Page 4 - Development of a Zeff diagnostic using visible and near-infrared bremsstrahlung light for the C-2W field-reversed configuration plasma

10D130-4 Nations et al.
Rev. Sci. Instrum. 89, 10D130 (2018)
shot (#104693) together with measured (line-integrated) bremsstrahlung intensity. After the CTs collide and merge at ∼50 μs, the emission is strongly edge dominated by neutral pollutants. At ∼800 μs, the FRC stabilizes and the intensity of pollutant edge light drops significantly. The amplitude of the measured bremsstrahlung signals inside the separatrix corre- late well with line-integrated measurements of electron density obtained with a far-infrared (FIR) interferometry diagnostic20 [shown in Fig. 4(b)]. This correlation is expected due to the ne2 dependence of bremsstrahlung in Eq. (2). As a result, bremsstrahlung signals are stronger inside of the separatrix where electron density is higher. Signals remain fairly flat near the centerline, yet it is possible to identify a slow rise in intensity in the FRC core as the shot progresses, center- line ne increases, and plasma impurity content builds up. Data rapidly sampled at 1 MHz enable intricate plasma futures to be resolved. Note that the high frequency temporal fluctuations near the separatrix (r ≈ r∆Φ) follow the fluctuations in ne (from n = 2 mode). The low frequency fluctuations near the edge (r > 50 cm), however, reflect signals dominated by line radiation from edge-localized neutral pollutants.
B. Bremsstrahlung local emissivity
Bremsstrahlung local emissivity can be obtained by inverting measured bremsstrahlung intensity. The Fourier- based inversion algorithm21 used in the present analysis assumes axial symmetry and fits the measured profile to a set of cosine-expansion-based integrals. This method is less prone to error propagation than the conventional “onion peel- ing” approach, where the radial distribution is obtained by iteratively moving from the edge toward the center. Signals are averaged over a small time window (100 μs), and statistical smoothing (moving median) is applied to reduce channel-to- channel variance. A linear interpolation on a fine grid (0.1 cm inter-channel spacing from the center to wall) is applied prior to inversion.
Figures 5(a) and 5(b) show measured bremsstrahlung intensity as a function of the chord impact parameter at t = 2 ms.
FIG. 5. Measured (line-integrated) bremsstrahlung intensity for the (a) VIS and (b) NIR systems at t = 2 ± 0.05 ms (100 μs time-window average). Local emissivity for the (c) VIS and (d) NIR systems. The dashed lines represent the size of the separatrix radius at t = 2 ms.
FIG.6. Radialprofilesof(a)electrondensityand(b)electrontemperatureat t = 2 ms (shot #104693).
Note the significant amount of edge-localized pollutant emis- sion measured outside of the separatrix, in the outer chords probing the open-field-line region. This effect appears to be more pronounced for the NIR system, yet also noticeable for the VIS. As a result, bremsstrahlung emissivity profiles are double-peaked, hollow at the core, and non-zero near the wall [see Figs. 5(c) and 5(d)]. Given the relatively moderate pollution-to-signal ratio, the reconstructed emissivity in the core (r < r∆Φ) is slightly sensitive (∼20%–25%) to the edge- localized pollution (more so for the NIR than the VIS system). Nevertheless, the presence of pollutants complicates but does not prohibit reliable inversions as the line-averaged profiles are fairly peaked.
For the particular plasma shot (#104693) discussed in the present analysis, a single multi-point Thomson scattering mea- surement22 of local T e was made at the axial mid-plane (z = 0) of the confinement vessel at t = 2 ms [shown in Fig. 6(a)]. Point measurements span from the core to the SOL. Local electron density at t = 2 ms is readily obtained by inverting line-integrated ne measurements from the FIR interferometry diagnostic20 [shown in Fig. 6(b)]. Note that the bremsstrahlung emissivity [shown in Figs. 5(c) and 5(d)] peaks inside of the separatrix at approximately the same location where the electron density peaks (at r ≈ 27 cm), which is in agree- ment with Eq. (2). After peaking inside of the separatrix, the electron density continues to drop (with increasing r) as one moves outside of the separatrix and into the open-field-line region.
C. Zeff measurements
Local Zeff can be calculated with ne(r), Te(r), and εbrems(r) using Eq. (2). The local bremsstrahlung emissivity is interpolated to the radial locations of the Thomson scat- tering measurements. Since measurements of bremsstrahlung emissivity are highly polluted outside of the separatrix, Zeff calculations are performed only for r < rs ≈ r∆Φ. Further- more, accurate determination of Zeff for r > r∆Φ is complicated by the lack of electron density and temperature measurements near the wall (to be performed using insertable triple Langmuir probes in future experiments).