Abramovic, I.

Lopes Cardozo, N. J.

English

Collective Thomson scattering (CTS) is a microwave diagnostic allowing measurements of a number of plasma parameters such as the bulk ion temperature, the plasma composition, drift velocities and fast ion velocity distribution function. A CTS system has been successfully installed and commissioned on the Wendelstein 7-X (W7-X) stellarator. The measured spectra are analyzed by the means of the CTS forward model eCTS and the Minerva scientific framework enabling the use of Bayesian inference of relevant plasma parameters. Here we discuss the options for further optimization of the CTS diagnostic and focus on two topics of importance for the inference of bulk ion temperature values from CTS spectra: influence of impurities on the CTS spectra and the width of the notch filters that are employed to protect the receiver from high-power radiation. In addition to that we discuss the possibility of effective charge measurements by CTS. We explore the existence of an optimal notch filter width.</p

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 Optimization of the Collective Thomson scattering diagnosticfor future operationCitation for published version (APA):Wendelstein 7-X Team, Abramovic, I., & Lopes Cardozo, N. J. (2019). Optimization of the Collective Thomsonscattering diagnostic for future operation. Journal of Instrumentation, 14(10), Article C10021.https://doi.org/10.1088/1748-0221/14/10/C10021Document license:TAVERNEDOI:10.1088/1748-0221/14/10/C10021Document status and date:Published: 01/10/2019Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 05. Oct. 2023Journal of Instrumentation     Optimization of the Collective Thomson scattering diagnostic for futureoperationTo cite this article: I. Abramovic et al 2019 JINST 14 C10021 View the article online for updates and enhancements.This content was downloaded from IP address 131.155.144.47 on 15/01/2020 at 07:282019 JINST 14 C10021Published by IOP Publishing for Sissa MedialabReceived: June 30, 2019Revised: September 1, 2019Accepted: September 30, 2019Published: October 15, 20193rd European Conference on Plasma Diagnostics (ECPD2019)6–10 May 2019Lisbon, PortugalOptimization of the Collective Thomson scatteringdiagnostic for future operationI. Abramovic,a,b,1 D. Moseev,b T. Stange,b S. Marsen,b W. Kasparek,c S.K. Nielsen,dA. Tancetti,d M. Salewski,d A. Pavone,b J. Svensson,b R.C. Wolf,b H.P. Laqua,bN.J. Lopes Cardozoa and the W7-X TeambaEindhoven University of Technology,De Zaale, 5612 AJ Eindhoven, The NetherlandsbMax-Planck Institute für Plasma Physik,Wendelsteinstraße 1, D-17491 Greifswald, GermanycUniversity of Stuttgart,Keplerstraße 7, 70174 Stuttgart, GermanydTechnical University of Denmark, Fysikvej,2800 Kgs. Lyngby, DenmarkE-mail: i.abramovic@tue.nlAbstract: Collective Thomson scattering (CTS) is a microwave diagnostic allowing measurementsof a number of plasma parameters such as the bulk ion temperature, the plasma composition, driftvelocities and fast ion velocity distribution function. A CTS system has been successfully installedand commissioned on the Wendelstein 7-X (W7-X) stellarator. The measured spectra are analyzedby the means of the CTS forward model eCTS and the Minerva scientific framework enabling theuse of Bayesian inference of relevant plasma parameters. Here we discuss the options for furtheroptimization of the CTS diagnostic and focus on two topics of importance for the inference ofbulk ion temperature values from CTS spectra: influence of impurities on the CTS spectra and thewidth of the notch filters that are employed to protect the receiver from high-power radiation. Inaddition to that we discuss the possibility of effective charge measurements by CTS. We explorethe existence of an optimal notch filter width.Keywords: Nuclear instruments and methods for hot plasma diagnostics; Analysis and statisticalmethods1Corresponding author.c© 2019 University of Technology Eindhoven. Published by IOPPublishing Ltd on behalf of Sissa Medialab https://doi.org/10.1088/1748-0221/14/10/C100212019 JINST 14 C10021Contents1 Introduction 12 Impurity content and temperature inference 23 Notch filter width and temperature inference 34 Summary and conclusion 41 IntroductionThe Wendelstein 7-X, the world’s largest optimized stellarator, has completed two operationalperiods OP 1.1 (in 2015–2016) and OP 1.2 (in 2017–2018). Collective Thomson scattering (CTS)is a microwave diagnostic capable of measuring a number of plasma parameters [1]. CTS hasrecently been installed and commissioned on Wendelstein 7-X (W7-X) during OP 1.2, and