atoms

Article Evaluation of an Oxygen Transport Coefficient in the Aditya Using the Radial Profile of O4+ Emissivity and the Importance of Atomic Data Used Therein

Malay Bikas Chowdhuri 1,* , Joydeep Ghosh 1, Ritu Dey 1, Sharvil Patel 2, Nandini Yadava 3 , Ranjana Manchanda 1, Amrita Bhattacharya 4 , Izumi Murakami 5 and Aditya Team 1

1 Institute for Research, Bhat 382 428, Gandhinagar, India 2 Birla Institute of Technology-Mesra, Jaipur Campus, Jaipur 302 017, Rajasthan, India 3 The National Institute of Engineering, Mysuru 570 008, Karnataka, India 4 Nuclear Engineering and Technology Programme, Indian Institute of Technology Kanpur, Kanpur 208 016, Uttar Pradesh, India 5 National Institute for Fusion Science, Toki 509-5292, Gifu, Japan * Correspondence: [email protected]

 Received: 30 June 2019; Accepted: 30 August 2019; Published: 9 September 2019 

Abstract: Oxygen impurity transport in the typical discharges of the Aditya tokamak was investigated 3 3 using emissivity radial profile of emissivity of the spectral line (2p3p D3–2p3d F4) at 650.024 nm from the Be-like oxygen ion. This O4+ spectral line was recorded using a 1.0 m multi-track spectrometer capable of simultaneous measurements from eight lines of sight passing through the plasma. The oxygen transport coefficients were determined by reproducing the experimentally measured emissivity profiles of O4+, using a one-dimensional impurity transport code, STRAHL, and photon emissivity coefficient (PEC) belonging to that transition. The PEC values were obtained from both ADAS and NIFS atomic databases. Using both the databases, much higher values of diffusion coefficients compared to the neo-classical values were observed in both high and low magnetic field edge regions of typical Aditya tokamak Ohmic plasma. Although, almost similar profiles of diffusion coefficients were obtained using PEC values from both databases, the magnitude differs considerably. The maximum values of diffusion coefficients in the plasma edge at low field side of tokamak were ~45 and ~25 m2 s 1 when modeling was done using the ADAS and NIFS databases, respectively. · − Further analysis on the atomic data used in the calculation indicates that the difference in diffusion coefficients is mainly related to the variation in the values of atomic data of the two databases.

Keywords: visible emission; Be-like oxygen ion; impurity transport; Aditya tokamak; atomic data

1. Introduction Impurity transport in the tokamak needs to be understood to minimize and control the impurities inside the tokamak plasma, since it affects plasma performance through radiation loss and dilution of fuel particle [1]. Not only that, higher levels of impurities inside the plasma core enhance the occurrence of density limit disruption [2]. Yet, the controlled amount of impurity seeding inside the edge plasma helps to achieve the mitigation of disruption, reduction the heat load on the diverter, and improved confinement, such as Radiative Improved (RI) mode [3]. In the present day, with having high electron temperatures, spectral emissions in the extreme and vacuum ultraviolet (EUV and VUV) wavelength ranges have been utilized to study impurity transport. However, visible emissions are still employed for this purpose in tokamaks with lower central temperature or in the diverter region of

