Telesca, Giuseppe

Van Oost, Guido

Verdoolaege, Geert

English

Ghent University Academic Bibliography

Optimization of the relative calibration for a visible bremsstrahlung Zeffdiagnostic on TEXTOR via requirements of profile consistencyG. Verdoolaege1, G. Telesca1, G. Van Oost1 and the TEXTOR-team1Department of Applied Physics, Ghent University, Ghent, BelgiumThe bremsstrahlung Zeff diagnosticOn TEXTOR a new diagnostic was commissioned for the determination of the ion effectiveFigure 1: The viewinggeometry of the brems-strahlung system.charge Zeff from bremsstrahlung emissivity measurements in the vis-ible [1]. The line-integrated bremsstrahlung emissivity is measuredalong 24 lines of sight within a single poloidal cross-section. The to-tal field of view is indicated by the red lines in Figure 1. The lightfrom the plasma is passed through an interference filter, selecting anarrow wavelength band in the visible that is free of line emissionon TEXTOR. The light from the 24 channels is then focused on aCCD array. From the measured bremsstrahlung line-integrals, a ra-dial bremsstrahlung profile is reconstructed using (regularized) Abelinversion. Together with profiles of electron density and electron tem-perature, Zeff profiles can be calculated.Calibration of the camera systemThe absolute calibration of the camera system was performed bytaking an integrating sphere inside the TEXTOR vessel. This calibration is a delicate operation,requiring the careful design of a dedicated calibration set-up. Access to the tokamak vessel isneeded, or the fibre support at the TEXTOR side has to be dismounted to position the integratingsphere in front of the fibres.In order to avoid the disadvantages of a calibration using an integrating sphere, an alterna-tive calibration method was devised. This alternative technique also allows the optimizationof an existing calibration. First, the relative (channel-to-channel) calibration of the system wasassessed, based on the requirement of consistency of line-integrated bremsstrahlung profilesduring horizontal shifts of the plasma column. Here, in principle the plasma is used as a calibra-tion light source. For two channels, say A and B, the principle of the method is the following.Suppose A and B measure along the same physical line of sight through the plasma. We call thetwo corresponding measurements with the camera mA and mB, respectively, both expressed inanalog-to-digital units. Either measurement should, apart from any measurement error, lead to33rd EPS Conference on Plasma Phys. Rome, 19 - 23 June 2006 ECA Vol.30I, P-2.165  (2006)the same line-integrated emissivity Lff:Lff =mAa=mBb. (1)Here, a and b are the calibration factors associated with channels A and B, respectively. If ais fixed to an arbitrary value, then the relative calibration of this two-channel system can becalculated. This procedure can be repeated for the other channels, and eventually the completerelative calibration of the 24-channel system can be assessed.In practice, the question rises how to feed the same physical line-integral Lff to differentchannels. Here, we assume that the line-integrated emissivity profile is sufficiently smooth.In this case, the relative calibration factors can be estimated as follows. The line-integratedbremsstrahlung emissivities along the 24 channels are measured in two discharges with verysimilar plasma parameters (which we assume to be identical), but with a relative shift H inhorizontal plasma position. In practice a few cm is sufficient, while H is taken positive when theshift is towards the high field side of the machine. This results in two sets of measurements (mi,respectively ni) along two chord fans with different intercepts on the equatorial plane, relativeto the plasma1, (bi, resp. bi + H, i = 1 . . .24), but with the same calibration factors ci. Everymeasurement mi, resp. ni, corresponds with a calibrated line-integral Mi =mici, resp. Ni =nici.The Mi are now interpolated as a function of intercept using a curve f (b). Alternatively, wemay use a low order polynomial fit, which is less biased towards individual points Mi(bi). Thelatter is particularly useful in the case were the number of channels within the field of view isrelatively low. In both cases, to a good approximation, the following equalities should hold:Ni = f (bi +H), i = 1, . . . ,24. (2)These equations simply express the fact that in both cases the same line-integrated profile wasmeasured. To avoid extrapolation of the emissivity profile, and depending on H, the equationsfor some outer channels are not taken into account. In the case of linear interpolation of the line-integrated emissivity profile, the calculation of the relative calibration coefficients amounts tothe solution of a system of linear equations. The shift H should then not be too large, otherwisethe system may become unsolvable.Figure 2(a) gives a visual representation of equations (2). The geometry is shown of a lineof sight, viewed by channel k, under a plasma shift H towards the high field side. In the figure,the plasma is depicted stationary, and instead an equivalent shift of the line of sight is shown.The blue line represents the chord Ck (intercept bk) viewed by channel k before the shift has1Naturally, the intercept relative to the machine does not change under