Introduction
Laser-produced plasmas have been studied as a source of X-ray radiation since the very early days of the laser (Ref. Reference Schwarz and Hora1). The field has advanced largely to address two related goals: laser-driven inertial confinement fusion and laser-produced X-ray probes. To achieve those goals, a signification portion of laser X-ray generation research was performed at large facilities such as Shiva (Ref. Reference Matthews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinsky, Turner and Ze2), Argus (Ref. Reference Matthews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinsky, Turner and Ze2), Nova (Refs Reference Back, Davis, Grun, Suter, Landen, Hsing and Miller3, Reference Back, Grun, Decker, Suter, Davis, Landen, Wallace, Hsing, Laming, Feldman, Miller and Wuest4), J-KAREN (Ref. Reference Aoyama, Yamakawa, Akahane, Ma, Inoue, Ueda and Kiriyama5) and Trident (Ref. Reference Workman, Cobble, Flippo, Gautier and Letzring6), with ongoing experiments at NIF, (Refs Reference Hill, Williams, Zylstra, Stan, Lockard, Gumbrell, Rudd, Powell, Swift, McNaney, Galloudec, Remington and Park7, Reference Landen, Farley, Glendinning, Logory, Bell, Koch, Lee, Bradley, Kalantar, Back and Turner8) OMEGA (Refs Reference Back, Davis, Grun, Suter, Landen, Hsing and Miller3, Reference Bullock, Landen and Bradley9), ALEPH (Ref. Reference Hollinger, Bargsten, Shlyaptsev, Kaymak, Pukhov, Capeluto, Wang, Rockwood, Wang, Townsend, Prieto, Stockton, Curtis and Rocca10), ELI-NP (Ref. Reference Lureau, Matras, Chalus, Derycke, Morbieu, Radier, Casagrande, Laux, Ricaud, Rey, Pellegrina, Richard, Boudjemaa, Simon-Boisson, Baleanu, Banici, Gradinariu, Caldararu, Boisdeffre, Ghenuche, Naziru, Kolliopoulos, Neagu, Dabu, Dancus and Ursescu11), SULF (Ref. Reference Li, Gan, Yu, Wang, Liu, Guo, Xu, Xu, Hang, Xu, Wang, Huang, Cao, Yao, Zhang, Chen, Tang, Li, Liu, Li, He, Yin, Liang, Leng, Li and Xu12) and many others. These laser systems typically operate with either kJ-class ns beams at ∼1016 W/cm2, or 1–100 J-class ultrashort beams with intensities of ∼1020–21 W/cm2. In comparison, experiments with J-class ns lasers with intensities of ∼1013 W/cm2 are a less explored area of laser–plasma interactions. However, modest laser intensities hold promise for their significant X-ray yield in the 1–5 keV range which can be used for biological imaging (Ref. Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13) and detector calibration (Ref. Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi, Tomassini and Di Cocco14).
Intense laser radiation on a metal foil ablates the material, forming a solid density plasma. Depending on the laser intensity, thickness of the foil and the hydrodynamic disassembly process, a portion of the foil remains intact while the laser pulse heats the plasma formed on the front surface. For ns class lasers <1015 W/cm2, inverse bremsstrahlung is the dominant mechanism of laser absorption (Ref. Reference Nishimura, Eliezer and Mima15). Laser energy is absorbed by the electrons most efficiently at densities with n e < n c, where the critical density is n c = 3.9 ×1021 cm−3 for 532 nm radiation (Ref. Reference Zel’dovich and Raizer16). At greater densities, the plasma becomes opaque, and these plasma regions are heated by thermal conduction of the hot electrons (Ref. Reference Chen17). After the plasma is sufficiently hot, it radiates the absorbed energy out as bremsstrahlung X-rays and line spectra from the highly ionized metal atoms. Inner shell ionization of cold atoms to produce K-line emission generally requires much higher laser intensities and hotter election populations. The opacity of the plasma and condition of the foil heavily influence the transport of X-ray radiation to the sample and detectors (Ref. Reference Nishimura, Eliezer and Mima15).