Atoms 2019, 7, 90; doi:10.3390/atoms7030090 www.mdpi.com/journal/atoms Atoms 2019, 7, 90 2 of 10 large tokamaks [4]. An impurity transport study is generally done using the experimentally observed spatial profile of absolute intensities of spectral emissions, either from intrinsic or injected impurity, in combination with an impurity transport code. It computes the radial profiles of impurity density through the ionization balance on the basis of given plasma parameters and using the coupled set of radial transport equations for every ionization stage [5,6]. Spectral emissivity of a transition of a charge state is then calculated using the photon emissivity coefficient (PEC), which comes from the calculation of population balance in the different excited states of the ion using collisional-radiative (CR) modeling. This model not only includes bound excited populations originating exclusively from the ground state via electron impact excitation, but also the secondary processes like excitation transfer, recombination, and ionization involving all excited states [7]—and all these calculations involve atomic physics data sets. Then, the accuracy in the transport study relies on the application of an appropriate atomic model and the accuracy of the atomic data, such as energy level, Einstein A-coefficient, ionization, and excitation rate coefficient used therein. The strong spectral line emissions of the Be-like oxygen ion mostly lie in the UV and VUV regions. As a result, in earlier times, the CR model (CRM) code developed to calculate the PEC values of different transitions from this ion were included to only the lowest 10 to 20 energy levels, excluding almost all ∆n = 0 (3 3) and (4 4) transitions [8]. However, considering the relatively low value → → of the ionization potential of the Be-like oxygen ion, which is equal to 113.9 eV, visible radiation of this ion due to ∆n = 0 transition within n = 3 and n = 4 levels does exist, and this was first observed in the DIII-D tokamak [9]. Then the spectral line brightness was calculated by developing a CRM using detailed atomic structure to reproduce the observation by retaining the n = 3 and 4 energy levels. This was also subsequently done by other groups [10,11]. Nevertheless, the PEC values obtained from these codes differ due to not only the differences in the fundamental atomic data, but also due to the non-inclusion of many transitions populating the 2p3d upper level of the observed visible spectral lines from tokamak plasma. In the Aditya tokamak [12], an intense visible line from Be-like oxygen at 650.024 nm 3 3 (2p3p D3–2p3d F4) is routinely observed [13]. Therefore, this emission was used to study the impurity transport in the Aditya tokamak by utilizing the advantage of visible , which is the use of optical fiber for the space resolved measurement. In the Aditya tokamak, the experimental spatial profile of brightness of this transition was modeled to obtain the oxygen diffusion coefficient using STRAHL impurity transport code [14] and the required PEC from the ADAS database [10]. The obtained higher value of the diffusion coefficient was explained by fluctuation-induced transport [15]. The radial profile of this emission was also employed to validate the impurity transport code developed using a semi-implicit numerical technique for the study of impurity transport in tokamak plasmas [16]. Later, the O4+ emissivity profile was modeled using this code [17], in which the PEC data were taken from ADAS and from a CRM code [10] developed by the National Institute of Fusion Science (NIFS), Japan. In this paper, the oxygen transport was studied using STRAHL code and the two above-mentioned PEC data to understand the role of atomic data used in impurity transport modeling. It was found that the oxygen diffusion coefficient obtained using NIFS PEC data is lower as compared to the one obtained using the PEC provided by ADAS. The paper is organized as follows: Section2 deals with the experimental setup used in this study. The detail of the modeling of the oxygen emissivity is described in Section3. In Section4, a brief discussion of the role of atomic data used in the transport code is presented, and a conclusion is presented in Section5.

2. Experimental Setup Aditya is a medium size tokamak, with major (R) and minor (a) radii of 0.75 m and 0.25 m respectively. It has a poloidal ring limiter made of graphite at a toroidal location. It is operated with a toroidal magnetic field, Bt, of 0.75 to 1.2 T and has a plasma current of 80 to 150 kA depending upon the operation scenario. The vacuum vessel is pre-filled with hydrogen gas at a pressure of ~1 10 4 mbar using a gas feed system consisting of mainly a Piezo-electric valve and a pulse generator. × − Atoms 2019, 7, 90 3 of 10

