2 Principle and design

The 60-channel optical spectroscopy system has been designed to align with the configuration of the laser beams and target chamber in the SG-II UP facility. As shown in Figure 1(a), four nanosecond laser beams, denoted as #1, #3, #5 and #7 (with only three shown for clarity), are focused axisymmetrically at the same polar angle of 50° in the sphere, converging toward the target chamber center from the top. In addition, a picosecond laser, Beam #9, propagates in the equatorial plane and is focused at the center. There are 60 reflective collectors mounted on the inner wall above the equatorial plane, covering one-quarter of the sphere, among Beams #1, #3 and #7. The polarization angles of Beams #1 and #7 are 23° clockwise from the $\mathrm{p}$ -polarization, while those of Beams #3 and #5 are 7.5° counterclockwise. Since the polarization angles of the four beams are rotationally symmetrical, measurements covering a quarter of the spherical space can reveal the distribution in the 2 $\pi$ solid angle. Each collector is equipped with a 90° ultraviolet (UV)-enhanced aluminum mirror that reflects light from the center to the input end of a fiber with a 192-μm-diameter core. The 60 fibers are bundled together at a flange, and these components are permanently installed at the SG-II UP facility.

Figure 1

Schematic diagram of the 60-channel optical spectrometer. Sixty reflective collectors are set on the inner side of the chamber wall, as shown in (a), collecting the lights emitted from the laser–target interactions. The angles of the laser beams are in the format of ( $\theta$ , $\phi$ ), where the polar angle is indicated as $\theta$ and the azimuthal angle as $\phi$ . The polarization angle from $\mathrm{p}$ -polarization of Beams #1 and #7 is 23° clockwise, and that of Beams #3 and #5 is 7.5° anti-clockwise. The collectors reflect the lights to a fiber bundle, which is extended for 20 m outside the chamber to a spectrometer, as shown in (b), and the spectra are recorded by a CCD camera.

The fiber bundle extends 20 m outside the vacuum chamber to protect electronic devices from radiations induced by high-power lasers. It is then coupled through a linear fiber array (see Figure 1(b)) to the 200-μm slit of the IsoPlane 160 imaging spectrometer, which has a focal length of 203 mm. The spectrometer is equipped with a triple turret that allows for the selection of gratings based on different experimental requirements. In one of our regular operating modes, with a 150-G/mm ruled grating, optical spectra in the 300–800 nm range can be recorded by a 13.3 mm × 13.3 mm area charge-coupled device (CCD) camera, achieving a spectral resolution of 6.3 nm. To obtain wider spectral ranges and higher resolution, two additional gratings with 50- and 1200-G/mm ruled lines can also be employed, with the main parameters shown in Table 1. The spectrometer slits are set to a width of 200 μm to ensure the detection of relatively weak light signals from the experiments. A fine spectral resolution of 0.3 nm has been calibrated using a 20-μm slit and a 1200-G/mm grating.

Table 1

List of the spectral ranges and resolution with a 200-μm slit using different ruled gratings.

3 Calibration and analysis

Since the diagnostic system measures a wide spectrum from UV to near-infrared, the calibration of the spectral response covered the range from 340 to 750 nm. Two light-emitting diode (LED) sources with known power and spectrum characteristics were selected: a continuum white LED emitting lights with wavelengths from 450 to 750 nm and a deep UV LED near 340 nm. The LED chips were set at the target chamber center respectively. Using the 150-G/mm grating in the spectrometer, the CCD recorded spectra of the LED lights collected by the fibers at different orientations. For the white LED, the CCD chip was filtered with a laminated neutral density film with 0.01 $\%$ transmission for 400–700 nm, and the exposure time was 1000 s. For the UV LED, no filter was used in the spectrometer system considering the lower CCD quantum efficiency in the UV range, and the exposure time was 1 s. The signal of UV and white LED lights on the CCD is shown in Figure 2, where the horizontal axis represents light wavelengths and the vertical axis corresponds to different orientations of the fiber channels, with 15 pixels (full width at 1/e of maximum intensity) for each channel. Due to optical damage or target splashing after laser shots and obstruction by other diagnostics, 43 of the 60 channels were able to collect lights during this experimental campaign.

The light power at the input end of the reflecting mirror was measured using a power meter. The products of the power and the exposure time provided the energy input to each channel, establishing a response relationship with the recorded spectral intensity on the CCD. The spectral response of the system is influenced by various factors, including the reflectivity of the aluminum mirror, the transmission attenuation of the fibers, the grating efficiency and the CCD quantum efficiency. Each component’s attenuation acts as a constant neutral density. Based on the calibrated LED spectra, the response of the entire optical system, $R$ ( $i$ , ${\lambda}_j$ ), for a specific wavelength ${\lambda}_j$ (with $j$ denoting the CCD pixel on the spectral dimension) in channel $i$ , can be derived using the following procedure.

