A novel hydrogenic spectroscopic technique for inferring the role of plasma-molecule interaction on power and particle balance during detached conditions
K Verhaegh, B Lipschultz, C Bowman, B P Duval, U Fantz, A Fil, J R Harrison, D Moulton, O Myatra, D Wünderlich, F Federici, D S Gahle, A Perek, M Wensing, TCV team, EuroFusion MST1 team
AA novel hydrogenic spectroscopic technique forinferring the role of plasma-molecule interaction onpower and particle balance during detachedconditions
K. Verhaegh , , , B. Lipschultz , C. Bowman , B.P. Duval , U.Fantz , , A. Fil , , J.R. Harrison , D. Moulton , O. Myatra , D.W¨underlich , F. Federici , D.S. Gahle , , A. Perek , M.Wensing , the TCV Team ∗ and the EuroFusion MST1 team ∗∗ Culham Centre for Fusion Energy, Culham, United Kingdom York Plasma Institute, University of York, United Kingdom Swiss Plasma Centre, ´Ecole Polytechnique F´ed´erale de Lausanne, Lausanne,Switzerland Max Planck Institute for Plasma Physics, Garching bei M¨unchen, Germany Augsburg University, Augsburg, Germany SUPA, University of Strathclyde, Glasgow, United Kingdom DIFFER, Eindhoven, The Netherlands ∗ See author list of ”S. Coda et al 2019 Nucl. Fusion 59 112023” ∗ ∗ See author list of ”B. Labit et al 2019 Nucl. Fusion 59 086020”E-mail: [email protected]
Abstract.
Detachment, an important mechanism for reducing target heat deposition,is achieved through reductions in power, particle and momentum; which are inducedthrough plasma-atom and plasma-molecule interactions. Experimental research inhow those reactions precisely contribute to detachment is limited. In this work, weinvestigate a new spectroscopic technique to utilise Hydrogen Balmer line measurementsto 1) disentangle the Balmer line emission from the various plasma-atom and plasma-molecule interactions; and 2) quantify their contributions to ionisation, recombinationand radiative power losses.During detachment, the observed Hα emission often strongly increases, which couldbe an indicator for plasma-molecule interactions involving H +2 and/or H − . Our analysistechnique quantifies the Hα emission due to plasma-molecule interactions and usesthis to 1) quantify the Balmer line emission contribution due to H +2 and/or H − ; 2)subsequently estimate its resulting particle sinks/sources and radiative power losses.Its performance is verified using synthetic diagnostic techniques of both detached TCVand MAST-U SOLPS-ITER simulations.Experimental results of this technique on TCV data show a bifurcation occursbetween the measured total Hα and the atomic estimate of Hα emission, indicative ofthe presence of additional Hα due to plasma-molecule interactions with H +2 (and/or H − ). An example analysis shows that the hydrogenic line series, even Lyα as well as themedium-n Balmer lines can be significantly influenced by plasma-molecule interactionsby tens of percent during which significant Molecular Activated Recombination (MAR)is expected. a r X i v : . [ phy s i c s . p l a s m - ph ] A ug pectroscopy inferences of plasma-molecule interactions Keywords : Tokamak divertor; Molecules; plasma; SOLPS-ITER; Plasma spectroscopy;Power/particle balances; Detachment
1. Introduction
Divertor detachment is predicted to be crucial for handling the power exhaust of futurefusion devices, such as ITER [1, 2, 3]. In this detached state, a collection of atomicand molecular processes ultimately results in the simultaneous reduction of the targettemperature ( T t ) and the ion target current (Γ t ), which facilitates large reductions in thetarget heat flux ( q t ) as shown in equation 1 where γ is the sheath transmission coefficientand (cid:15) is the surface recombination energy where an H + ion converts to an atom (13.6eV) and then to a molecule (15.8 eV) [4]. q t = Γ t ( γT t + (cid:15) ) (1)Given the sheath-target conditions (equation 2), a simultaneous reduction of theion target current and the target temperature requires target pressure ( p t ) loss. Thattarget pressure loss can be facilitated through volumetric momentum losses [5, 6] as wellas an upstream pressure loss as indicated in previous research on TCV [7], in agreementwith analytic model predictions and SOLPS-ITER simulations [7, 8].Γ t ∝ p t /T / t (2)That ion target current is predominantly determined through a competition ofion sources (e.g. ionisation - Γ i ) and sinks (e.g. recombination) in the divertor (ionflows from upstream to the target are generally considered to be small compared to Γ t )[9, 10, 11, 6, 7]. Each ionisation event, however, requires a certain amount of energy( E ion ) - strongly connecting particle balance with divertor power balance [9, 10, 11, 6, 7].Particle/power balance are also interconnected with momentum balance through equation2 [6, 5, 7]; and all three balances play an important role in the detached state [12, 7].Investigating detachment thus, ideally, requires a detailed characterisation of divertor 1)particle balance (ion sinks/sources); 2) power balance and 3) momentum balance.Previous experimental research [7, 13] investigated these balances from the viewpointof atomic processes . This showed that the initial ion target current reduction during thedetachment onset is facilitated by a reduction of the divertor ion source, which starts attarget temperatures of 4-7 eV [7]. That reduction in ion sources was driven by ’powerlimitation’: the ion source becomes ’limited’ by the power flowing into the ionisationregion when this becomes comparable to the power needed for ionisation which occurredsimultaneously with the onset of volumetric momentum losses [7, 14].One characteristic of detachment that has been observed in a number of devices [5]is that the observed Hα emission strongly increases after the detachment onset and ioncurrent roll-over [15, 16]. This is contrary to expectations based on excitation emission: Hα should be correlated with the drop in ion current. While this anti-correlation pectroscopy inferences of plasma-molecule interactions Hα enhancement observed on TCV is not consistent with ”atomic” processes(electron impact excitation (of H ) and electron ion recombination (of H + )) but ratheris indicative of reactions related to H plasma-chemistry. Previous modelling workand experimental work from linear devices has shown that H plasma chemistry couldinfluence the Hα emissivity through various interactions including interactions with H , H +2 and H − [17, 18, 19, 20, 21, 22]. These plasma-molecule interactions can result in excited hydrogen atoms , which then emit Hα emission and other hydrogenic line emission.This is consistent with suspicions raised at DIII-D and JET where experimental resultssuggested that the Hα brightness may not be fully explainable with purely atomicinteractions [23, 16].Power, particle and momentum balances are crucial aspects of detachment [5, 12]. Reactions between the plasma and H +2 & H − , as well as collisions between theelectrons and H can alter all three of those balances beyond the atomic predictions[17, 24, 25, 12, 22]. A chain of reactions can lead to the ’activation’ of recombinative orionisation processes of the plasma neutrals: ’Molecular Activated Recombination - MAR’and ’Molecular Activated Ionisation - MAI’ [26, 27, 19]. Plasma-molecule interactionscan result in radiative losses (thus possibly influencing divertor power balance) through1) molecular band emission (such as the Fulcher, Werner bands), arising from the plasmacolliding with and exciting H molecules [17, 24, 28, 22]) and 2) atomic line emission(arising from excited atoms after plasma-molecule interactions [17, 28, 29] - mostly with H +2 and/or H − . Apart from radiative losses, collisions between the plasma and H cantransfer power from the plasma to the molecules, effectively acting as a power sink tothe plasma [30, 25, 12].. Both collisions between the plasma and H [12, 31] as wellas ’molecular ion conversion’ reactions ( H + H + → H +2 + H ) can result in significantplasma momentum loss [30, 25, 12].Experimental investigations into such processes in tokamak divertors, in general,are few and are typically based on measuring the molecular spectra, such as the Fulcherband [17, 24, 23, 22]. The H Fulcher band emission arises from electronically excitedstates of H and provides useful information about the rovibrational distribution of H ( ν ) [17], H density and can be used to estimate H dissociation [23]. H becomeselectronically and rovibrationally excited through collisions between the electrons