The central chord average plasma electron density and temperature of the plasma are in the ranges of 1 to 3.5 1019 m 3 and 300 to 650 eV, respectively. The electron density profile was measured × − by a seven-channel microwave interferometer spanning over the whole plasma cross-section [18], and the core electron temperature was measured by the absorption foil ratio technique using soft X-ray emissions monitored by a silicon surface barrier detector. The edge electron density and temperature Atoms 2019, 7, x FOR PEER REVIEW 3 of 10 were measured using Langmuir probes. Standard magnetic diagnostics were used to measure the plasma current, loop voltage, plasma position, and magneto-hydrodynamic (MHD) activities [12]. Thechannel spatial microwave profile ofinterferometer 650.024 nm spanning spectral over line emittedthe whole by plasma the O cross-section4+ ion was measured[18], and the using core a space resolvedelectron visible temperature spectroscopic was measured system by [ 13the]. absorpti It wason equipped foil ratio technique with a 1using m visible soft X-ray spectrometer emissions with monitored by a silicon surface barrier detector. The edge electron density and temperature were 1800 grooves/mm grating blazed at 500 nm. A charge coupled device (CCD) with 1024 256 pixels measured using Langmuir probes. Standard magnetic diagnostics were used to measure the plasma× was placedcurrent, at loop the voltage, focal plane plasma on position, the existing and magneto-hydrodynamic port of the spectrometer (MHD) to detectactivities the [12]. spectrum. The CCD 2 pixel sizeThe was spatial 26 profile26 µm of 650.024and the nm spectral spectral resolutionline emitted by of the O system4+ ion was in measured terms of using full a width space at half × maximaresolved (FWHM) visible was spectroscopic 0.023 nm atsystem 650 nm [13]. when It was operated equipped withwith a 50 1 µmm visible entrance spectrometer slit width. with The 1800 entrance slit widthgrooves/mm of 250 µgratingm was blazed used at during 500 nm. this A charge experiment. coupled Adevice vertical (CCD) array with of1024 nine × 256 fibers pixels was was attached alongplaced the entrance at the focal slit plane height, on the enabling existing multi-track port of the spectrometer measurement. to detect The the fiber spectrum. had a The core CCD diameter pixel (d) of size was 26 × 26 µm2 and the spectral resolution of the system in terms of full width at half maxima µ µ 400 m(FWHM) and numerical was 0.023 aperturenm at 650 (NA)nm when of 0.22, operated and with thegap 50 µm between entrance the slit fibers width. was The 700entrancem. slit Light was collectedwidth simultaneously of 250 µm was used from during the eightthis experiment. vertical chords, A vertical viewed array of through nine fibers a 2.0was cm attached width along and 50 cm long rectangularthe entrance slit window, height, whichenabling was multi-track placed measurement. on the top triangular The fiber had port a core of the diameter Aditya (d) tokamak of 400 µm and can observeand the numerical whole plasmaaperture cross-section.(NA) of 0.22, and The the light gap between was collected the fibers from was four 700 µm. lines Light of sight, was collected placed in both inboardsimultaneously (high magnetic from field) the eight and vertical outboard chords, (low viewed magnetic through field) a sides 2.0 cm of thewidth plasma, and 50 as cm shown long by the rectangular window, which was placed on the top triangular port of the Aditya tokamak and can schematic diagram of viewing geometry in Figure1. The lines of sight locations for the experimental observe the whole plasma cross-section. The light was collected from four lines of sight, placed in both measurementsinboard (high in terms magnetic of ρ field)were and 0.53, outboard 0.66, 0.80, (low and magn 0.93etic for field) both sides high of the and plasma, low field as shown sides ofby thethe plasma. The lightschematic collection diagram optics of viewing consisted geometry of optical in Figure fibers 1. The with lines d ofof 1sight mm locations and NA for= the0.22, experimental and collimating lens withmeasurements a diameter in ofterms 11 mmof ρ were and focal0.53, 0.66, length 0.80, of and 19 mm.0.93 for As both a result, high and a spatial low field resolution sides of the of 25 mm at theplasma. horizontal The light mid collection plane of optics the Aditya consisted tokamak of optical was fibers achieved. with d of The 1 mm data and were NA collected= 0.22, and with an exposurecollimating time of lens 10 mswith during a diameter the currentof 11 mm flat and top focal region length of of the 19 Adityamm. As plasma,a result, a and spatial the resolution data acquisition of 25 mm at the horizontal mid plane of the Aditya tokamak was achieved. The data were collected was triggered by the loop voltage. The spectroscopic system was absolutely calibrated for the intensity with an exposure time of 10 ms during the current flat top region of the Aditya plasma, and the data to carryacquisition out the quantitativewas triggered by data the analysis. loop voltage. From The the spectroscopic recorded spectra,system was the absolutely chord integrated calibrated brightnessfor was obtainedthe intensity by to integrating carry out the the quantitative fitted curve data analys of theis. spectral From the line recorded using spectra, a Gaussian the chord profile. integrated The radial emissivitybrightness profiles was obtained were obtained by integrating using the an fitted Abel-like curve of matrix the spectral inversion line using technique a Gaussian [19 profile.] from The the chord integratedradial brightnessemissivity profiles of O4 +wereemissions. obtained using The detailsan Abel-like of this matrix conversion inversion technique have been [19] described from the in the chord integrated brightness of O4+ emissions. The details of this conversion have been described in the references [15,20]. The error estimation was done by incorporating the statistical error present in the references [15,20]. The error estimation was done by incorporating the statistical error present in the absoluteabsolute calibration calibration and and the the one one due due to to thethe spectral line line fitting fitting using using a Gaussian a Gaussian profile profile to obtain to obtainthe the brightness,brightness, which which is theis the area area under under the the curvecurve of th thee spectral spectral line line profile. profile. The uncertainties The uncertainties in the in the emissivitiesemissivities remain remain within within 15%. 15%.

FigureFigure 1. Schematic 1. Schematic for for viewing viewing geometry geometry used for for a aspace-resolved space-resolved visible visible spectroscopic spectroscopic system. system. Atoms 2019, 7, 90 4 of 10

3. Modeling of the O4+ Emissivity Profile The modeling of the radial profile of the O4+ emission was carried out using an empirical one-dimensional impurity transport code, STRAHL. This code numerically solves the radial continuity equation of each ionization stage of an impurity, and calculates the radial profile of the density of impurity ions by taking into account the tokamak magnetic field geometry, as well as the plasma electron temperature and density profiles. It also takes impurity source rate, transport coefficients (diffusion coefficient, D, and convective velocity, v), and source and sink terms as input parameters. For a charge state Z, the radial transport equation is expressed as: ! ∂n 1 ∂ ∂n Z = r D Z v n + Q (1) ∂t r ∂r ∂r − Z Z where nZ is the impurity density, DZ is the diffusion coefficient, and vZ is the convective velocity of ionic charge Z. QZ is the source/sink term relating each ionization stage with the neighboring ionization stages of impurity ions according to:

QZ = (neSZ + neαZ + nHCZ) nZ + neSZ 1nZ 1 + (neαZ+1 + nHCZ+1) nZ+1 (2) − − − where S, α, and C are the reaction rate coefficients for ionization, recombination (radiative and di-electronic), and charge exchange, respectively. The required electron density profile is taken from the seven-channel microwave interferometer diagnostics and the radial profile was obtained from the chord integrated profile measurement using Abel inversion [21]. As the electron temperature is available only for the core and the edge regions of the plasma, its radial profile was generated using the following equation: !β r2 Te(r) = Te,a + (Te,0 Te,a) 1 (3) − − a2 where Te(0) and Te(a) are the central and edge electron temperatures, respectively. The value of β was taken to be 1.75. This value of β was found to be appropriate to get the best matched Te profile for describing the observed positive and negative loop voltage spikes in similar discharges [22]. After calculating the radial profile of the density of each impurity ionization stage, the emissivity radial profile of a radiative transition from an initial state, i, to a final state, j, was calculated using following equation: ε (r) = n (r) ne(r) PEC (r) (4) z,i,j z,i · · z,i,j where nz and ne are, respectively, densities of the impurity ion of a particular charge state and of the electron and the PEC (photon emissivity coefficient), which is a function of both electron temperature and densities, obtained from CR modeling calculation based on the detail population balance of the excited states of an ion, carried out by considering the contributions from excitation, ionization, and recombination processes. Here, PECs from two different atomic databases were used in the modeling: Those labeled PEC1 were taken from the ADAS database [10], while those called PEC2 were provided by the NIFS code [11] (developed at the National Institute of Fusion Science (NIFS), Japan). The emissivity radial profile of the spectral line at 650.024 nm of O4+ ion was obtained using a space-resolved visible spectroscopy system during current flat top region of the Aditya tokamak plasma. The temporal evolution of the plasma current (Ip), loop voltage (Vloop), central chord average electron density (ne), and core plasma electron temperature (Te) of the analyzed discharge are shown in Figure2. The data acquired with a CCD exposure time of 10 ms was started at 45 ms of plasma discharge, and this time section is marked by two vertical lines in the figure. One can see from the figure that all major parameters were mostly constant during the time segment of the emissivity profile measurement. Figure3 shows the n e and Te profiles with respect to normalized plasma radius, ρ = r/a, where a is the plasma minor radius of the analyzed plasma. The values of core electron density and temperature are, respectively, 2.02 1019 m 3 and 350 eV. The Ohmic input power was ~180 kW and × − Atoms 2019, 7, x FOR PEER REVIEW 5 of 10 Atoms 2019, 7, x FOR PEER REVIEW 5 of 10 Atoms 2019, 7, 90 5 of 10 auxiliary heating was used in this discharge. It should be noted that the option of calculating the neo- classicalauxiliaryno impurity auxiliary heating heating wastransport used was wasin used this kept in discharge. this switched discharge. It off should Itin should the be code noted be notedcalculation. that that the the option option of of calculating calculating thethe neo- classicalneo-classical impurity impurity transport transport was kept was switched kept switched off in o theff in code the code calculation. calculation.

Figure 2. Temporal evolution of (a) plasma current (Ip) and loop voltage (Vloop), and (b) electron density Figure 2. Temporal evolution of (a) plasma current (I ) and loop voltage (V ), and (b) electron (nFiguree) and 2. core Temporal electron evolution temperature of (a (T) plasmae) of an Adityacurrent tokamak (Ip) andp loopplasma. voltage Spectroscopy (Vlooploop), and data (b) acquired electron densityduring density (n ) and core electron temperature (T ) of an Aditya tokamak plasma. Spectroscopy data time(ne) and segment core electron aree within temperature the two vertical (Te) of anbars. Aditya e tokamak plasma. Spectroscopy data acquired during time segmentacquired duringare within time the segment two vertical are within bars. the two vertical bars.

