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Abstract
The non-uniformity and transient nature of laser-produced plasma are critical factors that affect the analysis of the extreme ultraviolet spectra of highly charged ions and the diagnosis of plasma states. This paper systematically investigates the characteristics of extreme ultraviolet radiation and the hydrodynamic evolution of laser-produced nickel plasmas from two perspectives: high-spatio-temporal-resolution extreme-ultraviolet spectroscopic measurement and radiation hydrodynamics simulation. The consistency between the four-band experimental spectra and their theoretically simulated spectra confirms the accuracy of the atomic structure parameters and plasma state parameters. We also analyze the significant contribution of the 3d-4f double-excited state radiation to the spectral profile and discuss the influence of the self-absorption caused by plasma opacity on the characteristics of extreme ultraviolet radiation. The findings are crucial for accurately understanding the characteristics of extreme ultraviolet radiation, the hydrodynamic evolution, and the application of medium- and high-Z laser-produced plasma as a pulsed short-wavelength light source.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser-produced plasma (LPP) is generated by focusing a high-energy laser pulse onto the surface of a target material and is characterized by high temperature and density. It has been widely studied as an ideal source of pulsed short-wavelength light [1] and ions [2], especially in the fields of extreme ultraviolet (EUV) lithography [1], soft-X-ray bioimaging [3,4], and EUV metrology [5,6]. The EUV radiation and the hydrodynamics of medium- and high-Z-element LPPs have become widely studied topics [7–11]. However, the main constraints of the above-mentioned studies are the lack of atomic data and the absence of analytical models and codes. The spectral data for highly charged ions of most medium and high-Z elements are either incomplete or missing. [12–17]. Meanwhile, the theoretical simulation codes capable of processing the generation, expansion, cooling, and radiation transport of LPP throughout the process are also inadequate owing to the non-uniformity and transient characteristics [18]. These two issues are the primary challenges in studying the radiation characteristics and hydrodynamics of medium- and high-Z-element LPP.
In general, the energy levels and transitions of highly charged ions of medium- and high-Z elements are extremely complex. This complexity arises primarily from the coupling of multiple open subshells, resulting in hundreds or even thousands of nearly degenerate levels. Additionally, these factors result in unresolved transition arrays (UTA) [19], which are the main characteristics of narrowband and quasi-continuous spectra in the EUV region. In LPPs, the EUV radiations from ions of various charge states typically overlap, and because of the collisional broadening and opacity within the plasma, the spectral profiles are usually a mix of bands and narrow peaks. Analysis of such spectral structures requires not only accurate atomic structure calculations but also a thorough consideration of the influence of plasma radiation hydrodynamics on the emitted radiation.
Currently, codes such as Cowan [20], Grasp [21], and FAC [22] are widely used for atomic structure calculations. The Cowan code, in particular, offers unique advantages for lightweight calculations of complex configurations of highly charged ions and is compatible with experimental benchmarks. It has been extensively applied to analyze complex experimental spectra in the EUV range, including elements such as Sn [23] and Ag [24]. However, in these studies, the contributions of multiply-excited states are often overlooked, leading to significant discrepancies between the continuous background features in simulated spectra and the experimental spectra. Torretti et al. found a significant impact of 4p-4d and 4d-4f multiply-excited states on the spectrum through their simulation calculations for Sn [23]. One of the most challenging aspects is constructing medium- and high-Z-element configuration models that incorporate multiply-excited states, owing to their open 3d and 4d subshells and the existence of strong configuration interaction (CI) between levels in the n = 3 or 4 manifold. Moreover, a crucial issue for achieving accurate atomic structure calculations is including a suitable experimental benchmark to determine whether sufficient configurations were included in the atomic structure models.
The emissivities computed by 0D codes such as ATOMIC [25] and THERMOS [26] cannot be compared with experimentally obtained spectra, because the assumptions of homogeneity and optical thinning do not hold for LPPs. This is because these codes do not account for the impact of plasma parameter distribution on radiation. Currently, researchers have developed various 2D or 3D radiation hydrodynamics (RHD) codes [27–33] to simulate LPP states, enabling more realistic plasma modeling. However, to generate simulated spectra that can be directly compared with experimental spectra, the RHD code requires a post-processing spectral simulation module [31,33,34], such as FESTR [35] and SPECT3D [36]. These codes consider radiation emission, scattering, and radiation transport within the plasma.
