1. Introduction

Laser-generated multi-keV X-ray sources are robust diagnostic tools for high-energy-density physics [1], real-time diffraction measurements in dynamic compression experiments [2], and laboratory astrophysics [3]. Recently, multi-keV X-rays generated from laser-produced photoionized or radiation-dominated plasmas associated with accretion-powered astrophysical objects [4] have received significant attention. However, these experiments typically require higher efficiencies when converting drive beams into multi-keV X-rays to ensure that the backlight source is significantly brighter than the self-emission of the object as a probe light beam. In the conventional method for generating multi-keV X-ray sources, nanosecond laser pulses are used to heat solid targets. However, this method exhibits low efficiency [5] because the emission region of hot and underdense coronal plasma is relatively small. Compared to solid targets, X-ray sources from laser-driven clusters have the advantage of high coupling efficiency between laser energy and plasma [6]. Several studies have utilized underdense gaseous targets that emit multi-keV X-rays with high efficiency, but only within a relatively restricted spectral range, to generate multi-keV photons efficiently [7]. Additionally, doped low-density aerogel targets have demonstrated an order of magnitude improvement in laser-to-X-ray conversion efficiency (ξ_x) over laser-irradiated disks, where ξ_x is the ratio of the measured multi-keV X-ray energy (energy multiplied by 4π for multi-keV radiation) produced by the heating pulse to the heating pulse incident laser energy. A laser prepulse improves the conversion efficiency of laser energy to X-rays [8]. However, this technique is limited to a small number of materials based on the necessity of complex fabrication techniques [9]. A further increase in conversion efficiency can be achieved by selecting an optimal tile angle for the laser target and optimizing its spatial shape [10]. Pre-exploded metallic thin foils can be used to generate metallic plasmas to provide a bright X-ray source, which achieves strong multi-keV emission with values of ξ_x that are several times greater than those obtained using traditional solid targets [11]. In 2013 and 2018, we conducted experiments to investigate the development of an X-ray source using laser-irradiated metallic materials [12,13] at the Shenguang II (SGII) laser facility.

Generally, multi-keV studies have been limited to low- and mid-Z materials because researchers have primarily concentrated on ξ_x values for Ti He-like lines as functions of the ratio of the intensities of the pre-pulse and main pulse, pre-pulse/heating pulse time delay, wavelength, and intensity. However, in high-Z plasmas, L- and M-shell ionized plasmas are typically not fully resolved and tend to produce broad spectral features with the majority of spectral energy being produced within a narrow band. The resulting spectra contain a myriad of transition arrays and individual lines, and these features are particularly important for the production of multi-keV X-ray sources. Therefore, the control and optimization of multi-keV X-ray sources produced using high-Z materials is a subject of significant interest. Constantin et al. [14]. obtained a maximum multi-keV X-ray conversion efficiency of 36% for L-shell Krypton (12% critical density) and 14% for L-shell Xenon (9% critical density). Several studies on Sn L-shell emissions have also been conducted. Back et al. [15]. improved the ξ_x value of laser energy conversion into L-shell radiation using underdense laser-produced plasma. Plasma sources were generated through the laser irradiation of a confined high-Z gas. However, to the best of our knowledge, there has been no systematic experimental study of L-shell X-ray emission from multiple pre-exploded thin foils using a single-pulse laser beam.

In this study, we focused on optimizing X-ray emission in the 3 to 5 keV range, for which we selected the photon-energy-matched Sn L-shell. Unfortunately, the atomic kinetics calculations for L-shell emissions involve many more energy levels than those for the K-shell, making simulations more computationally demanding [16]. Additionally, ξ_x measurements for the X-rays of Sn L-shell emissions are not well documented in the literature. Therefore, this study primarily aimed to catalog the values of ξ_x for three-layer thin Sn targets under various laser conditions. Previous studies [17] have reported and experimentally demonstrated an optimal foil thickness for multi-keV emission. In this paper, we report our findings regarding the ξ_x values of Sn L-shell band emissions in the 3.7 to 4.3 keV range, as well as detailed spectra and multi-keV emission zones based on the irradiation of thin Sn foils using a single-pulse laser beam. Experimental data were obtained from two types of diagnostic instruments, namely a broadband time-integrated elliptically bent crystal spectrometer (EBCS) and X-ray pinhole camera (XPHC). The representative spectral lines that we observed primarily stemmed from the M→L shell spectra.

