CDNWA (MH) target for focal spots of 22, 30, 40, and 107 μm were 6.77, 2.31, 0.4, and 0.31 μJ, respectively. The exponential fitting of the normalized total E_EMP (y₁) and the focal spot size (x) showed an exponentially decaying relationship expressed by the function y₁ = 25.65 × e^(-x/6.73) + 0.03. The normalized total N_e (y₂) decreased as the focal spot size increased (i.e., y₂ = 5.15 × e^(-x/10.78) + 0.33), which indicates a similar trend between the intensity of EMPs and the number of hot electrons with varying focal spot sizes, thus further emphasizing that hot electrons are one of the primary sources contributing to EMPs. Additionally, the results suggest the potential of controlling the EMP radiation energy and the number of hot electrons by adjusting the focal spot of the laser, which offers valuable insights into the investigation and application of EMPs in various fields.

Fig. 6Full-screen View

(Color online) (a) Total integrated energy of CDNWA (MH) target from four different focal spots measuring 22, 30, 40, and 107 μm; (b) electron spectroscopy results for the four spots; (c) two exponential fits among total number of hot electrons (N_e), total energy of EMP (E_EMP) and focal spot size, where N_e and E_EMP are normalized with their respective highest values

Simulation result discussion

We employed the two-dimensional PIC software EPOCH to simulate thermal electron emission from three targets. The simulation box measured 40 µm × 20 μm and comprised a 4000 × 2000 grid, with each grid containing 30 superparticles. The spatial resolution was 10 nm × 10 nm. A linearly polarized 800 nm laser beam with a pulse width of 10 laser cycles and an FWHM of 4.3 μm was utilized; it was incident on the targets at an angle of 25° with respect to the target normal. The focal spot was located between -1 to -7 µm on the vertical axis in the figure, with a peak intensity of 1 × 10²⁰ W/cm². Three different targets were utilized in the simulation: carbon-hydrogen nanowire-array (CHNWA), CH, and Al targets, whose thicknesses were 10, 10, and 4 μm, respectively. The atomic number densities of C/Al were 37.5, 37.5, and 35 n_c, where n_c = 1.7 × 10²¹ cm^-3 represents the critical plasma density for an 800 nm laser. The initial ionization conditions were C²⁺, H⁺, and Al⁹⁺ for the CHNWA, CH, and Al targets, respectively. Additionally, we considered the effect of pre-pulses on the targets. The pre-plasma distribution for all targets can be expressed as shown in Eq. 2: $n=n_0{e}^{\frac{-\Delta x}{L}},$ (2) where the ionized particles for the CHNWA and CH targets is H⁺, and Al⁹⁺ for Al. Here, n₀ represents the initial atom number density; L is the plasma scale length, which is 0.16 μm; and Δx is the distance from the target surface. A similar simulation method was used in previous studies^{[43, 44]}.

A graphical representation of our findings is presented in Fig. 7, where (a)–(c) show the electron densities of the Al, CH, and CHNWA targets, respectively, at a simulation time of t = 133 fs, and (d)–(f) show the corresponding momentum space distribution of electrons at the same simulation time. The results show a relatively uniform distribution for the Al target, which is consistent with the insignificant distribution difference of the EMP shown in Fig. 2. Comparatively, the CH target tended to propagate toward the rear side of the target in the direction of laser propagation. During the interaction between the laser and NWA targets, the self-generated electromagnetic field exhibited the behavior of a lens, i.e., it confined and trapped hot electrons between the nanowires. This reduced the scattering and diffusion of hot electrons, thus enabling them to acquire relativistic energy via a direct laser-acceleration mechanism^{[45, 46]}. Therefore, the microstructure of the NWA targets results in the collimation of hot electrons, thus causing them to propagate in the target’s normal direction. This analysis highlights the close relationship between the spatial distribution of hot electrons (Fig. 7) and EMPs (Fig. 2), thus confirming that hot electrons are the primary source of EMPs.

