A S Jacobsen

B Geiger

F Leipold

J Rasmussen

M Salewski

M Stejner

M Weiland

null null

S B Korsholm

S K Nielsen

Jacobsen, A.

Salewski, M.

Geiger, B.

Korsholm, S.

Leipold, F.

Nielsen, S.

Rasmussen, J.

Stejner, M.

Weiland, M.

MPG.PuRe

5 January 2016Benchmark and combined velocity-spacetomography of fast-ion D-alpha spectroscopy andcollective Thomson scattering measurementsA.S. Jacobsen1, M. Salewski1, B. Geiger2, S.B. Korsholm1,F. Leipold1, S.K. Nielsen1, J. Rasmussen1, M. Stejner1,M. Weiland2 and the ASDEX Upgrade team21 Technical University of Denmark, Department of Physics, DK-2800 Kgs. Lyngby,Denmark2 Max Planck Institute for Plasma Physics, D-85748 Garching, GermanyE-mail: ajsen@fysik.dtu.dkAbstract. We demonstrate the combination of fast-ion D-alpha spectroscopy (FIDA)and collective Thomson scattering (CTS) measurements to determine a common bestestimate of the fast-ion velocity distribution function by velocity-space tomography.We further demonstrate a benchmark of FIDA tomography and CTS measurementswithout using a numerical simulation as common reference. Combined velocity-spacetomographies from FIDA and CTS measurements confirm that sawtooth crashes reducethe fast-ion phase-space densities in the plasma center and affect ions with pitches closeto one more strongly than those with pitches close to zero.1. IntroductionASDEX Upgrade is equipped with several fast-ion diagnostics [1]. Collective Thomsonscattering (CTS) [2–5] and fast-ion Dα (FIDA) spectroscopy [6–9] are sensitive to thefast-ion velocity distribution function in small measurement volumes. Neutron emissionspectroscopy (NES) [10], neutral particle analyzers [11] and gamma-ray spectroscopy(GRS) [12] are sensitive to the fast-ion velocity distribution function along their lines-of-sight. Fast-ion loss detectors are sensitive to ions ejected from the plasma [13].FIDA measurements can be interpreted using velocity-space tomography [14–17].With this method one determines the velocity distribution function F from themeasurements S by solving the discrete inverse problem S = WF where W is amatrix composed of so-called weight functions [18, 19]. These reveal the velocity-space sensitivity of the measurements. The method has recently been demonstratedexperimentally [7] and has since been applied to study sawtooth crashes [9, 17, 20].Theoretical expectations [21,22] and previous experiments on TEXTOR using CTS [23]and on DIII-D and ASDEX Upgrade using FIDA [8,24] indicated that sawtooth crasheseject fast ions with pitches close to one more strongly than those with pitches close toA.S. Jacobsen et al. 2#30382      036MWNBI power      0361019/m3ne      048keVTe      048keVTi2.0 2.2 2.4 2.6 2.8 3.0Time [s]012100 krad/srotationρ t = 0.1 ρ t = 0.3 ρ t = 0.6Figure 1. Overview of discharge #30382 showing the neutral beam injection (NBI)power, electron density, electron temperature, ion temperature and plasma rotation.zero from the plasma center. FIDA tomographies of 2D fast-ion velocity distributionfunctions allow the calculation of the sawtooth-induced redistribution as a function ofenergy and pitch of the fast ions, confirming the pitch dependence of sawtooth crashes[9, 17, 20]. Simultaneous FIDA tomographies inside and outside the sawtooth inversionradius showed that this decrease of the phase-space densities inside the inversion radius isaccompanied by a corresponding increase outside [20]. A reduction of the fast-ion densityabove a threshold energy of 10 keV in the plasma center could further be calculated [9].Here we experimentally demonstrate firstly a method to benchmark and secondly amethod to combine different fast-ion diagnostics using simultaneous FIDA and CTSmeasurements at ASDEX Upgrade. Consistency checks across fast-ion diagnosticsare difficult as the diagnostics observe different regions in position space as well asin velocity space. Therefore, consistency has usually been assessed by comparing themeasurements with synthetic measurements based on TRANSP/NUBEAM simulationsas common reference [4,18,25]. Velocity-space tomography allows us to benchmark CTSand FIDA measurements without simulations. Further, we experimentally demonstratea combination of different fast-ion diagnostics using velocity-space tomography ofsimultaneous FIDA and CTS measurements [15].2. Benchmark of FIDA tomography and CTSIn this section we calculate synthetic CTS measurements implied by a FIDA tomographyfrom simultaneously acquired spectra from four views and compare