and H [26, 17, 24, 20, 23, 22, 27, 32]. Such interactions also raise the molecular gas (rotational)temperature - a direct indicator for plasma-molecule interaction - implying more highervibrational excitation of the molecules. Higher vibrational levels strongly promote thecreation of H − and H +2 (for T e between 1-4 eV). Those species undergo reactions withthe plasma resulting in most of the MAR and MAI ion sinks/sources [20, 27, 10, 33, 21]as well as excited atoms, which can lead to strong modifications to the Hydrogenicline series [17, 24, 28, 20, 21]. Such modifications to the Balmer line series and theirassociated radiative losses have not yet been studied experimentally before on tokamakdivertors and may provide an alternative way of estimating MAR/MAI as well as atomicradiation related to H plasma chemistry. pectroscopy inferences of plasma-molecule interactions atomic process contributions based on the characteristics of the medium-n inputBalmer line emission (generally n=5,6,7). That information is now used to determine theatomic contributions to Hα and Hβ emission. The excess of experimental measurementsover what is expected from atomic processes is attributed to excited atoms arisingfrom plasma-molecule interactions (e.g. excited atoms related to H plasma chemistry).Using collisional radiative model results from Yacora (on the Web) [28, 29], Balmer lineemission attributed to plasma-molecule interactions involving H +2 , H − is quantitativelyseparated using the ratio between the molecular parts of the Hα and Hβ emissions. The Hα emission estimate due to excited atoms from plasma interactions with H +2 , H − , H are then used individually to: • Estimate Molecular Activated particle sinks (Recombination) /sources (Ionisation) -MAR/MAI for each emission channel. • Estimate the contribution of plasma-molecule interactions to: – the entire hydrogenic spectra providing radiative loss estimates for excitedatoms arising from plasma interactions with H , H +2 and H − . – the medium-n Balmer lines, which is accounted for self-consistently.The technique is verified using synthetic diagnostic data from TCV and MAST-USOLPS simulations, where YACORA has been used to ’post-process’ the contributionsof plasma-molecule interactions to the entire Balmer line emission. We refer to thistechnique as: Balmer Spectroscopy Plasma-Molecule Interaction - BaSPMI.Our example analysis on TCV data shows that a bifurcation occurs between theatomic prediction of Hα and the total measured Hα trend starting at the detachmentonset. We find that this mismatch cannot be explained by H dissociating into excited( ∗ ) atoms (e.g. e + H → H + H ∗ ): at the expected H densities, this makes up less than1 % of the measured Hα emission. Instead, the applied analysis illustration indicatesthat the hydrogenic line series (including the medium-n Balmer lines as well as Lyα ) hasstrong contributions from plasma-molecule interactions involving H +2 and H − ; which areformed from H . This has important repercussions for the interpretation of the Balmerline spectra. As will be shown in a companion paper [35] where this model is applied toexperimental measurements, molecules in the TCV divertor can influence particle/powersignificantly and thus may have a significant contribution to detachment after the initialdetachment onset. pectroscopy inferences of plasma-molecule interactions
2. Spectral analysis techniques of inferring information on plasma-moleculeinteraction from the Balmer spectra
The goal of our analysis technique BaSPMI is to quantify the contribution of plasma-molecule interactions to Hα and use this to provide quantitative estimates on the influenceof molecules on power losses; particle (ion) gains/losses and Balmer line emission. Aschematic overview of the contribution of the various plasma-atom and plasma-moleculeinteractions to excited hydrogen neutrals (which emit hydrogenic line emission) areshown in 1. + HH - HH H H H α Figure 1.
Schematic overview of the various reaction channels resulting in hydrogenicatomic line emission; schematic adopted from [28].
The analysis developed in this work builds upon the Balmer line analysis techniquesdeveloped previously by the authors in [34], of which we provide a summary in section2.1. For the analysis we utilise the measurements of Hα , Hβ in addition to twomedium-n Balmer lines (n=5,6,7) [34]. The analysis works on the basis of assigning all measured Balmer line emission to the sum of the expected
Balmer line emission based onboth plasma-atom interactions (involving
H, H + ) and H plasma chemistry (involving H , H +2 , H − ). Contributions from H +3 are ignored (see section 2.3). A flowchart of theanalysis scheme is provided in figure 2 and consists of several steps.(i) We apply the analysis technique from [34] on the medium-n Balmer lines, whichconsiders only atomic processes (e.g. electron-impact excitation of H and electron-ion recombination of H + ). Initially we attribute all medium-n Balmer line emissionto only atomic processes. The analysis from [34] consists of several sub-steps andmore information can be found in section 2.1:(a) We infer the electron density from the Balmer line shape through Starkbroadening [34, 15].(b) The fraction of the medium-n Balmer line ratio due to electron-impact excitation F exc ( n ) and electron-ion recombination F rec ( n ) = 1 − F exc ( n ) is determinedfrom the ratio of two medium-n Balmer lines. This uses an assumed possiblerange of neutral fractions n o /n e .(c) These fractions are multiplied with the measured medium-n Balmer linebrightness to obtain the Balmer line brightnesses due to electron-impactexcitation ( B excn → ) and electron-ion recombination ( B recn → ).(d) The (line-integrated) ionisation rate I L , radiative power loss due to electron-impact excitation P excrad,L and respective excitation region temperature T Ee is pectroscopy inferences of plasma-molecule interactions B excn → using an assumed range of possible neutral fractions n o /n e and pathlengths ∆ L .(e) The (line-integrated) recombination rate R L , radiative power loss due to electron-ion recombination P recrad,L and respective recombination region temperature T Re is estimated from B recn → using an assumed range of possible pathlengths ∆ L .(ii) The sum of the contributions of H plasma chemistry (involving H , H +2 and H − )to Hα and Hβ are estimated using the measured Hα, Hβ brightnesses and outputsfrom the ”atomic particle/power sink/source analysis” as will be explained in section2.2.(iii) The individual contributions ( H , H +2 and H − ) of plasma-chemistry to Hα are separated using the sum of those contributions to Hα and Hβ as will be explainedin section 2.3.(iv) The individual contributions of H plasma-chemistry to Hα are used to estimatethe individual contributions of H plasma-chemistry to the medium-n Balmer lineas will be explained in section 2.4. This information is used to modify the atomicprocess contributions to the medium-n Balmer line brightnesses in step 1, which isthen iterated up until step 4 until a converged result is obtained.(v) After a converged result is obtained, the individual contributions of Hα associatedwith H plasma-chemistry are used to estimate (line-integrated) MAI ion sources( I LM ), MAR ion sinks ( R LM ) as well as the (line-integrated) radiated power due toexcited atoms after plasma-molecule reactions involving ( H , H +2 andH − ) - P molrad,L ).This will be explained in sections 2.5.2 and 2.5.1. pectroscopy inferences of plasma-molecule interactions rec R T e Atomic particle/power sink source analysis
Recombination rateIonisation rateIonisation rateIonisation rateIonisation rateIonisation rate + Da [D ] Balmerline shape(n>6) Stark broadeningn e Balmerline ratio F rec (n) F rec (n)B n->2 B n->2exc B n->2rec Recombination raten e ΔL n e n o /n e I L P rad,Lexc R L ΔL n /n o e P rad,Lrec F exc (n) InputOutput E T e Molecular particle/power sink source analysis H α ( ) x + - H , H , H rad./reac per H α photon ratios R T e B n->2rec n e T eE T e exc B n->2 + - H α [H , H , H ] H α [total] n e T eE T e+ - H α [H , H , H ] H α [H , H , H ] H β [H , H , H ] H β [total] + H α [H ] H α [H ]H α [H ] Obtain molecular = -total atomic molecular H α , Hβ: Separate mol. H α in parts + - H , H , H
Estimate mol. contributions other Balmer lines
MAI MAR mol P rad n e T eE T e n e eE T Analysis exc steps + - H α [H , H , H ] B [H , H , n->2 H ] H α [H , H , H ] B [H , H , n->2 H ]
Figure 2.