2. Experimental setup

The experimental configuration and subsequent tests at the SGII laser facility were designed according to optimized parameters determined using the results of XRL-2D code [12] simulations. In this study, we targeted the enhancement of Sn L-shell-band emissions between 3.7 and 4.3 keV by exploiting a thin foil target using a laser. A three-layer planar target was used in this study. The middle layer consisted of a thin Sn film that varied in thickness from 400 to 800 nm. The first layer (i.e., plastic layer on the side of laser incidence) consisted of a 20-µm-thick CH film. We placed the Sn thin foil behind the CH thin film to ensure that the unabsorbed laser beam energy would generate another high-flux X-ray pulse on the Sn thin foil. The target was irradiated by up to four overlapping beams of laser pulses (at wavelengths of 0.35 µm) using a one-sided irradiation scheme with spot diameters of 150 µm. Figure 1 illustrates the position of each beam. The beams are tilted 60° relative to the target normal and oriented with a 42° azimuthal separation between each beam. This figure also shows the relative lines of sight of the diagnostic instruments that monitor the spectral content of the L-shell radiation and size of the focal spot. The beams are timed in such a manner that they are coincident on the face of the target. The temporal pulse is a 1 to 2ns square pulse, the average energy per beam is approximately 250 J, and the beams are focused to deliver energy to the target. The laser intensities are set to approximately 10¹⁵ W/cm² for the direct drive target by accounting for the angles of incidence of the beams on the target and assuming uniform irradiation over a focal spot. This value was crudely evaluated based on the beam aperture (f/3). The real laser intensity profile was not measured under the actual experimental conditions. Measurements of the intensity of the multi-keV line spectra and X-ray emission source sizes were performed simultaneously using an EBCS and XPHC, respectively, in a single shot. An elliptically bent α-quartz crystal (1011, 2d = 6.687 Ǻ) was coupled to a Fujifilm BAS MS imaging plate (IP). The two EBCSs were in good agreement in terms of their common spectral ranges. X-rays from the laser-produced plasma were filtered by a titanium foil to remove the bremsstrahlung components. The elliptical crystal had a focal length of 860 mm. The X-ray source was placed at the focal point of the ellipse. X-rays that were reflected by the crystal at angles specified by Bragg’s Law (22°≤θ≤ 60°) were focused through the other focal point. Within the first Bragg diffraction order, this setup covered a wide range of photon energies from 2.14 to 4.95 keV. The spectrometer was oriented at 30° with respect to the target normal. The known geometry of the spectrometer, crystal reflectivity (measured elsewhere [18]), attenuation by the differential filters in front of the dispersive crystals, and known response of the IP [19] were used to compute the energy within a given spectral band. The exposed IPs were read using Fuji IP scanners with the following user settings: sensitivity S4000, latitude L5, and scan resolution R25 µm. Because the IP responses, spectral transmission of the filters, and crystal reflectivity are known, the spectra can be calibrated to determine the absolute X-ray yield. An XPHC fitted with a 10-µm-diameter pinhole was utilized to measure the emission zone of the plasma through 10 µm Ti foil and 10 µm Saran (CH2-CHCl)_n foil filters. This ensured that the energy was restricted to approximately 3 to 5 keV with a magnification of 10.0 ± 0.2. The X-ray emission region was detected using a time-integrated XPHC set to 0° with respect to the target normal. The spatial resolution was estimated according to standard PHC theory. The spatial resolution was found to be greater than 12 µm. The intensity profile function obtained by converting the scanned image from the IP into an X-ray intensity image was fitted using a Gaussian distribution function that was calculated as the pixel size divided by the instrument magnification. Thereafter, the observed size of the X-ray emission source from the plasma was calculated based on the full width at half maximum (FWHM) of this function.

 

Fig. 1. Schematic of the experimental setup. The geometries of the EBCS and XPHC are drawn from the top view and show the 30°, −30°, and 0° orientations of the detectors with respect to the target axis. Additionally, the driven laser beams are drawn from the side view and show the orientations of 60° and −60°cones with respect to the target axis.

