During the past few years, the Orion high-resolution x-ray spectrometers have been successful tools for measuring x-ray spectra from plasmas generated in the Orion laser facility. Duplicate spectrometers also operate successfully at the Livermore EBIT-I and SuperEBIT electron beam ion traps for measuring x-ray polarization. We have recently implemented very high-quality, optically bonded, spherically bent quartz crystals to remove the structure in the x-ray image that had been observed in earlier measurements. The structure had been caused by focusing defects and limited the accuracy of our measurements. We present before and after images that show a drastic improvement. We, furthermore, have implemented a spherically bent potassium acid phthalate (KAP) crystal on one of our spectrometers. The KAP crystal was prepared in a similar fashion, and we present measurements of the N Ly-β and Ne Lyβ lines taken in first- and second-order reflections at 600 and 1200 eV, respectively. These measurements confirm that KAP crystals can be produced at a quality suitable for extending the spectral coverage to wavelengths longer than those accessible by different quartz crystals, especially those that cover the astrophysically important lines of iron.

In recent years, an increasing number of focusing crystal spectrometers have been implemented on various high-temperature plasma facilities that utilized spherically bent crystals with a relatively large collection area. Large crystals enable the collection of more photons, which makes it possible to situate spectrometers farther away from a noise-generating source, such as on the outside of the vacuum chamber of a high-intensity short-pulse laser,1,2 to obtain increased time resolution, for example, on tokamaks and related magnetically confined plasma machines,3–7 or to perform novel measurements on low-intensity x-ray sources, such as electron beam ion traps.8 The availability of large-area spherically bent crystals that are free of focusing defects is clearly crucial to the successful implementation of such high-resolution spherical crystal spectrometers, and several studies of the quality of the crystal bent have recently been reported.9,10

In the following, we report on using improved-quality spherically bent quartz crystals at the Orion laser facility at Aldermaston in the United Kingdom11 as well as the first spherically bent potassium acid phthalate (KAP) crystals at the Livermore EBIT-I electron beam ion trap12 facility. The new quartz crystals eliminate most of the non-uniformities noted in the reflection of the quartz crystals employed earlier in the ORION high-resolution x-ray (OHREX) spectrometer, which we had noted as a limiting factor in our line profile and plasma line shift measurements.16 The EBIT-I measurements with the new KAP crystal were carried out with the EBIT high-resolution x-ray (EBHIX) spectrometer,8 which is in design nearly identical to OHREX and, thus, serves as a testbed for crystals used subsequently in the Orion laser facility.13–15 The measurements confirm that spherically bent KAP crystals can be produced at a quality suitable for extending the spectral coverage to wavelengths longer than those accessible by different quartz crystals, especially those that cover the astrophysically important L-shell lines of iron.

A detailed description of the OHREX and EBHIX spectrometers is given by Beiersdorfer et al.1,8 The instruments are designed so that the spectral (meridional) focus and the spatially imaging (sagittal) focus of a given crystal coincide on the detector. This requirement concentrates the x-rays onto a small detector area and, thus, maximizes the signal-to-noise ratio. As mentioned above, crystals with a large collection area further improve photon collection, and the instruments are designed to employ crystals that are about 4 × 6 cm2 in size. Furthermore, the spectrometers were designed to be located outside the 4 m-diameter Orion target chamber. To achieve this, the crystals are bent to a nominal 67.2 cm radius of curvature and are set to a nominal Bragg angle of 51.3°.1 

The choice of crystal material and cut determines which range of x-ray energies can be observed with the spectrometer. Because of availability, most of our measurements have been performed with quartz crystals, in particular, quartz (101̄0), quartz (111̄0), quartz (112̄0), and quartz (213̄1).1,2,8,13,16–18 However, we have also used Ge and HAPG crystals.8,14,15 We note that none of these crystals has a lattice spacing 2d above 10 Å. This has so far precluded measurements in the ultra-soft x-ray region, especially of the astrophysically important neon-like Fe16+ spectrum19–22 with these instruments.