For channel $i$ set at a specific orientation, the input power measured in front of the collector is ${P}_{\mathrm{src}}$ ( $i$ ). Given the known spectrum $\eta$ ( $\lambda$ ) of the LED emission source, the power at wavelength ${\lambda}_j$ per unit wavelength d $\lambda$ is calculated as ${P}_{\mathrm{src}}\left(i,{\lambda}_j\right)={P}_{\mathrm{src}}(i)\frac{\int_{\lambda_j}^{\lambda_j+\mathrm{d}\lambda}\eta \mathrm{d}\lambda }{\int_{-\infty}^{\infty}\eta \mathrm{d}\lambda }$ , which results in an intensity on the detector ${I}_{\mathrm{src}}\left(i,{\lambda}_j\right)$ . Thus, the response (intensity per unit input energy) of the system in channel $i$ and at wavelength ${\lambda}_j$ is given by $R\left(i,{\lambda}_j\right)={I}_{\mathrm{src}}\left(i,{\lambda}_j\right)/\left({P}_{\mathrm{src}}\left(i,{\lambda}_j\right){\tau}_{\mathrm{exp}}\right)$ , where ${\tau}_{\mathrm{exp}}$ is the CCD exposure time. When the experimental signal ${I}_{\mathrm{sig}}\left(i,{\lambda}_j\right)$ is recorded, the energy of the signal in front of the fiber collectors can be calculated as $E\left(i,{\lambda}_j\right)={I}_{\mathrm{sig}}\left(i,{\lambda}_j\right)/R\left(i,{\lambda}_j\right)=\frac{I_{\mathrm{sig}}\left(i,{\lambda}_j\right)}{I_{\mathrm{src}}\left(i,{\lambda}_j\right)}{P}_{\mathrm{src}}\left(i,{\lambda}_j\right){\tau}_{\mathrm{exp}}$ .

Figure 2

Mosaic image of the UV and white LED spectra recorded by the spectrometer with the 150-G/mm grating. Here the white LED light was recorded with an OD4 filter and 1000-s exposure. The UV one was recorded with 1-s exposure and the intensity was artificially reduced by a factor of 10 for better visibility.

4 Experimental results

The spectrometer system has been employed to measure the laser absorption in the conical compression stage of the double-cone ignition scheme^[ Reference Zhang, Wang, Yang, Wu, Ma, Jiao, Zhang, Wu, Yuan, Li and Zhu^29] at the SG-II UP facility. In this setup, the four laser beams overlapped on a C₁₆H₁₄Cl₂ (CHCl) spherical shell within a gold cone (shell-in-cone target), and drove a conical implosion of the shell, as shown in Figure 3(a). Each beam delivered 1500 J of energy at a UV wavelength of 351 nm (tripled frequency $\omega =3{\omega}_0$ ), and was focused onto the shell through a 700-μm diameter spot determined by a $\Phi$ 700 continuous phase plate. The temporally shaped laser pulse is shown in Figure 3(b). The resulting intensity of the four overlapped beams reached a maximum of 5.7×10¹⁴ W/cm². The CHCl shell had a thickness of 50 μm and an inner radius of 500 μm, with the shell cap having a full opening angle of 100°. The orientations of the laser irradiation and the fiber collectors are shown in the angular coordinates in Figure 3(c), with the 90° polar angle defined as the equatorial plane and the 0° azimuthal angle as the incidence of Beam #3.

Figure 3

(a) Schematic diagram of the conical irradiation. The spherical CHCl shell is initially embedded in the gold cone, and four laser beams overlap at the shell surface through 700-μm continuous phase plates. (b) Laser temporal profile on the target. (c) The coordinates of the collectors in the 2D angular map, with Beams #1, #3 and #7 incident angles.