Figure 3. Figure 3. RadialRadial profile profile of of ne n ande and T Te eusedused for for the the calculation using using transport transport code. code. Figure 3. Radial profile of ne and Te used for the calculation using transport code. The experimental and best-fit-matched simulated radial profiles of O4+ emissivity are shown in 4+ TheFigure experimental4. The experimental and best-fit-matched emissivity radial simulated profiles in radial the low profiles (outboard) of O and emissivity high field (inboard)are shown in The experimental and best-fit-matched simulated radial profiles of O4+ emissivity are shown in Figuresides 4. The are representedexperimental by emissivity circles, and theradial horizontal profiles error in the bar inlow the (outboard) experimental and data high represents field (inboard) the sidesFigure areobservation 4. representedThe experimental chord by width circles, emissivity at the and horizontal the radial horizontal mid profil plane eserror ofin the thebar tokamak. lowin the (outboard) experimental The peak and emissivity highdata fieldrepresents is slightly (inboard) the observationsides higherare represented inchord the high width fieldby atcircles, side the but horizontal and the peaksthe horizontal liemid around plane ρerror =of0.64 the bar on tokamak. bothin the sides experimental The of the peak plasma. emissivity data Experimental represents is slightly the higherobservationprofiles in the chordhigh from bothfield width theside highat but the and the horizontal lowpeaks field lie sidesmid around wereplane ρ matched =of 0.64 the on tokamak. with both simulated sides The of peak profilesthe plasma. emissivity by varying Experimental is the slightly ρ profileshigherdi in fffromusion the highboth coeffi fieldthecient high side and impurityandbut thelow peaks sourcefield liesides rate. around Forwe modelingre matched = 0.64 purposes, on with both simulated sides at first of the the experimentalprofiles plasma. by Experimental varying profile the diffusionprofilesof thefrom coefficient low both field the side and high was impurity matchedand low source with field a rate. di sidesffusion For we coemodelingreffi matchedcient profile, purposes, with and simulated thenat first STRAHL the profiles experimental code by was varying again profile the ofdiffusion the runlow to coefficientfield obtain side best-fit was and formatched impurity the high with fieldsource a side diffusion rate. separately, For co modelingefficient as discussed profile,purposes, in details and at then in first the STRAHL paperthe experimental by Chowdhuricode was profile again et al. [17]. The simulated best-fit emissivity profiles obtained using code in both the low and high field runof the to obtainlow field best-fit side wasfor the matched high field with side a diffusion separate coly,efficient as discussed profile, in detailsand then in theSTRAHL paper codeby Chowdhuri was again sides of the Aditya tokamak plasma to the measured profiles are represented by a line in the figure. etrun al. to [17]. obtain The best-fit simulated for the best-fit high emissivityfield side separate profilesly, obtained as discussed using in code details in both in the the paper low byand Chowdhuri high field Here, Figure4a,b illustrates the modeling of the experimental data using STRAHL, where PEC values sideset al. [17].of the The Aditya simulated tokamak best-fit plasma emissivity to the profilesmeasured obtained profiles using are represented code in both by the a lowline andin the high figure. field Here,sides Figureof the Aditya4a,b illustrates tokamak the plasma modeling to the of measuredthe experimental profiles data are representedusing STRAHL, by a where line in PEC the valuesfigure. areHere, taken Figure from 4a,b the illustratesADAS database the modeling and from of thethe NIFSexperimental code, respectively. data using TheSTRAHL, convective where velocity PEC values term wasare takenkept zerofrom in the the ADAS code databasecalculation. and However, from the NIFSit was code, found respectively. that the results The convectivedo not change velocity much term by was kept zero in the code calculation. However, it was found that the results do not change much by Atoms 2019, 7, 90 6 of 10

Atoms 2019, 7, x FOR PEER REVIEW 6 of 10 are taken from the ADAS database and from the NIFS code, respectively. The convective velocity term was kept zero in the code calculation. However, it was found that the results do not change much by includingincluding the the convective convective term. term. In In the the previous previous study study on on the the Alcator-C Alcator-C tokamak, tokamak, a a similar outcome regardingregarding inward inward convention convention was was mentioned mentioned [4]. [4]. In In both both cases, cases, almost almost similar similar percentages percentages of oxygen concentration ~2% of ne were needed to match the experimental data. concentration ~2% of ne were needed to match the experimental data.

FigureFigure 4. 4.CalculatedCalculated (line) (line) and and experimental experimental emissivity emissivity (circle) (circle) plotted plotted with with normalized normalized radius radius ( ρ)) for bothboth high high (-ve (-ve ρ) ρand) and low low (+ve (+ veρ) fieldρ) field sides; sides; when when calculation calculation done done with with (a) ( aPEC1) PEC1 and and (b) ( bPEC2.) PEC2.