Unless the instruments are used in imaging mode, where high spatial resolution is a necessity, it is not necessary to set up the spectrometer in perfect focus. The reason is that the size of the laser-produced plasma in the Orion is typically not much larger than 10–100 μm, and diffracted photons from such a small x-ray emitting region remain in spectral focus even if the detector is not placed at the nominal focus where spectral and spatial foci coincide. This means that the placement of the detector can be deliberately set away from the best spatial focus in order to broaden the spatial width of the recorded spectrum. This allows us to examine the quality of the reflected image, as we show below.

Upon implementation of a charge coupled device (CCD) camera on the OHREX-1 spectrometer in the Orion, we noted that the crystal reflection was not uniform but formed a sort of netted image.16 This was attributed to local focusing defects spread across the crystal. We, therefore, decided to procure and implement a new quartz crystal from Inrad Optics, which had also supplied the high-quality spherically bent Ge crystals used on the EBIT-I device15,16 but not the quartz crystals used before.

For the present experiments, we have operated the OHREX-1 spectrometer concurrently with both the “old” and the “new” quartz (112̄0) crystals. A typical image of the reflections from the two crystals is shown in Fig. 1. We note that the image formed by the new crystal is almost twice as wide because the crystal was mounted slightly more out of best spatial focus.

FIG. 1.

Images recorded with the CCD camera on the OHREX-1 spectrometer. The images were produced by irradiating a 3 μm thick parylene dichloride (PyD) foil target with a single, 177 J, 0.5 ns, 3 − ω, square beam during Orion shot no. 10144. The laser spot diameter was about 300 μm. Heβ denotes the 1s3p → 1s2 transition in Cl15+, while A and B denote lithium-like Cl14+ satellite lines.

FIG. 1.

Images recorded with the CCD camera on the OHREX-1 spectrometer. The images were produced by irradiating a 3 μm thick parylene dichloride (PyD) foil target with a single, 177 J, 0.5 ns, 3 − ω, square beam during Orion shot no. 10144. The laser spot diameter was about 300 μm. Heβ denotes the 1s3p → 1s2 transition in Cl15+, while A and B denote lithium-like Cl14+ satellite lines.

Close modal

The crystals were both set to observe the 1s3p → 1s2 Heβ emission of helium-like Cl15+, which forms the brightest feature in each image. Less intense features are formed by innershell and dielectronic satellite lines from lithium-like Cl14+, two of which are labeled A and B Fig. 2. A spectral lineout generated by integrating the emission from each crystal over the spatial direction is shown in Fig. 2. A detailed discussion of the Heβ spectrum, including the associated satellite lines, was reported earlier.23 

FIG. 2.

Spectral lineouts from the images produced by the “old” and “new” quartz crystals in Fig. 1. The lineouts are generated by integrating over the full spatial extent of the image produced by each crystal. The spectral features are labeled in the same notation as that used in Fig. 1. The inset shows the residuals when fitting the Heβ peaks.

FIG. 2.

Spectral lineouts from the images produced by the “old” and “new” quartz crystals in Fig. 1. The lineouts are generated by integrating over the full spatial extent of the image produced by each crystal. The spectral features are labeled in the same notation as that used in Fig. 1. The inset shows the residuals when fitting the Heβ peaks.

Close modal

The structure in the reflection formed by the old crystal is readily apparent in Fig. 1. There are bright lines that enclose dark areas, forming a netted pattern. This netting seems to be caused by nonuniform x-ray reflection across the crystal surface. The crystal focusses x-rays better in some regions (bright areas) than in other regions (dark areas). We, thus, assume that the crystal surface locally deviates from a uniform curvature.

By contrast, the new crystal produces an overall smooth image. A few striations can be noted that are situated mostly on the right side of the image. However, these are minor compared to the features seen in the image produced by the old crystal.

We can quantify the brightness variations caused by nonuniform reflections by plotting lineouts along the spatial direction, i.e., perpendicular to the spectral direction. In Fig. 3, we show such a lineout across the weak satellite feature labeled A in Figs. 1 and 2. The average intensity variation is about 8% in the new crystal and about 70% in the old crystal. In other words, the variations associated with the new crystal are almost an order of magnitude smaller.

FIG. 3.

Spatial lineouts of feature A from the images produced by the “old” and “new” quartz crystals in Fig. 1.

FIG. 3.

