Open Access
Add to BibSonomy
Abstract
The quantitative measurement of plasma soft x-ray spectra is an important diagnostic problem in indirect-drive laser inertial confinement fusion (ICF). We designed, built, and tested a compact multichannel soft x-ray spectrometer with both spatial and temporal resolution capabilities for the detection of the spatiotemporal distribution of soft x-ray spectra. The spectrometer occupies a small solid angle, and the close measurement angle used for each channel enables the measurement of the angular distribution of emitting soft x-rays in ICF experiments. The spectrometer comprises pinhole, filter, and multilayer flat mirror arrays, and an x-ray streak camera. Its energy range is 0.1 – 3 keV. The dispersive elements of the spectrometer were calibrated at the Beijing Synchrotron Radiation Facility. The accuracy of the calibration was ≤ 5%, and the combined energy resolution (E/ΔE) of the calibrated dispersive elements of each channel was higher than 10. Finally, the instrument was tested at the Shenguang-III Laser Facility. The measurement results of x-ray radiation flux are agreed well with the experimental results of the M-band flat-response x-ray diode, demonstrating the feasibility of the proposed spectrometer configuration.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the study of indirect-drive inertial confinement fusion (ICF), the construction of a high-temperature, symmetric, near-Planckian soft x-ray radiation field is a crucial process to achieve fusion ignition [1]. The precise quantitative diagnosis of soft x-ray spectra of the field is the key to understanding the formation and properties of the radiation field, such as the radiation temperature, laser x-ray conversion efficiency, and total x-ray flux [2–4].
The conventional diagnostic instruments currently in use include multichannel Dante-type spectrometers, which are composed of filters working on K- or L-absorbing edges, x-ray mirrors, and x-ray diodes. These spectrometers offer a broad energy range and can absolutely measure x-ray spectra and thus are widely used for x-ray detection in large laser facilities, such as National Ignition Laser Facility and Omega Laser Facility [5,6]. However, those spectrometers lack spatial resolution and have poor temporal ($\sim$150 ps) resolution, and the characteristic of their dispersive elements result in the high-energy tail noise in the recorded signal. Besides, the inconsistency of observation angle of each channel of Dante-type spectrometers also cause the difficulties in measuring the angular distribution of x-rays.
Various x-ray spectrometers have been developed to solve these problems, such as crystal or grating spectrometers coupled with an x-ray streak or framing camera [7,8]. However, although these spectrometers eliminate high-energy tail noise and offer high-energy and temporal resolution, they still have shortcomings. For examples, the bulky size of crystal spectrometers makes them unsuitable for the measurement of the angular distribution of x-rays, and the small lattice constant of the crystal makes it difficult to apply to the soft x-ray range. In addition, grating spectrometers are difficult to calibrate and coupled with streak camera due to their uneven dispersion. For the other dispersive elements like x-ray zone plate, because the ICF experimental target is a mm-scale extended x-ray source, it is difficult to use as a dispersive element in a spectrometer. To overcome these difficulties and develop a spectrometer with both temporal and spatial resolution, we introduced multilayer mirror (MLM) arrays as dispersive elements. Compared with the K–L-edged filter, the MLM arrays have higher energy resolution (E/$\Delta$E $\approx$ 10-50) and can effectively minimize high-energy tail noise. Compared to crystal or grating spectrometers, the optical properties of MLM arrays can be tuned artificially for x-rays of different energies, and their response to specific x-rays can be precisely calibrated. At the same time, the ease of fabrication and assembly of multilayer flat mirrors simplifies a compact multichannel design, which helps to achieve a consistent field of view (FOV) and observation angle for each channel and facilitates coupling with an x-ray streak or framing camera.
In view of these points, we propose a compact multichannel soft x-ray spectrometer (CSXS) with both spatial and temporal resolution capabilities in the measurement range of 0.1–3 keV. The proposed instrument uses a pinhole array (PHA) as the imaging and collimation element, calibrated filter and MLM arrays as the absorbtive and dispersive elements, and an x-ray streak camera as the detector. The optical design of the spectrometer was explained in detail. Simulations and mathematical analyses were performed to verify the feasibility of the design. The calibration methods and results for the dispersive components were demonstrated. Finally, the instrument was tested in both the laboratory and the Shenguang-III Laser Facility. The experimental results demonstrate that the spectrometer can measure soft x-ray energy spectra with both spatial and temporal resolutions, and the agreement between the experimental results of CSXS and the M-band flat-response x-ray diode (MXRD) verifies the feasibility of the proposed spectrometer configuration.