Schematic overview of the full analysis routine. The atomic analysis part hasbeen adopted from [34]. The nomenclature used is adopted from [34]: n o /n e - neutralfraction; ∆ L - emission pathlength; n e - electron density (from Stark broadening [34]); T Ee - estimated electron temperature in the excitation region; T Re - estimated electrontemperature in the recombination region; B excn → - atomic Balmer line emission due toexcitation; B recn → - atomic Balmer line emission due to recombination. The steps withinthe blocks ’Obtain molecular Hα ’; ’Separate mol. Hα ’; ’Estimate mol. contributions’;’ Hα ( H , H +2 , H − ) x rad./reac per Hα photon ratios’ are shown in more detailed infigures 3, 4, 6, 7 respectively. There are two different versions of the analysis we can apply, ranging in complexity:1) a ’simple’ version: include only ’atomic’ emission channels for the medium-n Balmerlines (e.g. no iteration applied) and optionally estimate the molecular component of Hα and assume this is purely due to H +2 to obtain MAR/MAI/radiative loss rates (seesection 5.3); 2) the complex ’full’ version, which does apply the iterative technique andseparates Hα into its H , H +2 , H − contributions. We have applied the ’full’ version tothe results unless otherwise specified.We summarise the reactions on which BaSPMI provides estimates, in terms ofradiative loss and particle sinks/sources in table 1. Note that this table is not anoverview of all the important plasma-molecule interactions. Most notably, the table doesnot contain the reactions where H +2 & H − are being ’created’ as these do not directly pectroscopy inferences of plasma-molecule interactions Reactions Ion bal. Emission Comment e − + H → e − + H N/A (cid:88)
Electron impact excitation (of H ) e − + H → e − + H + (cid:88) (cid:88) Ionisation e − + H + → H (cid:88) (cid:88) (Radiative) Electron-Ion Recombination(of H + ) - EIR e − + H + → e − + H (cid:88) (cid:88) (Three body) Electron-Ion Recombination(of H + ) - EIR e − + H → e − + H + H N/A (cid:88)
Dissociation e − + H → e − + H + H + (cid:88) (cid:88) Electron impact dissociative ionisation(part of MAI chain) e − + H +2 → e − + H + + H + (cid:88) N/A
Electron impact dissociative ionisation(part of MAI chain) e − + H +2 → H + H + + e − N/A (cid:88)
Dissociation (part of MAD (or MAI ‡ )chain) e − + H +2 → H + H (cid:88) (cid:88) Dissociative recombination (part of MAR(or MAD ‡ ) chain) H + + H − → H + H + + e − N/A (cid:88)
Proton impact ionisation (part of MADchain) H + + H − → H + H (cid:88) (cid:88) Mutual neutralisation (part of MARchain)
Table 1.
Overview of the various reactions on which the analysis provides information interms of particle (ion) balance (bal.) and radiative power loss (radiation). If the analysisprovides information on it, it is denoted with a ’ (cid:88) ’ (whereas N/A implies not applicable).MAR/MAI/MAD mean Molecular Activated Recombination/Ionisation/Dissociation lead to Balmer line emission (but the destruction of these species, as shown in table 1,does).
The basic steps of the the atomic Balmer line analysis technique of the upper block offigure 2 were discussed above and some important additional details are discussed belowhere. More information can be found in [34].In this analysis the emission is modelled using a collisional-radiative model by a 0D’semi slab-like’ plasma model. Here the emission region has a pathlength (e.g. width)∆ L , and an electron density n e , while a different temperature ascribed to the excitation( T Ee ) and recombination ( T Re ) regions (essentially a ’dual slab’ model). For simplicity,this model assumes that the H + density equals the electron density ( n H + = n e , ignoringimpurities); which is expected to have a negligible impact [13, 15, 34] on this analysis.The emission for the excitation/recombination region is determined using results fromcollisional radiative modelling from ADAS [36, 37] in the form of Photon Emission ‡ Whether interactions with H +2 are part of a MAR, MAD or MAI chain depends on the reactionprocess which created H +2 (e.g. whether it is molecular charge exchange H + + H → H +2 + H or H ionisation e − + H → e − + H ). This is explained in section 2.5.2 pectroscopy inferences of plasma-molecule interactions m s − ). The PEC is defined as the population coefficient( n p n e n ground where n p is the population density of the p state and n ground is the populationdensity of the ground state) multiplied with the respective Einstein coefficient A pq for a p → q transition: P EC ( p, q ) = A pq n p n e n ground [36, 37].All the analysis shown in this work is done in a ’probabilistic’ manner, which isalso employed for all plasma-molecule interaction related estimates [34]. For each inputparameter in figure 2, depending on their uncertainty, a ’Probability Density Function’(PDF) is ascribed. The peak of this parameter corresponds to the measured inputparameter, whereas its width and shape corresponds to the expected uncertainty of thisparameter. According to those PDFs, samples of input values for each parameter infigure 2 are obtained through Monte Carlo sampling. These are then propagated to theoutput parameters, yielding a PDF for the output parameters from which the estimatesand their uncertainties are obtained.The full atomic & molecular analysis requires implementing Hα & Hβ brightnessesin addition to the two medium-n Balmer lines used in the atomic analysis in [34]. Thisrequired modification to the PDF description of the relative brightnesses with respectto [34], which has to be similar for all possible line ratios. This was achieved usingmultivariate normal distributions with a set correlation strength according to [38]; whichleads to normal distributions for all the various line ratios ( σ = 0 .
15) as well as theline intensities ( σ = 0 . Hα emission After the medium-n Balmer lines are analysed from the viewpoint of ”atomic” interactions,those results are used with measured
Hα, Hβ brightnesses to estimate the contributionof H plasma chemistry to Hα and Hβ , which is illustrated in figure 2.This is achieved by assuming that the total measured Hα ( B total → ) equals its atomic part ( B atom → ) plus its molecular part ( B molecule → ) - as shown in equation 3. That assumptionis further discussed for TCV and MAST-U in sections 4.2 and 5.2. B molecule → = B total → − B atom → (3)The output information from the atomic analysis of the medium-n Balmer lines(figure 2) is utilised to extrapolate the atomic parts of the medium-n Balmer linebrightnesses of a Balmer line (typically n = 5 , ,
7) to Hα , yielding the atomic parts of the Hα brightness. Utilising the recombination/excitation inferred temperatures( T Ee , T Re ) and the Stark inferred density ( n e , the ratios of B excn → and B recn → to theexcitation/recombination parts of Hα are computed and used together with B exc,recn → to pectroscopy inferences of plasma-molecule interactions Atomic H α estimate H α [atom] E T e R T e B n->2rec B n->2exc Measured H α n e B n->2 - E T e + - H α [H , H , H ] Obtain molecular = -total atomic
Atomic H α estimate H α [atom] E T e R T e B n->2rec B n->2exc Measured H α n e B n->2 - E T e + - H α [H , H , H ] estimate H α [atom] E T e R T e B n->2rec B n->2exc Measured H β n e B n->2 - E T e + - H α [H , H , H ] Atomic H β estimate H β [atom] E T e R T e B n->2rec B n->2exc Measured H β n e B n->2 - E T e + - H β [H , H , H ] molecular H α , Hβ: Figure 3.