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3. Experimental results

Figure 2 presents the case using the 400-nm-thick Sn foil with a laser intensity of 4 × 10¹⁵ w/cm². Figure 2(a) presents the raw spectrum for the typical X-ray power emitted by the 400 nm Sn foil target, which was captured using an elliptically bent α-quartz crystal (1011, 2d = 6.687 Ǻ) spectrometer and corresponds to the lineout of the spectral data. This figure represents the spectral intensity profiles obtained by averaging over a band of pixels along the spatial direction, which is perpendicular to the direction of spectral dispersion. Because the EBCS covers a broad energy range, the entire bandwidth of the diagnostic setup can be calibrated at once. An analysis of the relationship between the Bragg angle θ for reflection at the elliptically bent crystal and the spectrum angle β, which was presented by Henke et al. [20]., further elucidates the presented results. When ignoring the small crystal refraction effects, the photon energy E is given by the Bragg equation in terms of the relationship between the Bragg angle θ and spectrum angle β as follows:

 

Fig. 2. X-ray emission profiles. (a) Time-integrated X-ray spectra obtained from a thin planar Sn target irradiated by a 0.35 µm laser. (b) Pinhole image trace showing simultaneously obtained X-ray emission zones.

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For additional constraints, the spectral data were configured to focus on the narrow energy band of the Sn L-shell excited electron transitions from 3.7 to 4.3 keV, demonstrating that the emission predominantly stems from the L-shell band. The spectral dispersion was calibrated using K-shell Ti X-ray lines as references. We observed strong Sn Ne-like M→L lines in the energy range of 3.7−4.3 keV. Emissions from various transitions in a more complicated Sn L-shell cannot be fully resolved and tend to produce broad spectral features with the majority of the spectral energy concentrated within the narrow 3.7 to 4.3 keV energy range. In the Sn spectra, the total energy coverage of the L-shell emission spectrum was found to be over 600 eV. The spectral features presented in Fig. 2(a) are mainly associated with groups of unresolved transition arrays such as 3d-2s, 3d-2p, and 3p-2s. Figure 2(b) presented a scanned gray scale X-ray image from an XPHC, which provides the spatial profile of the X-ray emission zone recorded by the IP. The vertical and horizontal spot dimensions are approximately 120 and 150 µm, respectively, at FWHM and 270 µm at full width with 10% of the maximum intensity averaged over the vertical and horizontal directions. The widths, which are defined as 10% of the peak intensity, are163 µm (vertical) and 214 µm (horizontal).

4. Sn L-shell-band 3.7 to 4.3 keV X-ray conversion efficiency

The ξ_x value for converting laser energy into Sn L-shell-band X-ray emissions was measured using data from the time-integrated spectra obtained by the EBCSs. The laser-to-X-ray energy conversion efficiency ξ_x is defined as the ratio of the energy emitted by the source within a particular spectral bandwidth to the total delivered laser energy. We converted the X-ray image stored on an IP after its exposure into X-ray photons. The estimated ξ_x was determined using the following functional formula:

Here, E_L-band is the total energy emission in the L-shell band, E_{3.7-4.3 keV} (measured) is the measured energy in the L-shell-band (3.7 to 4.3 keV) X-rays, η_IP is the quantum efficiency of the IP, R_int is the integrated reflectivity of the crystal, T_filter is the transmission factor through the filter materials, and Ω_IP is the solid angle of the IP.

The raw spectroscopic data from the exposed IPs were converted into gray scale levels in digital images using Fuji IP scanners and then corrected for the geometry, filters, and crystal reflectivity. The background was subtracted from the pixel intensity histogram by fitting it to a polynomial function. The value of η_IP was calibrated in previous experiments to be within a 20% error level [19]. The rocking curve for elliptically bent α-quartz crystals is presented as a function of the actual measured angle relative to the Bragg angle [18]. The R_int of the elliptically bent α-quartz crystal was measured using a laboratory “Manson” X-ray source, which provided corrections for insufficient information regarding the R_int of the bent crystals. Based on a previous study, we used R_int = 0.209 ×E^1.34mr for the R_int of the α-quartz crystal with E in keV. T_filter was calculated using information from the X-ray optics database [21] with the targeted thin filters being laboratory calibrated and checked in situ for self-consistency [22]. The term Ω_IP is determined by the crystal curvature and geometry of the spectrometer. Ω_IP was calculated as a function of the photon energy (Bragg angle) using geometric formulas. There is an overall uncertainty of ±30% in the value of ξ_x measured using the IP. This overall uncertainty primarily stems from the results of measured uncertainties in the crystal reflectivity across the width of the crystal, relative transmissivity of differential filters, measured focal spot sizes, and level of the IP background.