The spatial growth of LPIs is influenced by the laser polarization directions. The polarization angles of Beams #1 and #7 are identical, as are those of Beams #3 and #5. Consequently, measurements in one-quarter of the sphere can reveal the light distribution in the entire hemisphere. The total scattered energy proportion ${f}_{\mathrm{scatt}}$ can be calculated from the spectral and angular integration, allowing the laser absorption efficiency ${f}_{\mathrm{abs}}$ to be deduced using the following equations:

$$\begin{align*}{f}_{\mathrm{scatt}}=2{\int}_0^{\pi /2}{\int}_0^{\pi}\frac{\mathrm{d}{E}_{\mathrm{scatt}}}{\mathrm{d}\Omega}\left(\theta, \phi \right)\sin \theta \mathrm{d}\theta \mathrm{d}\phi /{E}_{\mathrm{las}},\end{align*}$$

$$\begin{align*}{f}_{\mathrm{abs}}=1-{f}_{\mathrm{scatt}}.\end{align*}$$

Here $\theta$ and $\phi$ represent the polar and azimuthal angles in the sphere, respectively, while ${E}_{\mathrm{las}}$ is the incident laser energy on target. Linear interpolation of intensity is used in the angular integration for the directions between adjacent collectors. Furthermore, the spectrum of scattered light contains valuable information on various laser–plasma interaction processes and parametric instabilities.

4.1 Laser–plasma instabilities

Figure 4(a) shows a typical result of global scattered light recorded by the spectrometer system using the 150-G/mm grating and the ND4 filter. According to the frequency matching conditions between the parent laser wave and the daughter waves, the spectra of the scattered light can characterize different LPI processes. The lights around 351 nm consist of the direct reflection of the incident laser, SBS and CBET. The contributions from the three main parts are currently indistinguishable, but these would be resolved by using gratings with denser lines for better spectral resolution to observe wavelength shifts. The lights around 527 nm, primarily from the 2 ${\omega}_0$ remnant of the laser, are randomly reflected from the chamber and excluded from the scattered energy calculation. The continuum spectrum from 500 to 650 nm is from SRS, which occurs in sub-critical plasma with a density lower than the quarter critical density, and dominates the side scattering in this configuration^[ Reference Glize, Zhao, Zhang, Lian, Tan, Wu, Xiao, Yan, Zhang, Yuan and Zhang^20]. TPD re-scattering in the branch around $\omega$ /2 (680–720 nm) has also been observed. The red-shifted peak in the $\omega$ /2 spectra at a polar angle around 8° indicates electron temperature at quarter critical density of 1.6 ± 0.4 keV. In addition, the 3 $\omega$ /2 spectra (230–238 nm) from TPD re-scattering are generated by Thomson up-scattering of the incident laser, which requires a broad spectrum of plasma waves^[ Reference Seka, Myatt, Short, Froula, Katz, Goncharov and Igumenshchev^15]. Since the 3 $\omega$ /2 spectra have been observed to occupy less than 0.3 $\%$ of the total scattered energy (equivalent to 10⁻⁴ of the laser energy) in a prior experiment with a similar configuration, the spectrometer system has not been used with the 50-G/mm grating for simultaneous measurements of the spectra at 3 $\omega$ /2.

Figure 4

(a) Raw image for the multi-channel spectra of the scattered lights from the laser-driven shell-in-cone target implosion. Here the longitudinal axis represents collectors at different orientations, and the wavelength in spectra indicates different processes of LPIs (the spectral response needs to be taken into account for absolute energy calculation). The corresponding angular distributions of the 351-nm lights, SRS and $\omega$ /2 re-scattering TPD are shown in (b), (c) and (d), using linear interpolation for the directions in between two adjacent collectors. The incident angles for the laser beams are shown in the angular distribution maps.

Typical results for the two-dimensional (2D) angular distributions of energy in the three main spectral components are presented in Figures 4(b)–4(d), corresponding to 351-nm scattering, broadband SRS (around 500–650 nm) and the $\omega$ /2 branch of TPD (680–720 nm), respectively. The nonuniformity and asymmetry in these distributions could be attributed to beam energy and pointing imbalances, as well as laser polarization effects on LPIs. The 351-nm lights were primarily distributed in the polar directions around the laser incidence (40°–70°), with very weak emissions in larger or smaller angles, covering a broad span in azimuthal directions between every two beams (see Figure 4(b)). Among the shots in this experiment, the integrated energy of the 351-nm lights is ${0.9}_{-0.3}^{+0.8}\%$ (in the format $\mathrm{average}_{\mathrm{lower\kern0.17em limit}}^{\mathrm{upper\kern0.17em limit}}$ ) of the laser energy. For the broadband SRS, the emissions are close to the laser incidence (Figure 4(c)), indicating they are likely driven by single-beam-induced scattering. The energy conversion to SRS is ${2.9}_{-0.4}^{+2.6}\%$ of the laser energy. The TPD emissions near $\omega$ /2 are observed at polar angles less than 50° (Figure 4(d)), which can be explained by the light refraction due to the density gradient^[ Reference Seka, Myatt, Short, Froula, Katz, Goncharov and Igumenshchev^15]. The total energy of the $\omega$ /2 emissions is ${0.3}_{-0.1}^{+0.4}\%$ of the laser energy.