2. System design
2.1 Characteristics of laser plasma x-rays and key points of measurement
During the indirect-drive ICF experiment, the generation of the x-ray radiation field in the hohlraum involves various physical processes, including the deposition of laser energy by laser plasma interaction, the generation of x-rays by atomic dynamics, and the transport, absorption, and re-emission of x-rays.
The primary x-rays originate from atomic dynamics, and more than 95$\%$ of the total energy is the line emission generated by the bound–bound transition. However, only 10-20$\%$ of the total energy of x-rays can be emitted directly, this part of x-rays results from the coronal plasma, which has a high electron temperature and a low electron density. For the Au hohlraum commonly used in the laser ICF, the typical spectral lines include the 3d – 5f, 3d – 4f, and 3d – 4p lines of highly ionized Au ions. These spectral lines merge into indistinguishable bands since many transition lines between the two electron configurations are close and because of various broadening effects. This part of x-ray is also known as M-band x-ray in the field of ICF. For simplicity, we approximated this part of x-ray spectra ($L_{AuM}$) as multiple Gaussian peaks with certain broadening.
The rest of the primary x-rays are concentrated in the ablation region of the plasma. Because of the low electron temperature and high electron density in this region, x-rays are continuously absorbed and re-emitted; thus, the radiation field spreads in space and becomes isotropic. In this process, the state of the plasma satisfies local thermal equilibrium, and this part of the x-ray spectra ($P$) is regarded as the Planckian spectra. Therefore, the total soft x-ray spectra to be measured at time $t$ can be expressed as
In the indirect-drive ICF study, the x-rays close to Planckian spectra ($P$) with isotropic properties played a primary role in the uniform compression of the target. According to previous measurements conducted at the Shenguang-III Laser Facility [9], in this region, x-rays are concentrated at the energy range of 0.1–1.5 keV. In this study, we adjusted the measurement region of the CSXS system to be close to the peak energy position to obtain the key parameters and details of the soft x-ray spectrum. On the other hand, the set of line spectra of x-rays cannot be ignored either. Considering the generation mechanism, in this region, x-rays have a higher energy and earlier generation time than those close to Planckian spectra, causing a preheating effect on the target and disrupting the expected adiabatic isentropic compression. Besides, these x-rays have nonuniform distribution in the hohlraum space, exacerbating the Rayleigh–Taylor instability [10] of the target. Therefore, The CSXS system should have high temporal resolution to analyze the preheating effects and favorable spatial resolution to detect the nonuniform distribution of this part of x-rays in the hohlraum space. In addition, to reflect the characteristics of the Au M-band spectra ($L_{AuM}$), the central energy region of the representative line spectrum should be measured first, such as the 3d – 4p ($\sim$2090 eV), 3d – 4f ($\sim$2550 eV), and 3d – 5f ($\sim$3010 eV) lines of highly ionized Au ions.
2.2 Optical design
The basic structure and measurement method of the CSXS system are shown in Fig. 1(a). The PHA was used as the imaging element, endowing the spectrometer with a spatial resolution of ($\sim$100 $\mathrm{\mu}$m for the object surface) to distinguish spectra from different emission regions. The filter arrays were used to shield the scattered laser and the low-energy x-rays generated by the Bremsstrahlung effect. The MLM arrays were used as the main dispersive elements. The image of an individual channel is shown in Fig. 1(b). The images of all channels are arranged in a straight line on the slit of the x-ray stream camera (XSC). The XSC with the flat-response cathode was used as the detector. [11]. The XSC record the results by an optic CCD camera (2048 $\times$ 2048 pixels) with a full-screen time window of 5 ns. The temporal resolution of XSC was $\sim$20 ps. Therefore, spectral, temporal, and spatial information could be obtained from each channel of the CSXS system, as shown in Fig. 1(c).
Fig. 1. (a) Schematic design of the compact multichannel soft x-ray spectrometer; (b) image of laser entrance hole (LEH) before shooting into the streak camera, where the white dashed circle indicates the clear aperture of the LEH; (c) signal recorded by one of the channels of the spectrometer.
According to the characteristics of the energy spectra to be measured, the energy range of the spectrometer was divided into ten channels with energies of 0.27, 0.38, 0.51, 0.75, 0.84, 1.14, 1.55, 2.09, 2.55, and 3.01 keV. The channels ($\leq$ 1.55 keV) of the CSXS system are primarily used to diagnose Planckian spectra which is concentrated at 0.1 – 1.5 KeV. The channels ($\geq$ 2.09 keV) of the CSXS system are primarily used to diagnose the Au M-band spectra, especially the three characteristic transitions (3d – 4p, 3d – 4f, 3d – 5f) of Au ions. Consequently, we divided them into two array channels. Each array channel consisted of five channels and shared the same grazing incidence angle. The central grazing incidence angles were 3.5 $^{\circ }$ and 10 $^ {\circ }$, respectively, for the array channels of high ($\geq$ 1.14 keV) and low ($\leq$ 0.84 keV) energy ranges. The schematic design of the beam path is shown in Fig. 2.
