Bindselv, H.

Furtula, V.

Korsholm, S.B.

Leipold, F.

Meo, F.

Michelsen, P.K.

Moseev, D.

Nielsen, S.K.

Salewski, M.

Steijner, M.

TEXTOR, Team.

Stejner Pedersen, Morten

Nielsen, Stefan Kragh

Korsholm, Søren Bang

Bindslev, Henrik

Furtula, Vedran

Leipold, Frank

Meo, Fernando

Michelsen, Poul

Moseev, Dmitry

Salewski, Mirko

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Expected accuracy of fuel ion ratio measurements by collective Thomson scattering atTEXTORPedersen, Morten Stejner; Nielsen, Stefan Kragh; Korsholm, Søren Bang; Bindslev, Henrik; Furtula,Vedran; Leipold, Frank; Meo, Fernando; Michelsen, Poul; Moseev, Dmitry; Salewski, MirkoPublished in:ProceedingsPublication date:2010Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Stejner Pedersen, M., Nielsen, S. K., Korsholm, S. B., Bindslev, H., Furtula, V., Leipold, F., ... Salewski, M.(2010). Expected accuracy of fuel ion ratio measurements by collective Thomson scattering at TEXTOR. InProceedings (pp. P5.126)Expected accuracy of fuel ion ratio measurements bycollective Thomson scattering at TEXTORM. Stejner, S. K. Nielsen, S. B. Korsholm, H. Bindslev, V. Furtula, F. Leipold,F. Meo, P. K. Michelsen, D. Moseev, M. SalewskiAssociation EURATOM-Risø National Laboratory for Sustainable Energy,Technical University of Denmark, DK-4000 Roskilde, DenmarkIntroductionIn magnetically confined fusion experiments and for future reactors, measurements of thefuel ion ratio – the ratio between fuel ion densities – are of intrinsic scientific interest and willfurther be important for plasma control and machine protection. The techniques currently usedfor fuel ion ratio measurements – most notably neutral particle analysis – may not be applicablein the core of a fusion reactor [1]. It is therefore important to develop alternatives. Microwavebased collective Thomson scattering (CTS) diagnostics are well suited for reactor environmentsand provide access to the dynamics of confined ions by measuring the spectrum of probe ra-diation scattered by plasma fluctuations excited by ion motion. CTS measurements thus yieldinformation on the ion velocity distribution and on certain plasma waves. For specific scatter-ing geometries, CTS spectra contain signatures of ion Bernstein waves (IBWs) which are highlysensitive to the ion species mix. Measurements of IBW signatures in CTS spectra have thereforebeen suggested as a new diagnostic principle for measurements of the fuel ion ratio. Previousfeasibility studies have found that such a diagnostic could fulfill the measurement requirementsfor ITER [2], and that it could be integrated in the CTS system foreseen to measure fast ionvelocity distributions on ITER [3]. The next natural step is to perform proof-of-principle experi-ments in current machines demonstrating the ability to measure IBW signatures in CTS spectra,their sensitivity to plasma composition, and the ability to infer the fuel ion ratio – or in currentmachines the equivalent hydrogen to deuterium density ratio RH = nH/(nD+nH). The CTS re-ceiver at TEXTOR was recently modified for such experiments, which require higher frequencyresolution than was possible with the existing system [4]. Here we discuss the theoretical sen-sitivity to RH of spectra measured with the modified receiver, and the expected accuracy withwhich RH could be inferred from such spectra. Results of experiments to measure IBW signa-tures will be reported elsewhere.IBW signatures in CTS spectraIn CTS experiments, probe radiation (the CTS system at TEXTOR uses microwave gyrotronradiation at 110 GHz) with frequency and wave vector (ν i,ki) scatters off plasma fluctuations,and scattered radiation (νs,ks) is picked up by a receiving antenna. The probe launching an-37th EPS Conference on Plasma Physics P5.126−0.3−0.25−0.2−0.15−0.1909294960200400600800φFrequency relative to probe [GHz]Spectral power density [eV]0100200300400500600(a) Variation with