Determination of tungsten and molybdenum

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET T. Nakano1 , A. E. Shumack2,3 , C. F. Maggi4 , M. Reinke5 , K. D. Lawson2 , I. Coffey2 , T. P¨ utterich4 , S. Brezinsek6 , B. Lipschultz5 , G. Matthews2 , M. Chernyshova7 , K. Jakubowska7,8 , M. Scholz9 , J. Rzadkiewicz7,10 , T. Czarski8 , W. Dominik11 , G. Kasprowicz12 , K. Pozniak12 , W. Zabolotny12 , K.-D.Zastrow2 and JET EFDA contributors∗ JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB, UK 1 Japan Atomic Energy Agency, 801-1, Naka, Ibaraki, 311-0193, Japan 2 CCFE, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK 3 FOM Institute DIFFER, Edisonbaan 14, NL-3439 MN, Nieuwegein, The Netherlands 4 Max-Planck-Institut f¨ ur Plasmaphysik, 85748 Garching, Germany 5 University of York, Heslington, YO10 5DD, England 6 Association Forschungszentrum J¨ ulich GmbH 52425 J¨ ulich Germany 7 Instiute of Plasma Physics and Laser Microfusion, Hery 23, 01-497 Warsaw, Poland 8 Université Bordeaux, CNRS, CEA, CELIA, UMR 5107, F-33405 Talence, France 9 Institute of Nuclear Physics PAN ul. Radzikowskiego 152 31-342 Kraków, Poland 10 ´ Narodowe Centrum Bada´ n J¸adrowych ul. Andrzeja Soltana 7 05-400 Otwock,Swierk, Poland 11 Warsaw University, Faculty of Physics, Institute of Experimental Physics, 00-681 Warsaw, Poland 12 Warsaw University of Technology, Institute of Electronic Systems, 00-665 Warsaw, Poland ∗ See the Appendix of F. Romanelli et al., Proc. of the 24th IAEA FEC 2012, San Diego, US E-mail: [email protected] Abstract. The W45+ and W46+ 3p-4d inner shell excitation lines in addition to Mo32+ 2p3s lines have been identified from the spectrum taken by an upgraded high-resolution X-ray spectrometer. It is found from analysis of the absolute intensities of the W46+ and Mo32+ lines that W and Mo concentrations are in the range of ∼ 10−5 and ∼ 10−7 , respectively. Comparison of the W concentration from the X-ray spectrometer with those from a vacuum-ultra-violet spectrometer and from soft X-ray cameras indicates that the W concentration from the X-ray spectrometer is lower by a factor of ∼ 2 and > 7, respectively. In contrast, comparison of a plasma effective charge determined from the X-ray spectrometer with that from a visible range continuum intensity shows that the plasma effective charge from the X-ray spectrometer is higher by a factor of ∼ 3. Hence it is probable that the W concentration from the X-ray spectrometer is valid within a factor of ∼ 3, while the W concentrations from the vacuum-ultra-violet spectrometer and from the soft X-ray cameras are further higher.

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET2 Submitted to: J. Phys. B: At. Mol. Phys.

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET3 1. Introduction It has been decided that ITER will be operated from day one with tungsten (W) divertor and beryllium (Be) first wall [1,2] mainly in order to reduce tritium retention inside the vacuum vessel. In JET, in order to provide the physics and engineering basis for the exploitation of ITER, the original carbon plasma-facing components were all replaced by tungsten ones for the divertor and beryllium ones for the main chamber. JET with this new ITER-like wall configuration (hereafter, JET-ILW) has been in operation since 2011 [3, 4]. In such a wall configuration, one of the most significant issues is impact of W accumulation on plasma fusion performance. Hence quantitative W concentration monitoring is one of the important targets in the JET-ILW project. In JET-ILW, tungsten concentrations were first determined from line intensities of W44+ and W45+ around 6.2 nm and a quasi-continuum intensity of W27+ − W35+ around 5 nm, measured by a Vacuum Ultra Violet (hereafter, VUV) spectrometer [5]. This measurement found tungsten accumulation at the plasma core in JET-ILW in the case of low gas puffing. However, in toroidally rotating plasmas, it was found that the VUV spectrometer failed to measure the W emission from the plasma core [6]. This is because the W ions distributed from the plasma core toward outboard due to the centrifugal effect. This W redistribution was found by multi-chord soft X-ray (hereafter, SXR) measurement [6, 7]. This SXR measurement also provided spatial distribution of tungsten concentrations. However, the sensitivities of these two instruments, the VUV spectrometer and the SXR cameras, were adjusted so that the total radiative power from these instruments agreed with that from the bolometric measurement. In other words, these measurements were not independent and was not quantitatively cross-checked with another measurement. This was one of the drawbacks of these measurements although they certainly played central roles for W transport studies in JET-ILW. In parallel to JET modification into JET-ILW, an existing high-resolution X-ray crystal spectrometer was upgraded for the purpose of W concentration monitoring. This X-ray spectrometer was originally prepared to measure ion temperature [8] and toroidal plasma rotation [9] from, respectively, Doppler shift and broadening of the spectral line of He-like Ni ion (Ni26+ ). The X-ray spectrometer has now also started monitoring W concentration since a second crystal and detector for W were installed [10–12]. Because the sensitivity of the X-ray spectrometer is given as a photon throughput [12], it is possible to determine W concentration and compare it with those from independent measurements, for example, the VUV spectrometer and the SXR cameras, for the purpose of quantitative cross-checking. Further, the X-ray spectrometer has sufficiently high wavelength resolution to determine ion temperature and toroidal rotation velocity determined from Doppler broadening and shift, respectively. Thus, comparison of these quantities with those from other diagnostics such as charge exchange recombination spectroscopy is possible. This paper describes, line identification, comparison of W concentrations determined from the line intensities of two different charge states of W ions, and