Schematic analysis flow chart for separating the atomic and molecularcontributions from the Hα and Hβ emission. This represents the step ’Obtain molecular Hα, Hβ ’ in figure 2. estimate the total ’atomic’ part of the Hα emission ( B atom,upscaled → ) as shown in equation4, [34]. B atom,extrapolated → = B excn → P EC exc → ( n e , T Ee ) P EC excn → ( n e , T Ee ) + B recn → P EC rec → ( n e , T Re ) P EC recn → ( n e , T Re ) (4)Once H α and Hβ brightnesses associated with H plasma chemistry have beenestablished through equations 3 & 4, the various molecular contributions have to beseparated. However,before discussing our algorithm for the separation, first we must establish how we canmodel the brightness of a Balmer line due to the various plasma-molecule interactions,which can arise from interactions with H , H +2 , H +3 and H − (figure 1). In addition,Balmer line emission from H − can arise due to reactions involving H − + H +2 and/or H − + H + reactions. Using a slab model for the plasma, we can describe the ’molecular’part of the Balmer line brightness using equation 5. Such plasma-slab models assumethat all processes occur at the same location physically and implications of this havebeen discussed in detail for atomic reactions in literature [7, 34, 15, 13].The PEC coefficients in equation 5, obtained through Yacora (on the Web) [28, 29],are functions of the electron density, electron temperature, as well as the temperatures ofthe molecular species ( H , H +2 , H +3 , H − ). Those latter temperature dependencies have,however, been found to be insignificant ( (cid:28) H − § ) and § The additional temperature dependencies for H − only impact the the ”MAR/ Hα emission coefficient”ratios employed in section 2.5.2. The other processes of this analysis only depend on the ratio of the H − PEC coefficients between different transitions - where this dependence is divided out. For this, a randomtemperature between 0.5-3 eV is assumed for H − as H − can get some of the Franck-Cordon energy ofthe H bond (2.2 eV) when H dissociatively attaches with an electron to form H − ( e − + H → H − + H ).The H + temperature is assumed to be a random value between 0.8 to 1.5 times T Ee , as estimated fromSOLPS-ITER simulations [8, 42, 43]. pectroscopy inferences of plasma-molecule interactions H , H +2 , H +3 has been assumed. B moleculen → =∆ Ln e n H P EC H n → ( n e , T e )+∆ Ln e n H +2 P EC H +2 n → ( n e , T e )+∆ Ln e n H +3 P EC H +3 n → ( n e , T e )+∆ Ln H + n H − P EC H − + H + n → ( n e , T e , T + H , T H − )+∆ Ln H +2 n H − P EC H − + H +2 n → ( n e , T e , T H +2 , T H − ) (5)To further simplify equation 5, we ignore the emission contribution from H +3 (whichwe estimate to be negligible based on post-processing of SOLPS simulations - section 3)and we assume that all emission from H − occurs from H − interacting with H + (ratherthan H +2 ) as the H + density is far larger than the H +2 density while their PECs aresimilar at the region where we would expect emission from such processes to occur. Withthose simplifications, we now obtain equation 6 for B moleculen → . B moleculen → ≈ ∆ Ln e n H P EC H n → ( n e , T e ) (cid:124) (cid:123)(cid:122) (cid:125) B H n → + ∆ Ln e n H +2 P EC H +2 n → ( n e , T e ) (cid:124) (cid:123)(cid:122) (cid:125) B H +2 n → +∆ Ln e n H − P EC H − + H + n → ( n e , T e ) (cid:124) (cid:123)(cid:122) (cid:125) B H − n → (6) Hα emission Now that we have established a model for the Balmer line emission contributions fromplasma-molecule interactions (involving H , H +2 and H − ), we can work on separatingthe various contributions. The steps for this are highlighted in figure 4, which willbe discussed in more detail below. First, the H contribution of Hα and Hβ areestimated using the relation between the H density and the electron temperatureobtained from SOLPS. Secondly, this H contribution is subtracted from the total Hα and Hβ brightnesses attributed to plasma-molecule interactions to obtain the Hα and Hβ brightnesses attributed to H +2 and H − . Thirdly, the ratio of those Hα and Hβ brightnesses are used to separate the Hα emission attributed to H +2 and H − .We find that the expected H densities in the divertor (estimated from SOLPSsimulations) are expected to only have a small contribution ( < Hα and Hβ brightnesses. We find that the dominant contributions of the Hα emissionattributed to H chemistry are from H +2 and H − . We have used SOLPS-ITER simulationresults from TCV and MAST-U to establish a relation between the expected H densitytimes the pathlength ∆ L and the (excitation) electron temperature [12] - f H ( T Ee ), whichis used to estimate the Balmer line brightnesses attributed to H - B H n → as shown inequation 7. This is further discussed in section 5.1. pectroscopy inferences of plasma-molecule interactions H α [H ] SOLPS estim. H α [H ] H α [H H ] Separate (with H α/ H β) + - H β [H H] H α [H ] H α [H ] Separate mol. H α in parts + - H , H , H H β [H ] T eE T eE T eE T e H β [H ] SOLPS estim. E T eE T e T eE T e E T eE T eE T eE T e n e + - H α [H , H , H ] H β [H , H , H ] H α [H , H , H ] H α [H , H , H ] - - Figure 4.
Schematic analysis flow chart for separating the various pathways of themolecular Hα emission. This represents the step ’Separate mol. Hα in H , H +2 , H − parts’ in figure 2. B H n → = f H ( T Ee ) n e P EC H n → ( n e , T Ee ) (7)After having estimated B H , → , this is used to estimate the Hα and Hβ emissionattributed to H +2 and H − : B , → + B , → = B molecule , → − B H , → . Plasma-moleculeinteractions involving H +2 and H − lead to different Hβ/Hα ratios as shown in figure 5.This distinction can be used to quantitatively separate emission contributions from H − and H +2 using equation 8. The dependency of the PEC coefficients for H − on the H − and H + temperatures is eliminated in the division of this equation. We have chosen the Starkinferred electron density ( n e ) and excitation temperature ( T Ee ) to interrogate the requiredPEC coefficients as this is a more reliable overall temperature (with uncertainty) indicatorof the plasma - especially for a hotter plasma [34] - which ultimately is important forMAI estimates (section 2.5.2). However, using the recombination temperature insteadfor any of the molecular estimates would not change any of the obtained conclusionsfrom the analysis (apart from reducing MAI rates). f H +2 ,mol.Hα ≡ B H +2 → B H +2 → + B H − → = 11 + CC = P EC H − → ( n e , T Ee ) (cid:20) P EC H +2 → ( n e , T Ee ) ( Hβ/Hα ) | H − ,H +2 − P EC H +2 → ( n e , T Ee ) (cid:21) P EC H − → ( n e , T Ee ) − P EC H − → ( n e , T Ee ) ( Hβ/Hα ) | H − ,H +2 (8)Now we have all the information required to determine all the emission contributions pectroscopy inferences of plasma-molecule interactions + H
2- - +
H (through H + H)
19 -3
10 m
20 -3
10 mn e T e (eV) H / H Figure 5.
Hβ/Hα ratio using YACORA PEC coefficients for H +2 and H − + H + fortwo different electron densities as function of T e (note any influence of T + H , T H − on P EC H − + H + n cancels). to Hα , which are summarised in equation 9. B atom,extrapolating → = B excn → P EC exc → ( n e , T Ee ) P EC excn → ( n e , T Ee ) + B recn → P EC rec → ( n e , T Re ) P EC recn → ( n e , T Re ) B molecule → = B total,measured → − B atom,upscaled → B H → = f H ( T Ee ) P EC H n → ( n e , T Ee ) B H +2 → = ( B molecule → − B H → ) × f H +2 ,mol.Hα B H − → = ( B molecule → − B H → ) × (1 − f H +2 ,mol.Hα ) (9) n > Balmer line emission
The molecular contributions to Hα must be consistent with molecular contributions toall Balmer lines in the analysis, including the medium-n Balmer lines used in the atomicpart of the analysis. To achieve this, we use the separation of the molecular part of Hα (equation 9) to extrapolate those brightnesses to the medium-n Balmer lines utilized inthe atomic part of the analysis (section 2.1) as illustrated in figure 6. This is achievedby modeling the ratio between the medium-n Balmer line and Hα for each Balmer lineemission process attributed to plasma-molecule interactions using T Ee and n e . Thoseratios are multiplied with the separated Hα brightnesses attributed to H , H +2 and H − , pectroscopy inferences of plasma-molecule interactions Estimate mol. contributions other Balmer lines + H α [H ] H α [H ]H α [H ] n e T eE T e B / H α [H ] ratio n->2 2 x n e T eE T e + B / H α [H ] ratio n->2 2 x n e T eE T e - B / H α [H ] ratio n->2 x + - H α [H , H , H ] B [H , H , n->2 H ] Σ + - H α [H , H , H ] B [H , H , n->2 H ]
Figure 6.
Schematic analysis flow chart for estimating the molecular contributions tothe other Balmer lines based on the various Hα ’molecular’ emission channels. Thisrepresents the step ’Separate mol. contributions other Balmer lines’ in figure 2. which are then summed to obtain the total brightness of the medium-n Balmer linesattributed to plasma-molecule interactions. This is similar to how the atomic part of Hα was extrapolated using the medium-n Balmer lines in section 2.2.Molecular contributions to the medium-n Balmer line reduce their atomic estimatesas shown in equation 10. This modifies the inferred temperature from the atomic partof the analysis and subsequently all molecular estimates. Therefore, the molecularcontributions to the medium-n Balmer lines according to equation 10 are fed back intothe atomic analysis (section 2.1) after which the analysis covered in sections 2.1 through2.4 is repeated iteratively (see appendix Appendix A) as is schematically shown in Fig 2with the blue arrow, connecting the molecular part of the analysis to the atomic part ofthe analysis. The result is a self-consistent separation of all the used Balmer lines intoits atomic (electron-impact excitation (of H ) and electron-ion recombination (of H + ))and plasma-molecule interaction ( H , H +2 and H − ) related contributions. B tot,measuredn → = B moleculen → + B atomn → B atomn → = B tot,measuredn → − B H n → − B H +2 n → − B H − + H + n → B atomn → = B tot,measuredn → − B H → P EC H n → ( n e , T Ee ) P EC H → ( n e , T Ee ) − B H +2 → P EC H +2 n → ( n e , T Ee ) P EC H +2 → ( n e , T Ee ) − B H − → P EC H − + H + n → ( n e , T Ee ) P EC H − + H + → ( n e , T Ee ) (10) The separated brightnesses of Hα are used to determine the various atomic reactionrates/power losses (as is done in [34]), as well as the various MAR/MAI ion sinks/sources pectroscopy inferences of plasma-molecule interactions Hα are multiplied with the ”effectiveradiative loss (or MAI/MAR reaction rate) per emitted Hα photon”, providing radiativeloss (or MAI/MAR reaction rates) for that process. Those are then summed together foreach process providing the total hydrogenic radiative power loss estimates and MAR/MAIrates. H α ( ) x + - H , H , H rad./reac per H α photon ratios + H α [H ] H α [H ] n e T eE T e + MAR/H α [H ] x n e T eE T e - MAR/H α [H ] x MAR Σ + H α [H ] H α [H ] n e T eE T e MAI/H α [H ] x n e T eE T e + MAI/H α [H ] x MAI Σ + H α [H ] H α [H ]H α [H ] n e T eE T e mol P rad /H α [H ] x n e T eE T e mol P rad + /H α [H ] x n e T eE T e mol P rad - /H α [H ] x mol P rad Σ Figure 7.