The distance of the PHA from the target was 300 mm, and the distance from the PHA to the cathode slit of the XSC was 930 mm, resulting in 3.1$\times$ magnification. The effective photocathode length of the XSC used in our design was 30 mm, and the typical light source size was $\sim$1.5 mm (LEH). To prevent the overlapping of the image spots of each channel on the cathode slit, each channel was arranged to occupy at least a 4.65 mm region. Limited by the length of the cathode, the two array channels were not able to work simultaneously. In the case, they used independently, and each channel occupied a cathode region of 6 mm, which determined the pinhole spacing, $d_1$, in the PHA.
The pinhole diameter is the main factor that determines the light collection efficiency and spatial resolution. To ensure that the system efficiency were in the same order of magnitude and the spatial resolution was higher than 100 $\mathrm{\mu}$m, the pinhole diameter was carefully designed. The system efficiency can be defined as the ratio of the number of photons with uniform distribution around the center energy point of each channel within a fixed solid angle and the number of photons in the same limits which can be detected. A comparison of system efficiency calculated by the designed parameters is given in Table 1. The theoretical spatial resolution of each channel was calculated too, and also shown in Table 1.
Table 1. Main parameters related to system efficiency of CSXS
Two filter arrays were introduced behind the PHA. Each filter array consisted of three filters, two of which were responsible for the two channels near the working energy range. The sizes of the two types of filters were 7 mm $\times$ 7 mm and 3.5 mm $\times$ 7 mm. The specific material and calibrated thickness of the filter of each channel are presented in Table 1.
The MLM arrays were arranged in a 350 mm $\times$ 200 mm mirror pack. To leave enough space, the MLM arrays were installed at positions $s_2$ = 900 mm and $s_3$ = 1050 mm from the object point, respectively. The exit angles of the object point and the array pinhole were 2.82 $^{\circ }$ and 1.93$^{\circ }$. The MLM array was composed of five multilayer mirrors. The mirror widths of two MLM arrays were 4.35 mm and 5.17 mm, determined by a simple triangle-like geometric relationship. The mirror lengths of the MLM arrays must satisfy the following equation to receive the full beam size:
where $\phi$ is the diameter of the object surface, $s$ is the axial distance between the center of the array mirror and the object surface, $p$ is the object distance, and $\alpha$ is the center grazing incidence angle. The target of the system is usually the LEH of the hohlraum, and its diameter is $\sim$ 1.5 mm. By substituting the rest of the parameters into Eq. (2), the minimum mirror lengths of the two MLM arrays were found to be 21.6 mm and 49.1 mm. Considering the adjustment and aiming errors, the mirror lengths of the MLM arrays were set to 30 mm and 55 mm.The working surfaces of MLMs for all channels were coated with dual-period x-ray multilayers. The material pair of multilayer were selected based on the corresponding energy points of each channel as shown in Table 1. Since the energy point and the central grazing incidence angle were determined, the multilayer mirror design considered the reflectivity and energy resolution. Through iterative optimization by IMD code [12], the multilayer mirror of each channel had peak reflectivity better than 0.19. The combined energy resolution of each channel is greater than 10. The designed parameters of the multilayer film for each channel are shown in Table 1.
2.3 Simulation
To ensure that the spectrometer can resolve different regions of the x-ray energy spectrum, a single channel of the spectrometer must possess a flat-response of the FOV, and different channels of the spectrometer must share the same FOV. These two characteristics of the spectrometer were analyzed by means of ray tracing simulation.
For a single channel, the difference in the FOV response of the dispersive system is due to the difference in the grazing incidence angle of MLMs. Through ray tracing simulations, the response of the LEH image on the slit of the XSC was analyzed. The source spectra of the simulation are the x-rays with a uniform energy intensity distribution and a certain bandwidth (FWHM of channel response) centered on the designed energy point. The simulation results of channel 4 (in the low-energy array channel) and channel 9 (in the high-energy array channel) are shown in Fig. 3. The coordinate system of Fig. 3 is the same as that of Fig. 2. These two channels have the largest FOV response difference in their arrays. For the low-energy array channel, due to the relatively large central grazing incidence angle (10 $^{\circ }$), response differences across the full FOV were less affected by angular changes, while high-energy channels were greatly affected, as shown in Fig. 3(a),(c). These results also indicate that when using this spectrometer as a soft x-ray imager coupled with an x-ray imaging plate or CCD camera, the FOV response needs to be calibrated.