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET4 comparison of plasma effective charge determined from continuum intensities at two different photon energies, in order to confirm self-consistency within the X-ray spectrometer. Further, for the purpose of quantitative cross-checking, comparison of the W concentrations from the X-ray spectrometer with those from the VUV spectrometer and the SXR cameras is given. Additionally, comparison of the W concentration with the Mo concentration is mentioned because Mo spectral lines are coincidentally found in the same wavelength range as the W spectral lines. The present report provides the first detailed comparisons from the upgraded X-ray spectrometer. 2. Experimental 2.1. Spectrometer setup The purpose of the upgrade of the high-resolution X-ray spectrometer is to measure the W46+ 3p-4d line at 0.52004 nm (the wavelength from the on-line database [13]) to determine W concentrations. Figure 1 (a) shows a bird’s eye view of the X-ray spectrometer. The X-ray spectrometer is built in Johann mounting with a Rowland circle radius of 12.5 m. X-ray emissions from the plasma pass through a 300-µm-thick Be window at the vacuum vessel and a 20-m-long beam line, and then inject into a cylindrically bent SiO2 crystal (1011) (2d = 0.668 nm, d: lattice spacing) with a width of 230 mm and a height of 35 mm. At the crystal, the injected X-ray is dispersed at a Bragg angle of 51o and then detected by a new Gas Electron Multiplier (GEM) detectors [10–12, 14, 15] with a width of 205 mm (256 strips × 80 µm) at a temporal resolution of 10 ms. Because each strip is energy sensitive, the second order diffraction spectrum in addition to the first order diffraction spectrum can be measured at the same time. As shown in Figs. 1 (b) and (c), the diagnostic line-of-sight is on the mid-plane of the torus, 0.2 m below the magnetic axis of typical diverted plasmas, and the line-ofsight is in the opposite direction to the plasma current. Thus, in the case of co-rotating plasmas, blue-shifted spectrum is observed due to Doppler shift. The measurable spectral band is 0.0043 nm at a wavelength of 0.52 nm, or a photon energy of ∼ 2.4 keV, and an inverse linear dispersion of 2.1 × 10−5 nm/mm. The sensitivity is calculated as a product of photon-throughputs at each component of the spectrometer: X-ray reflectivity of the crystal, transmittance of a 300-µm-thick Be window at the torus, a 9-cm-long He gas buffer in front of the detector, a 12-µm-thick Mylar window at the detector, resulting in 1.6 × 10−11 [counts ph−1 m2 sr] for the first order diffraction spectrum and 2.9 × 10−12 [counts ph−1 m2 sr] for the second one [12]. Figure 1 (c) also shows line-of-sights of other diagnostics: a vacuum ultra violet (VUV) spectrometer, soft X-ray (SXR) cameras, and a high-resolution Thomson scattering (HRTS) system. The VUV spectrometer measures a spectral line complex at 6.2 nm, which consists predominantly of W45+ and W44+ lines. From the intensity of the line complex, a W concentration is evaluated [5]. The SXR cameras measure a spatial profile of X-ray emissions in an energy range above 3.3 keV and 3.6 keV, respectively,

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET5 with a Be filter thickness of 250 µm (vertical cameras) and 350 µm (horizontal cameras). This measurement also gives W concentrations [6]. Later, W concentrations from the VUV spectrometer and the SXR cameras are compared with that from the X-ray spectrometer. The HRTS system measures spatial profiles of electron temperature and density along the line-of-sight with a spatial resolution of 16 mm at the plasma core [16]. These are used to calculate spatial profiles of the W and Mo emissions, which depends on electron temperature and density. 2.2. Measurement An X-ray spectrum analysed for line identification is taken in an ELMy H-mode discharge with a plasma current of 2.0 MA and a toroidal magnetic field of 2.7 T. Waveforms of the parameters of this discharge are shown in Fig. 2; plasma heating is performed by a neutral beam (NB) with an injection power of 14 MW. During the steady state NB injection, the radiation power in the main plasma is about 3 MW. From the radiation power signal in the divertor plasma, regular ELM activities at a frequency of 47 Hz are seen. The D2 puff rate is modulated at 3 Hz between 1.2 × 1022 D/s and 3.0 × 1022 D/s, although the modulation does not play a role for the line identification. The electron temperature at the plasma core measured by the HRTS system is 4 keV and the electron density 6 × 1019 m−3 . At 18.0 s, molybdenum (Mo) is injected by laser ablation (Laser-blow-off, LBO) [17] in order to confirm identification of Mo lines. As shown in Fig. 3, the intensities of the central two spectral lines increase rapidly after the Mo injection, while those are lower than the spectral line at a strip number of 40 before the Mo injection. This confirms that the central two spectral lines are emitted from Mo ions while the others not from Mo ions. Figure 4 (a) shows time-averaged spectra between 13.0 s and 15.0 s taken in the discharge shown in Fig. 2. As already shown in Fig. 3, five spectral lines, two of which are confirmed to be Mo lines, are seen in the first order diffraction spectrum, which are used for detailed analysis for line identification, later. In contrast, no spectral lines are seen in the second order diffraction spectrum. This feature is desirable for analyses of the continuum intensity, for example, to determine a plasma effective charge (Zeff ). 3. Analysis 3.1. Spectrum analysis for line identification One of the difficulties in high resolution spectroscopy is line identification. This is due to the difficulty in determining the wavelength; slight misalignment of the instrument results in large uncertainties in wavelength and also known lines rarely fall in a very narrow spectral band, making the experimental wavelength calibration uncertain. To overcome these drawbacks, we employed the following two methods: i) Mo laser-blowoff experiment and ii) validation of the modelled spectrum using Flexible Atomic Code (FAC) [18], by comparing it with published spectra [19].