TheThe obtained obtained diffusion diffusion coefficient coefficient profiles profiles for for bo bothth the the low low (outboard) (outboard) and and high high (inboard) fieldfield sidessides are are shown shown in in Figure Figure 5.5 .Here, Here, the the red red dashed dashed li linene represents represents the obtained didiffusionffusion profile profile when calculatedcalculated with with STRAHL STRAHL and and PEC PEC data data (PEC1) (PEC1) fr fromom ADAS, ADAS, and and the the blue blue solid solid line line refers refers to the calculationcalculation using using STRAHL STRAHL and and PEC PEC data data (PEC2) (PEC2) from from NIFS NIFS code. code. One One can can see see that that although the diffusiondiffusion coefficient coefficient profiles profiles remain remain almost almost similar similar in in nature nature in in both both cases, cases, the the magnitudes magnitudes of of D D differ differ veryvery much. much. The The modeling modeling with with PEC2 PEC2 requires requires a alower lower D D to to get get the the best-fit best-fit between calculated and experimentalexperimental emissivity emissivity profiles profiles as as compared compared to to the the modeling modeling results results with with the the equivalent equivalent PEC PEC values, values, 2 1 PEC1.PEC1. In Inthe the low low field field side side of of the the plasma plasma edge, edge, the the peak peak value value of D becomesbecomes ~45~45 mm2·ss−−1 whenwhen modeling modeling 2 1 · is done with PEC1 than that of ~25 m2 −s1 in the case of PEC2. Similarly, lower value of D with reduced is done with PEC1 than that of ~25 m ·s· − in the case of PEC2. Similarly, lower value of D with reduced magnitudemagnitude is isalso also found found in in the the high high field field side side with with PEC2 PEC2 as as compared compared to to that that with with PEC1. This This higher valuevalue of ofD Dcompared compared to to the the calculated calculated one one by by neo- neo-classicalclassical transport transport theory theory is is explained using the fluctuationfluctuation induced induced transport. transport. It Itwas was found found that that th thee transport transport driven driven by by the the ion ion temperature temperature gradient (ITG)(ITG) and and dissipative dissipative trapped trapped electron electron (DTE) (DTE) modes modes wa wass good good enough enough to explain to explain the thediffusivity diffusivity in the in highthe field high side, field and side, the and further the further higher higher value valueof diff ofusivity diffusivity in the inlow the field low side field was side explained was explained by using by theusing combination the combination of ITG and of ITG resistive and resistive ballooning ballooning modes modes (RB) [15]. (RB) The [15]. error The errorbars barsin D inrepresent D represent the modificationthe modification of the of required the required diffusion diffusion coefficien coefficientsts to toget get the the best-fit best-fit between between experimental experimental and calculatedcalculated emissivity emissivity profiles profiles due due to to the the charge charge in in the the T Te eprofileprofile peaking peaking factor. factor. This This sensitivity sensitivity study of ofD Dwith with different different temperature temperature pr profilesofiles was was carried carried out out since since there there were were measurement measurement limitations in obtainingobtaining the the complete complete radial radial profiles profiles of of the the temperature. temperature. For For this this purpose, purpose, modeling modeling was was done with differentdifferent temperature temperature profiles profiles with with varying varying profile profile peaking peaking factor, factor, ββ (see(see Equation Equation (3)), (3)), from from 1.5 1.5 to 2.0 andand the the change change in inD Dis isshown shown in interms terms of oferror error bar bar for for the the best best matched matched condition. condition. Atoms 2019, 7, x FOR PEER REVIEW 7 of 10 Atoms 2019, 7, 90 7 of 10

FigureFigure 5. 5.RadialRadial profiles profiles of of diffusion diffusion coefficient coefficient using using PE PEC1C1 and and PEC2 PEC2 for for both both the high (inboard) andand lowlow (outboard) (outboard) field field sides sides of of plasma. plasma. Error Error bars bars re representpresent dependence dependence of of the magnitude of didiffusionffusion