firstmeasurements of bulk ion temperature, Ti, by CTS were obtained [2]. CTS and deuterium-basedcharge-exchange recombination spectroscopy measure the deuterium temperature [3], whereas themore common impurity-based charge-exchange recombination spectroscopy diagnostics measurethe impurity temperatures [4]. CTS diagnostics are in operation at the LHD device [5, 6] andASDEXUpgrade [7] and will be an important diagnostic at ITER [8]. The measured spectra at W7-X were extensively compared with numerical simulations made by the forward model eCTS [9, 10]whose input parameterswere inferred by theBayesianMaximum-A-Posteriormethod in theMinervaframework [11]. The obtained value of Ti is in agreement with the result obtained by the X-rayimaging spectroscopy [12], and agreement was obtained between synthetic and measured spectra,yet a few discrepancies in spectral shape and width were noted [2]. In this paper we will discussa possible cause of these discrepancies, namely, the plasma impurity content and its effect onsynthetic CTS spectra (section 2). Impurity ions, being heavier than the hydrogen ions, give riseto contributions to the scattering spectrum close to the central wavelength, thereby distorting thespectrum of the scattering on pure hydrogen.Additionally we will elaborate on an important consideration for future operation of CTS onW7-X: the influence of the notch filter width on the temperature inference quality. The CTS systemon W7-X features two notches at 137 GHz and 140 GHz which are 1000 MHz and 500 MHz wide,respectively. They protect the sensitive heterodyne receiver from high-power radiation. In additionwe also have a built-in interlock into the pin-switch which closes automatically if too strong a signalis detected behind the notch filters. The notch filters can be tuned to block a more narrow frequencyband which may be beneficial for the bulk ion temperature inference quality. However, as the riskof damaging the CTS receiver increases with the decrease in the notch filter width, it is worthwhileto investigate if an optimal width exists (section 3).– 1 –2019 JINST 14 C100212 Impurity content and temperature inferenceIn W7-X plasmas impurity concentrations have been measured by charge exchange recombinationspectroscopy and passive spectroscopy. The impurities with the largest concentrations in OP1.2were carbon, oxygen and argon. In particular the effect of carbon was clearly visible in CTSmeasurements [2] and needed to be accounted for in the inference of bulk ion temperature, Ti, fromthe measured spectra. The spectral width, from which Ti is inferred [13, 14], is sensitive also to theimpurity content. To further explore the implications of this for ion temperature measurements byCTS, it is of interest to answer two questions:1. How large is the error one makes if the plasma is assumed to be pure?2. How many impurity species should be accounted for in the analysis?To answer these questions we investigated how the spectra change if the concentration and thenumber of impurities are varied. We calculated synthetic spectra at Ti = 3 keV for differentconcentrations of the two main impurities: carbon and oxygen. The carbon concentration wasvaried from 1% to 5% in a hydrogen plasma. The result is depicted in figure 1 on the left. Theoxygen concentration was varied from 0.6% to 1% in a hydrogen plasma.1 The result is depictedin figure 1 on the right. In both figures the borders of the rectangular notch region are indicated.In figure 1 the electron density is a fixed parameter thus the hydrogen ion density decreases withthe increase of impurity ions. The change in ion density has a scaling effect on CTS spectra [13].Temperatures of all ion species are assumed to be equal and set to 3 keV. As can be seen in figure 1,the spectra consist of two parts: the narrow impurity feature (absent for pure hydrogen plasma) andthe broad feature (containing information about both the impurity ions and the bulk ions). It followsfrom theory that the heavier the impurity is, the more narrow the impurity feature is, at a given iontemperature. This means that often the impurity feature is completely within the notch region whichin practice is wider than indicated in figure 1. Effective widening of the notch in measurements isdue to the non-ideal characteristics of notch filters causing a poor signal-to-noise ratio in a widerspectral range. However, even if the impurity feature is within the notch, the impurities affectthe broad spectral feature outside the notch. The increase in impurity concentration, at a givenion temperature, leads to an overall narrowing