Spatial lineouts of feature A from the images produced by the “old” and “new” quartz crystals in Fig. 1.

Close modal

We present a lineout across the bright Heβ peak in Fig. 4. Similarly, the variation seen in the lineout from the new crystal is greatly reduced compared to the variation seen in the lineout from the old crystal. However, on first glance, the variation appears to be less than that shown in Fig. 3. The reason is that the bright areas concentrate so many x-rays that they locally saturate the CCD camera, which limits the height of the apparent peaks seen in Fig. 4. This saturation explains why the intensity of the Heβ peak recorded with the old crystal and shown in Fig. 2 is lower than that recorded with the new crystal. By contrast, however, the relative intensities of the satellite lines are commensurate for both crystals, as the weaker lines are not subject to saturation.

FIG. 4.

Spatial lineouts of the Heβ feature from the images produced by the “old” and “new” quartz crystals in Fig. 1.

FIG. 4.

Spatial lineouts of the Heβ feature from the images produced by the “old” and “new” quartz crystals in Fig. 1.

Close modal

Saturation was only observed on long-pulse, foil-target shots, which generate intense x-ray emission. In this case, the use of filters may be necessary, especially if the camera is brought into full spatial focus.

Integration over the spatial dimension largely evens out the intensity variations of the crystal reflections, as can be seen from the spectral lineout presented in Fig. 2. Some smaller variations, however, may persist. This is noted when fitting the spectral features and plotting the unfitted residuals. These residuals are typically twice as large for the spectral features recorded with the old crystal as those recorded with the new crystal; they are even larger for the Heβ peaks, as illustrated in the inset in Fig. 2.

We, furthermore, have implemented a spherically bent potassium acid phthalate (KAP) crystal on one of our spectrometers. The KAP crystal was prepared in a similar fashion to the quartz crystals, and we present measurements of the N and Ne Lyβ lines, which were taken in first- and second-order reflections at 592.9 and 1210.9 eV, respectively. These measurements were carried out at the EBIT-I electron beam ion trap using the EBHIX spectrometer with a charge coupled device (CCD) detector.

In an EBIT, a quasi-monoenergetic electron beam interacts with trapped ions, leading to the emission of x rays. The ions are confined axially in a 2 cm-long trap provided by a set of three electrodes and radially by the space charge potential of the electron beam. A 3 T magnetic field compresses the beam of EBIT-I to a diameter of 50–70 μm.24–26 These properties make EBIT a line source that acts like an entrance slit for diffractive spectrometers. However, due to the imaging and focusing properties of EBHIX, the spectrometer can be operated with the dispersion plane either perpendicular or parallel to the beam axis.16 Here, the perpendicular orientation was used, where the narrow electron beam width is focused in the spectral direction, making the spectral resolution largely independent of the exact focal position of the detector. EBIT operates in the coronal density limit, where, unlike for laser-produced plasmas, Stark broadening is not an issue. The only relevant broadening is Doppler broadening due to the temperature of the trapped ions.

With the EBIT, we are able to study x-ray emission one element at a time by choice of injection material and selectively breed desired charge states. The first- and the second-order reflections of the KAP crystal were, thus, examined individually by injecting N and Ne into the trap in separate measurements and integrating over five and ten 60-min exposures, respectively. The crystal and CCD positions remained fixed for both measurements. In Fig. 5, we present the resulting background-subtracted, co-added CCD images of the N and Ne Lyβ lines. The vertical extent of the spectral lines represents a demagnified image of the ions within the electron beam diameter along the length of the trap and is not indicative of the focusing properties of the crystal.

FIG. 5.

Unfiltered, but background-subtracted co-added images of the KAP measurements at the EBIT in the first (top) and the second (bottom) order.

FIG. 5.

Unfiltered, but background-subtracted co-added images of the KAP measurements at the EBIT in the first (top) and the second (bottom) order.