them with actualCTS measurements in discharge #30382 [26]. The discharge was heated by the 60 keVneutral beam injector Q3 at 2.5 MW. Figure 1 shows an overview of main plasmaparameters revealing the presence of sawteeth as periodic variations in electron density,ion temperature and toroidal rotation. Figure 2 shows simultaneously acquired spectrafrom four FIDA views before and after the large sawtooth crash at t = 2.29 s. Thesawtooth crash leads to reductions in the measured FIDA intensities. The measurementvolumes of the four FIDA views are at a normalized toroidal flux of ρt = 0.1. The FIDAspectra depend not only on the fast-ion phase-space densities but also on nuisanceA.S. Jacobsen et al. 3parameters such as the electron density which themselves show sawtoothing behaviour(figure 1). FIDA tomographies account for any changes in nuisance parameters. Thebeam deposition profile does not change significantly during a sawtooth crash as thebeam emission in the central measurement volume remains approximately constant [9].We reject spectral ranges dominated by beam emission or impurity lines. The beamemission typically dominates the FIDA emission at moderate Doppler shifts. Here thestrongest impurity transitions are Boron V (n = 10 → 8), Oxygen II, Oxygen V andHelium II. We also reject spectral ranges in the spectra that are sensitive to ions below10 keV (thermal ions) or only to ions above 80 keV as we do not attempt to reconstructthese regions. The rejected spectral ranges are shown in figure 2. As the NBI wasnot modulated, a standard subtraction of background noise and impurity lines in theFIDA spectra is not applicable. This decreases the usable wavelength ranges. The lowdensity (ne = 3 × 1019m−3) makes up for this shortcoming due to the resulting highsignal-to-noise ratio of the FIDA measurements.645 650 655 660 665101410151016101710181019wavelength [nm]Intensity [ph/(s nm m2  sr)]  BeforeAfter(a) φ = 14◦645 650 655 660 665101410151016101710181019wavelength [nm]Intensity [ph/(s nm m2  sr)]  BeforeAfter(b) φ = 129◦645 650 655 660 665101410151016101710181019wavelength [nm]Intensity [ph/(s nm m2  sr)]  BeforeAfter(c) φ = 70◦650 655 660101410151016101710181019wavelength [nm]Intensity [ph/(s nm m2  sr)]  BeforeAfter(d) φ = 155◦Figure 2. Simultaneously measured FIDA spectra in four views before and after asawtooth crash at t = 2.29 s in discharge #30382. The shaded regions are rejected. φis the angle between the line-of-sight and the magnetic field.E [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(a) BeforeE [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(b) AfterFigure 3. FIDA tomographies [ions/m3/keV] before and after a sawtooth crash att = 2.29 s in discharge #30382 based on the spectra from figure 2.Figure 3 shows FIDA tomographies before and after the sawtooth crash ascalculated from the FIDA spectra in figure 2 using the minimum Fisher informationregularization method on a 15 × 15 grid [17]. The FIDA tomographies allow theA.S. Jacobsen et al. 4computation of synthetic CTS measurements, i.e. 1D velocity-distribution functionsg(u) which are projections of the full distribution function onto the plasma fluctuationwave vector [27]. These synthetic CTS measurements are shown together with the actualCTS measurements before and after the sawtooth crash in figure 4. The syntheticand actual CTS measurements include the injected fast ions as well as the fast ionsfound in the tails of the thermal ion distribution. The synthetic CTS measurementsmatch the actual CTS measurements well within the uncertainties. The syntheticCTS measurements tend to lie marginally above the actual CTS measurements whichcould be explained by calibration uncertainty or by the presence of impurity lightthat is misinterpreted as FIDA light. Another possible explanation is that the FIDAmeasurement volume is slightly on the low field side whereas the CTS measurementvolume is slightly on the high field side. Hence trapped particles might not reach theCTS measurement volume. However, it should be noted that the measurements arecentral with ρt < 0.1.