Optimized continuum x-ray emission from laser-generated plasma

X-ray emission from matter pervades the universe and plays an important role in the high-energy density (HED) regime (∼10⁵ J/cm³). For example, the emission and absorption of x-rays controls the thermal state and evolution of stellar interiors.¹ Properties of solar flares are determined by analyzing keV x-ray emission.² In addition, studies of x-ray-matter interactions in extreme environments, such as radiation hardness studies,^3,4 radiation-dominated astrophysical phenomena,^5–7 and inertial confinement fusion,⁸ use multi-keV x-ray sources. Inertial confinement fusion implosions are also a strong source of keV-range continuum x-ray emission.⁹ 

Nanosecond pulses of keV-range continuum x-rays have generated significant interest as a backlighter probe^10–17 for high-pressure materials science experiments. Among many applications, material strength experiments^18–20 use nanosecond pulses of ∼10–100 keV x-rays for in situ sample radiography. EXAFS^21–23 and single crystal phase and strain anisotropy measurements^24,25 use nanosecond broadband multi-keV x-ray pulses. In general, increased x-ray flux in the given range improves data quality.

The National Ignition Facility’s (NIF) high-power lasers can be used to heat samples to multi-keV temperatures, generating nanosecond, multi-keV x-ray pulses. Inverse bremsstrahlung (IB) dominates laser absorption in this regime as electrons gain energy through collisions while oscillating in the laser field. The IB inverse absorption length scales as $∝Z*2neniTe−3/2 ln (Λei)$⁠,²⁶ where $Z*$ is the ionization state, n_e is the electron density, n_i is the ion density, T_e is the electron temperature, and $ln (Λei)$ is the Coulomb logarithm. However, light cannot propagate in plasma when $ne>nc≡1.1×1021 cm−3/λμm2$⁠, where $λμm$ is the laser wavelength in μm. At the NIF, $λμm=0.351$ μm and n_c = 8.9 $×1021$ cm⁻³. Since $ni=ne/Z*$ in charge neutral plasma, IB scaling in realistic laser plasma varies as $∝Z*ne2Te−3/2 ln (Λei)$⁠. This suggests that the volume adjacent to the critical surface (n_e = n_c contour) dominates laser absorption. Pre-heating solid-density samples with a picketed pulse increases this volume and can increase the keV-range x-ray yield in laser-heated plasma.²⁷ Low density foam and gas-pipe targets are another approach concurrently under development.^14,16,17

The two dominant modes of keV-range continuum emission in HED plasma are free–free (bremsstrahlung) and free–bound (recombination) x-ray emissions. Free–free emission scales as $∝Z*2neniTe1/2$ $∝Z*ne2Te1/2$⁠, following the above laser-plasma arguments. This naturally suggests that the increasing atomic number (Z) should increase continuum emission. Free–bound emission occurs by recombination of plasma electrons into open bound states; the emitted photon’s energy is the sum of the kinetic and bound state binding energies, producing continuum emission in plasma. The ratio of free–bound to free–free radiation for recombination into shell n is $ξn/n3En/Tee(En/Te)$⁠,²⁸ where ξ_n is the number of holes in shell n and E_n is the shell’s single-electron ionization energy (H-like in the K-shell, etc.). Free–bound emissions can become very strong as T_e becomes large enough to create vacancies in shell n (T_e ∼ E_n); however, the 1/T_e factors limit free–bound yield at high T_e creating optimal conditions for T_e ∼ E_n. The multi-keV T_e possible with NIF lasers ionizes up to period 4 transition metal K-shells, motivating their use for multi-keV continuum generation.

Here, we report results from NIF experiments investigating x-ray emission from Ti, Ag, and Au foils (⁠$Z=22, 47, 79$⁠, respectively). Figure 1 shows our experimental configuration. A total of 72 NIF lasers (44 on front and 28 on back) heat foil samples over several experiments (see Table I). The main pulse shape is a 2-ns quasi-square with a peak power of 150 TW and a peak irradiance of ∼4.4 × 10¹⁵ W/cm² (Fig. 1 inset); all but the Au^* shot also have a lower power picket (peak ∼35 TW, ∼1 × 10¹⁵ W/cm²).

Figure 2 shows time-integrated 6–25 keV x-ray spectra recorded using an NIF Survey Spectrometer²⁹ (NSS, see the supplementary material). In Au samples, the picketed pulse shape increases spectral intensity by ∼4X over Au^* across the NSS energy range. Ag samples produce similar continuum spectral intensity over this range. Below ∼21 keV, both experiments using Ti samples yield higher spectral intensity than Ag or Au by up to 4X. Based on the continuum emission slope, Au^* and Au are the hottest, followed by Ag, with Ti being the coolest. The repeated Ti experiment yields nearly identical spectra suggesting high repeatability.