coefficientcoefficient on on different different Te T profiles.e profiles. 4. Discussions on the Atomic Data towards the Difference in Diffusion Coefficients 4. Discussions on the Atomic Data towards the Difference in Diffusion Coefficients 3 3 The diffusion coefficients obtained using PEC (PEC1) data for the transition of 2p3p D3-2p3d F4 The diffusion coefficients obtained using PEC (PEC1) data for the transition of 2p3p 3D3-2p3d 3F4 from the ADAS database are larger as compared to those obtained using PEC data from NIFS (i.e., from the ADAS database are larger as compared to those obtained using PEC data from NIFS (i.e., PEC2). Ideally the transport analysis should be independent of the atomic processes, and the atomic PEC2). Ideally the transport analysis should be independent of the atomic processes, and the atomic data involved in the source and sink term used in the continuity equation (Equation (2)), and also data involved in the source and sink term used in the continuity equation (Equation (2)), and also in in the equation of emissivity calculation (Equation (4)). However, due to the complexity involved the equation of emissivity calculation (Equation (4)). However, due to the complexity involved in the in the atomic data generation and calculation of CR modeling, the atomic data used in the transport atomic data generation and calculation of CR modeling, the atomic data used in the transport analysis analysis differ very much. This is again mostly true for the processes involved with higher excited differ very much. This is again mostly true for the processes involved with higher excited states of low states of low Z material and for the complex configuration with higher atomic number. The observed Z material and for the complex configuration with higher atomic number. The observed emission of emission of O4+ at 650.024 nm in visible region belongs to a ∆n = 0 transition connecting the ionic O4+ at 650.024 nm in visible region belongs to a ∆n = 0 transition connecting the ionic emitter lower and 3 3 emitter lower and upper energy levels, which are 2p3p D3 and 2p3d F4, respectively. Then, it can upper energy levels, which are 2p3p 3D3 and 2p3d 3F4, respectively. Then, it can be seen that the be seen that the difference in the diffusion coefficient mainly arises due to the differences of the PEC difference in the diffusion coefficient mainly arises due to the differences of the PEC values from the values from the two databases, as shown in Figure6. At lower T e values, the NIFS PECs values are two databases, as shown in Figure 6. At lower Te values, the NIFS PECs values are lower than those lower than those provided by the ADAS database. As for example, the ratio of PEC1 to PEC2 is almost provided by the ADAS database. As for example, the ratio of PEC1 to PEC2 is almost five at the Te of five at the T of 30 eV. As a consequence, a lower value of the diffusion coefficient was found when 30 eV. As a consequence,e a lower value of the diffusion coefficient was found when using PEC2 to get using PEC2 to get the best-fit solution. The reason can be attributed to the difference in the basic the best-fit solution. The reason can be attributed to the difference in the basic atomic data, like atomic data, like ionization, recombination, and excitation rates, which are used by the CR model ionization, recombination, and excitation rates, which are used by the CR model calculation. Note also calculation. Note also that there might be differences in the inclusion of various transitions in the codes. that there might be differences in the inclusion of various transitions in the codes. For instance, ADAS 2 1 For instance, ADAS data do not include the forbidden transition between ground state 2s S0 and the data do not include the forbidden transition between ground state 2s2 1S0 and the upper state 2p3d 3F4. upper state 2p3d 3F . Note that this transition is forbidden in the frame work of the electrical dipole Note that this transition4 is forbidden in the frame work of the electrical dipole approximation and is approximation and is only of importance for radiation—and then does not see any spectral line having only of importance for radiation—and then does not see any spectral line having transition 2p3d 3F4-2s2 3 2 1 transition 2p3d F4-2s S0. In the ADAS case, the main excitation pathway to this upper state is likely 1S0. In the ADAS case, the main excitation pathway to this upper state is likely a two-step process, i.e., a two-step process, i.e., the ground state electron jumps to, at first, many other low-lying levels, such as the ground state electron jumps to, at first, many other low-lying levels, such as the 2s2p, then finally the 2s2p, then finally to the 2p3d level. In case of the NIFS CRM code, both the direct electron impact to the 2p3d level. In case of the NIFS CRM code, both the direct electron impact excitation from the excitation from the ground state to the 2p3d level and the indirect two steps excitation process from ground state to the 2p3d level and the indirect two steps excitation process from the ground state to the the ground state to the 2p3d level through the 2s2p one can contribute to populating that level. The 2p3d level through the 2s2p one can contribute to populating that level. The excitation rate coefficients 2 1 3 2 1 3 excitation2 1 → rate coe3 fficients for2 1 2s →S0 2s2p3 P2 and 2s S0 2p3d F4 transitions for both ADAS and for 2s S0 2s2p P2 and 2s S0 2p3d→ F4 transitions for both→ ADAS and NIFS data are plotted in FigureNIFS 7a,b, data arerespectively. plotted in It Figure can be7a,b, seen respectively. from Figure It can7b that be seenthere from are not Figure too7 bmany that theredifferences are not in too the 2 1 many differences in the excitation rate coefficients corresponding to the forbidden transition of 2s S0 excitation rate coefficients corresponding to the forbidden transition of 2s2 1S0 → 2p3d 3F4 between the 3 ADAS2p3d [23] Fand4 between NIFS data the [24]. ADAS Note [23 that] and the NIFS rate data coefficient [24]. Note values that are the almost rate coe threefficient orders values of magnitude are almost → 2 1 3 three orders of magnitude lower than the excitation2 1 → rate coe3 fficients of 2s S0 2s2p P2 transition for lower than the excitation rate coefficients of 2s S0 2s2p P2 transition for both→ ADAS and NIFS data, Atoms 2019, 7, x FOR PEER REVIEW 8 of 10