of the spectral width. Therefore, not accountingfor the impurity content will lead to underestimations of the inferred bulk ion temperature. Toquantify the underestimation we inferred the ion temperature assuming a pure hydrogen plasma,from the spectrum calculated for a hydrogen plasma containing 5% of carbon. The result of theinference yielded a value of Ti = 2.3 keV (instead of the correct value of Ti = 3 keV). The numberof different impurities to be accounted for was investigated by comparing spectra calculated withseveral impurity species to spectra calculated with one main impurity - carbon in our case. It wasfound that the spectral width, and thus the inference of Ti, is dominantly affected by impurity withthe largest concentration. This can be seen in figure 2 where we compare a spectrumwith 5% ofC6+ions to a spectrum with the same carbon concentration but with added 1% of O8+ ions. The changein width caused by the addition of 1% of O8+ ions is within the expected error bars and thus the1The oxygen concentration range was chosen based on preliminary measurements obtained by charge exchangerecombination spectroscopy during OP1.2.– 2 –2019 JINST 14 C10021Figure 1. Left: synthetic CTS spectra calculated for different carbon concentrations at bulk ion temperatureTi = 3 keV. The larger the amount of carbon, the more narrow the spectrum. Right: synthetic CTS spectralcalculated for different oxygen concentrations at bulk ion temperature Ti = 3 keV. The effect of oxygen onthe wings of the spectrum is small. A larger effect is in the central region which is not visible in measuredspectra as it falls within the notch.Figure 2. Comparison of a hydrogen plasma with carbon impurity and a hydrogen plasma with a mixture ofcarbon and oxygen impurities.inclusion of oxygen in the analysis will not improve the accuracy of theTi measurement significantly.However, the discrepancy visible in figure 2 can be understood in terms of the sensitivity of thespectra to the effective charge:Zeff =∑i Z2i nine(2.1)where the summation goes over the ion species, Zi and ni are the charge and density of thecorresponding ion i, ne is the electron density. The sensitivity to changes in Zeff can be used forimprovement of Ti inference2 provided information on impurities obtained from other diagnosticsis incorporated into the CTS analysis.3 Notch filter width and temperature inferenceThe CTS probing radiation on W7-X is supplied by one of the ECRH gyrotrons [15] operating at0.5–1 MW output power and 140 GHz probing frequency. The CTS uses a sensitive heterodynereceiver to measure a scattering signal in the frequency band 135 GHz to 145 GHz. The receiverneeds to be protected from incident gyrotron and stray radiation. To this end, notch filters are used2Or inference of Zeff from CTS measurements which is outside the scope of this paper.– 3 –2019 JINST 14 C10021Figure 3. Left: a synthetic spectrum with added noise from which regions of different widths have beenomitted and ion temperature inferred. The input temperature is Ti = 5 keV. The part of the spectrum withinthe notch does not carry information about the bulk ion temperature. Right: the ratio Toutput/Tinput is givenas a function of the omitted notch region widths.to attenuate signals in a frequency band around the probing frequency. For this reason the datapoints measured within the notch region have to be discarded in the data analysis process. Bayesianinference can be used on what remains of a spectrum after the notch region has been removed.To investigate how the notch width affects the inference of bulk ion temperature, we analysed aspectrum from which regions of increasing width have been removed. The synthetic spectrum andthe simulated notch widths are depicted in figure 3 where the narrowest notch region is 0.2 GHz andthe widest is 1.4 GHz.3 We initially inferred the ion temperature from the full spectrum obtainingconvergence after approximately 100 iterations and the result Ti = 5 ± 0.01 keV. Then we inferredthe ion temperature from the same spectrum from which notch regions of differing widths wereexcluded and the number of iterations pre-set to 500. The exercise was repeated with Gaussiannoise introduced into the notch region.4 It was found that the inference for a pre-set number ofiterations is improved by the addition of noise. We understand that in a Bayesian fashion in termsof the amount of information in this spectral region. Namely, the removed region is dominated bythe impurity contribution which is not very sensitive to the changes in bulk ion temperature.5 Thusthe presence of noise is