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET6 As already shown in Fig. 3, the Mo laser-blow-off experiment confirms the central two lines are from Mo ions. However, charge states and transitions are not known yet. In order to identify the observed spectral lines, atomic structure calculation is performed for W and Mo ions by FAC, which adopts the full-relativistic DiracFock-Slater iteration method with configuration interactions for calculation of atomic structures and the distorted wave approximation for calculations of electron-impact cross sections. For example, the following electron configurations are considered for W46+ , Ni-like W ion; 3p6 3d10

: ground state, Ni-like closed shell structure

3p

6

9

3d 4l

: singly excited state

3p

6

9

: singly excited state

3d 5l

3p5 3d10 4l 10

3p5 3d

8

: inner shell (3p) excited state

5l

: inner shell (3p) excited state ′

3p

6

3d 4l 4l : doubly excited state

3p

5

3d9 4l 4l′ : doubly and inner shell (3p) excited state

, where l and l′ are azimuthal quantum numbers. The atomic structure calculation gives about 6000 energy levels. Spontaneous transition rates and excitation/deexcitation rate coefficients between all the energy levels and ionization rate coefficients from all the energy levels to the W47+ ground level are calculated, and then used for collisionalradiative modelling to calculate W46+ spectra. Although similar calculations are performed for W25+ - W71+ , it is probable that predominant contributors are W44+ - W46+ . This is because of ionization potentials of Wq+ (q ≤ 43) are lower than the measurable photon energy range of the Xray spectrometer ( ∼ 2.4 keV). For example, the ionization potential of W43+ is 2.2 keV. Hence, no photons emitted from levels below the ionization potential fall in the measurable photon energy range of the X-ray spectrometer, except for photons from levels above the ionization potential, for example, auto-ionization levels. But emission intensities from the auto-ionization levels should be very low, compared to those from singly excited levels below the ionization potential. In addition, the ionization potential of W46+ (4.1 keV) jumps from that of W45+ (2.4 keV) due to the Ni-like closed shell structure. Because of this jump, W46+ is more difficult to ionize into W47+ while W45+ easier to ionize into W46+ at the central electron temperature of the discharge (∼ 4 keV). Hence, the W46+ population tends to be high compared to Wq+ (q ≥ 47). Therefore, by the above two reasons, main focus of the calculation is made on W44+ - W46+ . As for Mo ions, by similar reasons, a predominant contributor to the spectrum of the X-ray spectrometer is Mo32+ . First, the calculated spectra are compared to published spectra [19], which cover the spectral range of the X-ray spectrometer. This comparison results in good agreement within the spectral resolution of the published spectra, which is much lower than that of the X-ray spectrometer. The calculated spectrum for W45+ , W46+ and Mo32+ at a

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET7 density ratio of 1.0: 0.3 : 0.7 and an electron temperature of 4 keV is shown in Fig. 4 (b). This spectrum is compared to the measured spectrum in a next section. 3.2. Intensity analysis for W and Mo concentrations From the measured W46+ intensities, W concentration, cW = nW /ne (nW : tungsten density and ne : electron density) is determined from the following equation (a similar equation for the Mo32+ intensity to determine Mo concentration, cMo = nMo /ne ): 46+

nW

IW = ∫ W46+ ε (RLOS ) dRLOS

,

(1)

46+

cW = nW /ne = ∫ εW

46+

46+

(RLOS ) = FAW

εW

46+

IW (RLOS ) ne (RLOS ) dRLOS

(RLOS ) PECW

46+

(RLOS ) ne (RLOS )

, ,

(2) (3)

[ph s−1 ] the emissivity where I W [ph m−2 s−1 ] is the measured W46+ intensity, εW of W46+ , RLOS [m] the major radius along the line-of-sight of the X-ray spectrometer, 46+ 46+ [ph m3 s−1 ] the FAW (= nW46+ /nW ) the fractional abundance of W46+ , PECW 46+ photon emission coefficient for the same transition as I W . 46+ In order to evaluate W concentration cW , W emissivity εW , which is a product 46+ 46+ 46+ of FAW , PECW and ne , needs to be evaluated as a first step. Given that FAW 46+ and PECW are calculated with electron temperature and density, they can be plotted as a function of a normalised poloidal flux ψpol by using electron temperature and density profiles over ψpol . Figure 5 (a) shows measured electron temperature and density profiles with fitting curves (only ψpol ≤ 0.9) as a function of ψpol . From the electron temperature and density profiles, W45+ , W46+ and Mo32+ fractional abundance under ionization equilibrium are calculated with ADAS ionization/recombination rates [20] for W ion and with the data in Ref. [21] for Mo ions. As shown in Fig. 5 (b), the W45+ and W46+ fractional abundance increase toward the plasma core while Mo32+ fractional abundance is approximately constant within ψpol < 0.4 and is slightly hollow at the centre. Note that the fractional abundances are not calculated at ψpol ≤ 0.05 because the line-of-sight of the X-ray spectrometer does not pass through this range. Similarly to the fractional abundances, photon emission coefficients are calculated by FAC collisional-radiative modeling [18] from the measured electron temperature and density profiles shown in Fig 5 (a). Figure 5 (c) shows the calculated photon emission coefficients. The W45+ , W46+ and Mo32+ photon emission coefficients monotonically increase toward the plasma core. Secondly, the emissivity is calculated from eq.(3) with the fractional abundance and the photon emission coefficient and the measured electron density. As shown in Fig. 5 (d), the emissivity profiles are similar to those of the fractional abundances shown in Fig. 5 (b); the W45+ and the W46+ emissivity increase toward the plasma core while the Mo32+ emissivity is approximately constant within ψpol < 0.4 and is slightly hollow at the centre. 46+