In our experiments, we varied the target thickness and several laser parameters such as the laser energy, laser pulse width, and laser focus, resulting in different laser intensities. The values of ξ_x are presented in Table 1. Table 1 summarizes the results from individual laser shots to highlight the variation in ξ_x for the Sn L-shell X-ray emission band as the target thickness, laser intensity, and/or laser pulse width are changed. This table lists the measured ξ_x values relative to the listed energy of each shot (third column) based on the integration of ξ_x (ninth column) from various L-shell transitions over a 0.6-keV-wide band.

Table 1. Summary of the 3.7 to 4.3 keV L-shell band for Sn for different target thicknesses, pulse widths, laser focal spot sizes, and energies using 0.35 µm frequency-tripled laser beams.

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Figure 3 presents a plot of ξ_x using data from the 3.7 to 4.3 keV energy range, which were obtained using the time-integrated EBCS, as a function of the intensity of the laser irradiance on the three-layer (i.e., front 20µm CH substrate plus 400nm Sn plus back 2mm CH substrate) target for varying laser pulse durations. The data points were calculated as integrals of the IP exposure over a given energy band. One can see that ξ_x appears to increase slightly with the laser intensity until I_L≈ 4.8 × 10¹⁵ W/cm². The peak in the X-ray yield for Sn occurs at an irradiance of approximately 5.76 × 10¹⁵ W/cm² and drops off sharply above this value. Therefore, we can speculate that the cause of this phenomenon is that a sufficient plasma temperature was generated to reduce the number of plasma ions that radiate 3.7 to 4.3 keV X-rays with a higher laser intensity. The uncertainty in the irradiance is primarily attributed to the spot size and is maximized when the overlapping beams are tightly focused. Because tightly focused beams may not have perfect overlapping, the highest irradiance data point is bracketed on the low end by overexposed static pinhole images of the X-ray source. This may result in an overestimated laser spot size and further analysis of gated X-ray images is required. Figure 3 also presents ξ_x as a function of the laser pulse width at different laser intensities. We compared these results to the X-ray yield data obtained using the 0.35 µm frequency-tripled laser beams when the laser pulse width was varied with a fixed laser intensity and when the laser intensity was varied with a fixed laser pulse width. The measurements were integrated over the 3.7 to 4.3 keV energy range to obtain the total energy emitted from the L-shell radiation of the Sn plasma while assuming isotropic emission. As shown in Fig. 3, ξ_x is highly dependent on the laser pulse width, as well as the laser intensity. The multi-keV X-ray flux generated by the long laser pulse duration at a given laser intensity is 1.5 ± 0.52 times greater than that generated by the short laser pulse duration. The laser intensity ranges from 1.8 × 10¹⁵ to 6.5 × 10¹⁵ W/cm² and includes laser pulse widths of 1 or 2 ns. We found that ξ_x increases with an increasing laser pulse width at a fixed laser intensity. Additionally, at a fixed laser pulse width, over the laser intensity range from 1.8 × 10¹⁵ to 5.76 × 10¹⁵ W/cm², ξ_x initially increases and then decreases with increasing laser intensity. However, at the optimal ξ_x, no significant variation in laser intensity can be observed as the laser pulse width varies from 1 to 2 ns.

 

Fig. 3. Conversion efficiency versus laser intensity representing the Sn L-shell band for different laser pulse widths. The energy limits for integration were 3.7 to 4.3 keV.