recognized as an indication of a lack of useful bulk temperature informationwithin the notch. This led us to the conclusion that notches wider than the currently employed canbe used without causing loss of accuracy in Ti inference. The constraint on the notch width is givenby the lowest expected bulk ion temperature (the wings of the spectrum must remain outside of thenotch otherwise no signal can be detected).4 Summary and conclusionWe looked into two topics important for the data analysis and operation of the CTS diagnostic:impurities and the notch filter width.Study of the influence of impurities on synthetic CTS spectra led us to conclude that for bulkion temperature inference it suffices to account for the dominant impurity in the data analysis.3Note that the negative values of spectral power density in figure 3 are not physical. Gaussian noise is generatedindependently from the calculated synthetic spectrum and is then added to it which results in the spectrum shown infigure 3.4Introduction of Gaussian noise can be justified by considering that when background is subtracted from a measuredCTS signal, and calibration is applied, what remains is thermal noise.5The impurities affect the inference quality through plasma dilution as explained in section 2.– 4 –2019 JINST 14 C10021The minimum width of the hardware notch is constrained by the CTS receiver safety in givenexperimental conditions. On W7-X, the probing gyrotron is one of ten ECRH gyrotrons. Thisimplies that there can be unabsorbed ECRH radiation entering the receiver at frequencies close tothe probe frequency. Furthermore, the gyrotron frequency can be unstable and chirps in frequencyoccur when the source is turned on or off. For these reasons a hardware notch of several hundredMHz is currently necessary (at the moment 500 MHz). However, the notch width study showed thatnotch regions larger than the currently employed on W7-X are acceptable for bulk ion temperatureinference. The maximum width of a hardware notch which could be used depends on the widthof the expected spectra defined by the relevant ion temperature range and impurity content. Thereplacement of data within the notch region by Gaussian noise prior to the Bayesian inference ofTi, will reduce the number of iterations needed for convergence of the fit.The possible improvement of Ti inference by independent measurement of effective chargeshould be further investigated.AcknowledgmentsThis work has been carried out within the framework of the EUROfusion Consortium and hasreceived funding from the Euratom research and training programme 2014–2018 and 2019–2020under grant agreement No 633053. The views and opinions expressed herein do not necessarilyreflect those of the European Commission.References[1] D. Moseev et al., Recent progress in fast-ion diagnostics for magnetically confined plasmas, Rev.Mod. Plasma. Phys. 2 (2018) 7.[2] I. Abramovic et al., Core ion temperature measurements by collective Thomson scattering inWendelstein 7-X, to be submitted to Nucl. Fusion (2019).[3] M. Salewski et al., Deuterium temperature, drift velocity, and density measurements innon-Maxwellian plasmas at ASDEX Upgrade, Nucl. Fusion 58 (2018) 036017.[4] R. Fonck, D. Darrow and K. Jaehnig, Determination of plasma-ion velocity distribution viacharge-exchange recombination spectroscopy, Phys. Rev. A 29 (1984) 3288.[5] M. Nishiura et al., Spectrum response and analysis of 77 GHz band collective Thomson scatteringdiagnostic for bulk and fast ions in LHD plasmas, Nucl. Fusion 54 (2014) 023006.[6] M. Nishiura et al., Notch filter in 70 GHz range for microwave plasma diagnostics, Plasma FusionRes. 8 (2013) 402027.[7] M. Salewski et al., Comparison of fast ion collective Thomson scattering measurements at ASDEXUpgrade with numerical simulations, Nucl. Fusion 50 (2010) 035012.[8] M. Salewski et al., Alpha-particle velocity-space diagnostic in ITER, Nucl. Fusion 58 (2018) 096019.[9] I. Abramovic et al., Forward modelling of collective Thomson scattering for Wendelstein 7-Xplasmas: electrostatic approximation, Rev. Sci. Instrum. 90 (2019) 023501.[10] I. Abramovic, M. Salewski and D. Moseev, Collective Thomson scattering model for arbitrarilydrifting bi-Maxwellian velocity distributions, AIP Adv. 9 (2019) 035252.– 5 –2019 JINST 14 C10021[11] J. Svensson and A. Werner, Large scale Bayesian data analysis for nuclear fusion experiments, in theproceedings of the IEEE Workshop on Intelligent Signal Processing (WISP), Alcalá de Henares,España (2007).[12] N.A. Pablant et al., Core radial electric field and transport in Wendelstein 7-X plasmas, Phys.Plasmas 25 (2018) 022508.[13] I. Abramovic et al., Collective Thomson scattering data analysis for Wendelstein 7-X, 2017 JINST 12C08015.[14] D. Moseev and M. Salewski, Bi-Maxwellian, slowing-down, and ring velocity distributions of fastions in magnetized plasmas, Phys. Plasmas 26 (2019) 020901.[15] D. Moseev et al., Collective Thomson scattering diagnostic on Wendelstein 7-X, Rev. Sci. Instrum. 90(2019) 013503.– 6 –