Fig. 3. Energy response simulation for the image of the LEH ($\Phi$1.5 mm) of dispersive systems. (a) and (c) simulation results of channel 4 (840 eV) and channel 9 (3010 eV), where the black square corresponds to the part received by the XSC; (b) and (d) are the simulation result of XSC receiving part of channel 4 and channel 9
However, after restricting the incident beam aperture through a narrow cathode slit of the XSC (0.2 mm), the situation was effectively improved. The low-energy array channel had the great flat-response properties, as shown in Fig. 3(b). Likewise, the high-energy channel has only differ by a maximum of 2.63$\%$, as shown in Fig. 3(d). Simulation data for all channels are listed in Table 2. Based on these results, the final response of the spectrometer for the XSC can be considered a flat-response.
Table 2. Response difference and FOV center shift of each channel
When examining the consistency of the FOVs of different channels, it is necessary to understand that the slit of the XSC acts as the field stop of the system. The difference in the imaging area intercepted by the slit of the streak camera depends on the relative position of the pinhole and the mirror in each channel. According to the measurement results of the microscope and autocollimator, the position accuracy of the PHA was higher than 10 $\mathrm{\mu}$m, and the angle difference between the different mirrors of the assembled MLM array was smaller than 0.003 $^\circ$. Based on these data, the FOV shifts of different channels were evaluated by ray tracing simulation. The maximum shifts in the FOV centers of the two array channels were 72.3 $\mathrm{\mu}$m and 70.6 $\mathrm{\mu}$m, respectively.
3. Calibration
3.1 Calibration device and method
In the experiment of the spectrometer test, the final data obtained were the signal counts on the x-ray streak camera. The relation between the signal counts of a certain channel $C_i$ and the soft x-ray spectra $S(E,t)$ to be measured can be expressed as
For the calibration of the streak camera, the flat-response streak camera was used in the experiment. we mainly refer to the experimental results in reference [11], which can be regarded as a constant in the energy range covered by the system.
Therefore, the calibration experiment was conducted to determine the efficiency of the MLMs and filters. A specific calibration system was developed, as shown in Fig. 4, to calibrate the filter array and the MLM array at the same time. The device was mounted on the 4B7B beamline [13] of the Beijing Synchrotron Radiation Facility, which can provide a soft x-ray beam with an energy resolution higher than 1000 and an adjustment energy range of 0.1–5 keV. The calibration device consisted of two vacuum chambers. To match the working vacuum of the 4B7B soft x-ray beamline ($\leq 10^{-4}$ pa), each vacuum chamber was independently equipped with a turbo pump.
The two slits behind the monochromatic system were used to collimate and limit the beam aperture. The distance between two slits was about 500 mm, and the slit width was variable from 1 to 3 mm, depending on the working size of the MLM. Two standard silicon photodiodes (AXUV-100, IRD) were used as detectors [14]. The signals were recorded by two weak current meter (6517A, Keithley). Both detectors were equipped with stepping motors for lifting and panning.
In the calibration of the filter arrays. Only the front detector was used. We moved filters in and out of the light path and measured the beam intensity in both states. The filter holder could hold five filters, indicating that the set of array filters can be calibrated at once.
The scintillator was placed at the end of the optical path to accurately measure the grazing incidence angle of MLMs with a mounting camera. The distance between the scintillator and the center of the sample rack was measured to be 146.75 mm. The angle measurement process is shown in Fig. 5. After calculation, the angle measurement accuracy of this method was found to be higher than 0.01 $^ {\circ }$.
In the calibration of the MLM arrays. Firstly, the filter and the detector must be moved out of the optical path, and the MLMs must be adjusted to the correct grazing incidence angle using the method described above. Consequently, the rear detector must be reset, and the front detector must be moved in and out of the optical path, respectively, to obtain the intensity of the beam before and after passing through the mirror.
3.2 Calibrated results and error analysis
The characteristics of the individual components of the spectrometer were calibrated. The filters is calibrated at the normal incidence angle, and the two MLM arrays are calibrated at the designed angle, 3.5 $^{\circ }$ and 10 $^{\circ }$ respectively. The response of the low-energy array channel is shown in Fig. 6. The theoretical data are calculated by IMD software [12]. The calibration results and the theoretical results showed a similar trend, proving the reliability of the calibration experiments. At the same time, some differences existed in the numerical values.