46+

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET8 Finally, the normalised poloidal flux ψpol is converted to the major radius along the line-of-sight, RLOS , in order to evaluate line-integral emissivity along the line-of-sight. Figure 5 (e) shows the normalised poloidal flux ψpol as a function of the major radius along the line-of-sight of the X-ray spectrometer, calculated from a magnetic equilibrium reconstructed by EFIT code [22]. Given that the line-of-sight passes through the plasma tangentially between low- and high-field-side separatrix, the normalised poloidal flux is a downward-convex function of the major radius along the line-of-sight. Figure 5 (e) also shows the emissivity profiles of W45+ , W46+ and Mo32+ . The W46+ emissivity has a peak at RLOS of ∼ 3 m. This is the case for the W45+ emissivity. In contrast, the Mo32+ emissivity is approximately constant in an RLOS range between 2.5 and 3.3 m. The emissivity is integrated along the line-of-sight as shown in eqs.(1) and (2), and then, the W density and concentration, respectively, are evaluated. Because the W density and concentration can be determined from the measured W46+ intensity in addition to the measured W45+ intensity, they can be compared each other. In contrast, this is impossible for the Mo density and concentration because spectral lines from only one charge state of Mo ion (= Mo32+ ) is observed in the present measurement. The determined W and Mo concentrations are in the range of 10−5 and 10−7 , respectively, as already shown in Fig. 2 (f), and the ratio of Mo to W concentration is ∼ 5%. 3.3. Continuum intensity analysis for Zeff A plasma effective charge, Zeff , is evaluated from the measured continuum emission. As already shown in Fig. 4 (a), clear continuum spectrum is observed in both the first and the second order diffraction spectra. In particular, the second order diffraction spectrum is better for the continuum spectrum analysis because no spectral lines are seen. In the case that the continuum spectrum is dominated by Bremsstrahlung emission, Zeff can be evaluated with ease. But it is possible that recombination continuum emission contributes to the measured continuum. Hence it is necessary to evaluate contributions of Bremsstrahlung and recombination continua to the measured continuum. 3.3.1. Bremsstrahlung continuum As shown in Fig. 6, Bremsstrahlung continuum is emitted from a free electron, which final state is not bounded by ions in plasmas. Given that the spectral range of the X-ray spectrometer is ∼ 2.4 keV, transitions with energy difference between the initial level and the final level is ∼ 2.4 keV can only contribute to the measured continuum intensity. The Bremsstrahlung continuum intensity, P B [Wm−3 ] is calculated from the following equation [23]. 1 (4) P B (ν)dν = n2e JZeff (R/Te )0.5 exp(−hν/Te ) gff dν , 2 27 z2R with J = 1.5 (2πα)0.5 ( 2 )1.5 hc(a0 /z)2 , (5) 3 mc where ν indicates photon frequency, R Rydberg constant (=13.6 eV), h Planck’s constant (=6.6 × 10−34 Js), gff Gaunt factor [24], α fine structure constant (=1/137),

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET9 z a charge of an impurity ion, m a mass of electron (=9.1 × 10−31 kg), c a speed of light (=3.0 × 108 ms−1 ), and a0 Bohr radius (=5.3 × 10−11 m). Similarly to eq.(1), the line-integral Bremsstrahlung intensity is calculated with electron temperature and density profiles, and then a plasma effective charge Zeff is evaluated from the measured continuum intensity. 3.3.2. Recombination continuum As shown in Fig.6, recombination continuum is emitted from a free electron, which final level is bounded by ions in plasmas. Again, only transitions with energy difference between the initial and the final level is ∼ 2.4 keV can contribute to the measured continuum intensity. Because the photon energy is a sum of the kinetic energy of the free electron and the energy difference between the bound level and the ionization potential, electrons with a kinetic energy of less than 2.4 keV can contribute to the measured continuum intensity. For example, only electrons with a kinetic energy of 50 eV can contribute to the measured continuum intensity in the case the electrons recombine directly to the ground level of W44+ given that the ionization potential of W44+ is 2.35 keV. Population of such a low energy electron at electron temperature of 4 keV is very small, suggesting recombination continuum may be a minor contributor to the continuum emission. In general formulation, the intensity of recombination continuum to an impurity ion with a charge of q, for example Wq+ , PqR [Wm−3 ] is expressed with the following equation [23]; PqR (ν)dν = hνnWq+ ne f (ε)vσε,p (ε) dε R

P (ν)dν =

Σq PqR (ν)dν

,

,

(6) (7)

where nWq+ indicates a Wq+ density, f (ε) a electron velocity distribution function, v a electron velocity, σε,p (ε) a recombination cross section of the electron with a kinetic energy of ε to a bound level p of Wq+ , and P R (ν)dν a total recombination continuum intensity. The recombination cross sections are calculated by FAC; recombination to all the excited levels and the ground level, for example ∼ 6000 levels for W46+ , are considered for W26+ - W71+ . Above calculation indicates that the total recombination continuum contributes only a few percent to the measured continuum intensity in the present electron temperature range, ∼4 keV. Therefore, Bremsstrahlung continuum dominates the measured continuum intensity, determining plasma effective charge Zeff . In the present study, in case, Bremsstrahlung continuum intensity is evaluated by subtracting the calculated recombination continuum contribution from the measured continuum intensity. 4. Results and discussion 4.1. Line identification Figure 4 compares the experimental spectrum with the calculated spectrum, showing overall agreement; as already described in Sec.2.2, the Mo injection experiment