The abundance of nickel (Ni) is relatively high in astrophysical plasmas [37], and its content in the sun is second only to iron. By studying the opacity of highly charged nickel ions and utilizing appropriate stellar models, it is possible to estimate the state and age of stars [38]. Additionally, Ni is one of the impurity elements in the wall materials of nuclear fusion devices [39]. The study of spectral characteristics is highly beneficial for diagnosing the state of wall plasmas and investigating the quenching effects during the ignition process. Currently, EUV spectra of highly charged Ni ions are primarily obtained from spark discharge plasmas [40–45] and electron beam ion traps [46–48]. Computational analyses based on the assumptions of plasma homogeneity and optical thinness reveal that the spectral lines mainly arise from 3d-4p and 3d-4f transitions.
Therefore, this study focuses on LPP Ni and investigates the spatio-temporal evolution of EUV radiation from Ni plasmas using spatio-temporally resolved spectroscopy. The dominant transition arrays contributing to the experimental spectra are analyzed by employing a multi-configuration atomic calculation code. Additionally, the radiation hydrodynamics code RHDLPP and 3D post-processing spectral simulation code SpeIma3D are used to reconstruct the LPP spectra and diagnose the plasma state parameters. The aim is to accurately determine atomic parameters such as energy levels, wavelengths, and transition probabilities for highly charged nickel ions, assess the contributions of multiply-excited states to radiation characteristics, and investigate the spatio-temporal evolution of plasma state parameters. Furthermore, the influence of plasma opacity on the spectral profiles of nickel plasmas is analyzed. The objective is to gain a profound understanding of the intrinsic connection between the microscopic evolution mechanisms of non-uniform and transient LPPs and their macroscopic radiation characteristics. This study is expected to provide valuable data and methodological support for the application of pulsed short-wavelength light sources.
2. Experiment
2.1 Experimental setup
The experimental setup for this work is the same as a previously used spatio-temporally resolved laser-produced plasma spectroscopy system [49] and will be described only briefly here. As shown in Fig. 1, a tightly focused 1064-nm Nd: YAG laser with a 10-ns pulse width and 340 mJ energy was used to produce plasmas from a planar metallic Ni target. The EUV radiation was coupled into a entrance slit of a 1.0-m-focal-length grazing-incidence spectrometer, equipped with a 600-groove/mm grating, with resolution of 0.03 nm. Spectra were acquired with a 40-mm-diameter micro-channel plate (MCP) detector coupled via a fiber optic bundle to a 1024 × 255-pixel charge-coupled device detector. The MCP was gated on with a -2200-V pulse for temporal resolution. The time of laser pulse on the target surface was defined as time zero for plasma production, as monitored by an oscilloscope. The target holder was positioned on a 10-µm-resolution three-dimensional translation stage to provide a fresh surface for each laser shot to avoid forming deep craters. A lens positioned on a linear translation stage having the same resolution could be moved along the laser beam direction for convenient adjustment of laser focusing. When both the lens and target holder were moved simultaneously, emission spectra could be measured at various distances from the target surface. The slit had a width of 10 µm and a height of 10 mm, and it was located 185 mm from the plasma’s symmetry axis. Furthermore, a second slit with a width of 50 µm is placed 5 cm behind the first slit. These two slits collectively determine the resolution of spatially resolved spectroscopy. As shown in Fig. 1, the spectrograph collects radiation from a wedge-shaped region, with the thickness of the wedge approximately 232 µm at the plasma symmetry axis. Reference spectra of highly charged C, Al, and Si ions were used to calibrate the spectrometer wavelength.