−4 −2 0 2 4−0.500.511.52u [106 m/s]g(u) [1012  s/m4 ]  Measured CTSSynthetic CTSUncertainty(a) Before−4 −2 0 2 4−0.500.511.52u [106 m/s]g(u) [1012  s/m4 ]  Measured CTSSynthetic CTSUncertainty(b) AfterFigure 4. Comparison of real CTS measurements and synthetic CTS measurementsimplied by the FIDA tomographies in figure 3. The uncertainties include measurementnoise, uncertainties of nuisance parameters and, for the synthetic CTS measurementsbased on FIDA tomography, the bias due to the regularization [17].3. Combination of CTS and FIDA in velocity-space tomographyVelocity-space tomography allows us to combine measurements from different fast-iondiagnostics to calculate a common best estimate of the fast-ion distribution function[15]. Here we present the first experimental demonstration. For such a combination,the normalization of the measurements and of the weight function matrix with theestimated uncertainties becomes crucial [15]. These uncertainties need to be definedconsistently for the different diagnostics. CTS uncertainties account for uncertaintiesin the measured spectral power densities as well as in the nuisance parameters used inthe fit of g(u) [2, 4, 5]. Uncertainties in FIDA intensities can be calculated based onthe photon noise. However, the uncertainties in the nuisance parameters are often notaccounted for. Here we need to account for these uncertainties to treat FIDA and CTSA.S. Jacobsen et al. 5on an equal footing. They enter the problem as uncertainty in the weight functions.The FIDA weight functions depend on the electron temperature and density, the iontemperature and drift velocity and the effective charge. Here we estimate the uncertaintydue to these nuisance parameters as demonstrated in reference [17].E [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(a) BeforeE [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(b) AfterE [keV]pitch  20 40 60 80−1−0.500.51−1−0.500.51(c) ∆FrelE [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(d) TRANSP beforeE [keV]pitch  20 40 60 80−1−0.500.5100.511.52x 1017(e) TRANSP afterE [keV]pitch  20 40 60 80−1−0.500.51−1−0.500.51(f) TRANSP ∆FrelFigure 5. Velocity-space tomographies [ions/m3/keV] from combined FIDA and CTSmeasurements before and after the sawtooth crash at t = 2.29 s (as in figure 3) as wellas the relative change. The lower row shows corresponding TRANSP simulations. Inthe hatched area in (c) the uncertainties on the relative change (see figure 6) are largerthan the relative change.E [keV]pitch  20 40 60 80−1−0.500.5100.20.40.60.81Figure 6. Uncertainty of the relative crash size based on velocity-space tomographiesbefore and after the sawtooth crash. The uncertainties acount for photon noise,nuisance parameters and the bias due to the regularization [17]. Regions with largeuncertainties compared with the crash size are shown as hatched regions in figure 5.Figure 5 shows tomographies based on combined FIDA and CTS measurementsbefore and after the sawtooth crash together with a corresponding TRANSP simulation.A.S. Jacobsen et al. 6We neglect the small difference in the spatial locations of the measurement volumes asall volumes are central with ρt < 0.1. We further show the measured and simulatedrelative crash sizes ∆Frel = (Fafter − Fbefore)/Fbefore resolved in velocity space. Thefast-ion densities are strongly reduced due to the crash. This reduction is stronger forpitches close to one than for pitches close to zero for energies below about 40 keV.The tomographies confirm previous results based on FIDA tomographies from fiveviews which showed, however, a stronger pitch dependence [9,17,20]. The energy-pitchdependence of the sawtooth crash in the TRANSP simulation and the measurementis quite different. The relative crash size can be calculated throughout velocity spacesince the fast-ion densities in the tomography as well as in the TRANSP simulationthroughout velocity space are larger than zero. However, the values in the hatchedareas have large uncertainties. Figure 6 shows the estimated uncertainty of the relativechange based on uncertainties in the tomographies and standard error propagation. Theuncertainties represent photon noise, uncertainty due to nuisance parameters and thebias due to the regularization [17]. The relative change is reliable for positive pitch andenergies below the injection energy.A comparison of figure 5(a)–(b) and figure 3 shows that the addition of the CTSmeasurements does not change the tomographies appreciably. The inferred relative crashsizes as well as their uncertainties change marginally by about ±1%. Slight increases inuncertainty likely result from the systematic uncertainties discussed in section 2. Thesmall effect of CTS is expected in this discharge for three reasons. First, the FIDAmeasurements consist of 487 usable data points while the CTS measurements consistof 18. In the future the number of CTS measurements