Close modal

Figure 6 shows the lineouts for the first-order N Lyβ and second-order Ne Lyβ spectra in comparison. The spectra were extracted from the individual CCD images using single-photon counting. Consistent with expectation,27 the second-order spectrum displays much higher spectral resolution than the first-order spectrum. The spectra are calibrated in the Bragg angle using a linear scale between the two lines and taking into account higher order corrections to Bragg’s law due to small deviations of the index of refraction from unity,28 giving an effective lattice spacing of 2dn=2d(1(2d/n)2δ/λ2) for each order n with 2d=26.632Å and δ/λ2=2.25106Å2 for KAP.

FIG. 6.

Spectral lineouts of the H-like N and Ne Lyβ lines in the first and the second order, respectively, from the images produced from the KAP crystal at the EBIT.

FIG. 6.

Spectral lineouts of the H-like N and Ne Lyβ lines in the first and the second order, respectively, from the images produced from the KAP crystal at the EBIT.

Close modal

To characterize the crystal properties, we model both lines with Voigt profiles. Here, we attribute the Lorentzian component to the line spread function of the crystal reflection and possible charge bleeding of the CCD, as the natural line widths (N Lyβ: 0.26 meV; Ne Lyβ: 1.1 meV) are small compared to the observed Lorentzian widths, and the Gaussian component mainly to the thermal motion of the trapped ions. The results are summarized in Table I.

TABLE I.

Summary of KAP crystal parameters.

Spectral width (eV)
OrderGauss. comp.Lor. comp.VoigtE/ΔE
First 0.060.06+0.26 0.970.06+0.04 0.97 ± 0.07 611 ± 45 
Second 0.320.17+0.14 0.30 ± 0.12 0.52 ± 0.11 2350 ± 500 
Spectral width (eV)
OrderGauss. comp.Lor. comp.VoigtE/ΔE
First 0.060.06+0.26 0.970.06+0.04 0.97 ± 0.07 611 ± 45 
Second 0.320.17+0.14 0.30 ± 0.12 0.52 ± 0.11 2350 ± 500 

The line profile of the first-order spectrum of the N Lyβ line is strongly dominated by the Lorentzian component. While the best fit does allow for a small Gaussian contribution, its full-width-at-half-maximum (FWHM) is not constrained very well and consistent with zero at the 1-sigma confidence level. The upper limit of the Gaussian component suggests an ion temperature of below 790 eV, consistent with the typical range of temperatures of the ion cloud in EBITs.13,29–32 The FWHM of 0.97 eV of the Voigt profile corresponds to a resolving power of R = EE ∼ 611 and is limited by the crystal resolution. This is slightly lower than R ∼ 900 quoted in the Henke tables;33 however, some degradation compared to flat crystals is expected in bent crystals34 and can be significant, exceeding a factor of 2.35 

The higher-resolution second-order spectrum of the Ne Lyβ line shows more balanced contributions from the Voigt components. The Gaussian width translates to an ion temperature of ∼240 eV. The combined 0.52 eV FWHM of the Voigt profile corresponds to a resolving power of EE ∼ 2350. The second-order resolution is, thus, partially limited by the Doppler broadening of the trapped ions. Barnsley et al.36 observed R = 4400 for Ne Lyα at 1021.9 eV, i.e., a larger Bragg angle, in the second order with a lower radius of curvature of 107.3 cm and with a theoretical rocking curve calculation predicting 7000.37 

In principle, both N and Ne Lyβ lines are a blend of two transitions. However, for these low-Z ions, the energy splitting between Lyβ1 and Lyβ2 is very small (here, 0.03 and 0.14 eV38), i.e., much smaller than the measured spectral resolution. The line splitting, therefore, has no significant contribution to the observed line widths and does not affect the observed resolving power.

Like quartz crystals,39 KAP in the second order can achieve nominal resolving powers ≥10 000,27 while Ge can exceed 3000. Quartz crystals characterized with EBHIX at the EBIT have been observed with R ∼ 4000,14 while the newer Ge crystal from the same source as the present KAP crystal achieved R ∼ 2800.15 With R ∼ 2400, the second-order KAP crystal, thus, exhibits suitable quality to extend our spectral coverage to longer wavelengths than previously accessible through the quartz crystals.

This study was performed under the auspices of the U.S. DOE by LLNL under Contract No. DE-AC52-07NA27344 and supported, in part, by NASA’s APRA program. Orion experimental data are ©British Crown Owned Copyright 2018/AWE.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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