Marzi et al. (Ref. Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13) and Labate et al. (Refs Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi, Tomassini and Di Cocco14, Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi and Numico18, Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi, Numico and Salvetti19) describe a laser-driven soft X-ray source for both biomedical imaging applications and CCD camera calibration. They use a single beam of 3-J, 3-ns Full Width Half Max (FWHM), 1053-nm pulse for an intensity of 5 × 1012 W/cm2, incident upon a solid cylinder target. Cu produced the highest yield of 1–5 keV X-rays when compared with plexiglass, Al, Mo and W (Ref. Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13). Years prior, Eidmann and Kishimoto (Ref. Reference Eidmann and Kishimoto20) measured X-ray spectra from 50 eV to 1.2 keV with a 7-J, 3-ns (FWHM), 532-nm pulse for an intensity of 3 × 1013 W/cm2 with flat solid targets. Their results from Be, C, Al, Ti, Cu, Mo, Sn, W, Au and Pb also identified Cu with the highest intensity X-ray emissions (Ref. Reference Eidmann and Kishimoto20). Near 1 keV, the spectrum for Cu was dominated by L-shell emission. More recent work on Al, Cu and Au by Chaurasia et al. (Refs Reference Chaurasia, Munda, Tripathi, Gupta, Dhareshwar and Tallents21–Reference Chaurasia, Tripathi, Leshma, Murali and Pasley23), using a single 2- to 15-J, 500-ps, 1064-nm pulse for a maximum intensity of 4 × 1014 W/cm2 on target, described the variation of X-ray emission with focal position and thus the spot size. Shots that were slightly out of focus produced larger signals of soft X-rays (0.7–1.5 keV) from the larger volume of plasma. Shots that were in focus produced more emission of harder X-rays (3–5 keV). Gaeta et al. (Ref. Reference Gaeta, Rieger, Turcu, Forber, Campeau, Cassidy, Powers, Maldonado, French, Naungayan, Kelsey, Hark, Morris, Foster, Smith and Lim24) expanded a low-energy laser X-ray source to four beam lines of 2.8 × 1014 W/cm2 each with a 37-μm-thick copper tape target to produce ∼1 keV radiation for lithography applications at 300 Hz for 3.8 W/sr average power. They concluded that a laser system with a moderate energy and a small focal spot and short pulse width produces X-rays at a higher efficiency than systems with similar intensities and larger energy per pulse (Ref. Reference Gaeta, Rieger, Turcu, Forber, Campeau, Cassidy, Powers, Maldonado, French, Naungayan, Kelsey, Hark, Morris, Foster, Smith and Lim24).
We have begun developing a similar laser-driven benchtop X-ray source for detector and diagnostic development at the Dual Axis Radiographic Hydrodynamic Test (DARHT) Facility (Ref. 25). In comparison to previous work, our laser system uses thin (2.5–10.0 µm) foils with a 5-J, 8-ns, 532-nm pulse and an intensity of 4 × 1013 W/cm2. Our primary goal is to calibrate a suite of X-ray detectors and spectrometers before installation on DARHT. In this work, we detail initial experiments with multiple foil materials and thicknesses on the DARHT soft X-ray test stand to understand and commission this X-ray source to complement the future Bragg crystal spectrometer calibrations.
Materials and methods
The simple goal of the experimental apparatus (Fig. 1) is to put the most intense photon beam possible onto the metal foil target and detect the generated X-rays. The optical beam is produced in a flashlamp-pumped Nd:YAG (Ref. 26) and frequency doubled to 532 nm with a maximum energy of ∼5 J per 8-ns (FWHM) pulse. The beam is focused onto the foil with a 150-mm lens to a 1/e2 diameter of ∼40 μm; providing an intensity of 4 × 1013 W/cm2. The focal spot size was limited by experimental factors to protect the optics from metal debris. A photodiode (Ref. Reference Labs27) monitors the scattered laser light from an alignment mirror and is calibrated to provide the laser energy on every shot. The foils are mounted on an aluminum frame inside the target chamber at 10−7 Torr with a manipulator arm to move a new sample into the target position for each shot.