2.2 Experimental result
Figure 2 shows the spatially resolved EUV emission spectra from a Ni LPP at a distance of 140 µm to 320 µm from the target. Each spectrum is the result of time integration of 60 ns, which is the minimum operating time of the MCP, and the EUV emission time of the plasma is less than this time. The three strong peaks at about 9.2 nm, 10.3 nm, and 11.7 nm and one weak broad peak at 8.4 nm are dominant in the whole spectral profile. As the distance from the target increases, there is a noticeable decrease in spectral intensity. The intensity in the shorter-wavelength region decreases at a faster rate compared with that of longer wavelength. This is due to the rapid decrease in plasma temperature and density, as well as evolutions in the dominant ion species within the plasma. Additionally, minor shifts are observed in certain peaks such as the peak at 11.67 nm in Fig. 2. This shift can be attributed to the decrease in optical depth at farther distances, which will be further discussed later using Fig. 10.
Fig. 2. The spatially resolved EUV emission spectra from a Ni LPP at a distance of 140 µm to 320 µm from the target.
3. Spectral line identification
In order to identify the structures of the observed spectrum, ab initio atomic structure calculations of Ni6+-Ni9+ were performed using the Cowan suites of Hartree–Fock configuration interaction codes [20]. In the current work, CI effects are taken into account to ensure that the positions and oscillator strengths of levels are calculated to the highest possible accuracy. The list of configurations that included the main ground state and single- and double-excited states is presented in Table 1. In addition, the Slater–Condon integrals (Fk, Gk, and Rk) are reduced to about 80%, whereas the spin parameter (ξ) is fixed at 99%. These scaling factors resulted in the best agreement with the measured spectra.
Table 1. The main ground state, and single- and double-excited states included in the calculations
As is well known, the CI effects can alter the intensities and wavelengths of the lines. The study showed that the important interactions affecting the 3dn-14f configuration are with the 3p53dn + 1 configuration. For an example, Fig. 3(a) and (b) show the CI effects for the 3d-4f transition of Ni6+ ions, both without and with consideration of the 3p53d5 configuration, respectively. For clarity, the gf values are represented by vertical lines, and the distribution profiles are generated by convolving each line with a Gaussian profile with a full width at half maximum (FWHM) of 0.27 eV. This is done to display the complete contribution of the transition arrays. The number of lines in the 3d-4f transition increases from 2222 to 2386 with the 3p53d5 configuration. In addition, the CI effects slightly shift the positions of lines towards shorter wavelengths and significantly enhance the intensity of the lines, particularly at 13.63 nm and 14.14 nm. New spectral features appear at shorter wavelengths similar to those in the experimental spectrum.
Fig. 3. (a) and (b) show the configuration interaction effects on the 3d-4f transition array for Ni6+, both without and with consideration of the 3p53d5 configuration.
The challenge in identifying spectral lines stems from the intricate energy level structure of highly charged Ni ions. The ground configuration 3d of the Ni9+ ion is the simplest with only two levels, while the ground configuration 3d4 of the Ni6+ ion is the most complex with 34 levels. Because of the excitation configuration involving multiple open subshells such as 3p, 3d, and 4f subshells, there is a large number of nearly degenerate energy levels. The distribution range of these energy levels is wide, resulting in overlapping of energy levels from different configurations. However, the overlap between configurations weakens or disappears as the ionization degree increases.
To clarify the transition range in more detail, Fig. 4 show the average wavelength and distribution estimation for the considered transitions as a function of the ionization. The dots and error bars represent the average wavelength and width of the transition arrays, respectively, which were calculated using the UTA method [19]. The green shaded areas represent the wavelength range of the experimental spectrum, which is 8-14 nm. From the graph, it can be seen that most of the transitions fall within the experimental spectral region, except for the 3d-4p and 3p-3d transitions. The trend of the transitions’ average wavelength shift is generally the same, moving towards shorter wavelengths as the ionization degree increases. However, the giant resonance transitions for 3p-3d almost overlap in the same region, making highly charged Ni ions a promising source of EUV, as depicted in Fig. 4(c). Additionally, the width of the UTA decreases with increasing ionization degree, primarily owing to the reduction in the number of 3d shell electrons of Ni ions.
Fig. 4. Variations in the mean wavelengths (nm) of (a) 3d–mp, (b) 3d–mf, (c) 3p–ml, and (d) 3p53dn + 1–3p53dnmf in Ni6+ to Ni9+ ions. The error bars represent the widths of the transition arrays, and the green shaded areas represent the experimental wavelength range, which is 8-14 nm.