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET10 confirmed the central two lines were from Mo ions. These lines were well reproduced by the calculated spectrum and identified as both Mo32+ (2s-3p) lines. More exactly, from the shorter wavelength, the following two lines were identified: • Mo32+ (2p6 1 S0 − 2p5 3s 3 P1 : λ = 0.52069 nm [13], electric dipole (E1) transition) • Mo32+ (2p6 1 S0 − 2p5 3s 3 P2 : λ, not shown in Ref. [13], magnetic quadrupole (M2) transition) These two lines were already identified in Alcator-C [25] and FTU tokamaks [26]. Recently, theoretical treatment for the reason the M2 line intensity, which was thought to be very weak, was comparable to the E1 line intensity was given. The theory indicated that the M2 line was induced by a magnetic field, suggesting a possibility to diagnose the magnetic field strength [27]. Implementation of this effect, which was not included in the present calculation, may give a better agreement with the measured M2 intensity because the present measurement was performed under a magnetic field of 2.7 T at the magnetic axis. The remaining lines were well reproduced by the calculated spectrum, resulting in the following identification: • W46+ (3p6 3d10 1 S0 − 3p5 3d10 4d (3/2, 5/2)o1 : λ = 0.52004 nm [13]) • W45+ (3p6 3d10 4s 2 S1/2 − 3p5 3d10 4s4d (3/2, 2)o3/2 : λ, not shown in Ref. [13]) ) • W45+ (3p6 3d10 4s 2 S1/2 − 3p5 3d10 4s4d (3/2, 2)o1/2 : λ = 0.52289 nm [13]) • W45+ (3p6 3d10 4s 2 S1/2 − 3p5 3d10 4s4d (3/2, 3)o3/2 : λ = 0.52379 nm [13]) These transitions were due to inner shell excitation from 3p to 4d electron, which required a high excitation energy close to the ionization potential of W45+ , 2.41 keV. Note that the measured spectrum should be blue-shifted due to the Doppler shift while the calculated spectrum is plotted as calculated by FAC, or by stationary wavelength. Thus, the correspondence between the strip number and the wavelength, shown respectively at the top of Fig. 4 (a) and the bottom of Fig. 4 (b), always depends on the Doppler shift, or plasma toroidal rotation. This is the reason why the Mo32+ lines are shifted toward the longer wavelength; generally, plasma toroidal rotation speed is the highest at the plasma core and decreases with increasing plasma minor radius. As already shown in Fig. 5, the W45+ and W46+ emissions were from the plasma core while the Mo32+ emission from the outer. This results in smaller Doppler shift for Mo32+ lines. 4.2. W and Mo concentrations The W and Mo concentrations determined from the present analysis were already shown in Fig. 2 (f). The W and Mo concentrations were respectively in the range of 1 × 10−5 and 1 × 10−7 . Here, in order to discuss spatial profiles of the W concentration, the W concentration determined from the W45+ intensity, cW (45), was compared with that determined from the W46+ intensity, cW (46). As shown in Fig. 7 (a), cW (45) increased with increasing cW (46). However, cW (45) was systematically lower than cW (46). This was also the case for data taken in different types of discharges: a nitrogen seeded ELMy

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET11 H-mode discharge and a non-seeded ELMy H-mode discharge with the outer strike point on the horizontal target (bulk W target). As shown in eq.(2), cW (45) and cW (46) reflected the W concentrations at the W45+ and the W46+ emission location, respectively, and as shown in Fig. 5(d), the W46+ emissivity profile was slightly narrower than the W45+ emissivity profile. These resulted in more central W concentration information in cW (46) than in cW (45). Hence, the difference between cW (45) and cW (46) indicates a possibility that the W concentration increases toward the plasma core. To conclude this, sufficiently small uncertainty in the analysis is required. Because the ionization and recombination rates used in the present analysis is adjusted so as to reproduce the experimental measurement [5], it is probable that the systematic deviation between cW (45) and cW (46) indicates the non-uniform W concentration profile. The Mo concentration cMo increased very weakly with increasing cW (46) as shown in Fig. 7 (b). In JET, no Mo materials are used for the plasma-facing components except for only one marker tile at the inner divertor [28]. However, one of the possible sources is W coated CFC tiles, which have a W/Mo/W/Mo multilayer on a CFC substrate [29]. Once the top surface W coating is eroded or delaminated, the tile can be a Mo source. However, even higher Mo concentration is found from the plasma with the outer strike point on the horizontal target, which is made of bulk tungsten, as shown in Fig. 7 (b). This indicates that the W coated tiles at the outer divertor are not necessarily the Mo source. Hence the Mo source is not yet known. In-vessel inspection or post-mortem analysis after the current operational campaign may provide clues of the Mo source. 4.3. Plasma effective charge Figure 8 (a) shows a plasma effective charge determined from the 4.8 keV continuum intensity, Zeff (4.8 keV), as a function of that from the 2.4 keV continuum intensity, Zeff (2.4 keV), for non-, nitrogen-, neon- and argon-seeded plasmas. With increasing Zeff (2.4 keV), Zeff (4.8 keV) increased linearly within 50%, showing consistency between Zeff (2.4 keV) and Zeff (4.8 keV). However, as shown in Fig. 8 (b), a plasma effective charge determined from the visible range continuum intensity, Zeff (vis) , increased very weakly with increasing Zeff (2.4 keV). Overall, Zeff (2.4 keV) was higher compared to Zeff (vis) by a factor of ∼ 3. This is probably due to underestimate of the sensitivity of the X-ray spectrometer by a factor of ∼ 3. But still it can be said that the sensitivity of the X-ray spectrometer is valid within a factor of ∼ 3. Hence, uncertainty up to a factor of 3 is imposed for all quantitative discussion in the present study. 4.4. Comparison of W concentrations with that from other diagnostics Figure 9 (a) compares the W concentration determined from the VUV spectrometer, cW (VUV), with that from the X-ray spectrometer, cW (46). It has been shown that in toroidally rotating plasmas, the W emission tends to distribute toward the low field side due to centrifugal effect [6], and that further ICRF wave injection enhances this effect due to the anisotropical minority heating [30]. In such plasmas, thus the

