Two-color monochromatic x-ray imaging with a single short-pulse laser

X-ray imaging is an essential diagnostic technique to obtain density-related information of plasma in High Energy Density Physics (HEDP) and Inertial Confinement Fusion (ICF) experiments.^1–4 Most x-ray imaging diagnostics require three components: an x-ray source, a 2-D detector, and an x-ray optic to image the source onto the detector. For laser fusion plasma measurements, various x-ray imaging optics are utilized such as pinholes, slits, curved crystals, and multilayered Kirkpatrick-Baez mirrors.⁵ In particular, spherically curved crystals provide high throughput, narrow spectral bandwidth, and a long-working distance.⁵ At large high energy density (HED) facilities,^6–9 spherical crystal imagers were developed for single-color x-ray backlighting with nanosecond laser-produced x-ray sources.^10–12 More recently, picosecond short-pulse lasers have been used not only on foils as single-color backlighters for flash x-ray radiography of laser fusion implosion cores^13–15 but also to study fast electron transport within the target itself by imaging Kα emitted by the target after direct laser-target interaction.^16–19 Multi-color x-ray self-emission and backlighting imaging techniques were first demonstrated by combining independent imaging systems (i.e., two or more pairs of an x-ray source, an x-ray optic, and a detector).^10,20–24 Advantages of simultaneous multi-color x-ray imaging include improving the accuracy of electron temperature determination from emission measurements²² and increasing the detection range of areal densities (ρR) in backlighting experiments.^23,24

One of the challenges in performing multi-color x-ray backlighting has been the production of bright x-ray sources at different photon energies. Earlier laser implosion experiments at the Omega laser facility using x-ray backlighters at 4.7–5.0 keV and ∼2.5–4.5 keV required four beams for each source, precluding the use of all 60 OMEGA long-pulse beams for driving more symmetric implosions.²³ Recently completed high energy, petawatt (HEPW) lasers such as OMEGA EP²⁵, LFEX²⁶, Orion SP lasers,²⁷ and NIF ARC²⁸ now provide separate, bright backlighter sources for probing implosion cores and other targets. Experiments using OMEGA for implosion drive and OMEGA EP lasers for backlighting have been demonstrated on cryogenic deuterium-tritium (DT) capsules using single-color monochromatic x-ray crystal imaging at 1.865 keV (Si He-α)²⁹ and on warm deuterated plastic (CD) capsules using broadband bremsstrahlung in point-projection geometry (Compton radiography).^30,31 Production of multi-color x-ray sources with short-pulse lasers, however, has not been performed until now.

This paper presents details of two-color x-ray generation with a single high-intensity short-pulse laser as well as simultaneous monochromatic Kα imaging using two spherically curved crystals. Coincident Kα emissions at 4.5 keV and 8.0 keV were produced by irradiating a two-ply stack of Ti and Cu foils with the 50 TW Leopard short-pulse laser at the Nevada Terawatt Facility (NTF). Both Ti and Cu Kα x-rays produced by laser-produced fast electrons were imaged with separate crystals onto one image plate. An x-ray radiography experiment using the two-crystal imaging diagnostic was designed. Transmission calculations performed indicate that the range of areal densities that can be measured is extended from ∼70 mg/cm² using only Ti Kα up to ∼400 mg/cm² using both backlighter x-ray sources. Applications using multi-color x-ray generation with short-pulse lasers and two-crystal imagers are discussed.

The image formation of a spherically curved crystal system can be described using the paraxial lens equation as

where c is the distance from the Target Chamber Center (TCC) to the crystal, a is the crystal-to-detector distance, f is the focal length, θ_B is the Bragg angle of the crystal, and R is the crystal radius of curvature. For high spatial resolution imaging, spherically curved crystals must be operated at near normal angles between 80° and 90° in order to minimize aberrations.³² The focal length f is then given by f = R/2 since the sines of the near normal Bragg angle are approximately unity [sin(89.0°) = 0.999 85 for Ti and sin(88.7°) = 0.999 75 for Cu]. The principle and performance of spherical crystal imagers can be found elsewhere [Ref. 32 and references therein].