Fig. 6. Comparison of the theoretical and calibration values; (a) comtransmittance of combined filter (1, 2, and 3) shown in Table 1; (b) reflectivity of low-energy array MLMs at 10 $^\circ$ grazing angle;
In the calibration of the filters, the transmittances of the combined filters for most channels were in good agreement with the theoretical values. However, certain deviations existed. For example, for filter 2 of channels 3 and 4, as shown in Fig. 6(a), the deviation of theoretical transmittance can reach 5$\%$.
Comparing the theoretical and calibrated reflectivity of the MLMs, we found that the Full width at half height (FWHM) of the calibration curve was consistent with the theory. However, there was a certain shift in the energy points corresponding to the peak reflectivity for some channels, such as channels 1 and 5, as shown in Fig. 6(b). In addition, the calibrated reflectivity of all channels decreased, which is possibly due to the carbon deposition, the oxidation on the mirror surface or the increase in the surface roughness of the mirror. The transmittance of the combined filters and the reflectivity of the MLMs both showed errors deviating from the theoretical value, indicating the calibration experiments can greatly enhance the accuracy of system response.
The calibration error was analyzed. The primary factors include the signal-to-noise ratio of the detector ($\sim$ 100) and its dark current ($\sim$ 20 pA), and the secondary factor is the random flux error with the Keithley electrometer, which is simply the square root of the variance of the ten measurements at each spectral point. The electrometers were calibrated to 1.6$\%$ on the pA scale and 0.25$\%$ on the nA scale [14]. The magnitude of our measurement signal was usually on the nA scale, and these two points can be attributed to the systematic error. In addition, since two detectors were used for the reflectivity measurements of the MLMs, we compared the sensitivity of the front and rear detectors using the same beam at multiple energy points, and the deviation between them was found to be smaller than 2.2$\%$. Combined with the random errors of multiple measurements, the total error of filter calibration was less than 1.5$\%$, and the total error of MLM calibration was less than 3.2$\%$.
4. Testing
4.1 Experimental prototype
The spectrometer was designed to be fielded in the Diagnostic Instrument Manipulator (DIM) [15] of the Shenguang-III Laser Facility. DIM provides a vacuum diagnostic platform for the instrument to insert or retract chamber. To ensure stability and reliability in the working environment, an experimental prototype was prepared, as shown in Fig. 7.
Fig. 7. Mechanical structure of the compact multichannel spectrometer: (a) oblique view; (b) photograph
The boundary dimension of this spectrometer is 900 $\times$ 200 $\times$ 150 mm (excluding the target pointer). The overall structure is shown in Fig. 7. It includes a target pointer for indicating the object point, the PHA and the protection shield, the filter array and the support structure, the MLM array with a rotation stage, a monitoring camera, and an imaging plate in the mounting flange. Considering the possible damage to the equipment caused by high-velocity implosion debris and emitted high temperature plasma in process of the ICF experiment, A 5-mm thick Al shield with two slits was placed in front of the PHA to block the debris from the non-optical path direction. Moreover, the PHA and the array filter were designed to be easily replaced, and the corresponding spare parts were prepared before formal experiment. In addition, due to the high-vacuum requirements of DIM, all metal components in this spectrometer were cleaned of oil, and the adjustment frame and camera were suitable to work in vacuum.
Before the spectrometer could be equipped with a streak camera, the positions of the various parts of the device had to be calibrated. In the laboratory, the relative positions of spectrometer components were measured by a coordinate measuring instrument, and the error from the design value was less than 0.1$\%$. In addition, collimation experiments were performed using a laser coupled with a 50 $\mathrm{\mu}$m pinhole as the light source. The object pinhole (50 $\mathrm{\mu}$m pinhole) imaged in the image plate with annotated cathode slit locations. The relative position of the light spots and the annotated slit locations was iteratively adjusted. Through this collimation experiment, the centers of the image spots coincided with the centers of the annotated slit locations.
4.2 Validation of instrument performance
Before performing final experiments on Shenguang-III Laser Facility, it is necessary to evaluate the performance of the instrument in the laboratory. For the CSXS system, it needs to diagnose the spatiotemporal information of the soft x-ray of the laser plasma, so the temporal and spatial resolution are two indicators of particular concern.
The temporal resolution of the instrument is determined by the XSC. Therefore, the test experiment of the temporal resolution of the XSC was carried out to verify the temporal resolved performance of the instrument. The specific test method is shown in Fig. 8. The 263-nm UV laser with a laser pulse width of 8 ps was used as the light source. The digital delay pulse generator (DG645) is used to adjust the trigger time of the streak camera to receive the signal light. The adjustment mirrors are used to align the laser to the slit of XSC. An etalon consisting of two semi-transparent mirrors, the etalon can generate a series of pulse signals with decreasing amplitude and consistent time interval. the distance $d$ between the two parallel semi-transparent mirrors is 30 mm, the time interval can be calculated as 200 ps.