Figure 1. The laser beam enters the target chamber from the right striking the metal foil in the center. A group of DRDs is mounted facing the target front to detect backscattered radiation with different Al filters 10 cm from the target. A second group of DRDs is mounted around the filter object to detect forward-scattered radiation 18 cm from the target. The Sophia camera is mounted at the end of the chamber 45 cm from the target.
Diamond radiation detectors (DRDs), which are most sensitive to X-rays <6 keV and have an instrument response time of ∼200 ps, are the main detectors for the emitted X-rays (Refs Reference Spielman, Ruggles, Pepping, Breeze, McGurn and Struve28–31). These detectors are 3 × 1 × 1 mm and are mounted on an SMA connector that provides a −150 V bias and records the induced current. The DRDs on the right of Fig. 1 pointed at the front of the target surface measure the X-rays in the ‘backward direction’ and the DRDs on the left behind the target measure the X-rays in the ‘forward direction’, which we define here for the remainder of this work. The DRDs were cross calibrated, corrected for non-linearity in high-voltage signals and the signals compared here are using DRDs of the same size from the same manufacturer. Coarse X-ray spectroscopy measurements were made using eight different metal filters mounted to an anodized Al base and the Sophia-XO camera (Ref. 32). The camera has a square 2048 pixel array with square 13.5-µm pixels and a 200-µm-thick silicon sensor. The Sophia has a quantum efficiency >60% for X-rays between 0.5 and 5.0 keV (Supplemental Figure S1). The camera sensor was overexposed for 100 ns, integrating the entire X-ray pulse. Light-tight filters on both the DRDs and the Sophia camera are 500 ± 5 nm of Al on top of a 5 ± 0.25-µm polyimide support (Ref. 33). Thicker Al filters of 50 and 300 µm were used for higher energy X-ray measurements on two additional DRDs. Targets for this initial study included 10-µm-thick Al, Ti, stainless steel alloy number 304 (SS-304), Fe, Cu and Sn (Ref. 34). Also, 2.5- and 5-µm-thick foils of Ti, Fe and Cu were also shot to quantify the thickness dependence on X-ray yield.
Results and discussion
Time-resolved X-ray measurements
We performed a series of time-resolved X-ray measurements using DRDs with different foils at laser intensities from 0.8 × 1013 to 4.0 × 1013 W/cm2. Figure 2A shows the average DRD signals of the forward-scattered X-rays from each material for up to 15 shots with 4 × 1013 W/cm2 of laser intensity. Time zero in these and all other figures in this paper is set when 10% of the peak of the laser pulse arrives at the foil. Cu targets yield the brightest X-ray source, at the expense of larger shot-to-shot variation. Al generates much larger X-ray signals than the other higher Z materials, aside from Cu, in the forward direction. In the backward direction, Fig. 2B, Cu remains the strongest emitter. Al is the weakest X-ray emitter in the backward direction.
Figure 2. (A) Average DRD X-ray signals from up to 15 shots in the forward direction for Al, Ti, SS-304, Fe, Cu and Sn. (B) Average signals in the backward direction. The laser pulse is shown in grey and scaled for easy comparison. (C) Average numerically integrated signal for each material over five shots in the forward direction. (D) Average numerically integrated signals in the backward direction.