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We also measured the Sn L-shell band (3.7 to 4.3 keV) production efficiency as a function of the thickness of the thin foil target. Figure 4 presents the X-ray emissivity from 3.7 to 4.3 keV for 800, 600, and 400 nm Sn thin foil targets. The maximum emissivity of the 400 nm foil target is greater than that of the 800 or 600 nm foil targets. As shown in Fig. 4, the sensitivity of ξ_x depends on the thickness of the target. Furthermore, ξ_x increases as the foil thickness decreases from 800 nm to 600 nm and then to 400 nm. The preheating effect of the soft X-ray ablation wave before the arrival of the heat wave and the frequent collisions between the plasmoids generated by adjacent thin foils make the plasma conditions and energy partition of a multi-layer thin foil target very close to those of a low-density foam target. Consequently, the enhancement of ξ_x can be attributed to the greater amount of hot underdense plasma produced by the 400 nm foil. As shown in Table 1, when the 400 nm foil is irradiated, the X-ray emission region is significantly larger than those produced using the 800 or 600 nm foils. The thicknesses of the targets were selected based on the “optimal” thickness values described in a previous study [17].

5. Conversion efficiency analysis and discussion

The observed L-shell X-ray radiation was primarily in the 3.7 to 4.3 keV energy range and was used to identify (2s₀-3d₁, 2p_1/2-3d_3/2, 2s₀-3p₁) transition lines to fix the energy scale in Fig. 3(a). Because multi-keV X-rays are optically thin in the underdense emission region, the X-ray flux is proportional to the emission volume. The estimated values of ξ_x for three different thicknesses (400 nm, 600 nm, and 800 nm) of the Sn foil target are presented in Fig. 4. The scaling of the X-ray conversion efficiency in Sn under laser irradiation demonstrates the effects of the target thickness in our experiments. For all target thicknesses, the plasma electrons within the laser focal spot are ejected by the ponderomotive force. Therefore, they interact with a lower intensity of expanding plasma, resulting in weak radiation reaction effects. For a solid target, direct laser irradiation initiates surface ablation. This implies that the plasma expands to reduce the plasma temperature and generates X-rays because the material is continuously heated by the laser. Laser energy is distributed in relatively small plasma volumes close to the critical density region and the multi-keV X-ray emission region is spatially limited.

 

Fig. 4. Conversion efficiency versus laser intensity representing the Sn L-shell band for different thicknesses of thin foils. The energy limits for integration were 3.7 to 4.3 keV.

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We evaluated the 3.7 to 4.3 keV X-ray ξ_x value for laser-produced Sn plasma for Sn layers with thicknesses of 400 nm, 600 nm, and 800 nm, pulse durations, and laser intensities. Figure 3 presents the ξ_x values for two different laser pulse widths at various laser intensities. This figure reveals that ξ_x increases with the laser pulse duration. Figure 4 presents the measured values of ξ_x for three different target thicknesses as a function of the laser intensity at a fixed laser pulse width. For three-layer thin foil targets, our experimental data predict that an optimal thickness of the thin foil exists that enhances multi-keV X-ray emission. The changes in ξ_x with varying thicknesses of the target, pulse durations, and laser intensities maybe related to changes in the Sn ion concentration in the plasma. Therefore, it should be noted that to maximize 3.7 to 4.3 keV X-ray ξ_x production, we require a plasma with an appropriate ion concentration, which depends strongly on plasma density and temperature conditions. Montgomery et al. [23]. found that the X-ray flux is proportional to $n_e^2{T_e}$, where ${\textrm{n}_\textrm{e}}$ and ${\textrm{T}_\textrm{e}}$ are the electron density and temperature, respectively. Multi-keV X-rays were generated predominantly through the collisional excitation of electron-bound transitions and spontaneous free-bound radiative recombination. The emissivity of multi-keV X-rays is determined by the collisional excitation rate, which is proportional to the square of the electron density and is influenced by the electron temperature. To understand the results of our experiments, estimation was performed for two (${\textrm{n}_\textrm{e}}$, ${\textrm{T}_\textrm{e}}$) couples contributing to Sn L-shell band emission. We found that when ${\textrm{n}_\textrm{e}}$ is lower than the critical density ${\textrm{n}_{\textrm{cr}}}$, laser absorption occurs predominantly through inverse bremsstrahlung and a large volume of plasma can be heated by a supersonic bleaching wave [14]. A large heated volume with reduced hydrodynamic energy loss is an efficient mechanism for plasma heating at high electron temperatures. Therefore, it is important for multi-keV X-ray production.