Figure 1 shows a top view of the schematic of the two-crystal imager for 4.51 keV Ti Kα and 8.05 keV Cu Kα. The key design of the imager presented here is to form two images reflected from separate crystals on the same detector with the shared TCC-to-detector axis in the two imaging systems. With this design, existing crystal imagers can be readily converted to a two-crystal imager. The choice of a crystal for particular photon energy determines the Bragg angle. The angle, β, between the axes c and a is given by 2 × (90° − θ_B) (e.g., β = 2.0° for the Ti Kα crystal since the Bragg angle is θ_B = 89.0°). Once the TCC-to-detector distance, b, is chosen, the rest of the distances and magnification can be calculated from the lens equation and the law of cosines. The magnification of the imager is obtained through M = a/c. Here, the matching crystals to the photon energies of 8.048 keV Cu Kα and 4.510 keV Ti Kα are quartz (21-31) and quartz (20-23) with the Bragg deflection angles (β₁ = 2.6° and β₂ = 2.0°). The curvature of the crystals was 500 mm and 250 mm. In our design with b = 1240 mm, the distances of the crystals from the TCC are calculated to be c₁ = 298.5 mm and c₂ = 137.4 mm and the magnifications are calculated to be 5 and 10. The field of view of the crystal is limited either by the crystal diameter or an aperture. The Cu crystal with 32 mm diameter had a 10 mm diameter aperture, while the 20 mm diameter Ti crystal was used without any apertures because the crystal’s 20 mm diameter is small enough to achieve an acceptable spatial resolution, see below. In our experiment, the 2-D detector is a static image plate (IP), but it can be replaced by an electronic x-ray CCD camera,¹³ a time-gated x-ray framing camera,²⁹ or a time-resolved x-ray streak camera for 1-D imaging.³³ Pairs of magnets deflect fast electrons, reducing the noise on the IP.³⁴ Based on the crystal diameter, crystal curvature, magnification, and Bragg angle, the spectral bandwidth of each crystal is calculated using Eq. (11) in Ref. 35. The specification of the crystals and the imager design is summarized in Table I.

The two-crystal imaging system was tested using the 50 TW Leopard laser³⁶ at the University of Nevada Reno’s Nevada Terawatt Facility (NTF). The Leopard short-pulse laser at the wavelength of 1064 nm delivered ∼10 J in a 0.35 ps FWHM Gaussian pulse. The beam was focused by a f/1.5 off-axis parabola down to 8 μm FWHM spot size, achieving a peak intensity of ∼10¹⁹ W/cm². Figure 2 shows microscope images of the layered targets. The Cu and Ti foils were manually cut by a blade into pieces with the surface area of <1 mm². The laser was focused on the Cu foil at a 20° incident angle. The thickness of the Cu foil was kept to 10 μm to maintain the same laser-target interaction and the fast electron transport, whereas the Ti foil thickness was changed to 2, 5, or 10 μm. A slightly smaller piece of a Ti foil was placed on a Cu foil and glued together, allowing us to measure Cu Kα emission from the bare Cu foil and through the Ti foil. The layered target was then mounted on a glass stalk. The titanium side of the target faced the crystals so that the 4.5 keV Ti Kα x-rays were unattenuated by the Cu foil. The transmission of 8.0 keV photons through a 2, 5, and 10 μm thick titanium foil is 83%, 63%, and 40%, respectively. The Kα emission of Ti and Cu reflected by the spherically bent crystals was imaged on an image plate (IP) detector (IP type: BAS-SR). The reproducibility of the Leopard laser was monitored by measuring the escaping electrons with a magnet based electron spectrometer.³⁷ The slope temperature of the measured escaped electrons is sensitive to the generation of the fast electrons. A slope of 0.8 ± 0.1 MeV was inferred for all target shots considered here. The x-ray spectra for 4-6 and 7-11 keV ranges including Ti and Cu Kα line emission were measured with two x-ray spectrometers.³⁸ A discussion on the total amount of the measured Kα yields is omitted because the surface area of the foils, which is proportional to the total yield at a constant thickness, was not well controlled. We have not considered the intensity of the reflection just yet. Quantitative evaluation of the yields of the two sources requires separate investigations including characterization of fast electrons.