The average integrated signal versus atomic number Z is plotted in Fig. 2C, where there is not a clear dependence on Z for the forward-scattered X-rays. The expected increase in X-ray yield due to the Z 2 scaling of the inverse bremsstrahlung absorption coefficient (Ref. Reference Nishimura, Eliezer and Mima15) is evident in the integrated back-scattered X-ray flux, shown in Fig. 2D. Cu has the best combination of a high Z number for efficient absorption of laser energy by inverse bremsstrahlung and low ionization energies, allowing a large fraction of the plasma to ionize to the K and L shells which then emit keV X-ray radiation (Ref. Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13). Ti has lower ionization energies and would have a larger fraction of K and L shell ionization; however, it does not absorb the laser energy as efficiently. Sn exhibits the opposite phenomenon. It has a high Z and absorbs the laser energy strongly but has much higher ionization energies and much smaller fractions of K and L shell ionized atoms. Sn plasmas would be expected to have large fractions of M shell ions which emit in the extreme ultraviolet region and is blocked by the light filters on our DRDs. Similar trends were observed by Marzi (Ref. Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13), Eidmann (Ref. Reference Eidmann and Kishimoto20) and Chaurasia (Ref. Reference Chaurasia, Tripathi, Ryc and Dhareshwar22) who all found Cu had the largest X-ray yield with laser intensities near 1013 W/cm2.
The large differences in X-ray emittance and timing in the forward- and back-scattered directions (Fig. 2) are an effect of the hydrodynamic disassembly time and the opacity of the foil before disassembly. The forward-scattered X-rays arrive at the DRDs between 3.7 and 6.3 ns after the laser hits the foil. In the backward direction, the X-rays arrive between 0.5 and 0.9 ns after the laser pulse which is slightly longer than the 0.3 ns (10 cm) transit time for light from the plasma to the DRD array. Based on the X-ray arrival times, Al, Cu and Sn disassemble faster than the Ti, Fe and SS-304.
With detectors in both the forward and backward directions, an attenuation study was performed. Using the transmission equation, it is possible to calculate the time-dependent thickness of the foil and the speed of the ablation or hydrodynamic disassembly process.
\begin{equation}\frac{{{I_{\rm For}}}}{{{I_{\rm Back}}\,}}\left( t \right) = {{\rm e}^{ - \frac{\mu }{\rho }\,\rho \,z\left( t \right)}}\end{equation}where I For is the forward DRD signal transiting the foil corrected for distance, I Back is the backward DRD signal corrected for distance, µ/ρ is the mass attenuation coefficient (Ref. Reference Hubbell and Seltzer35), ρ is the material density and z(t) is the foil thickness. Signal intensity was corrected for the distance traveled using the inverse-square law. We believed that the X-ray radiation source was created by the laser on the front surface of the foil and the source radiates outwards isotropically into 4π steradians (sr) and the X-rays either transit the foil or are absorbed by the foil. There is no reflection. Mass attenuation coefficients depend on energy, and we have selected to use the values at 2 keV, the peak of the estimated Cu X-ray spectrum, as described below.
The Cu foil is initially 10 µm thick and has begun thinning when the first signals are detectable above the noise by the forward DRD (Fig. 3). A 10-µm-thick copper foil attenuates 2 keV X-rays by 10−6, while 5-µm-thick Cu foils attenuate by 10−4 where signals are first observed in the forward direction. The foil thickness over time was fitted to a fifth-order polynomial to provide a smooth function to calculate the ablation rate, dz/dt. Ablation rate has an average rate of 0.65 µm/ns and an instantaneous maximum of 1.78 µm/ns early in time. This speed is faster than the Maxwell–Boltzmann root mean squared speed of 1.05 µm/ns for a distribution of gaseous Cu at the boiling point (2835 K) and slower than the solid Cu bulk speed of sound, 3.75 µm/ns. Similar calculations were performed for Cu of 5 and 2.5 µm thick and different laser intensities. The slight trend towards faster ablation rates with more laser energy is encouraging; however, given the large uncertainties from shot to shot variation, measurement error with small signals, and the spectral estimation we do not believe these differences are meaningful. Cu, Ti, Fe and Sn samples with a thickness of 10 µm (Supplemental Figure S2) and the ablation speeds are compared in Table 1. If the rates were completely driven by the boiling material, we would expect a scaling with the square root of the atomic mass. These rates do not follow that trend. If the measured ablation speeds do represent the root mean squared velocity of the atoms, it implies a temperature for the sublimating atomic Cu material around 6900 K or 0.6 eV. This is not the electron plasma temperature that creates the bremsstrahlung X-rays. Simulations predict a maximum plasma temperature of ∼800 eV as described below. The ablation rates are a subject of ongoing study and research.