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET12 VUV spectrometer, whose line-of-sight passes through the very centre of the plasma, misses the significant part of the W emission. By this reason, figure 9 compares W concentrations taken only from plasmas with less centrifugal effect. The SXR tomography [6, 7] confirmed that the W emission profile was not distributed toward the outboard. As shown in Fig. 9 (a), cW (VUV) was systematically higher by a factor of ∼ 2 than cW (46). Possible reasons for the difference are i) atomic data, ii) sensitivities of the spectrometers and iii) spatial profile of the W emission: i) in the analysis for both cW (VUV) and cW (46), the identical ionization and recombination rates taken from ADAS [20], which are originally from Ref. [5] are used. ii) the photon emission coefficient for cW (46) is calculated by FAC while that for cW (VUV) is not explicitly used but is implemented together with the sensitivity of the VUV spectrometer, which is derived so as to reproduce the bolometric radiation power. In contrast, the sensitivity of the X-ray spectrometer is calculated and it has been shown that the sensitivity is valid within a factor of ∼ 3 as described above. iii) contribution of the W emission at the very centre of the plasma to cW (VUV) may be significant while such contribution is not possible for cW (46). This is because the X-ray spectrometer does not observe the plasma with ψpol of ≤ 0.05. Therefore, it is probable that the difference is due to both or either of the sensitivity and the spatial profile of the W emission. Figure 9 (b) compares the W concentration determined from the SXR cameras, cW (SXR) at the very centre of the plasma (ψpol =0.0), with that from the X-ray spectrometer, cW (46). It is found that cW (SXR) is higher by one order of magnitude than cW (46). This discrepancy is significantly large compared to the uncertainty of the sensitivity of the X-ray spectrometer. As described for the difference from cW (VUV), this may also be due to the contribution of the W emission from the very centre of the plasma. In order to exclude the contribution for the core W emission, cW (SXR) at ψpol =0.15 is compared with cW (46) in Fig. 9 (c). The discrepancy decreases down to a factor of ∼ 7. Still, however, the discrepancy is significantly large. The ionization and the recombination rates from ADAS [20] are also used to derive cW (SXR), reasoning that the atomic data does not create the discrepancy. The sensitivity of the SXR cameras is adjusted so as to reproduce the bolometric radiation power, similarly to that of the VUV spectrometer. Although this may be one of the reasons, another possibility is accuracy of the photon emission coefficients in the SXR measurement range; the analysis of the SXR intensity needs modelled spectrum with a photon energy range above 3.3 keV and 3.6 keV, respectively, for cameras with 250 µm- and 350 µm-thick Be filter because the SXR measurement loses the energy-dispersed information. Accurate spectrum of highly charged W ions is not necessarily calculated with ease, resulting possibly in a part of discrepancy. In addition, the SXR cameras do not measure only the W emission but also Bremsstrahlung continuum emission due predominantly to the presence of Be ions in the plasma. Hence to subtract the Bremsstrahlung continuum emission from the measured SXR intensity, it is required that Be concentration is assumed. This also contributes possibly to the discrepancy partly. In addition, Mo emission has some contribution to

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET13 the measured SXR intensity. 5. Conclusions The spectrum taken by the upgraded high-resolution X-ray spectrometer was analysed to identify the spectral lines for the purpose of determining W concentrations. The W45+ and W46+ 3p-4d inner shell excitation lines in addition to Mo32+ 2p-3s lines were identified at a wavelength of ∼ 0.52 nm. From the absolute intensities of the W46+ and Mo32+ lines, W and Mo concentrations were determined: respectively, ∼ 10−5 and ∼ 10−7 range for plasmas analysed in the present study. Similar level of Mo concentrations were found even in the case that the outer strike point on the bulk W tile, indicating that the W and Mo multilayer on the CFC outer divertor target was not necessarily a source of Mo ions. Comparison between a plasma effective charge Zeff determined from the first order diffraction spectrum and that from the second showed they were consistent within ∼50%. In contrast, they were higher by a factor of ∼ 3 than Zeff determined from the visible range continuum emission. Comparison of the W concentration cW from the X-ray spectrometer with that from the VUV spectrometer and that from the SXR cameras showed that cW from the X-ray spectrometer was lower by a factor of ∼ 2 and > 7. In the analysis of these three diagnostics, the identical ionization and recombination rates were used, reasoning that the atomic data did not create the discrepancy. Although the spacial profiles of the W emission might contribute to the discrepancy, it is probable that the sensitivity was one of the reasons for the discrepancy; the sensitivity of the Xray spectrometer was validated within a factor of ∼ 3 from the comparison of Zeff from the X-ray spectrometer with that from the visible range continuum intensity. Hence the determined W and Mo concentrations from the X-ray spectrometer were also valid with in a factor of ∼ 3. This spectrometer has sufficiently high-wavelength-resolution capability to determine Doppler shift and broadening as seen clearly from the measured spectrum. In the present work, absolute wavelength calibration for the X-ray spectrum is not yet finished. Once the absolute wavelength is determined, toroidal rotation velocity can be determined from the Doppler shift. Besides, once the instrumental function is determined, ion temperature can be also determined. Such works are ongoing and will be presented in near future. 6. Acknowledgments This work was supported by EURATOM and carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work was partly done with the Minerva framework [31].