a plasma shift.33rd EPS 2006; G.Verdoolaege et al. : Optimization of the relative calibration for a visible bremsstrahlung Ze... 2 of 4occurred. The black line is a second, adjacent chord Cl viewed by another channel l. Thesechannels view a physical line-integrated emissivity Mk, resp. Ml . The green line depicts theline of sight viewed by channel k, after the shift has occurred (intercept bk + H, relative to theplasma). Channel k now views an emissivity Nk. Next to a shift in intercept, there is also ashift of observation point (A to B), relative to the plasma. The red line represents the line ofsight for a fictitious channel, with associated emissivity f (bk +H), resulting from the fitting orinterpolation process of the initial set of line-integrated emissivities Mi. The intercept for thered chord is the same (bk +H) as for the green chord. Now, according to (2), Nk and f (bk +H)should be equal. However, it can be seen in Figure 2(a) that this is in reality not entirely true.On the other hand, it is also clear that in the present geometry, the difference δ in emissivityviewed by the red and the green chord, is relatively small. Simulations with a typical radialbremsstrahlung profile show that δ is typically a few percent or less of the emissivity along theshifted (green) chord. Therefore, it is allowed to neglect the shift of observation point relativeto the plasma.Up to this point, only the relative calibration of the channels was assessed. Indeed, if a setof calibration factors ci is found that satisfies (2), then it is easy to see that also the set a · ciwill satisfy these equations, for an arbitrary factor a. Although the relative calibration on itsown already allows the reconstruction of relative Zeff profiles on an arbitrary scale, an absolutecalibration is required for the assessment of absolute impurity concentration levels. The full ab-solute calibration can be fixed by the calibration of a single channel with an integrating sphere.This requires only a reduced experimental set-up, as compared to the calibration of all channelswith the sphere.Figure 2(b) concerns a preliminary result of this approach. The line-integrated bremsstrahlungprofiles are shown for two similar discharges with a relative horizontal plasma shift of 1 cm to-wards the high field side (from # 99431 to # 99430). The bremsstrahlung emissivity is plottedagainst the intercept b, relative to the plasma. The profiles were calibrated by the calibrationfactors that were calculated via linear interpolation of the starting profile. There is a good cor-respondence between the two profiles, implying that the equations (2) are well satisfied. Theoutermost channels at both sides were discarded, since the corresponding calculated calibrationfactors were not satisfactory. The absolute calibration was determined from the calibration of acentrally pointed channel using the integrating sphere. The thus determined calibration yieldsphysically acceptable radial Zeff profiles. Preliminary simulations using a known radial brems-strahlung emissivity profile, show a good accuracy of the retrieved calibration. Future simula-tions and experiments are planned to estimate the error bars of a set of calculated calibration33rd EPS 2006; G.Verdoolaege et al. : Optimization of the relative calibration for a visible bremsstrahlung Ze... 3 of 4(a) (b)Figure 2: (a) The geometry of a chord during a horizontal plasma shift. (b) The calibrated line-integrated bremsstrahlung profiles resulting from the requirement of profile consistency undera horizontal plasma shift H. H is indicated in the figure for two channels.factors.ConclusionAn alternative technique for the relative calibration of the bremsstrahlung Zeff system wasproposed. A satisfactory calibration can be obtained from the requirement of consistency ofline-integrated bremsstrahlung emissivity profiles during a horizontal plasma shift. The absolutecalibration of the system then comes down to the absolute calibration of one of the channels.The here outlined relative calibration method is of general applicability, and provides a simpleand self-consistent way for the relative calibration of any multi-channel spectroscopic diagnos-tic. It can in principle be carried out at any time, without requiring access to the tokamak vesselitself or the establishment of a calibration set-up. Since the plasma acts as a calibration lightsource, no specialized light sources are needed for the relative calibration. This is a consider-able advantage, especially in the case of spectroscopy outside the visible range. In addition, thismethod provides a valuable way for the check or optimization of an existing relative calibration.References[1] G. Verdoolaege, G. Telesca, E. Delabie, G. Van Oost, and the TEXTOR team, Rev. Sci.Instrum. (2006), accepted for publication.33rd EPS 2006; G.Verdoolaege et al. : Optimization of the relative calibration for a visible bremsstrahlung Ze... 4 of 4

Optimization of the relative calibration for a visible bremsstrahlung Zeff diagnostic on TEXTOR via requirements of profile consistency

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Optimization of the relative calibration for a visible bremsstrahlung Zeff diagnostic on TEXTOR via requirements of profile consistency

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