In the early stage, Raassen et al. [37,39–48] studied the spark discharge spectra of highly charged Ni ions and found that the EUV spectral range is mainly due to the 3d-4p and 3d-4f transitions. Figure 4(a) clearly indicates that 3d-4p is not within the experimental spectral range. Additionally, it was discovered that the 3d-mp (m = 4-6) transitions of Ni6+ to Ni9+ are weaker compared with the 3d-mf (m = 4-6) transitions. Our computational results also confirm this pattern. These transitions to mf final states become relatively stronger with increasing core charge as the mf wavefunctions contract to overlap more with the 3d wavefunction owing to the competition between the attractive Coulomb and repulsive centrifugal terms in the excited electron potential [50].
In order to evaluate the accuracy of the current calculations, the results obtained from the NIST-ASD database [12] were compared with those of the current work. The wavelengths, oscillator strengths, and corresponding transition probabilities of the 3d–4f transitions for Ni8+ and Ni9 + are summarized in Table 2. The difference in the wavelengths is approximately |Δλ|≤0.02 nm, which is less than the resolution of 0.03 nm in the experimental spectrum.
Table 2. The 3d–4f transition wavelengths for Ni8+ and Ni9+ from the NIST-ASD database (λnist) and the current work (λour).a
Figure 5 shows a comparison between the spectral line distribution and the experimental spectrum. The orange curves are the spectral Gaussian profiles of 3d–mf (m = 4-6) transition arrays of Ni6+–Ni9+ ions, and the black curve represents the experimental spectrum at a distance of 220 µm from the target. As depicted in the figure, the majority of the prominent spectral features observed in the experimental spectra primarily stem from the 3d-4f transition array. However, for a quasi-continuous structure in the experimental spectra, considering only the 3d-4f transitions is insufficient to fully explain the observed spectral features.
F. Torretti et al. found that the contribution of multi-excited configurations to the spectrum is greater than that of single excited configurations when studying the radiation characteristics of LPP tin (Sn) at 13.5 nm [23]. Similarly, we provided a comprehensive explanation of the experimental spectra by considering the doubly-excited 3p53dn4f states.
The energy level diagram of Ni6+–Ni9+ is presented in Fig. 6(a), which only includes the levels of 3d-4f transitions for clarity. From the figure, it can be observed that the transition energies of 3dn-3dn-14f and 3p53dn + 1-3p53dn4f are adjacent. Furthermore, the statistical weights of the double-excited 3p53dn4f states are much greater than those of the single-excited 3dn-14f states, which is confirmed in Fig. 6(b). The spectral distributions and oscillator strengths of the two transitions of the Ni8+ ion are shown in Fig. 6(b), where the double-excited state transition contains 14990 spectral lines, while the single-excited state has only 79 lines. To further evaluate the importance of the double-excited state, we assume that the excitation state of Ni8+ satisfies the normalized Boltzmann distribution and compare the Gaussian profiles of the two transitions at temperatures of 20 eV, 30 eV, and 40 eV, as shown in Fig. 6(c). It can be seen that as the temperature increases, the intensities of the two transitions also gradually increase. When the temperature exceeds 30 eV, the overall intensity that is dominant from the multiply excited states.
Fig. 6. (a) Schematic energy level diagram of the ions Ni6+–Ni9+, showing only 3d-4f transitions for clarity. (b) The spectral distributions and oscillator strengths of 3d2-3d4f and 3p53d3-3p53d24f transitions of Ni8+ ions. (c) Comparison of Gaussian profiles of 3d2-3d4f and 3p53d3-3p53d24f transitions of Ni8+ ions at various temperatures.
4. Simulation
We carried out simulations in order to benchmark our present calculations and to investigate the EUV radiation characteristics and hydrodynamic evolution of LPP Ni. The RHD code RHDLPP was used to calculate the temperature, density, charge state distribution, and electron density of the LPPs. The post-processing spectral simulation code SpeIma3D was then employed to simulate the spectra.