Schematic analysis flow chart for estimating MAR, MAI and radiative lossrates from the separated Hα ’molecular’ emission pathways. This represents the step’ Hα ( H , H +2 , H − ) x rad./reac per Hα photon ratios’ in figure 2. Although Hα emission does not lead to significant radiative losses directly, consideringmost plasma radiation is in the VUV [44], it can be an indicator for significant radiativelosses. Hα emission, corresponding to the 3 → Lyβ (3 →
1) emission. Utilising the associated Einstein coefficients andphoton energies, 6.5 times more radiative loss arises due to
Lyβ than Hα . Since Hα indicates a transition to the n = 2 excited state, the enhancement of Hα should alsolead to some enhancement of the n = 2 excited state, which subsequently results in Lyα emission - which carries 5.8 times more energy than a Hα photon.It is thus clear that, at a minimum, a power loss of the order of ten more than thepower loss of Hα itself is associated with related (V)UV emission. Since this only coversthe influence of plasma-molecule interactions on the n = 3 populated state, this is aconservative estimate of the radiative losses due to plasma-molecule interactions. Forexample, plasma-molecule interactions could potentially directly lead to an enhancementof the n = 2 populated state, and thus directly enhance Ly − α radiation losses.It is important to repeat that the power loss estimated here is radiation fromhydrogenic (atomic) emission lines arising from excited atoms after plasma-moleculeinteractions . This is different from radiative losses associated with molecular bandemission which as been the subject of previous research [22, 44], where the brightness pectroscopy inferences of plasma-molecule interactions n <
7) of the atomicBalmer and Lyman spectra associated with plasma-molecule interactions. These aremultiplied with their respective photon energies and summed to estimate the radiatedhydrogenic (atomic) power loss due to excited atoms after plasma-molecule interaction.This power is then divided by the Hα emission due to those channels, obtaining aratio representing ’total radiated energy (eV) per Hα photon’ for each individualemission channel (equation 11). We represent this as ( P H ,H +2 ,H − rad,L B H ,H +2 ,H − → ) where P H ,H +2 ,H − rad,L isa line-integrated radiation rate in W/m , which can be determined by multiplying therespective brightness with the respective ’total radiation per Hα photon’ coefficient: P H ,H +2 ,H − rad,L = B H ,H +2 ,H − → × P H ,H +2 ,H − rad,L B H ,H +2 ,H − → . In this, we make the same assumptions forinterrogating the molecular PEC coefficients as made in section 2.3. P H rad,L B H → = (cid:88) i =2 , , , , (cid:88) j =1 , i>j P EC H i → j ( n e , T e ) P EC H → ( n e , T e ) P H +2 rad,L B H +2 → = (cid:88) i =2 , , , , (cid:88) j =1 , i>j P EC H +2 i → j ( n e , T e ) P EC H +2 → ( n e , T e ) P H − rad,L B H − → = (cid:88) i =2 , , , (cid:88) j =1 , i>j P EC H − + H + i → j ( n e , T e ) P EC H − + H + → ( n e , T e ) (11)Examples of these coefficients are shown in figure 8 and are compared to theminimum power loss expected from a Hα photon due to molecular reactions (when alsoaccounting for associated Lyβ and
Lyα emission). This indicates roughly 20-100 eVpower loss per observed Hα photon that is due to H +2 and H − contributions to Hα . Similarly to how the radiative losses per Hα photon are calculated above, one canalso calculate ion sinks/sources (MAR/MAI) per Hα photon - equation 12 for H and H − . For the MAR/MAI rates we use AMJUEL [40, 39, 45, 41] rates H4 7.2.3a - MAR H − ; H4 2.2.10 - MAI H ; which are functions of electron density and temperature. M ARH molα (cid:12)(cid:12)(cid:12)(cid:12) H − = M AR H − ( n e , T e ) P EC H − + H + → ( n e , T e ) M AIH molα (cid:12)(cid:12)(cid:12)(cid:12) H = M AI H ( n e , T e ) P EC H → ( n e , T e ) (12) pectroscopy inferences of plasma-molecule interactions + H
2- - +
H (through H + H)
19 -3
10 m
20 -3
10 mn e T e (eV) R ad i a t i on ( e V ) pe r e m i tt ed D pho t on E Ly + E Ly A /A + E H Figure 8.
Radiative loss (eV) per emitted Hα photon derived from molecularcontributions associated with H +2 and H − (assuming H − emission comes from the H − + H + reaction) at different electron densities. The black curve shows the roughlyexpected power loss directly explainable by the Hα photon (e.g. if one would havethe power loss of a Hα photon (3 →
2) plus associated
Lyα (2 →
1) and
Lyβ photons(3 →
1) per emitted Hα photon (from a molecular process)). Calculating MAR/MAI ion sinks/sources for H +2 requires additional steps as notonly the destruction of H +2 matters, which can result in excited H atoms thus providingthe B H +2 n → we infer, but also the creation process of H +2 . H +2 can be created either throughmolecular charge exchange ( H + H + → H +2 + H ), which turns a plasma ion into aneutral , or ionisation of H ( e − + H → e − + H +2 ) which does not turn a plasma ion intoa neutral. When H +2 reactions with an electron, there are now 3x2=6 possible outcomes:1,2) e − + H +2 → H + H (AMJUEL reaction H4 2.2.14) is MAR for molecular CX andMAD for H ionisation; 3,4) e − + H +2 → H + + H (AMJUEL reaction H4 2.2.12) is MADfor molecular CX and MAI for H ionisation; 5,6) e − + H +2 → H + + H + (AMJUELreaction H4 2.2.14) is MAI for molecular CX and MAI (x2) for H ionisation.As neither of those H +2 creation processes results in excited atoms, we cannot extractinformation on which process is dominant using only the Balmer line spectra. Instead,we require using the reaction rates for the creation process of H +2 to model the relativestrength of the two H +2 creation processes, which is shown in equation 13 assumingthe electron density equals the hydrogen ion density. For < σv > H + + H → H + H +2 we usedata from [27] (for deuterium), whereas from < σv > H + + H → H + H +2 we use data fromAMJUEL H4 2.2.9. f H +2 fromCX = < σv > H + + H → H + H +2 < σv > H + + H → H + H +2 + < σv > e − + H → e − + H +2 (13) pectroscopy inferences of plasma-molecule interactions H α ratios for H +2 shown in equation 14. The notationMAR/MAI/MAD for the rates of equation 14 refers to what the process would be if H +2 is purely created through molecular charge exchange (e.g. f H +2 fromCX = 1). The impactof different reaction rates on f H +2 fromCX and subsequently the ”MAR and MAI to Hα emission coefficient ratios” are discussed in section 5.5. M ARH molα (cid:12)(cid:12)(cid:12)(cid:12) H +2 = f H +2 fromCX ( n e , T e ) M AR ( n e , T e ) P EC H +2 → ( n e , T e ) M AIH molα (cid:12)(cid:12)(cid:12)(cid:12) H +2 = (2 − f H +2 fromCX ( n e , T e )) M AI ( n e , T e ) + (1 − f H +2 fromCX ) M AD ( n e , T e ) P EC H +2 → ( n e , T e ) (14)Figure 9, which shows the calculated MAR/MAI per Hα photon, indicates atdetachment relevant temperatures ( T e < H +2 and H − have (within experimentaluncertainty) similar MAR per Hα photon rates (4-7). MAI starts to dominate overMAR for H +2 at T e > Figure 9.