Figure 3 shows the measured monochromatic x-ray images of the foils. The laser was focused at the area where two foils were layered. The laser-produced fast electrons generated Kα spot-like emission in both foils. The high energy MeV electrons propagate through the foil and are trapped around the foils by an electric sheath, inducing the Kα fluorescence from the foils. The different magnifications of the imagers with 5 for the Cu imager and 10 for the Ti imager produce a smaller Cu foil image than the Ti foil on the IP even though the actual Cu foil was larger as shown in Fig. 2(a). The emission from the Cu Kα images clearly shows the attenuation of the 8.0 keV x-rays by the Ti foil glued on the Cu foils. The attenuation of the Cu x-ray intensity approximately corresponds to the Ti foil thickness when comparing the Cu Kα signals from the bare Cu surface and through the Ti layer (i.e., 83% and 63% transmission at 8.05 keV through 2 and 5 μm thick Ti foils). Figure 3(b) shows Kα images of 2 μm Ti and 10 μm Cu foils. The thinner Ti foil produced less Kα emission, resulting in a faint Ti Kα image compared to the 5 μm Ti foil shown in Fig. 3(a). The spatial resolution of the imagers is evaluated as follows. Edge line profiles (lineouts) of the Ti and Cu foils shown in Fig. 3(a) were taken. The sharpness of the edge profiles was fit with a convolved step function using a Gaussian function for the Ti and Cu lineouts. As shown in Fig. 4, the spatial resolution is estimated from the FWHM of the derivative of the smoothed step function to be 27 ± 4 μm and 23 ± 4 μm for the Ti and Cu crystal imagers, respectively. Similar spatial resolutions were obtained from the images in Fig. 3(b). The slightly better resolution of the Cu imager than that of the Ti imager could be attributed to the use of the 10 mm diameter aperture in the Cu imager.

The same two-crystal imaging system can be used for x-ray backlighting by changing the x-ray source foil position and defocusing the laser beam to produce a uniform backlighter source. In recently published experiments, a short-pulse beam defocused to a ∼350 μm spot size creates a spatially uniform Kα backlighter.^14,15,29 Figure 5 depicts an experimental design of a crystal backlighting imaging setup for a dense plasma. The configuration of the crystal imagers is identical to the one for the x-ray emission imaging shown before. Here, the backlighter target is positioned at 2 mm from the TCC toward the detector. The dense plasma is assumed to be a deuterated carbon (CD) sphere having a Gaussian density profile with the FWHM of 100 μm. The peak values of the density profiles were 1, 13.5, and 74.5 g/cm³, corresponding to the areal densities of 5, 70, and 400 mg/cm². The motivation for using the Gaussian density profile and the range of the peak core densities is based on measurements of an imploded cone-in-shell fast-ignition target reported by Theobald et al.¹⁴ The plasma profile and the imager configuration were taken into account for calculating synthetic radiograph images at 4.510 and 8.048 keV with a radiation transport atomic physics code Spect3D.³⁹ The calculated radiograph images were normalized by incident backlighter intensity to obtain the transmission images. Figure 6 shows the results of the calculated transmission images and line profiles of the transmission at the center of the plasma. The spatial scales of the images are corrected to represent the transmission images at the TCC plane. The plasma with 5 and 70 mg/cm² areal densities transmits 80% and 5% of the 4.5 keV Ti Kα x-rays, respectively. For the higher density plasma with ρR of 400 mg/cm², the Ti Kα x-rays are completely attenuated, but the 8.0 keV photons are transmitted at 5%. The calculated transmission range for the 8.0 keV x-ray is consistent with measurements of an imploded fast-ignition target with the density of ∼70 g/cm³ and the areal density of ∼300 mg/cm² at the transmission of 22% on OMEGA.¹⁴ Assuming that the measureable transmission is in the range of 5%–80%, the ranges of areal densities to be inferred are 5–70 and 20–400 mg/cm² with the Ti and Cu Kα x-rays. The additional higher energy probe (i.e., Cu Kα) extends the diagnostic sensitivity from 70 to 400 mg/cm², increasing the dynamic range to 80 instead of ∼14 with only Ti Kα x-rays.

