A representative data sample from the pixel detector for one time bin for the He-like argon spectrum is shown in Figure 17. The spectral lines, bent into an elliptical shape by the spherical crystal, are clearly visible. The top detector has a broken detector panel, and there are some dead pixels scattered across all of the detectors. Data from the broken detector panel should be ignored. Slices from the detector showing the measured spectra and results of the spectral fitting done by THACO over a single chord are shown in Figure 18 and Figure 19. The resulting line-integrated profile data is shown in Figure 20.

An example of an inverted plasma temperature and toroidal velocity profile created by THACO from the He-like argon lines can be seen in Figure 21. The measured ion temperatures from HIREXSR agree with independent diagnostics in other measurement channels¹. Using argon, a recycling impurity, allows the ion profiles to be measured over the entire evolution of the plasma. This is critical for transport studies such as in Rice et al. 2013¹¹, which study plasma evolution over time scales longer than the impurity confinement time. If the detectors were instead positioned to measure a transient impurity, such as calcium, HIREXSR would provide transient profile data. See Howard et al. 2011¹⁰ for such a study.

Figure 1: Illustration of Bragg Reflection. Incoming rays will reflect and constructively interfere based on their angle of incidence and wavelength. Please click here to view a larger version of this figure.

Figure 2: A Rocking Curve for a Calcite Crystal. The black curve is the best fit to the observed data, while the dotted line is the idealized case where there is no absorption. Please click here to view a larger version of this figure.

Figure 3: A Johann Spectrometer with a Bent Crystal. Incoming rays incident on the same location on the circumference of the circle have the same angle of incidence on the crystal and end up on the same location on the detector. Please click here to view a larger version of this figure.

Figure 4: A Johann Spectrometer with a Spherically Bent Crystal. The spherical bending of the crystal allows for spatial resolution along the meridional plane, so spectra are captured along multiple line-averaged chords through the plasma. Please click here to view a larger version of this figure.

Figure 5: The detector-crystal alignment used in HIREXSR. In HIREXSR, the detector is angled slightly from the standard arrangement to allow for a larger range of wavelengths to be measured. Please click here to view a larger version of this figure.

Figure 6: Top-down CAD View of HIREXSR. This CAD drawing shows the relative positions of the two detector arrays and the spectrometer crystal to the tokamak vacuum vessel, which contains the plasma. The sightline of the spectrometer is angled slightly off-axis to allow toroidal rotation to be measured through the Doppler shift. Please click here to view a larger version of this figure.

Figure 7: Layout of Optical System. This figure shows the layout of the optical system for the laser blow-off system from Howard et al.¹⁰. Please click here to view a larger version of this figure.

Figure 8: Fractional Charge State Abundance for Various Noble Gases. This plot shows the fractional charge state abundances for various noble gases in coronal equilibrium. Fully stripped states are in shown with solid lines, H-like with dashed, He-like with dash-dot and Ne-like with dash-dot-dot. Please click here to view a larger version of this figure.

Figure 9: Ca¹⁸⁺ k/w Brightness Ratios. The measured chord-averaged brightness ratio of the dielectronic satellite k to the resonance line w in He-like Ca¹⁸⁺ (red dots) compared to the theoretical curve (green line). Please click here to view a larger version of this figure.

Figure 10: Measured He-like Ca¹⁸⁺ Spectrum. The measured He-likeCa¹⁸⁺ (w, x, y, and z) spectrum with satellites (most prominent '4', '3', q, r and k) is shown by the dots. A synthetic spectrum calculated with collisional-radiative modeling indicated by the solid line. Please click here to view a larger version of this figure.

Figure 11: Measured H-like Ar¹⁷⁺ Spectrum. The measured spectrum of the Ar¹⁷⁺ Ly_α doublet and nearby satellites (green dots), with synthetic spectrum (red line). Note the overlap between the Mo³²⁺ line and the Ly_α2^line. Please click here to view a larger version of this figure.

Figure 12: Measured He-like Ar¹⁶⁺ Spectrum. Measured X-ray spectra in the vicinity of the Ar¹⁶⁺ w resonance lines. Note the log scale. Please click here to view a larger version of this figure.

Figure 13: Internal View showing Crystals and Be Window. The beryllium window (a) and crystals (b) are displayed as viewed from within the housing. The Be window is labeled with green, the spherical crystal with red, and the rectangular crystal with purple. Please click here to view a larger version of this figure.

Figure 14: Internal View Showing Detectors. The three detector array for He-like spectra is shown on the left in (a), and for H-like spectra is shown on the right in (b). The three detectors used for He-like spectra allow for the capture of spectra from the core and edge of the plasma simultaneously. Please click here to view a larger version of this figure.

Figure 15: Side View of HIREXSR. This diagram illustrates the relative distances of the detectors, crystals, and the tokamak. Please click here to view a larger version of this figure.

Figure 16: Example View of dwscope. This figure shows a screenshot of an instance of dwscope. Line-integrated data from HIREXSR is highlighted by the red box. Please click here to view a larger version of this figure.

Figure 17: Example Detector Output. This figure shows example raw data collected by the detectors over a single time bin for He-like (top, middle) and H-like (bottom) argon spectra. The y-axis corresponds to wavelength, and the x-axis to meridional angle. The spectral lines, bent into an elliptical shape by the spherical crystal, are clearly visible. The top (1x gain) and bottom (2x gain) spectra are from the core, and the middle spectrum (8x gain) is from the edge. The dotted green lines separate different regions for the spectral fitting code. The top detector has a broken detector panel, and there are some dead pixels scattered across all of the detectors. Please click here to view a larger version of this figure.

Figure 18: Example Collected H-like Spectra. Measured line-averaged brightness over the argon H-like spectrum for a single chord and time bin (top, white), corresponding to a single column of pixels in the bottom detector in Figure 17. The removed background is shown in green, and a multi-gaussian fit is shown in cyan. The total fit composite spectrum is shown by the red line, and the residuals are in the bottom figure. Note the agreement with Figure 11. Please click here to view a larger version of this figure.

Figure 19: Example Collected He-like Spectra. Measured line-averaged brightness over the argon He-like spectrum for a single chord and time bin (top, white), corresponding to a single column of pixels in the top detector in Figure 17. The removed background is shown in green, and a multi-gaussian fit is shown in cyan. The total fit composite spectrum is shown by the red line, and the residuals are in the bottom figure. Please click here to view a larger version of this figure.

Figure 20: Example Line-Integrated Profile. This figure shows an example of the line-integrated data generated by THACO from the results of the line fitting. It needs to be tomographically inverted to return the full profile. Please click here to view a larger version of this figure.

Figure 21: Example Inverted Plasma Profiles. This figure shows example data that has been inverted by THACO to produce temperature and toroidal rotation profiles. HIREXSR allows for both spatial resolution (along the y-axis) and time resolution (along the x-axis). Please click here to view a larger version of this figure.

Table 1: Detector Specifications. This table lists detector specifications relevant to the design of HIREXSR.