MAR (negative) and MAI (positive) per emitted Hα photon for H +2 , H − at different electron densities. The black curve represents zero. The uncertainties areprovided by the default assumption of an uncertainty of 25 % on all used molecularreaction rates and emission coefficient in addition to an assumed H temperaturerange ([0.37 - 10] eV using a log-uniform distribution) - see section 5.5. The indicateduncertainties are 68% confidence margins pectroscopy inferences of plasma-molecule interactions
3. Verification using synthetic diagnostic techniques
The diagnostic techniques described above have been verified against ’direct’ outputsfrom SOLPS simulations of TCV and MAST-U plasmas by calculating the syntheticspectra using the diagnostic line of sight descriptions as well as the measured spectrometerinstrumental functions from TCV spectrometers. These ’synthetic’ spectra are analysedin an identical way as the experiment to provide estimates of the atomic and molecularprocesses. Those results are then compared to ’direct’ results obtained from directlyextracting these parameters from the SOLPS simulations. The methods used for thishave been developed in [34, 15], which contains more details of the implementation.To simulate the Balmer line brightnesses attributed to H chemistry involving H , H +2 , H − , H +3 , Yacora (on the Web) collisional radiative modelling results [29, 28] areused in conjunction with the simulated electron temperature, electron density, molecule( H ) density as well as the ion ( H + ) temperature; while ADAS is used for the electronexcitation impact (of H ) and electron-ion recombination (of H + ) Balmer line emissioncontributions [36, 37].The densities for H +2 , H − , H +3 must be known to accurately model the Balmerline emission due to their plasma-molecule interactions. Such species are, by default,not (’fully’) treated in SOLPS-ITER. Generally, only H +2 is included. However, it isdesignated as a ’test specie’ in Eirene where it remains static (e.g. there is no transport)after being created. Additionally, there is some discussion on the isotope dependencyof the rates leading to and/or breaking up H +2 , H − [46]; which is further discussed insection 5.5.We overcome the above limitations of the information from SOLPS-ITERcorresponding to H +2 , H +3 , H − to H by using a balance between the creation anddestruction rates of these species from H to ’post-process’ the H +2 , H +3 , H − densitiesafter obtaining the SOLPS-ITER results. This is similar to the ’neutral fraction ionisationbalance’ calculated for demonstration purposes in [34]. For instance H +2 H = SCD H → H +2 ACD H +2 → H where SCD H → H +2 is the sum of the creation (’ionisation’) rates of H +2 from H and ACD H +2 → H is the sum of the destruction (’recombination’) rates of H +2 . For the H +2 rates we employ the same rates as discussed in section 2.5.2 (using the reported H temperatures from the simulation). The temperature of H − is assumed to be equalto the H temperature plus a random number between 0 - 2.2 eV as H − arises fromreactions between the plasma and H and a part of the Franck-Cordon energy binding H is released to H − . Transport of the different molecular species is in this approachneglected. It is important to warn the reader that these ratios are still being heavilydebated in literature and may have large uncertainties - section 5.5. Therefore, significantdeviations can occur between the post-processed results, the direct SOLPS-ITER outputsand the experimental results. pectroscopy inferences of plasma-molecule interactions Under the assumptions/limits described above we first discuss how the Balmer lineemission associated with H plasma chemistry changes the synthetic brightnesses(compared to only accounting for electron-impact excitation and electron-ionrecombination) and how this compares to experimental observations. The simulationsused [8] have been compared previously against the accompanying experiment in [7]from a view point of atomic interactions. This provides us with qualitative arguments asto how representative the analysed synthetic diagnostic results are of the experiment.(i) The synthetic diagnostic brightnesses are in quantitative agreement with theexperiment if only electron-ion recombination and electron-impact excitation isconsidered for the medium-n Balmer lines. The total synthetic Hα brightness(related to atomic interactions and H plasma chemistry) is in rough agreementwith the total measured Hα brightness.(ii) However, the simulated results indicate a significant fraction of the n = 5 Balmerline emission is due to plasma-molecule interactions (mostly due to H +2 ). This lowersthe simulated n = 6 /n = 5 Balmer line ratio from its atomic estimate ( ∼ .
5) to ∼ . . Therefore, the application of the analysis is more complex (andhas higher uncertainties) in the synthetic diagnostic case than in the experiment .Figure 10 shows a comparison between various processes obtained ’Direct’(ly) fromsimulations of a TCV density scan and the same quantities evaluated (’Analysis’) throughsynthetic measurements. Each column of plots corresponds to different sets of constraintsthat are applied. The technicalities of these constraints are described in more detail inappendix Appendix B.Figure 10 a,b shows that the synthetically inferred MAR/EIR ion sinks as wellas the radiative power loss associated with H +2 and H − are in quantitative agreementwith the direct SOLPS output if no constraints are employed. There is, however, astrong difference in the atomic ionisation source as well as the radiation associated withelectron-impact excitation after the detachment onset (around an upstream density of3 . × m − ). This difference after detachment onset is traced to an overestimateof the atomic excitation emission caused by underestimating the (atomic only) lineratio n = 6 /n = 5 near the end of the discharge( ∼ .
45 instead of ∼ . pectroscopy inferences of plasma-molecule interactions Figure 10.
Comparisons between ’Direct’ output of SOLPS-ITER modelling of TCVdensity scan to detachment and the same quantities derived (’Analysis) from syntheticdiagnostic measurements of the same SOLPS-ITER cases: a) Inferred particle balance,including atomic ionisation, electron-ion recombination recombination, MAR from H +2 and H − . b) Inferred radiative loss channels from atomic (mostly line) emission,including atomic excitation, radiation due to excited atoms from reactions involving H +2 and H − c/d) Power and particle balance comparison between ’Direct’ outputs andoutputs from ’Analysis’ with the added constraint of target temperature. e/f) Powerand particle balance comparison between ’Direct’ outputs and outputs from ’Analysis’with an added constraint based on the CIII emission front. However, especially during detachment, the ion source inferences can become unreliableif no constraints are employed.The periods of poor inference of ion sources can be improved by including additionalconstraints. As explained in [34], the overestimation of excitation emission is a knowncomplication in cases where the excitation emission is relatively small. Since anoverestimation of the excitation emission manifests in an overestimation of the excitationtemperature, one can improve the analysis by enforcing temperature constraints [34]. Weinclude two temperature constraints: a) a constraint at the ’target’ (lines of sight near thetarget) on the excitation target temperature based on other target temperature estimates(for the synthetic case a ± pectroscopy inferences of plasma-molecule interactions T e dependence of the MAI/ Hα ratio (figure9), which is related to the change-over from H +2 being created from molecular chargeexchange to it being created from H ionisation (see section 2.5.2). This implies thatthe MAI estimates are sensitive to inaccuracies in the T e estimate, which also impliesthat they are relatively more sensitive to chordal integration effects. The uncertaintiesin MAI and atomic ionisation are however anti-correlated, and the total uncertainty isreduced when MAI and atomic ionisation is summed (as is done in figure 10).In the remainder of this work, both temperature constraints from the estimatedtarget temperature as well as the CIII front location are employed for the ionisation and(atomic) radiation estimates, unless stated otherwise. We can perform further synthetic testing on the simulations shown in the previous sectionthrough ’code experiments’ by removing certain emission channels from the input ofthe synthetic brightnesses, after which the full analysis is used to analyse the ’modified’synthetic brightnesses. This is an important part of testing the robustness of the analysisscheme as it enables us to see how well the analysis copes with excluding processes whichare not present. This is investigated by:(i) Removing all molecular emission channels (figure 11 a,b).(ii) Removing the H +2 emission channel (figure 11 c,d).(iii) Removing the H − emission channel (figure 11 e,f).These cases are shown in figure 11, together with a copy of the analysis in which allemission channels are included, previously shown in figure 10.Figure 11 generally shows a quantitative agreement between the various particlesinks/sources and power sinks estimated from the analysis and those obtained directlyfrom the code. One exception to this is the MAI estimate in figure 11e,f, where H − was not accounted for. This is related with the large uncertainties of MAI discussedpreviously. We observe that the upper uncertainty level of MAR from H +2 and/or H − are negligible (although not zero) even when they have been omitted in the syntheticdiagnostic brightness during detachment. Therefore, one should only interpret a certainprocess to be present if its effect is ’significant’. With this in mind, it does appear thatthe analysis can correctly point out the lack/presence of MAR and separate MAR from H +2 and H − - as long as their impacts are ’significant’.We also observe in figure 11 that the quality of the excitation-dependent inferencesas well as MAI deteriorates as more emission channels are present in the input synthetic pectroscopy inferences of plasma-molecule interactions Figure 11.