Optimization of the Collective Thomson scattering diagnostic for future operation

 Optimization of the Collective Thomson scattering diagnosticfor future operationCitation for published version (APA):Wendelstein 7-X Team, Abramovic, I., & Lopes Cardozo, N. J. (2019). Optimization of the Collective Thomsonscattering diagnostic for future operation. Journal of Instrumentation, 14(10), Article C10021.https://doi.org/10.1088/1748-0221/14/10/C10021Document license:TAVERNEDOI:10.1088/1748-0221/14/10/C10021Document status and date:Published: 01/10/2019Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 04. Oct. 2023Journal of Instrumentation     Optimization of the Collective Thomson scattering diagnostic for futureoperationTo cite this article: I. Abramovic et al 2019 JINST 14 C10021 View the article online for updates and enhancements.This content was downloaded from IP address 131.155.144.47 on 15/01/2020 at 07:282019 JINST 14 C10021Published by IOP Publishing for Sissa MedialabReceived: June 30, 2019Revised: September 1, 2019Accepted: September 30, 2019Published: October 15, 20193rd European Conference on Plasma Diagnostics (ECPD2019)6–10 May 2019Lisbon, PortugalOptimization of the Collective Thomson scatteringdiagnostic for future operationI. Abramovic,a,b,1 D. Moseev,b T. Stange,b S. Marsen,b W. Kasparek,c S.K. Nielsen,dA. Tancetti,d M. Salewski,d A. Pavone,b J. Svensson,b R.C. Wolf,b H.P. Laqua,bN.J. Lopes Cardozoa and the W7-X TeambaEindhoven University of Technology,De Zaale, 5612 AJ Eindhoven, The NetherlandsbMax-Planck Institute für Plasma Physik,Wendelsteinstraße 1, D-17491 Greifswald, GermanycUniversity of Stuttgart,Keplerstraße 7, 70174 Stuttgart, GermanydTechnical University of Denmark, Fysikvej,2800 Kgs. Lyngby, DenmarkE-mail: i.abramovic@tue.nlAbstract: Collective Thomson scattering (CTS) is a microwave diagnostic allowing measurementsof a number of plasma parameters such as the bulk ion temperature, the plasma composition, driftvelocities and fast ion velocity distribution function. A CTS system has been successfully installedand commissioned on the Wendelstein 7-X (W7-X) stellarator. The measured spectra are analyzedby the means of the CTS forward model eCTS and the Minerva scientific framework enabling theuse of Bayesian inference of relevant plasma parameters. Here we discuss the options for furtheroptimization of the CTS diagnostic and focus on two topics of importance for the inference ofbulk ion temperature values from CTS spectra: influence of impurities on the CTS spectra and thewidth of the notch filters that are employed to protect the receiver from high-power radiation. Inaddition to that we discuss the possibility of effective charge measurements by CTS. We explorethe existence of an optimal notch filter width.Keywords: Nuclear instruments and methods for hot plasma diagnostics; Analysis and statisticalmethods1Corresponding author.c© 2019 University of Technology Eindhoven. Published by IOPPublishing Ltd on behalf of Sissa Medialab https://doi.org/10.1088/1748-0221/14/10/C100212019 JINST 14 C10021Contents1 Introduction 12 Impurity content and temperature inference 23 Notch filter width and temperature inference 34 Summary and conclusion 41 IntroductionThe Wendelstein 7-X, the world’s largest optimized stellarator, has completed two operationalperiods OP 1.1 (in 2015–2016) and OP 1.2 (in 2017–2018). Collective Thomson scattering (CTS)is a microwave diagnostic capable of measuring a number of plasma parameters [1]. CTS hasrecently been installed and commissioned on Wendelstein 7-X (W7-X) during OP 1.2, and firstmeasurements of bulk ion temperature, Ti, by CTS were obtained [2]. CTS and deuterium-basedcharge-exchange recombination spectroscopy measure the deuterium temperature [3], whereas themore common impurity-based charge-exchange recombination spectroscopy diagnostics measurethe impurity temperatures [4]. CTS diagnostics are in operation at the LHD device [5, 6] andASDEXUpgrade [7] and will be an important diagnostic at ITER [8]. The measured spectra at W7-X were extensively compared with numerical simulations made by the forward model eCTS [9, 10]whose input parameterswere inferred by