García-Muñoz, M.

Geiger, B.

Heidbrink, W.W.

Jacobsen, Asger Schou

Korsholm, Søren Bang

Leipold, Frank

Madsen, Jens

Michelsen, Poul

Moseev, D.

Nielsen, Stefan Kragh

Rasmussen, Jesper

Salewski, Mirko

Stejner Pedersen, Morten

Tardini, G.

Jacobsen, AS

Salewski, M

Geiger, B

García-Muñoz, M

Heidbrink, WW

Korsholm, SB

Leipold, F

Madsen, J

Michelsen, PK

Moseev, D

Nielsen, SK

Rasmussen, J

Stejner, M

Tardini, G

eScholarship - University of California

How to compute velocity-space tomographies using several fast-ion diagnostics

Jacobsen, A.

Salewski, M.

Garcia-Munoz, M.

Heidbrink, W.

Korsholm, S.

Leipold, F.

Madsen, J.

Michelsen, P.

Nielsen, S.

Rasmussen, J.

Stejner, M.

MPG.PuRe

Bindslev, H.

How to compute velocity-space tomographies using several fast-iondiagnosticsA.S. Jacobsen1, M. Salewski1, B. Geiger2, M. García-Muñoz3, W.W. Heidbrink4,S.B. Korsholm1, F. Leipold1, J. Madsen1 P.K. Michelsen1, D. Moseev2,S.K. Nielsen1, J. Rasmussen1, M. Stejner1, G. Tardini2 and the ASDEX Upgrade Team21 Association Euratom - DTU, Technical University of Denmark,Department of Physics - DTU Risø Campus, DK-4000 Roskilde, Denmark2 Association Euratom - Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany3Universidad de Sevilla, 41004 Seville, Spain4 University of California, Irvine, California 92697, USAIntroductionASDEX Upgrade and LHD are equipped with collective Thomson scattering (CTS) [1–4]and fast-ion Dα (FIDA) [5, 6] diagnostics (or rather Hα in the case of LHD). These diagnosticsmeasure fast ions in small volumes compared with the plasma size. In either diagnostic onepre-selects a viewing direction through geometric arrangement of the experiment and measuresa 1D function, g, of the fast-ion 2D velocity-space distribution function f . In principle threeFIDA views and two CTS views are available at ASDEX Upgrade, and two additional FIDAviews are likely going to be installed in 2013. In the next ASDEX Upgrade campaign, sevenviews are thus expected to be available. Here we investigate the five-view FIDA system and theseven-view combined system through the use of synthetic measurements. Traditionally, fast-ionCTS or FIDA measurements are compared with simulated spectra to investigate whether themeasurements match the expectation [1, 7, 8]. However, if the real measurements disagree withthe synthetic measurements, it is often unclear what caused this discrepancy. Our final goal is toexperimentally determine f , and this might help establish where in 2D velocity space the mea-surements disagree with the theoretical prediction. Inference of velocity-space tomographiesfrom CTS or FIDA measurements was recently shown to be an achievable goal [9, 10]. We de-veloped methods to account for uncertainty in the measurements which allow the use of CTSand FIDA measurements together to compute a joint velocity-space tomography [11]. Applyingour prescription to a set of real 1D fast-ion measurements will yield an entirely experimentallydetermined 2D fast-ion velocity distribution.40th EPS Conference on Plasma Physics O6.512(a) CTS weight function. (b) FIDA weight function shown together with theoutline of the CTS weight function (black lines).Figure 1: Weight functions for CTS and FIDA for a projection angle of 32◦. The ranges of theprojected velocity, u, for the CTS weight function, and the wavelength, λ , for the FIDA weightfunction are chosen such that the weight functions are as similar as possible.Tomography of a velocity distribution function using a combination of diagnosticsFigure 1 shows weight functions for both CTS and FIDA for a viewing angle, φ , of 32◦. Theviewing angle is the angle between the magnetic field and the direction along which the velocitydistribution of the fast ion is resolved. Weight functions relate the 2D fast-ion velocity distri-bution function f to the 1D measurements g and are essential components of our developedtomography procedure [9–11]. The CTS weight function shown in figure 1(a) is calculated an-alytically [9]. The FIDA weight function shown in figure 1(b) cannot be calculated analyticallyand so is calculated numerically. The FIDA weight function takes into account Stark splitting,the charge-exchange reaction probability, the probability of the n=3 to n=2 electron transitionand instrumental effects in addition to the Doppler shift of the radiation. Figure 1(b) also showsthe outline of the CTS weight function, illustrated by the black lines, to ease the comparison ofthe two weight functions. It is clearly seen