Figure 3. Ablation rate for 10-µm-thick Cu foils. A fifth-order polynomial fit (black) to the thickness data (blue) was used to calculate the ablation rate, dz/dt (red). The maximum ablation rate is 1.78 µm/ns.
Table 1. Ablation rates
a Al and SS-304 rates were not calculated.
b Weighted average of the alloy.
We examined the effect of foil thickness on the X-ray intensity in the forward direction; a thinner foil has a shorter absorbance path length and disassembles faster, so it should produce stronger X-rays in the forward direction. We observed a slight increase in the percentage of forward-scattered X-rays with thinner foils shown in Fig. 4. The absolute magnitude of the observed X-rays was highest with 5-µm foils for Ti and Fe and with 2.5-µm foils for Cu. The drop in X-ray flux from 2.5-µm foils is likely due to a smaller plasma volume, thus producing less radiation. This is verified by a similar decrease in radiation in the backscattered direction for 2.5-µm foils versus 5-µm foils, along with Chaurasia’s (Ref. Reference Chaurasia, Tripathi, Ryc and Dhareshwar22) measurements that smaller plasma volumes produce less X-rays. In Cu, the improvement in the percentage of forward-scattered X-ray transmission for the 2.5-µm foil was large enough to offset the decreased radiation production. The timing of the arrival of the X-ray pulse at the DRDs is also shortened with thinner foils (Supplemental Figure S3) which is consistent with the ablation rates.
Figure 4. Average numerically integrated DRD X-ray signals for five shots in the forward (green) and backward (red) direction for 10-, 5- and 2.5-µm-thick targets of different materials. The percentage of the flux in the forward direction relative to the flux in the backward direction is given.
Filtered X-ray spectral estimation
Spectra of the emitted X-rays from Cu were estimated by using eight different foil filters imaged onto the Sophia camera as shown in Fig. 5A. The transmission of each of these filters, shown in Fig. 5B, is calculated from the Center for X-ray Optics online database (Refs Reference Gullikson36, Reference Henke, Gullikson and Davis37). To extract the estimated spectra, we employed an expectation–maximization method, used for medical computed tomography images (Refs Reference Sidky, Yu, Pan, Zou and Vannier38, Reference Duan, Wang, Yu, Leng and McCollough39). This method uses an estimate of the spectra, calculates the expected signal amplitude with each filter, compares the expected signal to the actual signal and adjusts the spectral estimate. We used a 400 eV black-body spectral guess with additional Cu K-alpha lines that was both wider and more intense than the actual spectra as required by the expectation maximization algorithm. Approximately 100 iterations are required to arrive at an estimated spectra that accurately reproduces the measured signal for each filter within a 10% error. Spectra were smoothed via a Gaussian basis set of 200 functions.
Figure 5. (A) X-ray image of the metal target filter with the filter type and average counts listed in each region. The image contrast and brightness has been adjusted for best visibility of each region. (B) X-ray transmission curves for Ti (blue), for Fe (green) and for Cu (orange). Note the strong K-edges in the chosen filter set and the small L edge for Ti at ∼500 eV.