φ−0.3−0.25−0.2−0.15−0.100.20.40.60.8150100150200250300350400RHFrequency relative to probe [GHz]Spectral power density [eV]050100150200250300350(b) Variation with RHFigure 1: Theoretical spectra calculated with parameters relevant for TEXTOR: ne = 3×1019 m−3, Te = 1.1 keV,Ti = 1.1 keV, Bt = 2.6 T. The spectrum is shown for frequencies from 300 MHZ to 100 MHz below the probefrequency corresponding to the range monitored with the modified CTS receiver. In (a) RH=0.5 while φ is variedfrom 91◦ to 95◦. In (b) φ = 93◦ while RH is varied from 0.01 to 0.99.tenna and the receiving antenna together determine the scattering geometry and the orientationof ks. The measurement resolves fluctuations in the plasma with frequency and wave vector(νδ ,kδ ) = (νs−ν i,ks−ki). When the length scale of the resolved fluctuations is greater thanthe Debye length, kδ λD < 1, the spectrum is sensitive to collective fluctuations in the plasmadriven by ion motion. νδ is essentially proportional to the ion velocity in the direction of kδ soCTS measurements are sensitive to one-dimensional projections of the ion velocity distributionalong kδ .IBWs are electrostatic solutions to the hot plasma dispersion relation and propagate at fre-quencies between the ion cyclotron harmonics of each ion species in the plasma. IBWs areweakly damped when propagating in directions close to perpendicular to the magnetic field.They are therefore readily excited by thermal ion motion and will, under usual circumstances,be intrinsically present in tokamak plasmas with no external drive. In directions away fromperpendicular the damping increases strongly, and it entirely suppresses the waves in direc-tions far from perpendicular. The CTS spectrum therefore only contains IBW signatures whenφ = 6 (kδ ,B)∼ 90◦. Figure 1(a) shows theoretical CTS spectra with IBW signatures. The spec-tra were calculated with a kinetic and fully electromagnetic model of CTS [5] assuming plasmaparameters and frequencies ranges relevant to the TEXTOR CTS system. The IBWs give rise topeaks in the CTS spectrum at intervals corresponding to the cyclotron frequencies of the domi-nant ion species – here hydrogen with νc,H = 40 MHz and deuterium with νc,D = 20 MHz. Thepeak amplitude is high for φ ≃ 90◦ but decreases rapidly for angles further from perpendicular.37th EPS Conference on Plasma Physics P5.126The relative heights of peaks related to different ion species depends on the relative densities ofthose ions. This is illustrated in Fig. 1(b) which shows spectra calculated for different values ofRH. At low RH the spectrum displays peaks at intervals of 20 MHz corresponding to νc,D. Athigher values of RH IBWs related to hydrogen contributes to every second peak. These peakslargely maintain their amplitude while peaks with contributions only from IBWs related to deu-terium gradually lose amplitude and disappear. Furthermore, radiation scattered by light ions,on average, has a higher Doppler shift due to the higher thermal velocity of those ions. Hydro-gen and IBWs related to hydrogen therefore contribute more to the spectrum at frequencies farfrom the probe than deuterium. IBWs related to ions with different masses will also be dampeddifferently since the damping is a finite Larmor radius effect. This means that the spectrum issensitive independently to both the charge and the mass of the ions. Therefore it is in principlepossible to distinguish ions with the same charge to mass ratio (and hence the same cyclotronfrequency) but with different masses. These are the properties which give CTS measurementsof IBW signatures the potential to become a diagnostic tool for the fuel ion ratio.Expected accuracy of fuel ion ratio measurementsBesides the fuel ion ratio and scattering geometry, the CTS spectrum depends in a non-trivialway on a number of parameters including bulk electron- and ion temperatures, electron density,magnetic field strength, impurity densities, and the velocity distributions of any