Figure 3(a) shows time-integrated Ti x-ray emission spectral intensity recorded by Virgil^30,31 (see the supplementary material). X-ray spectra predicted by the radiation hydrodynamics code hydra³² (see the supplementary material) run in one-dimensional geometry overlay the experimental data. We find good agreement with the continuum and many bound–bound features. Under these conditions, the large number of atomic energy levels necessitates the use of super-configurations³³ that lead to discrepancies seen in some emission energies [Fig. 3(a)]. We find that plasma conditions around $ne≃3×1021$ cm⁻³ and $Te≃3.2$ keV dominate keV-range radiation emission in Ti and correspond to Z^* = 20.7. Moreover, the strong Ly_α feature at ∼4.96 keV in the Virgil and hydra spectra arises from hydrogen-like states, confirming the K-shell vacancies predicted by hydra. In similar hydra simulations of Ag, we find $ne≃2.1×1021$ cm⁻³, $Te≃6.4$ keV, and $Z*=40.3$⁠, consistent with the assertion of hotter Ag plasma from the NSS data and a slightly vacant L-shell.

We investigate the continuum x-ray emission processes with the hybrid-structure atomic kinetics code scram.^34,35 Figure 3(b) shows scram simulation results for free–free and free–bound x-ray emission contributions for Ti and Ag in experimentally representative conditions (⁠$ne=3×1021$ cm⁻³ and T_e = 4 keV). As expected, Ag yields stronger free–free emission than Ti; however, this is a fraction of the total continuum. Above the Ti K-series limit (∼6.1 keV), Ti free–bound emission is 7–10 times larger than free–free, similar to the jump observed in the measured and predicted x-ray spectra in (a). The theoretical scaling for Ti using $Z*$ = 20.9 from the scram simulations and the hydrogen-like $En=6.626$ keV gives 7.9, in agreement with scram. The free–bound enhancement in Ag predicted by scram is only 2.2, similar to the ratio of 2.9 given by the analytic expression, and the continuum total is lower than that for Ti.

Figure 3(c) shows the ratio of free–bound to free–free x-ray emission calculated by scram at 18 keV (above the K-series limit across scanned materials) vs Z for $ne=3×1021$ cm⁻³ and T_e = 4 keV compared with the analytical expressions for the K- and L-shells (using $Z*$ from the corresponding scram calculation). Atoms lighter than Ti (Z < 22) have less than one bound electron, and the increase in E_n with Z increases the free–bound yield. The inner shell of atoms heavier than Ti have higher occupancy, and the free–bound contribution decays due to diminished hole quantity. The disagreement between the analytical and the scram calculations near $Z−Z*=2$ is due to the average $Z*$ not adequately describing the distribution of ionization states close to the filling of the K-shell.

Figure 4 shows temporally resolved x-ray emission in the photon energy ranges of 1.2–7.2 keV and 7–20 keV using Dante³⁶ and SPIDER,³⁷ respectively. Dante uses filtered fast x-ray diodes, and SPIDER uses a filtered streak camera. Each configuration yields different emission patterns to help understand the spectral results. The emission recorded by both instruments persists until the laser turns off on every experiment, ruling out sample burn through limiting the overall x-ray yield. Additionally, the two Ti shots show nearly identical SPIDER emission history, further indicating high repeatability.

Emission recorded by SPIDER from the non-picket laser pulse for Au^* initially rises with the quasi-square laser pulse (sharper than the pulse with a picket, see the inset of Fig. 1), increases in magnitude throughout its duration, and rapidly ceases with the end of the laser pulse. The Dante data show a similar trend, with lower x-ray energies (navy curves) rising earlier than higher energies (light blue curves), indicating a combination of increasing emitting volume and heating with time, as the laser remains on. The 2 ns pulse heats and expands the sample, increasing the radiation losses and the emitting volume. Comparing SPIDER sensitivity [inset of Fig. 4(a)] and NSS spectra, the SPIDER data for Au^* (and Au) are dominated by L-shell emission. While the L-shell is not expected to be ionized in these conditions,³⁸ the overall yield should nevertheless increase as the emitting volume increases. The rapid decay of keV x-ray emission with the end of the laser pulse is characteristic of systems in this regime.

The Au (picket drive) SPIDER signal closely mimics the laser pulse shape: emission rises over the first 0.6 ns (similar to the laser pulse), plateaus in the center, and quickly decays when the laser turns off. The Dante data show similar results, with all channels rising quickly, plateauing, and then falling quickly when the laser turns off. Whereas the Au^* Dante data suggest heating- and emitting-volume expansion throughout the main drive, the Au Dante data suggest rapid heating. The Au^* and Au x-ray spectra in Fig. 2 show the same slope (ignoring bound–bound transitions), suggesting that T_e is the same. Combined with no SPIDER signal between the picket and main pulses (1.5–4.5 ns in Fig. 4), this indicates that the picket primarily increases the emitting volume by pre-expansion.