The calculated spectra from 5 μm Cu targets at different laser intensities are shown in Fig. 6. The intensity setting was adjusted by lowering the laser output energy, keeping the spot size fixed. These spectra show an increase in amplitude with increasing laser intensity and a slight shift in the peak to higher energy emission from 1.7 to 1.9 keV. There is no evidence of emission at the Cu K-lines at 8.047, 8.027 and 8.905 keV or H and He-like lines near 8.666, 8.699, 8.347 and 8.392 keV (Ref. Reference Henke, Gullikson and Davis37). Cu K-alpha and K-beta lines were inserted into the initial spectral guess and are significantly reduced by the iterative algorithm. Omitting these spectral lines from the initial guess results in negligible change in the spectra <4 keV, and no signal >4 keV (Supplemental Figure S4). Additional measurements from DRDs with 50-μm Al filters, which have <1% transmission <3.5 keV and >50% transmission >7.8 keV, only recorded noise, further supporting that Cu K-line radiation is not produced (Supplemental Figure S5). It is possible that emission from the Cu L-lines at ∼900 eV and lines from Li-like ions at 1.3–2.6 keV, Ne-like ions at 1–1.5 keV and F-like ions at 1–1.2 keV (Ref. Reference Kramida, Ralchenko and Reader40) are not being resolved with this coarse spectral measurement technique (Ref. Reference Henke, Gullikson and Davis37).
Figure 6. Spectral estimation with intensities of 1.6 × 1013 W/cm2 (green), 2.4 × 1013 W/cm2 (blue), 3.2 × 1013 W/cm2 (red) and 4.0 × 1013 W/cm2 J (black). The features marked by the numbers are artifacts of the chosen metal filters. The peaks at 8.5 and 8.9 keV are the locations of the Cu K-alpha and K-beta lines, respectively. These lines are significantly decreased from the original guess by the algorithm and are likely not present in the real experimental spectra.
The estimated spectra have several features which are artifacts of the spectral estimation method due to the strong absorption edges in the available metal filters. At the low end of the spectra, we would expect the decline to be smooth, and the estimated peak at 500 eV is a result of the Ti L absorption edge in the same spectral range. The sharp discontinuities at 5 and 7 keV are from the Ti K-edge and the Fe K-edge.
Simulations
Hydrodynamic simulations were performed using the one-dimensional (1-D) radiation-magneto-hydrodynamic software HELIOS-CR (Ref. Reference MacFarlane, Golovkin and Woodruff41). HELIOS-CR utilized Lagrangian methods to solve conservation equations, frequently used in the inertial confinement fusion community for laser-produced plasma (Ref. Reference MacFarlane, Golovkin, Mancini, Welser, Bailey, Koch, Mehlhorn, Rochau, Wang and Woodruff42) and Z-pinch plasma simulations (Ref. Reference Bailey, Chandler, Slutz, Bennett, Cooper, Lash, Lazier, Lemke, Nash, Nielsen, Moore, Ruiz, Schroen, Smelser, Torres and Vesey43). HELIOS-CR simulations were performed using a 5-J, 10-ns (FWHM), 532-nm pulse with a 40 μm spot size resulting in an intensity of 4 × 1013 W/cm2 incident on 10-, 5- and 2.5-µm-thick foils of Al, Ti, Fe and Cu. The foils are divided into 100 zones of equal size, which are 0.1, 0.05 and 0.025 µm thick depending on the foil. The provided PROPACEOS (Ref. Reference MacFarlane, Golovkin and Woodruff41) equations-of-state and opacity values were used. These simulations agree with the measured temporal X-ray signals from the DRDs and support the conclusion that X-rays in the forward direction are being attenuated by the mostly intact foil until after disassembly.