Laser interactions with solids generate two-temperature electron energy distribution functions with positively correlated T_cold and T_hot values. If the value of T_hot is too low, then very few electrons are available that can ionize the L-shell to produce multi-keV X-rays. Similarly, if the value of T_cold is too high, a significant amount of energy is lost to the bulk particles below the ionization energy at T_cold. Therefore, the medium expands further and is brought to a higher temperature, which allows more volume to be excited in the Sn L-band. Therefore, the key is to heat medium-temperature particles to a high temperature to achieve a high degree of ionization. For the 3.7 to 4.3 keV energy range, the Sn thin foil functions almost the same as a gas-like target [24], where the electron density is below ${\textrm{n}_{\textrm{cr}}}$ relative to the laser wavelength. Therefore, the production of a large plasma region at a sufficiently low density facilitates efficient heating. Consequently, our experiments revealed that thin foil targets may provide an excellent mechanism for enhancing X-ray emissions. Additionally, a laser-exploded multi-thin-foil target helps overcome the limitations related to focus spots and increases the emission region along the target normal as a result of plasma expansion in both the forward and backward directions.

Our experiments revealed that the enhanced laser-to-X-ray ξ_x value can be attributed to two factors linked to underdense plasma in the target. The first is that the supersonic heat wave that generates a vast plasma region with multi-keV temperatures before the rarefaction wave destroys underdense plasma. The second is an enhanced emission region. Although our X-ray source development experiments were conducted with multi-thin-foil targets similar to low-density gas or foam targets in the same photon range, the laser parameters and thin foil thickness should be tuned carefully. Otherwise, ξ_x can only be enhanced by lower magnitudes using an exploded thin foil target because the peak yield stems from the efficient coupling of the laser energy with the desired ionization state. One limitation is that sufficient time is necessary for atoms to strip down to the required electron configurations. At very low irradiance, lateral and axial thermal diffusion in the target are significantly dominant. Furthermore, the plasma temperature becomes too low to facilitate a sufficient level of collisional excitation of electrons. At very high irradiance, the coupling of the laser energy to the hot electrons and other non-thermal modes may become significant as a result of free-bound radiative recombination emission. Detailed atomic kinetic models can explain that the majority of photons in the multi-keV range are produced by collisional excitations and recombination emissions.

However, whether the efficient conversion of SGII laser energy into Sn L-shell X-ray emissions can be achieved remains unknown. Regardless, the plasma should be in the charge state range of L-shell emission such that the number of electrons remaining in the L-shell orbits increases. Therefore, the plasma should not be over-ionized or under-ionized. Otherwise, the L-shell emission will drop significantly, possibly even enlarging the emission region. The X-ray emission spectra in Fig. 5 contain the characteristic lines of L-shell emission. A significant fraction of the L-band emission originates from the inner-shell transitions of Sn M-shell ions. Therefore, the laser intensity should be moderated and the spot size should be optimized at a fixed laser energy.

 

Fig. 5. Time-integrated emission X-ray spectra for a Sn-layer 400 nm thin foil under laser irradiance.

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As noted in the introduction, several parameters affect X-ray yields, including the properties of both the target and laser. Our experiments represent the beginning of the investigation of the effects of these parameters on the scaling of X-ray yields. The investigation of the scaling of X-ray yields under laser irradiance involves varying two important parameters: the laser intensity and laser pulse width. The size of the laser-heated region significantly affects the energy transport properties of the target. Only a small subset of scaling parameters can be investigated with a limited number of target shots available for diagnostic development. Table 1 lists the integrated 3.7 to 4.3 keV laser-to-X-ray ξ_x values for each of 30 shots. For a given laser wavelength and energy, one can see a relatively strong dependence of ξ_x on the pulse width, target thickness, and laser intensity. Regardless, the conversion efficiency appears to increase linearly with an increasing laser intensity until I_L≈ 4.8 × 10¹⁵ W/cm². The peak in the X-ray yield for Sn occurs at an irradiance of approximately 5.76 × 10¹⁵ W/cm² and decreases sharply above this value.