non-thermal ionpopulations. To infer the fuel ion ratio, the spectrum must be fitted with a forward model forCTS. Here we use a Bayesian least squares method of inference [6] previously used to infer fastion velocity distributions [7]. This allows the fit to be optimized taking into account any priorknowledge about all relevant parameters and their uncertainties. In this approach, the probabilitydistributions describing the measured spectrum, the prior information about model parameters,and the resulting posterior distribution (the state of knowledge after the measurement) are allassumed to be multivariate normal distributions. After the measurement, the uncertainty on agiven parameter is related to the width of the posterior distribution and it may be expressedas a function of the uncertainties in the prior information, the uncertainties in the measuredspectrum, and the Jacobian for the best fit spectrum. This means that for given assumptionsabout the uncertainties in the prior information and the measured spectrum, the uncertainty ofthe inferred fuel ion ratio can be estimated theoretically.Figures 2(a) and 2(b) show examples of theoretically expected posterior uncertainties for RHfor realistic ranges of RH, φ and Ti on TEXTOR. The model parameters kept fixed are identicalto those used in Figs. 1(a) and 1(b). Their uncertainties are given in the figure caption. Theuncertainties in the measured spectra are assumed to be 2% of the signal strength – as wasfound in initial experiments with the modified receiver and as is expected from theory [4]. Theprior uncertainty in RH was 0.5, and the posterior uncertainty is significantly reduced from37th EPS Conference on Plasma Physics P5.12692939495969700.20.40.60.8100.050.10.150.20.250.3φRHσRH0.050.10.150.20.250.3(a) σRH for varying φ and RH92939495961000150020002500300000.050.10.150.20.250.3φTiσRH00.050.10.150.20.250.30(b) σRH for varying φ and TiFigure 2: Theoretically calculated posterior uncertainties for model parameters as in Fig. 1 and prior uncertain-ties: σne = 3×1018 m−3, σTe = 0.4 keV, σTi = 0.4 keV, σBt = 0.1 T, σφ = 3◦, σRH = 0.5. In (a) RH and φ are variedwhile other parameters are kept constant. In (b) RH = 0.5 and φ and and Ti are varied while other parameters arekept constant. σRH is significantly reduced from its prior value when φ is close to 90◦.this value when φ is close to 90◦ – i.e. when the spectrum contains IBW signatures. In thefrequency range monitored by the CTS receiver at TEXTOR, the signatures related to hydrogentends to dominate over those related to deuterium due to the larger Doppler shift. At high RHthe spectum is therefore less sensitive to changes in RH and the posterior uncertainty is higher.The IBWs can be damped at high ion temperatures causing the IBW signatures to be weaker,which can also lead to higher posterior uncertainties in RH. Nevertheless, the calculations showthat, within broad parameter ranges, the diagnostic can be expected to measure RH with anuncertainty around or below 0.1 at TEXTOR. Initial studies indicate that similar accuracies canbe expected for ITER standard scenarios [2]. This will be investigated in detail elsewhere.References[1] Donné, A. J. H. et al, Nuclear Fusion, 47, S337 (2007)[2] Bindslev, H. et al, Final Report EFDA Contract 04-1213 - deliverable 4.1- D3 (2005).[3] Meo, F. et al, Rev. Sci. Instrum., 75, 3585 (2004).[4] Stejner, M. et al (2010), Accepted for publication by Rev. Sci. Instrum.[5] Bindslev, H., J. Atmos. Terr. Phys., 58, 983 (1996)[6] Bindslev, H., Rev. Sci. Instrum., 70, 1093 (1999)[7] Salewski, M. et al, Nuclear Fusion 50, 035012 (2010)37th EPS Conference on Plasma Physics P5.126

Expected accuracy of fuel ion ratio measurements by collective Thomson scattering at TEXTOR

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Expected accuracy of fuel ion ratio measurements by collective Thomson scattering at TEXTOR

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