A clear illustration of the laser–foil interactions is revealed by following different zones through the hydrodynamic disassembly process of a 10-µm Cu foil in Fig. 7A. As the laser pulse arrives at the foil, the first micron of material is ablated from the front surface. The leading edge of this plasma comprising the first 100 nm of the foil is heated to ∼800 eV by the laser pulse. The remaining foil material is shock compressed to higher densities and pushed backward, until disassembling around the time of the peak of the laser pulse. The middle of the foil, material between 4.0 and 4.1 µm, reaches temperatures of ∼60 eV from collisional heating by hotter electrons. The total mass density of the foil material and the simulated radiation flux from the front and back surface in Fig. 7B show that radiation in the backward direction begins almost immediately when the laser hits the foil. Radiation in the forward direction is not released until the foil has begun to disassemble and is significantly smaller in magnitude than the flux in the backward direction. Comparisons of simulations with different thicknesses of Cu in Fig. 7C show the expected trend towards more emission in the forward direction with thinner foils and slightly lower emission in the backward direction due to a smaller volume of high temperature plasma. Al, Ti and Fe foils exhibit all of the same general features, but comparisons of the magnitude of the radiation flux between materials in Fig. 7D do not match experiments or the Z 2 scaling from the inverse bremsstrahlung absorption coefficient. The timing of the simulated radiation pulses also deviates from experiments as the Al X-rays are simulated to show up the earliest as the lightest material disassembles the fastest, followed by Ti, Fe and then Cu. Experimental results measured Cu and Al X-ray pulses arriving at the detectors around the same time, followed a few nanoseconds later by Ti and then Fe.
Figure 7. Results of HELIOS-CR simulations for Cu hydrodynamics irradiated by a 532-nm 5-J pulse with a 40-μm spot and a 10-ns FWHM at an intensity of 4 × 1013 W/cm2. (A) Simulated foil motion from selected zones of a 10-μm-thick Cu foil with the laser pulse (grey). (B) On the same timescale, the mass density of the simulated foil and the simulated radiation flux in the forward direction (green) and radiation in the backward direction. (C) The simulated flux for different thicknesses of Cu compares favourably to experiment see Figure 4. (D) The simulated flux for different materials compares poorly with experiments, see Figure 2D.
We simulated the spectra of the emitted radiation from the 5-μm-thick Cu foil using the output of the HELIOS-CR hydrodynamic data with SPECT3D (Ref. Reference MacFarlane, Golovkin and Woodruff44). We chose to use the non-local thermodynamic equilibrium K-line emission model for Cu which is native to the code. This atomic model includes the fully detailed states for H-like, He-like and Li-like Cu ions with the ground state for Be-like Cu ions. The time-integrated simulated X-ray spectra is shown in Fig. 8. At low energies, there is a black-body continuum from 0 to 800 eV and peaks at 143 eV. The group of emission lines from 1.3 to 2.4 keV is due to Li-like Cu26+ ions (Ref. Reference Kramida, Ralchenko and Reader40). Using an estimated Boltzmann distribution and ionization energies tabulated by NIST (Ref. Reference Kramida, Ralchenko and Reader40), the Li-like state comprises ∼4% of the plasma at a temperature of 800 eV. There is no emission of K-alpha, H-like or He-like lines around 8 keV in the simulated spectra. At an electron temperature of 800 eV, He-like Cu27+ and H-like Cu28+ comprise only 0.000098% and 0.000026% of the plasma using the same estimated Boltzmann distribution. We are not able to generate a high enough temperature with a laser intensity of 4 × 1013 W/cm2 to produce Cu He-like and H-like ions in sufficient quantities to detect their characteristic X-rays. The simulated 1-D spectra roughly agree with the estimated spectra from the X-ray filtered imaging as the black-body emission is filtered out and there are no high energy lines. The simulated and estimated spectra do peak at different wavelengths, 1.4 keV vs. 1.9 keV, which may be due to emission from other ionized Cu species that are not included in the atomic model used by SPECT3D (Ref. Reference MacFarlane, Golovkin and Woodruff44). This also does not include the very real possibility of metal impurities or other absorbed elements contaminating the experimental spectra (Ref. Reference Ramey, Coleman, Hakel, Morris, Colgan, Barefield, Fontes, Gilgenbach and McBride45).