Fig. 7Full-screen View

(Color online) (a)–(c) Density distributions of hot electrons generated by interaction between laser and Al flat, CH flat, and CHNWA targets. (d)–(f) Space momentum distribution of hot electrons for three targets. Laser incidence occurred at t = 0 and reached target surface at t = 27 fs, whereas electron distribution presented in simulation results is relevant to t = 133 fs

Investigation into protection for EMPs

Early nuclear detonation experiments revealed that EMPs generated by nuclear explosions traversed the atmosphere, thus adversely affecting the terrestrial power infrastructure, electronic systems, and human personnel. This is due to the unique physical repercussions induced by the microwave irradiation of materials, including molecular heating, which can cause injury to biological cellular tissues. The coupling of microwaves with electronic systems engenders electromagnetic induction effects, thus resulting in disruptions to electronic equipment. Correspondingly, investigations into laser-driven nuclear fusion reactions and related applications showed that the coupling of lasers with targets results in high-intensity broadband EMPs. These EMPs not only cause severe perturbations in diagnostic data (even potentially submerging test signals entirely amidst electromagnetic interference) but also propagate electromagnetic disturbances onto the diagnostic apparatus both inside and outside the target chamber. This can result in the impairment of precision instruments and pose varying degrees of harm to a person present in environments characterized by robust electromagnetic fields.

Researchers have implemented shielding measures, such as using lead and concrete at Lawrence Livermore National Laboratory^[47], as well as employing metallic or iron oxide materials to create Faraday cages integrated with suitable grounding at the National Ignition Facility^{[17, 48]}. At China’s Laser Fusion Research Center^[49], researchers have investigated the shielding effectiveness of materials such as copper, lead, and copper meshes against EMPs. Building upon these efforts to mitigate EMP interference, we investigate the effectiveness of composite shielding materials in attenuating EMPs by focusing on copper + permalloy + lead composites of various thicknesses. Copper is selected owing to its excellent conductivity, whereas permalloy is selected for its high permeability, both of which contribute significantly to the shielding effect against electromagnetic fields. Meanwhile, lead is incorporated into the composite material for its strong shielding properties against high-energy radiation and neutrons, which reduces the generation of secondary electrons caused by their interaction with the metal, thereby reducing EMP radiation from the electron source. Therefore, this composite shielding material possesses comprehensive ability to shield against electric/magnetic fields as well as secondary electromagnetic fields caused by high-energy radiation, thus rendering it highly advantageous for certain applications.

To evaluate the spatial distribution of the EMP outside the target, we selected three representative locations: a7, a9, and a10. Fig. 8(a) shows the peak attenuation of the EMP passing through the target chamber for glass flanges, metal flanges, and spaces outside the target. Attenuation was quantified by calculating the ratio of the peak values of a5 to those of a7, a9, and a10. The attenuation ratios for glass flanges, metal flanges, and spaces outside the target were 5.21, 2183.98, and 136.81, respectively. This suggests that metal flanges and long-distance transmission can cause significant EMP attenuation, thus facilitating shielding, particularly through the increased utilization of metal flanges and the positioning of shielded equipment at greater distances from the glass flanges. Fig. 8(b) shows the shielding effect of four composite materials (copper + permalloy + lead) with four different thicknesses on EMPs, including 0.05 + 0.3 + 0.6, 0.9 + 0.9 + 0.9, 1.2 + 1.2 + 1.2, and 1.5 + 1.5 + 1.5, in units of micrometer. The shielding effects were 42.8, 290, 339.38, and 540 times, respectively. These results show that the shielding effect of the EMP improved as the thickness of the shielding material increased.

Fig. 8Full-screen View

(a) Spatial distribution of EMP outside target chamber; attenuation multiples of a7, a9, and a10 with respect to peaks of a5. (b) Shielding effect of composites (copper + permalloy + lead) with different thicknesses on EMP peak strength. Thicknesses include 0.05 + 0.3 + 0.6, 0.9 + 0.9 + 0.9, 1.2 + 1.2 + 1.2, and 1.5 + 1.5 + 1.5, in units of micrometer, and peak shielding was obtained by dividing the peak of a7 by that of a8. a5 is located closest to the propagation direction of laser. a7 is located on the glass flange outside target chamber and near exterior of shielding box. a8 is located inside shielding box. a9 is positioned on metal flange. 10 is located 3.8 m away from target chamber wall

Hu et al.^[50] developed a gated fiber detector that was resistant to strong EMP interference by employing optoelectronic isolation. Currently, additional shielding schemes are being actively verified in practical environments. These include the use of photoelectric conversion modules, magnetic rings, surge protectors, absorbing materials, and effective grounding techniques, all of which aim to mitigate the effects of strong EMPs. We plan to develop more comprehensive shielding solutions, which are anticipated to not only extend the service life of the equipment but also enhance electromagnetic compatibility.