could be significantly increasedby using high frequency resolution CTS measurements [28] and two simultaneous CTSviews. Second, the uncertainty in FIDA measurements is about 5% of the total signalwhereas the uncertainty of CTS measurements is about 20%. Third, the reasonablematches between the FIDA-implied synthetic CTS measurements and the actual CTSmeasurements suggest that the CTS measurements agree with the FIDA tomographyand thus should not change it much.4. Discussion and ConclusionsWe have experimentally demonstrated that FIDA measurements from four views andCTS measurements from one view can be combined to give a common best estimateof the 2D fast-ion distribution function using velocity-space tomography. We furtherbenchmarked CTS measurements against synthetic measurements implied by FIDAtomography without the need for fast-ion simulations as common reference. Ourmethods are directly applicable to LHD which is equipped with CTS [29, 30] and twoFIDA views [31]. The availability of six FIDA views and two CTS views at ASDEXUpgrade will further improve the inversion for studies of for example Alfvén eigenmodesor the effect of ion cyclotron resonance heating. As our approach relies on weightfunctions for FIDA [18, 19] and CTS [32], it will, together with recently derived NESA.S. Jacobsen et al. 7weight functions [33] and GRS weight functions [34], allow us to combine GRS and NESmeasurements at JET [35] in velocity-space tomography of fusion alphas in the upcomingJET D-T campaign [36]. Lastly, ITER will be equipped with GRS, NES and CTSdiagnostics. A helium variant of FIDA could provide additional measurements. Thus,the methods of benchmarking and combination of fast-ion diagnostics experimentallydemonstrated here will apply to ITER. We demonstrated our approach by benchmarkingand combining FIDA and CTS measurements before and after a sawtooth crash atASDEX Upgrade. Previous results of the crash size and the velocity-space resolvedejection of fast ions from the center based on FIDA tomography could be confirmed[8, 17, 20].AcknowledgmentsThis work has been carried out within the framework of the EUROfusion Consortiumand has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein donot necessarily reflect those of the European Commission.References[1] Stroth U et al 2013 Nucl. Fusion 53 104003[2] Salewski M et al 2010 Nucl. Fusion 50 035012[3] Furtula V et al 2012 Rev. Sci. Instrum. 83 013507[4] Rasmussen J et al 2015 Plasma Phys. Control. Fusion 57 075014[5] Nielsen S K et al 2015 Plasma Phys. Control. Fusion 57 035009[6] Geiger B et al 2011 Plasma Phys. Control. Fusion 53 065010[7] Salewski M et al 2014 Nucl. Fusion 54 023005[8] Geiger B et al 2015 Plasma Phys. Control. Fusion 57 014018[9] Geiger B et al 2015 Nucl. Fusion 83 083001[10] Tardini G et al 2012 Journal of Instrumentation 7 C03004–C03004[11] Schneider P A et al 2015 Rev. Sci. Instrum. 86 073508[12] Nocente M et al 2012 Nucl. Fusion 52 094021[13] Garćıa-Muñoz M et al 2007 Nucl. Fusion 47 L10–L15[14] Salewski M et al 2012 Nucl. Fusion 52 103008[15] Salewski M et al 2013 Nucl. Fusion 53 063019[16] Salewski M et al 2015 Plasma Phys. Control. Fusion 57 014021[17] Jacobsen A S et al Plasma Phys. Control. Fusion Inversion methods for fast–ion velocity–spacetomography in fusion plasmas[18] Heidbrink W W et al 2007 Plasma Phys. Control. Fusion 49 1457–1475[19] Salewski M et al 2014 Plasma Phys. Control. Fusion 56 105005[20] Weiland M et al Plasma Phys. Control. Fusion Enhancement of the FIDA diagnostic at ASDEXUpgrade for velocity space tomography[21] Kolesnichenko Y et al 2000 Nucl. Fusion 40 1325–1341[22] Jaulmes J et al 2015 14th IAEA Technical Meeting on Energetic Particles[23] Nielsen S K et al 2011 Nucl. Fusion 51 063014[24] Muscatello C M et al 2012 Plasma Phys. Control. Fusion 54 025006[25] Heidbrink W W et al 2014 Plasma Phys. Control. Fusion 56 095030A.S. Jacobsen et al. 8[26] Rasmussen J et al 2015 14th IAEA Technical Meeting on Energetic Particles[27] Moseev D et al 2011 Plasma Phys. Control. Fusion 53 105004[28] Stejner M et al 2015 Plasma Phys. Control. Fusion 57 062001[29] Kubo S et al 2010 Rev. Sci. Instrum. 81 10D535[30] Nishiura M et al 2014 Nucl. Fusion 54 023006[31] Ito T et al 2010 Rev. Sci. Instrum. 81 10D327[32] Salewski M et al 2011 Nucl. Fusion 51 083014[33] Jacobsen A S et al 2015 Nucl. Fusion 55 053013[34] Salewski M et al 2015 Nucl. Fusion 55 093029[35] Eriksson J et al 2015 Nucl. Fusion 55 123026[36] Romanelli F 2015 Nucl. Fusion 55 104001