Atomsas shown 2019, 7 ,in x FORFigure PEER 7a. REVIEW Then, the direct contribution to the population of the upper level 2p3d 83F of4 from10 Atoms 2019, 7, 90 8 of 10 2s2 1S0 → 2p3d 3F4 transition seems to be lower as compared to the contribution from the two-step process. It is usually seen that in the calculation of PEC values through the CR model, the importance as shown in Figure 7a. Then, the direct contribution to the population of the upper level 2p3d 3F4 from ofboth direct ADAS excitation, and NIFS followed data, asby shown immediate in Figure radiative7a. Then, decay the to directany lower contribution level, is tomostly the population observed at 2 1 → 3 2slow S electron0 2p3d densities F4 transition [25].3 In seems addition to2 1beto that,lower as as sh 3comparedown in Figure to the 7a, contributionthe excitation from rate coefficientthe two-step for of the upper level 2p3d F4 from 2s S0 2p3d F4 transition seems to be lower as compared to process. It is usually seen3 that in the calculation→ of PEC values through the CR model, the importance thethe ground contribution state to from 2s2p the P2 two-stepis fairly different process. between It is usually the cases seen (the that ADAS in the and calculation NIFS data) of PEC at the values lower of direct excitation, followed by immediate radiative decay to any lower level, is mostly observed at electronthrough temperature. the CR model, These the differences importance in of atomic direct excitation,data and processes followed make by immediate the PEC values radiative different decay at low electron densities [25]. In addition to that, as shown in Figure 7a, the excitation rate coefficient for theto anylow lowertemperature level, is region mostly between observed ADAS at low and electron NIFS co densitiesdes. This [25 might]. In additionbe the probable to that, reason as shown behind in 3 thegetting ground a lower state diffusionto 2s2p P coefficient2 is fairly different when the between calculat theion cases is done (the using ADAS3 NIFS and dataNIFS as data) compared at the lower to the Figure7a, the excitation rate coe fficient for the ground state to 2s2p P2 is fairly different between electron temperature. These differences in atomic data and processes make the PEC values different at ADASthe cases data. (the ADAS and NIFS data) at the lower electron temperature. These differences in atomic the low temperature region between ADAS and NIFS codes. This might be the probable reason behind data and processes make the PEC values different at the low temperature region between ADAS and getting a lower diffusion coefficient when the calculation is done using NIFS data as compared to the NIFS codes. This might be the probable reason behind getting a lower diffusion coefficient when the ADAS data. calculation is done using NIFS data as compared to the ADAS data.

Figure 6. Photon emission coefficient (PEC) from ADAS (PEC1) and NIFS (PEC2) databases plotted with

Te for different ne values.

Figure Figure 6. 6.PhotonPhoton emission emission coefficient coefficient (PEC (PEC)) from from ADAS ADAS (PEC1) (PEC1) and and NIFS NIFS (PEC2) (PEC2) databases databases plotted plotted with Tewith for different Te for di ffnerente values. ne values.

2 1 3 2 1 3 Figure 7. Excitation rate coefficient, Q, for (a) 2s S0 2s2p P2 and (b) 2s S0 2p3d F4 transition Figure 7. Excitation rate coefficient, Q, for (a) 2s2 1S0→ → 2s2p 3P2 and (b) 2s2 1S0→ → 2p3d 3F4 transition plotted with electron temperature, Te. plotted with electron temperature, Te.

5. Conclusions Figure 7. Excitation rate coefficient, Q, for (a) 2s2 1S0 → 2s2p 3P2 and (b) 2s2 1S0 → 2p3d 3F4 transition Oxygen impurity transport in the Aditya tokamak was studied using the emissivity radial profile plotted with electron temperature, Te. 3 3 of the 650.024 nm visible spectral line due to the radiative transition 2p3p D3-2p3d F4 emitted by Atoms 2019, 7, 90 9 of 10

Be-like oxygen ions. The brightness spatial profile has been recorded from eight lines of sight passing through the plasma using a spatially-resolved visible spectroscopic system. The emissivity radial profile was obtained using an Abel-like matrix inversion. The radial profiles from both low and high field sides of the plasma were simultaneously measured and also modeled using the STRAHL impurity transport code. For calculation purposes, the required photon emissivity coefficients (PEC) were taken from two separate databases, ADAS and NIFS. It was found that the experimental emissivity profiles of both the low and high field sides could be best-fitted using an almost similar profile of diffusion coefficients by using PECs from both databases. However, the values of diffusion coefficients differ in magnitude. It was observed that when the calculation is done using ADAS data, the diffusion coefficient profile of the high field region has a peak around the normalized plasma radius ρ = 0.73 with a maximum value of 30.0 m2 s 1, then it gradually decays further outsides of the plasma, but at low field · − region, its value gradually rises to the plasma edge, reaching a maximum value 50 m2 s 1. The obtained · − diffusion coefficients have lower values when the calculation is done using NIFS data. The maximum values of the diffusion coefficients in the plasma edges at the low field side of the tokamak are ~45 and ~25 m2 s 1 when modeling is done using the ADAS and NIFS databases, respectively. Further analysis · − of the atomic data used in CR modeling to obtain PEC values reveals that the difference in the diffusion coefficient is mainly due to the variation in PECs at low temperature regions. The differences in the PEC values are attributed to the dissimilarity in the excitation rate coefficient used in the two codes.

Author Contributions: Conceptualization, M.B.C. and J.G.; methodology, M.B.C.; atomic data, I.M., R.D., S.P. and A.B.; formal analysis, M.B.C.; writing, M.B.C. and J.G.; experiment, M.B.C., J.G., R.M., N.Y., S.P., and the Aditya Team. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflicts of interest.

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