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET14 References [1] M. Merola, F. Escourbiac, R. Raffray, P. Chappuis, T. Hirai and A. Martin, Fusion Engineering and Design 89 (2014) 890. [2] T. Hirai, F. Escourbiac, S. Carpentier-Chouchana, A. Fedosov, L. Ferrand et al., Fusion Engineering and Design 88 (2013) 1798. [3] F. Romanelli and J.E. Contributors, Nuclear Fusion 53 (2013) 104002. [4] G.F. Matthews, Journal of Nuclear Materials 438, Supplement (2013) S2 . [5] T. P¨ utterich, R. Neu, R. Dux, A.D. Whiteford, M G O’Mullane and the ASDEX Upgrade Team, Plasma Physics and Controlled Fusion 50 (2008) 085016 (27pp). [6] T. P¨ utterich, et al., Proc. of the 24th IAEA Fusion Energy Conference 2012, San Diego, US EX/P3-15 [7] T. P¨ utterich, R. Dux, R. Neu, M Bernert, M N A Beurskens et al., Plasma Physics and Controlled Fusion 55 (2013) 124036. [8] R. Bartiromo, F. Bombarda, R. Giannella, S. Mantovani, L. Panaccione and G. Pizzicaroli, Review of Scientific Instruments 60 (1989) 237. [9] L.-G. Eriksson, E. Righi and K.-D. Zastrow, Plasma Physics and Controlled Fusion 39 (1997) 27. [10] J. Rzadkiewicz et al., Nucl. Instrum. Methods in Phys. Research A 720 (2013) 36. [11] M. Chernyshova, et al., JINST 9 (2014) C03003. [12] A. E. Shumack et al., Rev. Sci. Instrum. Submitted ( 2014). [13] Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2013). NIST Atomic Spectra Database (ver. 5.1), [Online]. Available: http://physics.nist.gov/asd [2014, June 3]. National Institute of Standards and Technology, Gaithersburg, MD. [14] G. Kasprowicz, et al., Proc. SPIE, 8008 (2011) 80080J. [15] K. Pozniak, et al., Proc. SPIE, 8008 (2011) 800808. [16] L. Frassinetti, M.N.A. Beurskens, R. Scannell, T.H. Osborne, J. Flanagan, M. Kempenaars, M. Maslov, R. Pasqualotto, M. Walsh and J.-E. Contributors, Review of Scientific Instruments 83 (2012). [17] G. Magyar, B. Denne-Hinnov et al JET-P(93)43 (1993). [18] M. F. Gu, Can. J. Phys. 86 (2008) 675. [19] J. Clementson, P. Beiersdorfer, G. V Brown and M. F. Gu, Phys Scr 81 (2010) 015301. [20] H.P. Summers, JET-IR 06, 1994. [21] M Mattioli, G. Mazzitelli, K.B. Fournier, M Finkenthal and L. Carraro, Journal of Physics B: Atomic, Molecular and Optical Physics 39 (2006) 4457. [22] M. Brix, N.C. Hawkes, A. Boboc, V. Drozdov, S.E. Sharapov and J.-E. Contributors, Review of Scientific Instruments 79 (2008). [23] T. Fujimoto, Oxford University Press (2004). [24] Sutherland, Monthly Notices of the Royal Astronomical Society, vol 300, issue 2 (1998). [25] E. Källne, J. Källne and R.D. Cowan, Phys. Rev. A 27 (1983) 2682. [26] K.B. Fournier, W.H. Goldstein, et al., May, Phys. Rev. E 53 (1996) 1084. [27] J. Li, J. Grumer, W. Li, M. Andersson, T. Brage, R. Hutton, P. Jönsson, Y. Yang and Y. Zou, Phys. Rev. A 88 (2013) 013416. [28] K. Heinola et al., ”Fuel retention in JET ITER-Like Wall from Post Mortem Analysis” PSI 2014, Kanazawa, Japan O-10. [29] C. Ruset, E. Grigore, I. Munteanu, H. Maier, H. Greuner, C. Hopf, V. Phylipps, G. Matthews, JET-EFDA Contributors, Fusion Engineering and Design 84 (2009) 16621665 [30] F. Casson, C. Angioni et al., ’Theory of heavy impurity transport & application to modelling of tungsten in JET and ASDEX-Upgrade’ 41st EPS conference Berlin (2014). [31] J. Svensson and A. Werner, Proceedings IEEE workshop on intelligent signal processing WISP (2007).

Determination of tungsten and molybdenum concentrations from an X-ray range spectrum in JET15

(a)

(b)

LOS

θ

Plasma Current

SXR (vertical)

0

Height (m)

1

VUV spec.

2

(c)

Be

Thomson

X-ray spec.

-1

SXR (horizontal)

W coated CFC Bulk W 2

3 Major radius (m)

JPN85232 t=16.5s 4

Figure 1. (a) A bird’s eye view, (b) line-of-sight on the mid-plane of the torus and (c) line-ofsight on the poloidal cross-section of the X-ray spectrometer. In Fig. (c) line-of-sights of other diagnostics are also shown.