The two-crystal imager is primarily designed for simultaneous two-color monochromatic x-ray imaging with a single short-pulse laser. Alternative uses of the diagnostic and generation of multi-color x-ray sources are discussed here. As described in Sec. IV B, two-color x-ray backlighting increases the areal density sensitivity. The broad ρR sensitivity of the diagnostic could be useful for backlighting of a thin plastic shell implosion, where the imploding shell has a few times solid density by shock compression and a core formed by the collapsing shell is much denser than the initial shell density. X-ray images during these phases can be obtained on one target shot by using two separate short-pulse beams firing in each phase or on two target shot by delaying the backlighter timing with respect to the drive. Multiple short-pulse beams are available at OMEGA EP (2 beams), LFEX (4 beams), Orion (2 beams), and NIF ARC (8 beams) for time-gated x-ray source generation. In the latter case, the Ti channel is used to record the in-flight shell density on one shot while the Cu channel for the stagnation on another shot. Since two x-ray channels are available, no diagnostic replacement or alignment is necessary between the shots, which substantially reduces the diagnostics preparation time. This two x-ray channel capability is also useful when measuring an implosion core having increasing areal densities during the compression, for example, from 5 to ∼100 mg/cm² in the overlapping range between the Ti and Cu Kα probes. Another use of the two-crystal imager is to use one channel for backlighting and the other for self-emission imaging.

Hard x-ray sources above 10 keV using high-intensity short-pulse lasers were investigated as a new x-ray source.⁴⁰ For spherical crystal imaging, the backlighter energies are limited by reflectivity of crystals. Numerous combinations of laser-produced backlighter x-rays and curved crystals were studied for photon energies between 1 and 25 keV photons.⁴¹ Different cold Kα x-rays can be readily produced by changing the target material. A large difference of the target atomic numbers in a two-layered target is desired in order for the higher energy backlighter x-ray not to be attenuated by the low-Z foil. Multi-color x-ray sources (above 25 keV) produced by a single short-pulse laser may be used for point-projection or line-projection backlighting. The conversion efficiency from the laser to x-rays has been reported to be on the order of 10⁻⁵ ∼ 10⁻⁴ in the photon energies between 20 and 80 keV.⁴² 

According to a Particle-in-cell (PIC) simulation, the optimum short-pulse laser intensity desired for the production of cold Kα emission is on the order of 10¹⁸ W/cm², producing hundreds of keV electrons.⁴³ Additionally, no high laser contrast prior to the main pulse is required for the Kα production. With a high-energy (>kJ), multi-picosecond short-pulse laser, an x-ray source on the order of tens of picoseconds can be produced. Time-resolved x-ray measurements on a multi-picosecond time scale could be possible with such a long duration x-ray source and ultrafast x-ray cameras.^44–46 

The demonstration of simultaneous two-color monochromatic Kα crystal imaging using a single short-pulse laser is presented. 4.5 keV Ti Kα and 8.0 keV Cu Kα x-rays were produced by shining the 10 J, 0.35 ps Leopard short-pulse laser on a Ti–Cu layered target. The Kα emission from both foils was imaged with two separate spherically curved crystals on a single image plate detector, which demonstrated the production of x-rays with two different photon energies with a single short-pulse laser and simultaneous x-ray imaging. A design of the two-color imaging diagnostic applied for backlighting of a high density plasma shows the ρR range to be probed from 5 to 400 mg/cm² assuming a detectable transmission between 5% and 80%. The dynamic range of the two-color backlighting is ∼80 and has a 5 times broader range than that with only Ti Kα backlighter. Applications of the imaging diagnostic with multiple short-pulse beams and a long x-ray pulse duration (>10 ps) with electronic detectors are discussed for time-resolved measurements. Since numerous combinations of a short-pulse laser-produced x-ray and a crystal matching to its photon energy are available, the concept of the two-color monochromatic x-ray imaging with a single short-pulse laser can be widely applied to self-emission imaging and/or x-ray backlighting experiments for high energy density laboratory science.

The authors would like to acknowledge Dr. P. Wiewior and O. Chalyy for their support of the Leopard laser operations and A. Astanovitskiy, O. Dmitriev, V. Nalajala, A. Covington, and the NTF management for supporting the experiment. H.S. was supported by the UNR Office of the Provost (start-up funding). This collaborative work was partially supported under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract Nos. DE-AC52-07NA27344, DE-FG-02-05ER54834 (ACE), and DE-NA0002075 (NTF).