Power and particle balance, similar to figure 10, where certain emissionchannels have been disabled in the synthetic diagnostic to investigate its influence onthe analysis outputs brightnesses. As the contribution of molecules to the n = 5 , We have applied the similar synthetic testing procedure shown throughout this section toMAST-U SOLPS simulations [30] as shown in figure 12, which comprises a D fuellingand N seeding ramp (with intrinsic carbon impurities). In this case, we have not usedthe temperature exclusion constraint based on the CIII front introduced previously as,given the magnetic geometry of the MAST-U Super-X divertor, the CIII front cannotbe comfortably tracked using line integrated spectroscopy and instead requires cameradiagnostics, such as [47, 48].We observe that, generally, there is an agreement within uncertainty between theparameters inferred from the synthetic diagnostic and those obtained directly. Oneexception to this is excitation related estimates at the highest N puff rates, where the ionsource drops below what can be detected. Due to the lack of electron-ion recombination inthese conditions, the ’detection threshold’ for ionisation estimates is increased, explainingthe large ionisation estimate uncertainty. We re-iterate that the post-processing to obtain H +2 & H − densities likely overestimates the contribution of molecules to especially themedium-n Balmer lines.In general we see an improved quantitative agreement (especially for MAI) for theMAST-U synthetic testing than the TCV synthetic testing. This is likely attributed to pectroscopy inferences of plasma-molecule interactions Figure 12.
Power and particle balance from estimates from synthetic diagnosticanalysis and directly obtained from SOLPS MAST-U simulations [30], similar to figure10. The results of both a density ramp (with intrinsic carbon impurities) and that of afixed D puff with a N seeding ramp (with intrinsic carbon impurities) are shown. the closed divertor/higher electron densities in MAST-U, resulting in shorter mean freepaths and therefore a stronger spatial separation between the ionising and recombiningregions.
4. Experimental results on TCV
The experiment analysed in here is identical to the main experiment analysed in [7], whichis a conventional divertor L-mode reversed field (unfavourable for H-mode) density rampdischarge with a plasma current of 340 kA. In this study the TCV Divertor SpectroscopySystem (DSS) diagnostic is used for all spectroscopic measurements [13, 34]. The divertorgeometry with the lines of sight coverage for this diagnostic can be seen in figure 14,adapted from [7, 34]. Diagnostic repeat discharges are used in order to obtain sufficientdiagnostic coverage. The reproducibility of this has been demonstrated in [7]. It shouldbe noted that the discharge analysed in this section is a deuterium discharge. However,collisional radiative models such as ADAS [36, 37] and Yacora Online [28] are applicableto hydrogen . This will be further discussed in section 5.5. pectroscopy inferences of plasma-molecule interactions Electron-ionrecombination H ( ph / s ) H [measured]H [atomic "upscaled"] pa r t i c l e s / s Ion target currentIonisation
Time (s) H / H Integrated [measured]Target [measured]Integrated [atomic "upscaled"]Target [atomic "upscaled"]
Core Greenwald fraction 0.5Time (s)0.2 0.3 0.4
Figure 13. (a) Particle balance in TCV during a density ramp detached dischargefrom [7, 34] with ion target current, ionisation source, recombination rate. (b) Hα measurement [15] compared to the atomic estimate of Hα , integrated over the entireouter divertor leg. (c) The measured Hβ/Hα ratio compared to an estimated ’atomic’
Hβ/Hα ratio. The two vertical lines are the two times shown in figures 14 and 15 atomic only analysis and comparisons against the measured Hα brightnesses First, before applying the full analysis of figure 2, we will apply the atomic part of theanalysis only - identical to [7, 34]. This does not use
Hα, Hβ measurements and assumes pectroscopy inferences of plasma-molecule interactions all emission from the medium-n Balmer lines is due to atomic processes only. Theobtained particle balance for the outer divertor leg is shown in figure 13a (cid:107) in terms ofthe total divertor ion target current (measured by Langmuir probes); ionisation sourceand Electron-Ion Recombination (EIR) sink. This is accompanied with the measured Hα brightness compared to the atomic prediction of Hα in figure 13 b; based on theinformation obtained from the medium-n Balmer lines (equation 4) [34, 15].The total measured Hα increases and bifurcates from the shown ’atomic’ estimate ofthe Hα emission near the detachment onset phase of the discharge. The same is true forthe measured Hβ and ’atomic upscaled’ Hβ emission (not shown). This indicates thatan additional - ’non-atomic’ - process starts to contribute to the Hα (and Hβ ) emissionnear the detachment onset. The ’non-atomic’ increase in Hβ is, however, smaller thanfor Hα , causing the Hβ/Hα ratio to drop compared to the ’atomic upscaled’ estimate(figure 13c)s. Considering only atomic reactions using ADAS [36, 37], this ratio isexpected to go from a low value in excitation dominant conditions ( ∼ .
09) during theattached phase to a higher value ( ∼ .
14 (integrated) and ∼ .
29 near the target) asrecombinative emission starts to occur during the detached phase. However, we observethat the
Hβ/Hα ratio does not increase but decreases during the discharge from ∼ . ∼ .
07. Evidently, an additional process seems to contribute to the Hα (and the Hβ ) emission, which can be explained with plasma-molecule interactions (section 2.2)involving H +2 & H − . The expected H densities from simulations can only account forless than 1 % of the measured Hα emission (see section 5.1). Other possible influenceson Hα (hydrocarbons and opacity) are estimated to have a negligible impact 5.2. After having discussed the Hα trend and compared it to the extrapolated ’atomic only’ Hα trend by applying only the atomic part of the analysis in the previous section, wenow illustrate an example of the self-consistent results of the atomic and molecularanalysis to separate the hydrogen line brightnesses into its various atomic (excitation/ recombination) and molecular ( H , H +2 , H − ) contributions. For this, three differenttemperature constraints (for T Ee ) have been employed: 1) the upper temperature limit is25 eV (e.g. probability is strongly reduced for temperatures above 25 eV); 2) temperatureconstraint based on the CIII 465 nm emission line front which is measured throughoutthe discharge using line-of-sight spectroscopy (see details in Appendix B); 3) a targettemperature constraint based on the estimated target temperature by power balance( T P Bt ), which was shown and compared against various target temperature estimates(measured and modelled) in Figure 10 of [7] yielding a good agreement between thevarious temperature estimates.The results of the emission contributions are shown in figure 14 for one line of sightat two different times of the same discharge as presented in figure 13 as a bar-chart. (cid:107)
The ionisation calculation shown assumes a log-uniform n o /n e probability distribution [15] (as opposedto the uniform distribution assumed previously in [7, 34]). pectroscopy inferences of plasma-molecule interactions Hα , Hβ , Hγ , Hδ ) used in the analysisas well as an extrapolated analysis estimate of the Lyα ( B → ) line, whose totals andindividual contributions has been obtained through ’upscaling’ the experimental dataof the molecular contributions of Hα and the atomic contributions of the medium-nBalmer line n using equation 15 based on combining equations 10 and 4. B → = P EC H → ( n e , T Ee ) P EC H → ( n e , T Ee ) × B H → (cid:124) (cid:123)(cid:122) (cid:125) B H → + P EC H +2 → ( n e , T Ee ) P EC H +2 → ( n e , T Ee ) × B H +2 → (cid:124) (cid:123)(cid:122) (cid:125) B H +22 → + P EC H − → ( n e , T Ee ) P EC H − → ( n e , T Ee ) × B H − → (cid:124) (cid:123)(cid:122) (cid:125) B H − → + P EC exc → ( n e , T Ee ) P EC excn → ( n e , T Ee ) × B atom,excn → (cid:124) (cid:123)(cid:122) (cid:125) B exc → + P EC rec → ( n e , T Re ) P EC recn → ( n e , T Re ) × B atom,recn → (cid:124) (cid:123)(cid:122) (cid:125) B rec → (15)The illustration of the technique in figure 14 indicates that depending on the plasmaconditions (in this case dictated by the timestep in the discharge): • Plasma-molecule interactions can contribute considerably to hydrogenic line emission.It can dominate the Hα , Hβ emission and it can have a significant impact on Lyα emission as well as medium-n Balmer line emission ( Hγ, Hδ ). – This suggests plasma-molecule interaction can contribute strongly to thehydrogenic line radiation. – Contamination of plasma-molecule interactions of the medium-n Balmer lineemission may impact spectroscopic ionisation estimates and cause them todeviate from the atomic only analysis (shown in figure 13). This is discussed in[35] as well as the impact of MAR on particle balance. • A large range of different emission processes can be significant simultaneously;e.g. both electron-ion recombination, plasma-molecule interactions from H +2 and H − appear to be significant for Hβ at t = 1 .