theBayesianMaximum-A-Posteriormethod in theMinervaframework [11]. The obtained value of Ti is in agreement with the result obtained by the X-rayimaging spectroscopy [12], and agreement was obtained between synthetic and measured spectra,yet a few discrepancies in spectral shape and width were noted [2]. In this paper we will discussa possible cause of these discrepancies, namely, the plasma impurity content and its effect onsynthetic CTS spectra (section 2). Impurity ions, being heavier than the hydrogen ions, give riseto contributions to the scattering spectrum close to the central wavelength, thereby distorting thespectrum of the scattering on pure hydrogen.Additionally we will elaborate on an important consideration for future operation of CTS onW7-X: the influence of the notch filter width on the temperature inference quality. The CTS systemon W7-X features two notches at 137 GHz and 140 GHz which are 1000 MHz and 500 MHz wide,respectively. They protect the sensitive heterodyne receiver from high-power radiation. In additionwe also have a built-in interlock into the pin-switch which closes automatically if too strong a signalis detected behind the notch filters. The notch filters can be tuned to block a more narrow frequencyband which may be beneficial for the bulk ion temperature inference quality. However, as the riskof damaging the CTS receiver increases with the decrease in the notch filter width, it is worthwhileto investigate if an optimal width exists (section 3).– 1 –2019 JINST 14 C100212 Impurity content and temperature inferenceIn W7-X plasmas impurity concentrations have been measured by charge exchange recombinationspectroscopy and passive spectroscopy. The impurities with the largest concentrations in OP1.2were carbon, oxygen and argon. In particular the effect of carbon was clearly visible in CTSmeasurements [2] and needed to be accounted for in the inference of bulk ion temperature, Ti, fromthe measured spectra. The spectral width, from which Ti is inferred [13, 14], is sensitive also to theimpurity content. To further explore the implications of this for ion temperature measurements byCTS, it is of interest to answer two questions:1. How large is the error one makes if the plasma is assumed to be pure?2. How many impurity species should be accounted for in the analysis?To answer these questions we investigated how the spectra change if the concentration and thenumber of impurities are varied. We calculated synthetic spectra at Ti = 3 keV for differentconcentrations of the two main impurities: carbon and oxygen. The carbon concentration wasvaried from 1% to 5% in a hydrogen plasma. The result is depicted in figure 1 on the left. Theoxygen concentration was varied from 0.6% to 1% in a hydrogen plasma.1 The result is depictedin figure 1 on the right. In both figures the borders of the rectangular notch region are indicated.In figure 1 the electron density is a fixed parameter thus the hydrogen ion density decreases withthe increase of impurity ions. The change in ion density has a scaling effect on CTS spectra [13].Temperatures of all ion species are assumed to be equal and set to 3 keV. As can be seen in figure 1,the spectra consist of two parts: the narrow impurity feature (absent for pure hydrogen plasma) andthe broad feature (containing information about both the impurity ions and the bulk ions). It followsfrom theory that the heavier the impurity is, the more narrow the impurity feature is, at a given iontemperature. This means that often the impurity feature is completely within the notch region whichin practice is wider than indicated in figure 1. Effective widening of the notch in measurements isdue to the non-ideal characteristics of notch filters causing a poor signal-to-noise ratio in a widerspectral range. However, even if the impurity feature is within the notch, the impurities affectthe broad spectral feature outside the notch. The increase in impurity concentration, at a givenion temperature, leads to an overall narrowing of the spectral width. Therefore, not accountingfor the impurity content will lead to underestimations of the inferred bulk ion temperature. Toquantify the underestimation we inferred the ion temperature assuming a pure hydrogen plasma,from the spectrum calculated for a hydrogen plasma containing 5% of carbon. The result of theinference yielded a value of Ti = 2.3 keV (instead of the correct value of Ti = 3 keV). The numberof different impurities to be accounted for was investigated by comparing spectra calculated withseveral impurity species to spectra calculated with one main impurity - carbon in our case. It wasfound that the spectral width, and thus the inference of Ti, is dominantly affected by impurity withthe largest concentration. This can be seen in figure 2 where we compare a spectrumwith 5% ofC6+ions to a spectrum with the same carbon concentration but with added 1% of O8+ ions. The changein width caused by the addition of 1% of O8+ ions is within the expected error bars and thus the1The oxygen concentration range was chosen based on preliminary measurements obtained by charge exchangerecombination spectroscopy during OP1.2.