Figure 8. Simulated spectra from SPECT3D integrated over the full duration of the laser pulse exhibiting a black-body continuum from 0 to 800 eV and several Li-like Cu lines from 1.3 to 2.4 keV. Lines from He-like and H-like Cu atoms or Cu K-lines are not estimated to be emitted under these conditions. Spectra estimated from the filtered images at an equivalent laser intensity is scaled and shown for comparison in blue.
Conclusion
We have built and characterized a modest intensity of 4 × 1013 W/cm2, laser-produced plasma, soft X-ray source using a single 5-J, 8-ns (FWHM), 532-nm pulse on Al, Ti, Fe, SS-304, Cu and Sn foil targets. This work, in agreement with other studies (Refs Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13, Reference Eidmann and Kishimoto20), has found that Cu has the largest X-ray yield for laser-produced plasma at these intensities. Foil targets introduce additional X-ray emission complications due to the hydrodynamic disassembly process compared to a solid cylinder (Refs Reference Marzi, Giulietti, Giulietti, Gizzi and Salvetti13, Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi, Tomassini and Di Cocco14, Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi and Numico18, Reference Labate, Galimberti, Giulietti, Giulietti, Gizzi, Numico and Salvetti19), or a flat solid target (Refs Reference Eidmann and Kishimoto20–Reference Chaurasia, Tripathi, Leshma, Murali and Pasley23). X-ray emission begins with a material ablated from the front of the foils and is detected earlier on DRDs facing the front surface. X-rays reaching DRDs behind the foil are heavily attenuated by the foil until the hydrodynamic disassembly time with signals that are about 10 times smaller than DRDs facing the front surface. The ratio of forward/backward X-ray emission has been used to measure the ablation rate of the foils and suggests a thermal, boiling-like process with temperature of ∼0.6 eV. Spectral estimation of the emitted X-rays from Cu was calculated with an expectation–maximization algorithm by imaging eight filters with a Sophia X-ray CCD camera. The estimated spectra peaks at 2 keV with no X-rays observed beyond 4 keV. There is no evidence of Cu K-alpha lines or He-like and H-like emission. The intensity, timing and spectra of the X-rays compare favourably to simulations performed using HELIOS-CR.
For future experiments, we explore ways to increase the intensity of the laser pulse on the target by decreasing the spot size. Placing the final lens inside the vacuum and reducing the focal length by a factor of 3 would result in an increase in intensity by a factor of 9 from 4 × 1013 to 3.6 × 1014 W/cm2. HELIOS-CR simulations with 5 μm Cu targets suggest this would increase our maximum electron temperature to 1400 eV and our X-ray flux by ∼10 times if the irradiated area is equal. Future work will include fielding a mica Bragg spectrometer with a spectral range up to 4 keV, collected on calibrated image plates to obtain X-ray dose as a function of energy. Once this is implemented, the image plates will be replaced with a microchannel plate gated X-ray imager.
Supplementary Material
The supplementary material for this article can be found at https://doi.org/10.1017/lpb.2024.1.
Data Availability Statement
Raw DRD and Sophia camera image data used to support the findings of this study are available from the corresponding author upon request. The HELIOS-CR simulation package is available from Prism Computational Sciences, Inc at www.prism-cs.com (Ref. Reference MacFarlane, Golovkin and Woodruff41).
Acknowledgements
The authors appreciate the support and scientific discussions with Joseph Strehlow, Sasi Palaniyappan and Cort Gautier. They would like to take the opportunity to thank Ross Roybal and Sharon Dominguez for their manufacturing and design support.
Author Contributions
L. Tyler Mix: Investigation (lead); formal analysis (lead); visualization (lead); writing – original draft (lead). James A. Maslow: Investigation (supporting); resources (lead). M.A. Jaworski: Conceptualization (supporting); writing – review and editing (supporting). Joshua E. Coleman: Conceptualization (lead); writing – review and editing (lead); supervision (lead).
Funding Statement
This work was supported by the U.S. Department of Energy at Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
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