4.1 Code description
RHDLPP is a specialized RHD code uniquely tailored for LPPs. This single-fluid, two-temperature RHD code operates under the assumption that the temperatures of electrons and ions (${T_e}$ and ${T_i}$, respectively) are equivalent to each other but distinct from the radiation temperature (${T_r}$). The RHD equations are solved within an Eulerian framework, allowing for 1D or 2D Cartesian, spherical, or cylindrical coordinates. RHDLPP integrates a suite of modules covering hydrodynamics, heat conduction, radiation transport, laser energy deposition, equation of state (EOS), and charge state distribution. The code utilizes the Flux-Limited Diffusion (FLD) approximation [51] to model radiation transport, thereby approximating the free-streaming limit.
Laser propagation and energy deposition in RHDLPP are simulated through a hybrid methodology [52] that merges geometrical-optics ray-tracing in sub-critical plasma regions with a 1D solution of the Helmholtz wave equation in super-critical regions. Thermodynamic properties within the code are ascertained using an EOS based either on the real-gas approximation [53] or a quotidian equation of state (QEOS) [54]. The charge state distribution and average ionization degree are calculated employing a steady-state collisional-radiation (CR) model [55]. This model includes various atomic processes derived from the screened-hydrogenic approximation [56].
Because of the non-uniform and optically thick nature of LPPs, we have developed a post-processing code for spectral simulation called SpeIma3D. This code eliminates the need for assumptions regarding plasma uniformity and the dominance of either emissivity or opacity in spectral formation. Consequently, it is now capable of simulating transient evolution images [57,58], temporally and spatially resolved spectra, and integral spectra across varying wavelength ranges that are directly comparable to experimental results.
Here, we will solely focus on explaining the implementation of spectral simulations, for which the schematic is shown in Fig. 7. This method simulates the spectra in three stages. First, the distributions of plasma state parameters such as temperature, density, and ion abundance are calculated using the RHDLPP code. Then, the 2D state parameter distributions are transformed into 3D distributions along the symmetry axis using the axisymmetric properties of the plasma. The 3D plasma is encased by a bounding cylindrical surface, with the unperturbed background gas filling the space between them.
The second stage involves constructing ray paths based on a spatio-resolved spectral measurement system composed of a slit and a 3D plasma illumination source, i.e., ray tracing is executed. As shown in Fig. 7, the slit is divided into equal-area cells, each denoted by the symbol $\textrm{d}\sigma $. Following this, a rectangular region $\varepsilon $ that is symmetric and parallel to the slit is defined within the plasma. The size of $\varepsilon $ depends on the angular aperture of the slit and the distance between the slit and the plasma’s symmetry axis. Similarly, the region $\varepsilon $ is divided into smaller cells each denoted by $\textrm{d}S$. If the areas of $\textrm{d}S$ and $\textrm{d}\sigma $ are sufficiently small, ray paths can be constructed by connecting their geometric centers with a straight line. As illustrated in Fig. 7, each path terminates at the center of $\textrm{d}\sigma $ on the slit surface, while the starting point moves from the center of $\textrm{d}S$ along the ray to the bounding cylindrical surface, ensuring that the ray traverses the plasma.
In the third step, the specific intensity ${I_\nu }$ of the radiation with frequency $\nu $ at the endpoint of the ray at any given moment is calculated. This is achieved by resolving the 1D integral form of the steady-state radiative-transfer (RT) equation along each path [35]:
The radiant energy $E({\textrm{d}S \to \textrm{d}\sigma } )$ at frequency $\nu $ collected by the cell $d\sigma $ from $ds$ at any given moment is computed using the equation $E({\textrm{d}S \to \textrm{d}\sigma } )= {I_\nu } \cdot \mathrm{\Delta }S \cdot \mathrm{\Delta }\Omega \cdot cos\theta $. Here, $\mathrm{\Delta }S$ represents the area of $\textrm{d}\sigma $, $\mathrm{\Delta }\Omega $ denotes the solid angle subtended by $dS$ at the center of $d\sigma $, and $\theta $ is the angle between a ray and the normal of $d\sigma $. This equation is validity if the areas of $\textrm{d}S$ and $\textrm{d}\sigma $ are sufficiently small to ensure that the ray between their centers fully represents the rays between all points in the two cells. In the simulation, the adequacy of the areas is assessed through the convergence of the results. Finally, the total radiant energy $E({\varepsilon \to \mathrm{{\cal L}}} )$ collected by slit $\mathrm{{\cal L}}$ from region $\varepsilon $ within the time interval $\mathrm{\Delta }t$ at frequency $\nu $ can be calculated using the integral equation:
4.2 Simulation results
We simulated the 2D parameter distributions of LPP Ni using the RHDLPP code. The target had a thickness of 100 µm and a density of 8.9 g/cm3. The background gas used was hydrogen, with a density of 10−9 g/cm3. The initial temperature of both the target and the background gas was 300 K. A Gaussian laser pulse was chosen as the incident laser pulse with an energy of 340 mJ (peak power of 2.27 × 107 W). The pulse had a FWHM of 10 ns, a peak at 15 ns, a wavelength of 1064 nm, and a focal spot radius of 200 µm on the target surface, with a laser peak intensity of 1.81 × 1010 W/cm2.