– 2 –2019 JINST 14 C10021Figure 1. Left: synthetic CTS spectra calculated for different carbon concentrations at bulk ion temperatureTi = 3 keV. The larger the amount of carbon, the more narrow the spectrum. Right: synthetic CTS spectralcalculated for different oxygen concentrations at bulk ion temperature Ti = 3 keV. The effect of oxygen onthe wings of the spectrum is small. A larger effect is in the central region which is not visible in measuredspectra as it falls within the notch.Figure 2. Comparison of a hydrogen plasma with carbon impurity and a hydrogen plasma with a mixture ofcarbon and oxygen impurities.inclusion of oxygen in the analysis will not improve the accuracy of theTi measurement significantly.However, the discrepancy visible in figure 2 can be understood in terms of the sensitivity of thespectra to the effective charge:Zeff =∑i Z2i nine(2.1)where the summation goes over the ion species, Zi and ni are the charge and density of thecorresponding ion i, ne is the electron density. The sensitivity to changes in Zeff can be used forimprovement of Ti inference2 provided information on impurities obtained from other diagnosticsis incorporated into the CTS analysis.3 Notch filter width and temperature inferenceThe CTS probing radiation on W7-X is supplied by one of the ECRH gyrotrons [15] operating at0.5–1 MW output power and 140 GHz probing frequency. The CTS uses a sensitive heterodynereceiver to measure a scattering signal in the frequency band 135 GHz to 145 GHz. The receiverneeds to be protected from incident gyrotron and stray radiation. To this end, notch filters are used2Or inference of Zeff from CTS measurements which is outside the scope of this paper.– 3 –2019 JINST 14 C10021Figure 3. Left: a synthetic spectrum with added noise from which regions of different widths have beenomitted and ion temperature inferred. The input temperature is Ti = 5 keV. The part of the spectrum withinthe notch does not carry information about the bulk ion temperature. Right: the ratio Toutput/Tinput is givenas a function of the omitted notch region widths.to attenuate signals in a frequency band around the probing frequency. For this reason the datapoints measured within the notch region have to be discarded in the data analysis process. Bayesianinference can be used on what remains of a spectrum after the notch region has been removed.To investigate how the notch width affects the inference of bulk ion temperature, we analysed aspectrum from which regions of increasing width have been removed. The synthetic spectrum andthe simulated notch widths are depicted in figure 3 where the narrowest notch region is 0.2 GHz andthe widest is 1.4 GHz.3 We initially inferred the ion temperature from the full spectrum obtainingconvergence after approximately 100 iterations and the result Ti = 5 ± 0.01 keV. Then we inferredthe ion temperature from the same spectrum from which notch regions of differing widths wereexcluded and the number of iterations pre-set to 500. The exercise was repeated with Gaussiannoise introduced into the notch region.4 It was found that the inference for a pre-set number ofiterations is improved by the addition of noise. We understand that in a Bayesian fashion in termsof the amount of information in this spectral region. Namely, the removed region is dominated bythe impurity contribution which is not very sensitive to the changes in bulk ion temperature.5 Thusthe presence of noise is recognized as an indication of a lack of useful bulk temperature informationwithin the notch. This led us to the conclusion that notches wider than the currently employed canbe used without causing loss of accuracy in Ti inference. The constraint on the notch width is givenby the lowest expected bulk ion temperature (the wings of the spectrum must remain outside of thenotch otherwise no signal can be detected).4 Summary and conclusionWe looked into two topics important for the data analysis and operation of the CTS diagnostic:impurities and the notch filter width.Study of the influence of impurities on synthetic CTS spectra led us to conclude that for bulkion temperature inference it suffices to account for the dominant impurity in the data analysis.3Note that the negative values of spectral power density in figure 3 are not physical. Gaussian noise is generatedindependently from the calculated synthetic spectrum and is then added to it which results in the spectrum shown infigure 3.4Introduction of Gaussian noise can be justified by considering that when background is subtracted from a measuredCTS signal, and calibration is applied, what remains is thermal noise.5The impurities affect the inference quality through plasma dilution as explained in section 2.