30

Time-average for X-ray spectrum

JPN85232 (a)

20

NB (MW)

10 0

Mo injection

IC (MW) (b)

20

Radiation (div) (MW)

Radiation (main) (MW)

10 0

(c)

4

D2 puff rate ( 1022 D/s)

2 0

(d)

8

Te(0) (keV)

4 0 12

(e)

ne(0) (1019 m-3)

8 4 0

(f)

10-5

Mo conc.

10-6 10

-7

(g)

3 2 1

W conc.

Zeff(2nd)

Zeff(1st)

Zeff(Vis) 10

12

14

16

18

Time ( s ) Figure 2. Waveforms of (a) neutral beam (NB) injection power, ion cyclotron radio frequency (IC) wave injection power, (b) radiation power from the main plasma, that from the divertor plasma, (c) D2 puffing rate, (d) electron temperature and (e) electron density at the plasma core, (f ) tungsten and molybdenum concentrations, and (g) plasma effective charge, as a function of time.


JPN85232

(a)

18.5

800

18.0 Mo Injection 17.5

600 400

17.0

200

16.5 16.0

0

4

( 10 counts / s )

(b) Intensity

1000

8

Intensity (counts/s)

Time ( s )

19.0

After Mo injection

6 4 Before Mo injection

2 0

50

100

150

200

250

Strip number

Figure 3. (a) Time evolution of the measured spectrum with Mo injection, and (b) time-averaged spectra before and after the Mo injection.

Intensity ( counts / s )


0 8000 (a)

50

Strip number 100 150

200

250

JPN85232 13.0-15.0s

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0.519

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45+

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45+

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32+

Mo

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Mo

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46+

0.6

W

0.8

3

-1

(b)

-1

ph m s nm )

0

-13

Spectral photon emission coefficient

2000

Wavelength ( nm )

Figure 4. Comparison of the spectrum measured by the upgraded X-ray spectrometer [12] with that calculated by Flexible Atomic Code [18] for W45+ , W46+ and Mo32+ at an electron temperature of 4 keV and a density ratio of 1.0:0.3:0.7, respectively. Note that W and Mo concentration determined from the spectrum are 1 × 10−5 and 7 × 10−7 , respectively.

4

Te Mo

10

(b)

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-3

m )

45+

W

-3

10

46+

W

-5

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10

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46+

W 45+ W 46+

32+

W

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Mo

45+

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(e)

Ψpol

32+

3

Mo

10

2

46+

10

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45+

W

1

10

0

0.2 0.0 2.0

10

10

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(c)

32+

Mo

-1

(ph m s )

10

( ph s )

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Emissivity ε

32+

-1

19

3

2 0

Normailsed Poloidal flux Ψpol

8

ne

( 10

(a)

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Electron density

JPN85232 t=16.6s

( 10 eV )

Electron temperature


-1

2.4 2.8 3.2 3.6 Major radius of line-of-sight RLOS ( m )

10

Figure 5. Spatial profiles of (a) measured electron temperature and density, (b) calculated fractional abundances, (c) calculated photon emission coefficients, (d) calculated emissivities of W45+ , W46+ and Mo32+ as a function of normalised poloidal flux, and (e) normalised poloidal flux and the calculated emissivities of W45+ , W46+ and Mo32+ as a function of a major radius of the line-of-sight of the X-ray spectrometer.


-6

-5

Mo concentration, cMo, ( 10 ) W concentration, cW(45), ( 10 )

Figure 6. Schematic diagram of energy levels of W44+ and continuum emission processes. e− indicates a free electron, εe a kinetic energy of the free electron, and hν a photon energy.

3

+50%

(a)

2 Non-seeded (Horizontal target) 1

-50%

N2 seeded Non seeded

0 3

(b)

cMo / cW = 15%

10%

2 5% 1 2.5% 0

0

1

2 -5

W concentration, cW(46), ( 10 )

Figure 7. (a) W concentration determined from the W45+ 3p-4d line, cW (45), and (b) Mo concentration as a function of W concentration determined from the W46+ 3p-4d line, cW (46) .


Zeff (4.8 keV)

(a)

+33% Ar seeded

4 Ne seeded -50% 2

N2 seeded Non seeded

0

-50%

(b) 1.5 Zeff (vis)

Plasma effective charge

6

-67% -75%

1.0 0.5 0.0

0

2

4

Zeff (2.4 keV)

Figure 8. (a) Plasma effective charge determined from the continuum of the second order diffraction spectrum at 4.8 keV, Zeff (4.8 keV), and (b) that from the visible range continuum, Zeff (vis) as a function of that from the first order diffraction spectrum at 2.4 keV, Zeff (2.4 keV).


(a)

4x

3x

2x

-5

cW (VUV) ( 10 )

6 4

1x N2 seeded Non seeded Non seeded(Horizontal target)

2 0 (b)

70x

20x

-4

cW (SXR) (10 ) at Ψpol=0.0

W concentration

6 4 2

5x

0 (c)

10x

20x

-4

cW (SXR) (10 ) at Ψpol=0.15

3

7x 2 3x

1 0

0

1

2

3 -5

W concentration, cW(46), ( 10 )

Figure 9. (a) W concentration determined from the VUV spectrometer [5], (b) that from the soft X-ray cameras at a normalised poloidal flux of 0.0, and (c) that from the soft X-ray cameras at a normalised poloidal flux of 0.15 [6] as a function of the W concentration from the X-ray spectrometer.