that CTS weight functions are symmetric whereasthe FIDA weight functions are asymmetric due to the effects of the charge-exchange probability.The slope of the outline of the FIDA weight function is furthermore slightly different comparedto that of the CTS weight function due to the Stark splitting [11].Figure 2 shows a typical ASDEX Upgrade fast-ion distribution function and two tomographicreconstructions. The distribution function shown in figure 2(a) is simulated using TRANSP andNUBEAM [12]. It shows maxima at full and half injection energy (60 keV and 30 keV) ofneutral beam injector S3 at ASDEX Upgrade. The tomographic reconstructions are made usingsynthetic measurements calculated from the TRANSP simulation. Previously we used different40th EPS Conference on Plasma Physics O6.512(a) Central fast-ion velocity distribution functiontypical for a low density discharge without mode-activity simulated using TRANSP/NUBEAM.(b) Reconstruction of the distribution function usingfive synthetic FIDA views containing 5% noise.(c) Reconstruction of the distribution function usingfive synthetic FIDA views combined with two syn-thetic CTS views containing 5% noise.Figure 2: A TRANSP/NUBEAM simulated fast ion velocity space distribution function andtomographic reconstructions of this. The unit of the colorbar is [s2/m5]. The tomographic re-constructions are made using synthetic measurements from five and seven views respectively.grids for the original function and the tomography which added numerical noise. Here we useidentical grids (31×15) but add 5% Gaussian noise to the measurements. The noise makesan accurate reconstruction of fine details impossible. Figure 2(b) shows a tomography usingsynthetic measurements from five FIDA views. For each view, the part of the spectrum thatwould be obscured in a real experiment due to beam emission and halo emission is omitted.Three of the chosen viewing angles are the angles of the three existing FIDA views at ASDEXUpgrade, which are here 11◦, 21◦ and 67◦. The remaining two viewing angles are 42◦ and83◦. It is seen how the overall shape of the distribution reappears in the tomography togetherwith the two beam injection maxima. However, the 30 keV maximum is located further to the40th EPS Conference on Plasma Physics O6.512right than in the simulation. Figure 2(c) shows the tomography using synthetic measurementsfrom the five FIDA views combined with two CTS views. This system thus simulates the actualviews expected to be available at ASDEX Upgrade during the next experimental campaign. Theviewing angles for the CTS views are chosen to be 73◦ and 79◦ which are realistic angles. Thepart of the spectrum in the CTS measurements that would be obscured by bulk ions are omitted.Each FIDA and CTS view contains about 100 measurements. By comparing figures 2(b) and2(c) it is seen that the tomography improves when a combination of FIDA views and CTS viewsare used. Both the peak intensity and the locations of the two beam injection maxima are betterresolved in the tomography using a combination of views.ConclusionsTomographic reconstructions using five synthetic FIDA views and a combination of five syn-thetic FIDA views and two synthetic CTS views are inferred. It is seen that the tomographyimproves when a combination of FIDA and CTS is used compared to the tomography inferredonly from FIDA views.AcknowledgementsThis work, supported by the European Communities under the contract of Association be-tween Euratom and DTU, was partly carried out within the framework of the European FusionDevelopment Agreement. The views and opinions expressed herein do not necessarily reflectthose of the European Commission.References[1] M. Salewski et al, Nuclear Fusion 50, 035012 (2010)[2] F. Meo et al, Journal of Physics: Conference Series 227 012010 (2010)[3] M. Nishiura et al, Review of Scientific Instruments 79, 10E731 (2008)[4] S. Kubo et al, Review of Scientific Instruments 81, 10D535 (2010)[5] B. Geiger et al, Plasma Physics and Controlled Fusion 53, 065010 (2011)[6] T. Ito et al, Plasma and Fusion Research 5, S2099 (2010)[7] W. W. Heidbrink et al, Plasma Physics and Controlled Fusion 49, 1457-1475 (2007)[8] W. W. Heidbrink, Review of Scientific Instruments 81, 10D727 (2010)[9] M. Salewski et al, Nuclear Fusion 51, 083014 (2011)[10] M. Salewski et al, Nuclear Fusion 52, 103008 (2012)[11] M. Salewski et al, Nuclear Fusion 53, 063019 (2013)[12] A. Pankin et al, Computer Physics Communications 159, 157-184 (2004)40th EPS Conference on Plasma Physics O6.512