The computational domain for the 2D cylindrical simulation was defined as $- 700 < r < 700{\;\ \mathrm{\mu} \mathrm{m}}$ and $0 < z < 900{\;\ \mathrm{\mu} \mathrm{m}}$. For radiation modeling, the energy range from 1 eV to 100 keV was divided into six logarithmically distributed groups. The group Planck mean coefficient ${\kappa _{P,g}}$ and the Rosseland mean coefficient ${\kappa _{R,g}}$ were derived from the TOPS database [13] assuming local thermodynamic equilibrium. Given the plasma’s symmetry, the boundary condition at $r\textrm{} = \textrm{}0$ was set as an axisymmetric condition. For all other boundaries, we applied an extrapolation with zero gradient for the plasma and a zero incoming flux boundary condition for the radiation. The heat conduction flux limiter was set to 0.1.
Figure 8 illustrates the 2D temperature (left column), mass density (middle column), and electron density (right column) distributions of LPP Ni at delay times of 10 ns, 15 ns, and 20 ns. These delay times commence from the moment the laser pulse first contacts the target surface. The laser’s direction of propagation is from the top to the bottom in the figure. The data reveal that as the laser heats the plasma, the maximum temperature of the plasma gradually increases and reaches a peak value of 26.5 eV at a delay time slightly greater than 15 ns, corresponding to the peak laser power at a delay time of 15 ns. Moreover, as the delay time increases, the high-temperature region of the plasma gradually moves away from the target surface, suggesting a corresponding shift of the EUV emission region away from the target as well. In the later stage of the Gaussian time distribution of the laser pulse (after 20 ns), the plasma temperature rapidly decreases owing to factors such as reduced laser energy, rapid plasma expansion, conversion of internal energy into kinetic energy, and loss of thermal radiation energy. Because of the low ambient pressure and the conversion of laser energy into plasma kinetic energy upon deposition, there are notable spatial gradients in plasma mass density and electron density, particularly in close proximity to the target surface. These significant gradients result in substantial absorption effects during the transportation of radiation. Additionally, these gradients decrease as the delay time increases.
Fig. 8. The 2D temperature (left column), mass density (middle column), and electron density (right column) distributions of Ni plasma generated by a 340-mJ laser pulse at delay times of 10 ns, 15 ns, and 20 ns. The laser propagates from top to bottom in the figure.
Next, we conducted spectral simulations of LPP Ni using the currently calculated plasma state parameters and SpeIma3D code. The simulation parameters were meticulously aligned with these experimental conditions. The experimental apparatus incorporated a detector with a 60-ns gate width, enabling the capture of 60-ns time-integrated spectra. For more comprehensive experimental details, refer to our earlier publications [59]. Additionally, the emissivity and absorption coefficient (${j_\nu }$ and ${\kappa _\nu }$) were computed by summing the contributions of all bound-bound, bound-free, and free-free transitions using the presented atomic data and the detailed level accounting (DLA) model [60,61]. The scattering coefficient was determined using the classical Thomson scattering formula [60]. The process of calculating the population of an energy level is twofold: initially, it involves determining the abundance of ions using the CR model [55] with radiation field based on calculation by RHDLPP, followed by computing the energy level population for each ion through the application of the Boltzmann distribution formula [62].