The experimental results are shown in Fig. 9. Since the pulse signal basically has no intensity in the range beyond 2 ns, Fig. 9(a) only captures the experimental image in the range of 2 ns. After data processing, the average value of FWHM of all signal pulses was calculated as 22.8 ps. According to the inherent 8 ps broadening of the laser pulse, the temporal resolution of system can be calculated as 21.4 ps. This experimental result demonstrates the temporal resolved performance of the instrument.
Fig. 9. Test results for temporal resolved performance of system (a) image; (b) Received sequence signal pulse
For the spatial resolution of the system, it is difficult to find a broad-spectra soft x-ray light source with sufficient brightness to test the instrument in the laboratory. However, because the imaging method of the instrument is pinhole imaging, the spatial resolution of this imaging method is highly related to the pinhole size, object distance and image distance for a single channel. We have strictly checked these parameters through high-precision microscopes and coordinate measuring instruments to ensure that the error of pinhole size is better than 2 $\mathrm{\mu}$m, and the error of distances is better than 0.05 mm. After calculation, these factors can result the maximum variation of 6.13 $\mathrm{\mu}$m in spatial resolution of channel 2, and the channel 2 has the worst theoretical resolution 103.2 $\mathrm{\mu}$m. In addition, we calibrate the spatial resolution of the XSC by using the projection imaging of the standard resolution plate on the streak camera. The experimental results are shown in Fig. 10. The structure of the 25 lp/mm pair can be clearly reflected on the XSC, which means that the XSC can have a spatial resolution better than 13 $\mathrm{\mu}$m relative to the object surface after removing the influence of the system magnification (3.1 $\times$). Combined with the previous calculation data, each channel of the spectrometer can still have a spatial resolution better than 105 $\mathrm{\mu}$m.
Fig. 10. Test results for spatial resolution of XSC (a) image of the resolution plate; (b) intensity profiles along the bule lines in (a)
4.3 Experimental arrangement
To test the basic performance of the spectrometer, a dedicated shot (20220114017) at the Shenguang-III Laser Facility was fielded. A gold column hohlraum with a diameter of 3mm and a length of 5.1 mm was used as the experimental target, and the diameter of LEH was 1.7 mm. The shot used a square 3-ns laser pulse with 16 inner beams and 16 outer beams, and the total laser energy was 126.5 kJ.
This spectrometer was installed on a DIM in the northern polar region ($\theta$ = 16 $^\circ$, $\phi$ = 90 $^ \circ$) as shown in Fig. 11. All channels of CSXS have close elevation angles relative to the target hohlraum. The difference in azimuth angles between different array channels is 3.2 $^\circ$. An XSC was mounted on the last adapter flange of the spectrometer, and the length of the cathode slit was 20 mm, which could cover only three channels at 3.1 $\times$ magnification. Limited by the number of shots and detector conditions, only channels 7, 8, and 9 were tested in this experiment, and a 0.2-mm tantalum sheet was used to shield the other array channels.
The MXRD is used to measure the absolute M-band x-ray flux [16]. Considering that channels 7, 8, and 9 (2090, 2550, and 3010 eV) can cover the main structure of the M-band spectra of Au, and the emission characteristics of the target in the azimuth direction tend to be isotropic. An MXRD was installed on a dim on the other side ($\theta$ = 16 $^\circ$, $\phi$ = 0 $^\circ$) to analyze the experimental performance of the spectrometer.
4.4 Experimental results
The direct measurement results of the XSC are shown in Fig. 12(a). The imaging results of the three channels in the XSC can be clearly seen from the photograph. With 3.1 $\times$ magnification, each channel occupied 5.3 mm of the cathode slit of the XSC, and the spacing between the center spots of each channel was 6 mm, consistent with the theoretical design.
Fig. 12. Experimental results recorded by the XSC (a) image (b) average counts of all regions over time (c) Signal counts versus distance at 2.3 ns
In the direction of the horizontal axis, the streak camera recorded the changes in the signals of different channels ranging 0–5 ns, as shown in Fig. 12(b). The results showed the temporal distribution characteristics of the x-ray field. It can be observed that channel 8 at the position of the Au 3d–4f spectral line ($\sim$2550 eV) had the largest intensity, consistent with theoretical expectations [17]. The signal counts of all channels had a plateau, which differed by less than or equal to 5$\%$. The start times of the plateau region were different for different channels but had comparable properties. The slowest decline was in the signal counts of channel 9 because of the influence of the Planck spectrum.