Figure 3 presented the results for the different laser pulse widths considered in this study and summarized the multi-keV conversion rates for the laser-exploded metallic thin foils discussed in this paper. ξ_x increases with the laser pulse width and it decreases when the laser pulse width is reduced. The efficiency is heavily dependent on the laser pulse width and intensity. These results clearly indicate that plasma produced at a longer pulse width is heated more efficiently at various laser intensities. During the plasma heating phase, the size and uniformity of the source largely depend on the temperature until the bulk of the plasma is ionized to the L-shell. Optimal 3.7 to 4.3 keV X-ray conversion rates can be achieved at a laser intensity of 10¹⁵ w/cm². Furthermore, optimized laser irradiation conditions can improve efficiency because they have a significant effect on laser absorption, heating, and emission characteristics.

We have provided a brief overview of a study on X-ray sources from laser-exploded metallic thin foils and have examined the underlying physics of underdense sources. A promising target geometry that can be experimentally tested in future studies is a large number of very thin metallic foils. We have drawn (2s₀-3d₁, 2p_1/2-3d_3/2, 2s₀-3p₁) transition lines relating ξ_x to the photon energy hν for laser-exploded multi-thin-foil targets. The results indicate that the foil thickness and space interval between each parallel foil should be tuned such that the mean medium density is similar to that of a low-density gas target. Laser pre-exploded foil experiments have validated that the multi-thin-foil target approach generates underdense plasma under similar temperature and density conditions compared to gas targets and yields “metallic” gas-like performance. Another interesting phenomenon observed in our experiments on multi-keV X-ray sources using laser-exploded multi-thin-foil targets is that multi-keV X-ray emission increases as the thickness of the thin foil is reduced (Fig. 4). This implies that a higher X-ray conversion efficiency can be achieved by utilizing a thin foil with an optimal thickness. A detailed analysis of the range of foil thicknesses used in our experiments revealed that a 400 nm Sn layer performed better than thicker targets in terms of generating an efficient multi-keV X-ray source when using a 1 ns laser pulse width. The mechanism of X-ray emission depends on the duration of the laser pulse. Our main goal was to heat the thin Sn to a sufficient temperature to obtain a high degree of M-shell ionization such that the multi-keV X-ray emission was insensitive to the electron temperature while minimizing the hydrodynamic losses from the laser pulse width (volume heating and non-ablative running), thereby sufficiently expanding the Sn. However, if the target over-expands, its emissions are reduced because emissivity is proportional to the square of density (∝ρ²). Therefore, it is necessary to ensure an adequate density to obtain a sufficient number of emitters. A detailed analysis of the range of foil thicknesses revealed that the balance between electron temperature and density yields an optimal thickness to generate an efficient multi-keV X-ray source. We also experimentally demonstrated that varying the thickness of each layer in a thin foil can alter multi-keV X-ray emission (Fig. 4).

6. Conclusion

In this study, we investigated multi-keV X-ray emission as a function of the laser pulse width, laser intensity, and thickness of a thin foil target. This paper presented X-ray spectra and ξ_x values from Sn plasma induced by laser light. The ξ_x value of Sn L-shell-band (3.7 to 4.3 keV) emission was investigated as a function of the laser pulse width, intensity, and foil thickness. These three parameters allowed us to optimize a bright multi-keV X-ray source. By increasing the laser pulse width from 1 to 2 ns and focusing the laser onto a three-layer (i.e., front CH substrate plus Sn plus back CH substrate) thin foil target, we observed an increase in the magnitude of the X-ray yield by a factor of 1.5 ± 0.52. A large plasma scale length is the key factor contributing to these results. By reducing the thickness of a thin foil target irradiated with a laser intensity of approximately 5.8 × 10¹⁵ W/cm², we determined that the value of ξ_x at 400 nm is nearly twice that at 800 nm. Sn L-shell emission can provide a bright broadband (3.7 to 4.3 keV) source of X-ray photons by varying the target thickness and thin foil targets radiate significantly more than solid targets, and nearly as much as low-density foam targets [22]. As a result, we were able to generate a bright multi-keV X-ray source using a multi-layer thin metallic foil, similar to that produced using a gas-like target. The results of this study suggest that multi-layer thin foil targets can increase the size of the emission region. First, a radiation wave (soft X-ray) preheats a thin foil target. The preheated thin foil target can then expand into an underdense plasma before the arrival of the heat wave. Therefore, it is necessary to vary the target thickness to optimize a bright multi-keV X-ray source using multilayer thin metallic foil targets.