Like Au (picket drive), emission from Ag increases rapidly with the main pulse. However, unlike Au, the emission increases throughout the main pulse before rapidly decaying as the laser turns off. The 3.0 keV channel of Dante is sensitive to Ag L-series emission and correspondingly rises slightly faster than the other two channels that are more sensitive to the continuum; fluctuations in the 7.2 keV data are due to noise. The overall bound–bound emission is less efficient than in Au, due to having fewer electrons and comparatively lower binding energies. In our simulations, the end of the rapid increase in emission roughly corresponds to Ag becoming oxygen-like, indicating the onset of significant L-shell ionization and resulting in enhanced free–bound radiation.

Finally, the Ti SPIDER signal rises more slowly, reaching near-peak emission ∼1.3 ns after the main pulse’s leading edge. This is likely due to weak bound–bound transitions and/or lower IB absorption due to the low Z. The Dante data confirm this as the channels rise in order of increasing energy, indicating heating throughout the drive. The Virgil spectra show that the Ti K-series limit increases to ∼6.1 keV (from 4.966 keV), consistent with our hydra simulations. The high ionization state inferred from the hydra/scram calculations simultaneously depletes L- and M-shell bound–bound transitions and increases free–bound contributions. As with Ag, the temporal emission history from Ti is bimodal. Unlike Ag, the rate of change of Ti x-ray emission increases just after the laser pulse’s leading edge (∼5.15 ns). This may correspond to the onset of strong free–bound emission as the K-shell becomes ionized. In our simulations, this change approximately corresponds to the onset of He-like states in Ti; the average atomic configuration contains a distribution of ionization states that include many H-like atoms. This is especially likely as SPIDER is sensitive to energies associated with Ti K-shell free–bound emission (inset of Fig. 4).

Figure 5 shows raw data recorded using a Static X-ray Imager (SXI)^39,40 pinhole CCD camera, which is filtered to observe 3–5 keV x-rays. The lower signal in the Ti image is consistent with free–bound dominated emission, which is largely filtered by the SXI due to the K-series limit being just above the sensitivity range. The strong bound–bound emission from Au and Ag in this regime accounts for the higher signal levels. This is consistent with previous results comparing matched K- and L-shell emission at similar n_e and T_e.⁴¹ 

In the raw SXI images (Fig. 5), the vertical and horizontal directions correspond roughly to foil normal and transverse directions, respectively. The Au vertical spot size is ∼35% larger than Au^*, consistent with pre-expansion by the picket. We do not observe a significant difference across picketed pulse shape experiments, suggesting material independent expansion. The keV x-ray transverse emission volume also yields clues about the interplay between conduction out of the heated region and radiative losses. Thermal conductivity in the Lee–More [LM] model⁴² scales as $∝neTe5/2/Z*$⁠. For constant T_e and n_e, the LM thermal conductivity decreases with increasing Z. The combined lower radiative losses and higher conductivity are consistent with the larger emission size observed for decreasing Z.

In conclusion, we have observed 4X stronger multi-keV continuum x-ray emission from Ti than Ag or Au. The extraordinary energy density produced by the NIF lasers ionizes Ti samples into the K-shell, causing strong continuum emission from free–bound transitions. X-ray spectrometer data show direct evidence for both large free–bound emission enhancement in Ti and a significant population of hydrogen-like Ti atoms. Our conclusions are well-supported by analytical scaling, radiation-hydrodynamics simulations, and detailed spectroscopic calculations. Despite strong continuum emission, Ti has lower overall radiative losses due to fewer bound–bound transitions that dominate emission from high-Z atoms. This combined with thermal conductivity produces an emission volume that scales inversely with Z, further enhancing Ti continuum emission. The continuum spectral slopes suggest that T_e scales positively with Z due to a combination of increasing IB laser absorption and reducing thermal conductivity. In agreement with previous studies, we find that a picketed laser pulse shape increases the laser absorption efficiency. It may be possible to achieve higher free–bound contributions in higher-Z materials by taking advantage of the large number of potential vacancies in the L-shell. Achieving this would require higher T_e that might be possible using magnetic fields.^43,44 Additionally, initially sub-critical density targets (gas or foam) also produce very intense x-ray pulses,^14,16,17 but material availability for these types of samples is limited, and at a size of ∼4 mm, they are quite large and may not be practical for all applications.

See the supplementary material for the details that further describe our results. The first part includes information about the NSS and Virgil x-ray spectrometers. The second part are technical details about the hydrodynamics simulations.

This work was performed under the auspices of U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This document's release number is: LLNL-JRNL-817453. This document was prepared as an account of the work sponsored by an agency of the United States government. Neither the United States government nor the Lawrence Livermore National Laboratory, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.