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Downloaded from orbit.dtu.dk on: Dec 19, 2017How to compute velocity-space tomographies using several fast-ion diagnosticsJacobsen, Asger Schou; Salewski, Mirko; Geiger, B.; García-Muñoz, M.; Heidbrink, W.W.; Korsholm,Søren Bang; Leipold, Frank; Madsen, Jens; Michelsen, Poul; Moseev, D.; Nielsen, Stefan Kragh;Rasmussen, Jesper; Pedersen, Morten Stejner; Tardini, G.Published in:Europhysics conference abstractsPublication date:2013Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Jacobsen, A. S., Salewski, M., Geiger, B., García-Muñoz, M., Heidbrink, W. W., Korsholm, S. B., ... Tardini, G.(2013). How to compute velocity-space tomographies using several fast-ion diagnostics. In Europhysicsconference abstracts (Vol. 37D)How to compute velocity-space tomographies using several fast-iondiagnosticsA.S. Jacobsen1, M. Salewski1, B. Geiger2, M. García-Muñoz3, W.W. Heidbrink4,S.B. Korsholm1, F. Leipold1, J. Madsen1 P.K. Michelsen1, D. Moseev2,S.K. Nielsen1, J. Rasmussen1, M. Stejner1, G. Tardini2 and the ASDEX Upgrade Team21 Association Euratom - DTU, Technical University of Denmark,Department of Physics - DTU Risø Campus, DK-4000 Roskilde, Denmark2 Association Euratom - Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany3Universidad de Sevilla, 41004 Seville, Spain4 University of California, Irvine, California 92697, USAIntroductionASDEX Upgrade and LHD are equipped with collective Thomson scattering (CTS) [1–4]and fast-ion Dα (FIDA) [5, 6] diagnostics (or rather Hα in the case of LHD). These diagnosticsmeasure fast ions in small volumes compared with the plasma size. In either diagnostic onepre-selects a viewing direction through geometric arrangement of the experiment and measuresa 1D function, g, of the fast-ion 2D velocity-space distribution function f . In principle threeFIDA views and two CTS views are available at ASDEX Upgrade, and two additional FIDAviews are likely going to be installed in 2013. In the next ASDEX Upgrade campaign, sevenviews are thus expected to be available. Here we investigate the five-view FIDA system and theseven-view combined system through the use of synthetic measurements. Traditionally, fast-ionCTS or FIDA measurements are compared with simulated spectra to investigate whether themeasurements match the expectation [1, 7, 8]. However, if the real measurements disagree withthe synthetic measurements, it is often unclear what caused this discrepancy. Our final goal is toexperimentally determine f , and this might help establish where in 2D velocity space the mea-surements disagree with the theoretical prediction. Inference of velocity-space tomographiesfrom CTS or FIDA measurements was recently shown to be an achievable goal [9, 10]. We de-veloped methods to account for uncertainty in the measurements which allow the use of CTSand FIDA measurements together to compute a joint velocity-space tomography [11]. Applyingour prescription to a set of real 1D fast-ion measurements will yield an entirely experimentallydetermined 2D fast-ion velocity distribution.40th EPS Conference on Plasma Physics O6.512(a) CTS weight function. (b) FIDA weight function shown together with theoutline of the CTS weight function (black lines).Figure 1: Weight functions for CTS and FIDA for a projection angle of 32◦. The ranges of theprojected velocity, u, for the CTS weight function, and the wavelength, λ , for the FIDA weightfunction are chosen such that the weight functions are as similar as possible.Tomography of a velocity distribution function using a combination of diagnosticsFigure 1 shows weight functions for both CTS and FIDA for a viewing angle, φ , of 32◦. Theviewing angle is the angle between the magnetic field and the direction along which the velocitydistribution of the fast ion is resolved. Weight functions relate the 2D fast-ion velocity distri-bution function f to the 1D measurements g and are essential components of our developedtomography procedure [9–11]. The CTS weight function shown in figure 1(a) is calculated an-alytically [9]. The FIDA weight function shown in figure 1(b) cannot be calculated analyticallyand so is calculated numerically. The FIDA weight function takes into account Stark splitting,the charge-exchange reaction probability, the probability of the n=3 to n=2 electron transitionand instrumental effects in addition to the Doppler shift of the radiation. Figure 1(b) also showsthe outline of the CTS weight function, illustrated by the black lines, to ease the comparison ofthe two weight functions. It is clearly seen that CTS weight functions are symmetric whereasthe FIDA weight functions