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Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy and collective Thomson scattering measurements

We demonstrate the combination of fast-ion D-alpha spectroscopy (FIDA) and collective Thomson scattering (CTS) measurements to determine a common best estimate of the fastion velocity distribution function by velocity-space tomography. We further demonstrate a benchmark of FIDA tomography and CTS measurements without using a numerical simulation as common reference. Combined velocity-space tomographies from FIDA and CTS measurements confirm that sawtooth crashes reduce the fast-ion phase-space densities in the plasma center and affect ions with pitches close to one more strongly than those with pitches close to zero

Jacobsen, Asger Schou

Salewski, Mirko

Korsholm, Søren Bang

Leipold, Frank

Nielsen, Stefan Kragh

Rasmussen, Jesper

Pedersen, Morten Stejner

Online Research Database In Technology

Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy andcollective Thomson scattering measurements - DTU Orbit (08/11/2017) Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy and collective Thomson scatteringmeasurementsWe demonstrate the combination of fast-ion D-alpha spectroscopy (FIDA) and collective Thomson scattering (CTS)measurements to determine a common best estimate of the fastion velocity distribution function by velocity-spacetomography. We further demonstrate a benchmark of FIDA tomography and CTS measurements without using anumerical simulation as common reference. Combined velocity-space tomographies from FIDA and CTS measurementsconfirm that sawtooth crashes reduce the fast-ion phase-space densities in the plasma center and affect ions with pitchesclose to one more strongly than those with pitches close to zero. General informationState: PublishedOrganisations: Department of Physics, Plasma Physics and Fusion Energy, Max Planck Institute for Plasma PhysicsAuthors: Jacobsen, A. S. (Intern), Salewski, M. (Intern), Geiger, B. (Ekstern), Korsholm, S. B. (Intern), Leipold, F. (Intern),Nielsen, S. K. (Intern), Rasmussen, J. (Intern), Pedersen, M. S. (Intern), Weiland, M. (Ekstern)Number of pages: 5Publication date: 2016Main Research Area: Technical/natural sciences Publication informationJournal: Plasma Physics and Controlled FusionVolume: 58Issue number: 4Article number: 042002ISSN (Print): 0741-3335Ratings: BFI (2017): BFI-level 1 Web of Science (2017): Indexed yes BFI (2016): BFI-level 1 Scopus rating (2016): CiteScore 1 SJR 0.583 SNIP 0.617 Web of Science (2016): Indexed yes BFI (2015): BFI-level 1 Scopus rating (2015): SJR 0.734 SNIP 0.864 CiteScore 1.1 Web of Science (2015): Indexed yes BFI (2014): BFI-level 1 Scopus rating (2014): SJR 1.318 SNIP 1.235 CiteScore 1.61 Web of Science (2014): Indexed yes BFI (2013): BFI-level 1 Scopus rating (2013): SJR 1.088 SNIP 1.227 CiteScore 1.54 ISI indexed (2013): ISI indexed yes Web of Science (2013): Indexed yes BFI (2012): BFI-level 1 Scopus rating (2012): SJR 1.391 SNIP 1.142 CiteScore 1.63 ISI indexed (2012): ISI indexed yes Web of Science (2012): Indexed yes BFI (2011): BFI-level 1 Scopus rating (2011): SJR 1.512 SNIP 1.592 CiteScore 2.69 ISI indexed (2011): ISI indexed yes Web of Science (2011): Indexed yes BFI (2010): BFI-level 1 Scopus rating (2010): SJR 1.477 SNIP 1.41 Web of Science (2010): Indexed yes BFI (2009): BFI-level 1 Scopus rating (2009): SJR 1.589 SNIP 1.32 Web of Science (2009): Indexed yes BFI (2008): BFI-level 1 Scopus rating (2008): SJR 1.872 SNIP 1.603 Web of Science (2008): Indexed yes Scopus rating (2007): SJR 1.971 SNIP 1.389 Web of Science (2007): Indexed yes Scopus rating (2006): SJR 1.833 SNIP 1.403 Web of Science (2006): Indexed yes Scopus rating (2005): SJR 1.73 SNIP 1.55 Scopus rating (2004): SJR 2.232 SNIP 1.377 Scopus rating (2003): SJR 2.016 SNIP 1.247 Web of Science (2003): Indexed yes Scopus rating (2002): SJR 1.667 SNIP 1.022 Web of Science (2002): Indexed yes Scopus rating (2001): SJR 1.507 SNIP 1.23 Web of Science (2001): Indexed yes Scopus rating (2000): SJR 1.388 SNIP 1.124 Scopus rating (1999): SJR 2.148 SNIP 1.515 Original language: EnglishVelocity-space tomography, Collective Thomson scattering, Fast-ion D-alpha spectroscopy, Sawtooth crash, TokamakDOIs: 10.1088/0741-3335/58/4/042002 Source: FindItSource-ID: 2291842031Publication: Research - peer-review › Journal article – Annual report year: 2016 

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Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy and collective Thomson scattering measurements

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