In addition, in the direction parallel to the slit, the experimental results showed the spatial distribution characteristics of the x-ray radiation field, as shown in Fig. 12(c). At 2.3 ns, the signals of all channels were divided into the coronal region and the ablation region in the Au plasma. It can be seen that the coronal region was the main producing region of the energy spectra of the Au M-band, and the Au M-band intensity of the coronal region in channel 8 accounted for the largest proportion, whereas the proportion in channel 9 was the smallest, which are consistent with the theory [17]. Moreover, the results revealed the inhomogeneity of the spatial distribution of the energy spectrum.
In terms of measurement spectrum, since the energy points of all test channels are in the Au M-band, the soft x-ray spectra to be measured can be regarded as a combination of multiple discrete Gaussian peaks. The response of each channel can also be regarded as a Gaussian peak due to the influence of the periodic multilayer. The signal counts of each channel can be regarded as the integral result of the multiplication of two Gaussian peaks. Combined with Eqs. (1) and (3), the corresponding spectrum of each time point $t$ can be obtained through the property of integral of the Gaussian function. Through this method, we can reconstruct the broadband spectra in the Au M-band with a small number of data points. This method is very convenient and efficient. In addition, it can also accurately reflect the spectral characteristics of Au M-band. The spectrum corresponding to 1.5 ns is shown in Fig. 13(a) as an example. A clear effect of Planck spectra can be seen at 2100 eV. The calculated x-ray radiation flux at each moment was obtained by integrating the unfolded x-ray spectra, as shown by the black line in Fig. 13(b), and the measurement result of the MXRD is shown by the red line. The peak intensity of the CSXS is low compared to the MXRD. This may be due to the lack of 3–4 keV spectral measurements. However, the calculated results agreed well with the measured results of the MXRD in terms of temporal characteristics.
Fig. 13. (a) Unfold spectra calculated by the experiment result at 1.5 ns (b) Measured x-ray flux with the MXRD and the CSXS, respectively
5. Conclusion
In this study, we proposed a compact soft x-ray spectrometer for simultaneous temporal, spatial, and spectral diagnosis of soft x-ray energy spectra of a hohlraum. MLMs were used as dispersive elements, which led to a highly efficient spectrometer and eliminated the high-energy noise. Pinholes and x-ray streak cameras were used as imaging components and detectors, endowing the spectrometer with both temporal and spatial resolution capabilities. Owing to the compact array design, each channel provided a consistent FOV and detection angle. The dispersive elements were calibrated using a synchrotron beamline, and a special calibration device was developed. This device can calibrate the filter and MLM arrays at the same time, improving the calibration efficiency. Finally, we tested the partial channels of the spectrometer at the Shenguang-III Laser Facility. The experimental results confirmed that the spectrometer can measure the spatiotemporal distribution of the soft x-ray spectra of a hohlraum. In addition, the x-ray radiation flux calculated from the measured signal of CSXS agreed well with the measurement results of MXRD, verifying the reliability of the spectrometer configuration.
The introduction of additional measurement channels with the development of dual-channel or long-slit streak cameras and the improvement of spectrometer configuration can further improve the measurement accuracy. Overall, the demonstrated measurement method and instrument are highly promising for soft x-ray energy measurements.
Funding
Ministry of Science and Technology of the People's Republic of China (2017YFA0403300); National Natural Science Foundation of China (12005157); National Natural Science Foundation of China (11905281).