are asymmetric due to the effects of the charge-exchange probability.The slope of the outline of the FIDA weight function is furthermore slightly different comparedto that of the CTS weight function due to the Stark splitting [11].Figure 2 shows a typical ASDEX Upgrade fast-ion distribution function and two tomographicreconstructions. The distribution function shown in figure 2(a) is simulated using TRANSP andNUBEAM [12]. It shows maxima at full and half injection energy (60 keV and 30 keV) ofneutral beam injector S3 at ASDEX Upgrade. The tomographic reconstructions are made usingsynthetic measurements calculated from the TRANSP simulation. Previously we used different40th EPS Conference on Plasma Physics O6.512(a) Central fast-ion velocity distribution functiontypical for a low density discharge without mode-activity simulated using TRANSP/NUBEAM.(b) Reconstruction of the distribution function usingfive synthetic FIDA views containing 5% noise.(c) Reconstruction of the distribution function usingfive synthetic FIDA views combined with two syn-thetic CTS views containing 5% noise.Figure 2: A TRANSP/NUBEAM simulated fast ion velocity space distribution function andtomographic reconstructions of this. The unit of the colorbar is [s2/m5]. The tomographic re-constructions are made using synthetic measurements from five and seven views respectively.grids for the original function and the tomography which added numerical noise. Here we useidentical grids (31×15) but add 5% Gaussian noise to the measurements. The noise makesan accurate reconstruction of fine details impossible. Figure 2(b) shows a tomography usingsynthetic measurements from five FIDA views. For each view, the part of the spectrum thatwould be obscured in a real experiment due to beam emission and halo emission is omitted.Three of the chosen viewing angles are the angles of the three existing FIDA views at ASDEXUpgrade, which are here 11◦, 21◦ and 67◦. The remaining two viewing angles are 42◦ and83◦. It is seen how the overall shape of the distribution reappears in the tomography togetherwith the two beam injection maxima. However, the 30 keV maximum is located further to the40th EPS Conference on Plasma Physics O6.512right than in the simulation. Figure 2(c) shows the tomography using synthetic measurementsfrom the five FIDA views combined with two CTS views. This system thus simulates the actualviews expected to be available at ASDEX Upgrade during the next experimental campaign. Theviewing angles for the CTS views are chosen to be 73◦ and 79◦ which are realistic angles. Thepart of the spectrum in the CTS measurements that would be obscured by bulk ions are omitted.Each FIDA and CTS view contains about 100 measurements. By comparing figures 2(b) and2(c) it is seen that the tomography improves when a combination of FIDA views and CTS viewsare used. Both the peak intensity and the locations of the two beam injection maxima are betterresolved in the tomography using a combination of views.ConclusionsTomographic reconstructions using five synthetic FIDA views and a combination of five syn-thetic FIDA views and two synthetic CTS views are inferred. It is seen that the tomographyimproves when a combination of FIDA and CTS is used compared to the tomography inferredonly from FIDA views.AcknowledgementsThis work, supported by the European Communities under the contract of Association be-tween Euratom and DTU, was partly carried out within the framework of the European FusionDevelopment Agreement. The views and opinions expressed herein do not necessarily reflectthose of the European Commission.References[1] M. Salewski et al, Nuclear Fusion 50, 035012 (2010)[2] F. Meo et al, Journal of Physics: Conference Series 227 012010 (2010)[3] M. Nishiura et al, Review of Scientific Instruments 79, 10E731 (2008)[4] S. Kubo et al, Review of Scientific Instruments 81, 10D535 (2010)[5] B. Geiger et al, Plasma Physics and Controlled Fusion 53, 065010 (2011)[6] T. Ito et al, Plasma and Fusion Research 5, S2099 (2010)[7] W. W. Heidbrink et al, Plasma Physics and Controlled Fusion 49, 1457-1475 (2007)[8] W. W. Heidbrink, Review of Scientific Instruments 81, 10D727 (2010)[9] M. Salewski et al, Nuclear Fusion 51, 083014 (2011)[10] M. Salewski et al, Nuclear Fusion 52, 103008 (2012)[11] M. Salewski et al, Nuclear Fusion 53, 063019 (2013)[12] A. Pankin et al, Computer Physics Communications 159, 157-184 (2004)40th EPS Conference on Plasma Physics O6.512

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How to compute velocity-space tomographies using several fast-ion diagnostics

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