Generation of Simulated Data

4.1.1 Line-integrated spectra

For the testing of tomographic inversion techniques it is desirable to have synthetic line-integrated data corresponding to known profiles of local plasma conditions. Us-ing realistic plasma profiles means that such images should have similar features to those seen in the real data, making them suitable for testing all stages of the anal-ysis chain. To this end, simulated line-integrated spectra were generated based on MAST simulation results from the OSM-EIRENE code package [Lisgo et al., 2005].

This is not a predictive code but an interpretive model constrained by experimental data. It uses an onion skin model (OSM) for the deuterium plasma and the Monte-Carlo neutral hydrogen code EIRENE for neutrals. The particular simulation used here is for MAST shot 25028 at t = 0.31s; this was an L-Mode LSND plasma with 1MW of NBI heating, performed to investigate divertor detachment on MAST [Har-rison, 2010]. The simulation results were provided by Dr James Harrison at CCFE.

While they do not include impurities, which are what we actually measure with the CIS diagnostic, the general structure in the 2D profiles should be sufficiently

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4.1. Generation of Simulated Data 70 similar to what appears in real data for the development and testing purposes here.

The simulation outputs of interest were ion temperature, parallel flow speed and D_α emissivity, used in place of impurity emissivity. The vector magnetic field was ob-tained from the EFIT magnetic equilibrium reconstruction code for the same shot and time. Both the plasma parameters and magnetic field profiles were specified in 2D in the poloidal (R, Z) plane and assumed to be toroidally symmetric. Line of sight vectors for the simulated diagnostic were generated using a simple pinhole camera model, with the design values for the field of view and positioning of the camera. Since the main application of the diagnostic was in the divertor, the simu-lated diagnostic view considered here corresponds to the wide-angle lower divertor view from port HL07.

Calculation of the line integrated spectra proceeded by iterating over each line-of-sight (i.e. each virtual detector pixel), and for each one stepping along the line of sight away from the camera. The lines of sight were considered to be narrow pencil beams, i.e. the finite depth of field and pixel size of the real system were not taken into account. At each step along the sight-line, the current position in the R, Z plane was calculated, and the local plasma parameters were obtained by interpolating the input plasma and B field data to that R, Z location. The positions and intensities of the spectral line components emitted at that plasma position were determined from the line multiplet structure, Zeeman splitting model described in 2.1.1 and line-of-sight Doppler shift, determined by the parallel flow velocity and the angle between the local magnetic field and the sight-line. Note that the flow is assumed to be entirely parallel to the magnetic field for the purposes of generating the simulated spectra. Gaussian line profiles, with widths given by Doppler broadening for the local ion temperature, were then used to represent each line component. These local spectra along the line of sight were all calculated at the same sampling points in wavelength, and the final line integrated spectrum was computed by integrating the intensity at each wavelength along the line of sight.

An example line integrated spectrum for C III is shown as the blue line in Fig. 4.1, along with the spectrum which would be emitted from a homogeneous source with the same average flow, temperature and magnetic field for comparison (grey line).

The line-integrated profile is highly distorted, and visibly consists of a double peak at each line component: this is due to contributions from distinct brightly emitting plasma regions with different flow speeds. While this example is an extreme case of distortion of the line shape, the same principle applies to all sight-lines and illustrates why line-of-sight spectroscopic measurements can be very difficult to interpret when only limited spatial coverage of the plasma is available.

4.1. Generation of Simulated Data 71

Wavelength (nm)

Relative Intensity

464.60 464.7 464.8 464.9 465 465.1 465.2 465.3

0.2 0.4 0.6 0.8 1

Figure 4.1: Example synthetic line integrated spectrum for C III in the MAST divertor (blue line). The dotted grey line shows the spectrum for a single point with the average conditions along the line-of-sight, for comparison.

After repeating this procedure for all simulated sight-lines, the result is a set of simulated line-integrated spectra for the light arriving at each virtual detector pixel. In order to use these results for data analysis development, they must then be converted into simulated data images.

4.1.2 Image generation from simulated spectra

Simulated data images were created pixel-by-pixel from the calculated line-integrated spectra. For each pixel, the position on the detector was mapped to incidence angles through the interferometer components (θ, ω) according to θ = arctan(px²+ y²/f₃) and ω = arctan(x/y), where x, y are the pixel’s position on the detector in the same units as f₃. For each wavelength sample in the spectrum, the detected spectral intensity at that wavelength was calculated according to:

S(λ) = I(λ)

2 (1 + ζ_Icos(φ_Delay(θ, ω, λ) + φ_Savart(θ, ω, λ)), (4.1.1) where φDelay and φSavart are given by equations (2.5.39) and (2.5.41) respectively and I(λ) is the line integrated spectral intensity from the plasma. Filter effects can be included by multiplying I(λ) by the filter transmission profile, based on data from the manufacturer and the θ-dependent band pass shift from equation (3.4.2).

The instrument contrast ζ_I is an input parameter accounting for the real instrument contrast, since realistic contrast reducing effects in the optics were not included in these simulations. The total intensity in the pixel is then given byR S(λ)dλ. Once