Acknowledgments
The authors are grateful to the researchers and technicians of the China Academy of Engineering Physics and the operation group of BSRF for their suggestions and assistance in the experimental design and operation. The authors thank Y.G. Wu and Q.S. Huang for the fabrication of dispersive elements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the national ignition facility,” Phys. Plasmas 11(2), 339–491 (2004). [CrossRef]
2. S. Glenzer, B. MacGowan, N. Meezan, et al., “Demonstration of ignition radiation temperatures in indirect-drive inertial confinement fusion hohlraums,” Phys. Rev. Lett. 106(8), 085004 (2011). [CrossRef]
3. R. E. Olson, L. J. Suter, J. L. Kline, D. A. Callahan, M. D. Rosen, S. N. Dixit, O. L. Landen, N. B. Meezan, J. D. Moody, C. A. Thomas, A. Warrick, K. Widmann, E. A. Williams, and S. H. Glenzer, “X-ray conversion efficiency in vacuum hohlraum experiments at the national ignition facility,” Phys. Plasmas 19(5), 053301 (2012). [CrossRef]
4. H. F. Robey, T. S. Perry, H.-S. Park, P. Amendt, C. M. Sorce, S. M. Compton, K. M. Campbell, and J. P. Knauer, “Experimental measurement of au m-band flux in indirectly driven double-shell implosions,” Phys. Plasmas 12(7), 072701 (2005). [CrossRef]
5. E. L. Dewald, K. M. Campbell, R. E. Turner, J. P. Holder, O. L. Landen, S. H. Glenzer, R. L. Kauffman, L. J. Suter, M. Landon, M. Rhodes, and D. Lee, “Dante soft x-ray power diagnostic for national ignition facility,” Rev. Sci. Instrum. 75(10), 3759–3761 (2004). [CrossRef]
6. C. Sorce, J. Schein, F. Weber, K. Widmann, K. Campbell, E. Dewald, R. Turner, O. Landen, K. Jacoby, P. Torres, and D. Pellinen, “Soft x-ray power diagnostic improvements at the omega laser facility,” Rev. Sci. Instrum. 77(10), 10E518 (2006). [CrossRef]
7. M. May, R. Heeter, and J. Emig, “Convex crystal x-ray spectrometer for laser plasma experiments,” Rev. Sci. Instrum. 75(10), 3740–3742 (2004). [CrossRef]
8. N. M. Ceglio, R. L. Kauffman, A. M. Hawryluk, and H. Medecki, “Time-resolved x-ray transmission grating spectrometer for studying laser-produced plasmas,” Appl. Opt. 22(2), 318–327 (1983). [CrossRef]
9. S. Jiang, F. Wang, Y. Ding, S. Liu, J. Yang, S. Li, T. Huang, Z. Cao, Z. Yang, X. Hu, W. Miao, J. Zhang, Z. Wang, G. Yang, R. Yi, Q. Tang, L. Kuang, Z. Li, D. Yang, and B. Zhang, “Experimental progress of inertial confinement fusion based at the ShenGuang-III laser facility in china,” Nucl. Fusion 59(3), 032006 (2019). [CrossRef]
10. L. F. Wang, W. H. Ye, Z. M. Sheng, W.-S. Don, Y. J. Li, and X. T. He, “Preheating ablation effects on the rayleigh–taylor instability in the weakly nonlinear regime,” Phys. Plasmas 17(12), 122706 (2010). [CrossRef]
11. C. Wang, J. Li, X. Hu, Z. Hu, X. Zhu, B. Deng, T. Yi, Q. Fan, Z. Cao, S. Liu, S. Jiang, Y. Ding, C. Xie, and G. Jiang, “Realization of a flat-response photocathode for x-ray streak cameras,” Opt. Express 23(15), 19793–19798 (2015). [CrossRef]
12. D. L. Windt, “Imd—software for modeling the optical properties of multilayer films,” Comput. Phys. 12(4), 360–370 (1998). [CrossRef]
13. R. Yi, Y. Zhao, Q. Wang, L. Zheng, J. Yang, X. He, C. Li, S. Jiang, Y. Ding, and M. Cui, “Characteristic study and application of the soft x-ray beam line 4b7b on bsrf,” Acta Opt. Sin. 34(10), 1034002 (2014). [CrossRef]
14. K. M. Campbell, F. A. Weber, E. L. Dewald, S. H. Glenzer, O. L. Landen, R. E. Turner, and P. A. Waide, “Omega dante soft x-ray power diagnostic component calibration at the national synchrotron light source,” Rev. Sci. Instrum. 75(10), 3768–3771 (2004). [CrossRef]
15. Y. Zhenghua, L. Shenye, C. Zhurong, J. Shao’en, D. Yongkun, H. Junhua, Z. Min, W. Mingzhi, W. Wei, and Y. Zhiwen, “Development of shenguang iii facility general diagnostic instrument manipulator,” High Power Laser Part. Beams 23(1), 115–120 (2011). [CrossRef]
16. L. Guo, S. Li, J. Zheng, Z. Li, D. Yang, H. Du, L. Hou, Y. Cui, J. Yang, S. Liu, S. Jiang, and Y. Ding, “A compact flat-response x-ray detector for the radiation flux in the range from 1.6 keV to 4.4 keV,” Meas. Sci. Technol. 23(6), 065902 (2012). [CrossRef]
17. J. Zhang, G. Yang, B. Zhang, Y. Zhou, A. Lei, H. Liu, J. Li, J. Yang, Y. Ding, and X. Yang, “Modeling the spectra of laser-produced au plasmas in the range 0.3-0.4 nm,” High Power Laser and Particle Beams 13(2), 186–190 (2001).