– 4 –2019 JINST 14 C10021The minimum width of the hardware notch is constrained by the CTS receiver safety in givenexperimental conditions. On W7-X, the probing gyrotron is one of ten ECRH gyrotrons. Thisimplies that there can be unabsorbed ECRH radiation entering the receiver at frequencies close tothe probe frequency. Furthermore, the gyrotron frequency can be unstable and chirps in frequencyoccur when the source is turned on or off. For these reasons a hardware notch of several hundredMHz is currently necessary (at the moment 500 MHz). However, the notch width study showed thatnotch regions larger than the currently employed on W7-X are acceptable for bulk ion temperatureinference. The maximum width of a hardware notch which could be used depends on the widthof the expected spectra defined by the relevant ion temperature range and impurity content. Thereplacement of data within the notch region by Gaussian noise prior to the Bayesian inference ofTi, will reduce the number of iterations needed for convergence of the fit.The possible improvement of Ti inference by independent measurement of effective chargeshould be further investigated.AcknowledgmentsThis work has been carried out within the framework of the EUROfusion Consortium and hasreceived funding from the Euratom research and training programme 2014–2018 and 2019–2020under grant agreement No 633053. The views and opinions expressed herein do not necessarilyreflect those of the European Commission.References[1] D. Moseev et al., Recent progress in fast-ion diagnostics for magnetically confined plasmas, Rev.Mod. Plasma. Phys. 2 (2018) 7.[2] I. Abramovic et al., Core ion temperature measurements by collective Thomson scattering inWendelstein 7-X, to be submitted to Nucl. Fusion (2019).[3] M. Salewski et al., Deuterium temperature, drift velocity, and density measurements innon-Maxwellian plasmas at ASDEX Upgrade, Nucl. Fusion 58 (2018) 036017.[4] R. Fonck, D. Darrow and K. Jaehnig, Determination of plasma-ion velocity distribution viacharge-exchange recombination spectroscopy, Phys. Rev. A 29 (1984) 3288.[5] M. Nishiura et al., Spectrum response and analysis of 77 GHz band collective Thomson scatteringdiagnostic for bulk and fast ions in LHD plasmas, Nucl. Fusion 54 (2014) 023006.[6] M. Nishiura et al., Notch filter in 70 GHz range for microwave plasma diagnostics, Plasma FusionRes. 8 (2013) 402027.[7] M. Salewski et al., Comparison of fast ion collective Thomson scattering measurements at ASDEXUpgrade with numerical simulations, Nucl. Fusion 50 (2010) 035012.[8] M. Salewski et al., Alpha-particle velocity-space diagnostic in ITER, Nucl. Fusion 58 (2018) 096019.[9] I. Abramovic et al., Forward modelling of collective Thomson scattering for Wendelstein 7-Xplasmas: electrostatic approximation, Rev. Sci. Instrum. 90 (2019) 023501.[10] I. Abramovic, M. Salewski and D. Moseev, Collective Thomson scattering model for arbitrarilydrifting bi-Maxwellian velocity distributions, AIP Adv. 9 (2019) 035252.– 5 –2019 JINST 14 C10021[11] J. Svensson and A. Werner, Large scale Bayesian data analysis for nuclear fusion experiments, in theproceedings of the IEEE Workshop on Intelligent Signal Processing (WISP), Alcalá de Henares,España (2007).[12] N.A. Pablant et al., Core radial electric field and transport in Wendelstein 7-X plasmas, Phys.Plasmas 25 (2018) 022508.[13] I. Abramovic et al., Collective Thomson scattering data analysis for Wendelstein 7-X, 2017 JINST 12C08015.[14] D. Moseev and M. Salewski, Bi-Maxwellian, slowing-down, and ring velocity distributions of fastions in magnetized plasmas, Phys. Plasmas 26 (2019) 020901.[15] D. Moseev et al., Collective Thomson scattering diagnostic on Wendelstein 7-X, Rev. Sci. Instrum. 90(2019) 013503.– 6 –

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Optimization of the Collective Thomson scattering diagnostic for future operation

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