Figure 9 compares experimental and simulated Ni plasma spectra in the 8-14 nm range at various distances from the target. The experimental data are represented by a dotted line, while the simulated results are depicted using a solid line. From the graph, it is evident that the simulated spectrum and experimental data show good consistency. Specifically, the distinct spectral lines in the experimental spectrum were accurately replicated in the simulation. Furthermore, at given distances, the intensity ratios of spectral lines are consistent between the experimental and simulated spectra. Lastly, the spatial variation patterns of spectral intensity are consistent. Note that the resolution of the simulated spectra is lower than that of the experimental spectra due to the use of a uniform FWHM value of 0.6 eV during the convolution process. At a distance of 230 µm from the target surface, the best overlap between the experimental and simulated spectra was obtained at the peaks at 10.18 nm and 10.39 nm.
Fig. 9. The experimental (dotted line) and simulated (solid line) Ni plasma spectra at various distances from the target and within the 8-14 nm wavelength range.
5. Discussion
The self-absorption effect significantly influences the EUV emission of LPPs, and relevant research has been conducted on LPPs Sn. Fujioka et al. conducted precise experiments to thoroughly investigate the influence of opacity on the emission characteristics of LPPs Sn in the EUV region [63]. Additionally, Pan et al. employed the Thomson scattering method for accurate diagnosis of plasma temperature-density parameters and further studied the specific effects of self-absorption on EUV spectral intensity [64]. Here, we also investigate the influence of self-absorption on the radiative properties of the LPP Ni. Figure 10 compares the simulated spectra with and without consideration of self-absorption at various distances from the target. The dashed lines represent spectra without self-absorption, while the solid lines represent spectra that account for self-absorption effects. The data indicate that self-absorption causes the most significant decrease in spectral intensity at 140 µm. As the distance increases, the impact of self-absorption decreases, and at 740 µm, the spectra from both cases almost overlap. Moreover, as the wavelength moves towards longer waves, self-absorption leads to a greater decrease in spectral intensity. This is because the EUV radiation needs to pass through an absorption layer characterized by low-temperature and low-charged ions (such as Ni6+ and Ni7+) in order to be collected by the spectrometer. On the other hand, the radiation in the longer wavelength region primarily originates from low-charged ions. Finally, a shift in the peak at 11.67 nm is observed, especially noticeable at 140 µm, with the shift magnitude decreasing as the distance increases. Similar behavior is observed in the experimental spectrum depicted in Fig. 2. This can be explained by the rapid decrease in electron density, and thus, self-absorption, with an increase in distance. Certainly, these pronounced self-absorption effects primarily depend on the large spatial gradients of the state parameters of the LPP Ni. As depicted in Fig. 8, the spatial gradients of the state parameters decrease as the distance increases, leading to a corresponding reduction in the self-absorption effect.
Fig. 10. Comparison of the simulated spectra with and without consideration of self-absorption at various distances from the target. The dashed lines represent spectra without self-absorption, while the solid lines represent spectra that account for self-absorption effects.
6. Summary
In this study, we comprehensively investigated the radiation characteristics and hydrodynamics of LPP Ni using spatio-temporally resolved LPP spectroscopy and a radiation hydrodynamics code package. Specifically, we conducted the identification and reconstruction of experimental spectra, plasma state diagnostics, and investigation of the impact of self-absorption effects on the EUV radiation features. The results indicate that the experimental spectra primarily originate from 3d-4f transitions of Ni6+-Ni9+ ions, with a significant contribution from doubly-excited states. Furthermore, self-absorption effects have a notable impact on the EUV radiation characteristics, which diminish as the plasma parameter gradients decrease. However, a more in-depth understanding of this impact requires further experimental and theoretical investigations. This study is significant in advancing our understanding of the radiation transition properties and transport characteristics of complex media, particularly in the context of high-temperature and high-density plasmas.
Funding
National Key Research and Development Program of China (2022YFA1602500); National Natural Science Foundation of China (11874051, 11904293, 12064040, 12204282, 12374384, 62335016); Major Science and Technology Project of Gansu Province (22ZD6FA021-5); Central Leading Local Science and Technology Development Fund Projects (23ZYQA293); Science and Technology Department of Gansu Province (22JR5RA137, 22JR5RA151, 23YFFA0074); Industrial Support Project of Gansu Province (2021CYZC-22, 2023CYZC-19).
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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