12 s. This shows the importance ofseparating the various emission channels. • The emission processes can change strongly between each hydrogenic transition.We observe that the sensitivity to plasma-molecule interactions diminishes withincreasing n of the hydrogenic transition while the sensitivity to electron-ionrecombination increases [34]. Plasma-molecule interactions involving H − seemto excite the n = 3 populational state (e.g. Hα emission) in particular. • An anti-correlation seems to exist in the sample output of the analysis (whichdescribes the uncertainties) between atomic excitation emission and emission frominteractions with H +2 . This illustrates why the various temperature constraintsintroduced in Appendix B are important: without such constraints it is uncertainto distinguish, given the measured data and its uncertainties, atomic excitation andemission from interactions with H +2 . pectroscopy inferences of plasma-molecule interactions Figure 14.
Shows a bar-chart of the contributions (%) of various processes (atomicexcitation, atomic electron-ion recombination, plasma-molecule interaction with H , H +2 and H − with uncertainties for various hydrogenic series lines at two different timesfor a chord close to the target together with the estimated electron temperature ranges.A schematic illustration of the various emission regions as well as the divertor geometryand line of sight is shown. The used times are highlighted in figure 13. After having shown a brief illustration of the analysis technique on experimentaldata to separate the emission into its different contributions, we show a brief illustrationof line-integrated ion sinks/sources obtained through this technique in figure 15 at thetwo different phases in the discharge highlighted in figure 14 and 13. pectroscopy inferences of plasma-molecule interactions Figure 15.
Analysis illustration of estimated ion sources (positive) and sinks (negative)along one chord at two different plasma conditions corresponding to the two timesindicated in figures 14 and 13 with indicated temperature ranges. Next to the result isa schematic illustration of the emission regions (figure 14) together with the indicatedused line of sight.
The illustration in figure 15 shows the presence of MAR through both H +2 and H − and indicates their magnitude to be significant (larger than Electron-Ion Recombination- EIR). The estimated MAI contribution (from H +2 ) is significant (similar to the atomicion source) at the earlier time phase and is completely negligible at the later one. Acomplete study of the ion sources and sinks is presented in [35].
5. Discussion H We find that the contribution of H to Hα in the studied divertor conditions is very small,especially during detached conditions; instead the contribution of H plasma chemistryto Hα is mainly through H +2 and/or H − (figure 14). This may be in contrast to previousstudies in limiter devices at the SOL, although H +2 contributions were speculated to be pectroscopy inferences of plasma-molecule interactions H .First, we obtain a functional form for the ’effective’ H density ( n H ) timespathlength (∆ L ) as function of the (impact excitation region) electron temperature T Ee - f H ( T Ee ) ≈ ∆ L × n H . This provides us with a way to estimate the Balmer linebrightness associated with H using equation 7. We obtain this functional form f H ( T Ee )by combining TCV [8] and MAST-U [30] SOLPS-ITER simulations in combination withsynthetic spectroscopy diagnostics [34, 15] (see section 3). Given that in a plasma-slabmodel the Balmer line brightness associated with H is B H n → ≈ ∆ Ln H P EC H → ( n e , T Ee ),we can compute f H found in the simulations as function of T Ee using equation 16. Forthis we use the n e obtained through synthetic Stark broadening analysis and we use theatomic excitation emission-weighted temperature for T Ee (see [34]). f H ≡ B H → P EC H → ( n e , T Ee ) ≈ ∆ L × n H (16) f H found in the simulations is shown in figure 16 for both MAST-U and TCV withcorresponding lines of sight for all lines of sight and various simulations (representative ofa density ramp (TCV [8] and MAST-U [30]) and seeding scan (MAST-U [30]). We findthat that for both cases there is a strong relation between f H and T Ee . This indicatesthat having information about the kind of device (e.g. TCV vs MAST-U), the electronexcitation temperature and the electron density are sufficient for providing estimates onthe Balmer line brightness attributed to H .We use the f H values obtained from the simulations to estimate the relation between f H and T Ee using a fit (linear in log-log space) to which we ascribe an of a factor 100uncertainty (from a factor 0.1 to 10 - log-uniformly distributed).For the particular experimental case analysed in this work (section 4), B H n → B moleculen → issuch that less than 0.5 % of the Balmer line emission is due to H (which correspondsto the upper level of the 68 % confidence interval). This occurs in the attached regionwhere the molecular contribution of the Balmer line emission is practically negligible.In the detached phase, the contribution of H to the Balmer line emission becomesless than 0.01 %. Therefore, even if f H ( T Ee ) obtained from SOLPS-ITER is stronglyunderestimated, it would be unlikely that this would influence the obtained solutions. Hα emission contributions not related to plasma-atom interaction and H chemistry In a carbon machine such as TCV and MAST-U, reactions with hydrocarbons could leadto excited atoms leading to additional Hα (and Hβ ) emission beyond atomic processes.Additionally, moderate levels of opacity (fairly opaque for Lyβ, Lyγ while being mostlytransparent for
Hα, Hβ ) can also lead to enhanced
Hα, Hβ emission. We discuss thesetwo processes here and estimate their importance for TCV.To obtain an upper limit estimate for the possible atomic emission of hydrocarbons, pectroscopy inferences of plasma-molecule interactions T e (eV) - excitation emission weighted n H L ( m - ) TCVMAST-U T1SOLPS simulation synthetic diagnosticData points Fits
TCV
MAST-U
Figure 16.
Relation between the excitation Balmer line emission weighted temperature T Ee and f H ( T Ee ) ≡ B H → P EC H → ( n e ,T Ee ) ≈ n H × ∆ L (where n e is the synthetic Stark density).Fits through each of the data sets are shown. The TCV data set consists out of 5simulations [8] (density scan) (26 lines of sight) while the MAST-U data set consistsout of 35 simulations [30] (density scan and N seeded) with 20 lines of sight. Thecorresponding SOLPS grid cells and spectroscopy lines of sight for MAST-U and TCVare also shown. we assume that all neutral carbon from validated SOLPS simulations for TCV [8, 42]exists in the form of hydrocarbons. Since neutral carbon recombination has beendeactivated for most of these simulations ([8] - the SOLPS-ITER default at the time),the sum of the neutral and C + densities is utilised as an upper estimate of the neutralcarbon density. To map these hypothetical hydrocarbon densities to the Hα emission weutilise reaction cross-sections from [49] for CH (the cross-sections for Hα emission from[49] are similar for the full range of hydrocarbons presented: CH , C H , C H , C H ).For this extreme case, the estimated total Hα emission over the entire plasma due tohydrocarbons is estimated to be less than 10 photons/s: more than an order of foursmaller than the estimated Hα emission from atomic or hydrogenic molecular reactions.It is thus unlikely that hydrocarbon chains contribute significantly to the Hα emission.According to SOLPS simulations for TCV [8], which have been compared in depth tothe experiment discussed [7], the integrated neutral density along the spectroscopic linesof sight remains smaller than 10 m − - at which not much opacity is expected [33, 50].This is indeed confirmed by post-processing the SOLPS simulations using ray-tracingtechniques. These indicate very minor modifications to the population escape factorsdue to opacity, indicating ultimately modifications to the 2D profile of the Hα emissivityof up to 3%. Therefore, opacity is not expected to significantly alter the Hα emission onTCV. pectroscopy inferences of plasma-molecule interactions Hα as a monitor for molecular events The increase of Hα during detachment, or more specifically the ’anti-correlation between Hα and the ion target current’ during detachment is a well-known detachment observationobserved on several devices [5]. In this work, we have shown that this behaviour cannotbe explained through electron-ion recombination on TCV, but is explained throughplasma-molecule interactions with H +2 and H − . Although electron-ion recombinationcan be higher on higher divertor density machines, it is likely that the increase of Hα insuch machines is also, at least partially, due to plasma-molecule interactions with H +2 and H − .In fact, the suspicion that Hα was increase due to H chemistry was also rased basedon experiments in both JET [16] and DIII-D [23] experiments. During DIII-D similar Hβ/Hα ratios as measured on TCV and shown in figure 13c were observed, whilst theexpected
Hβ/Hα ratio based on
Hγ, H(cid:15) was much higher as EIR recombination wasbecoming an important contributor.We have observed that comparing Hα with estimates from only the atomic part ofthe analysis is a quick and useful monitor for plasma-molecule interactions involving H +2 and/or H − . This can be achieved with the atomic part of the analysis, which requiresless measurements and can be more easily applied. Additionally, this comparison can beused as a quantitative estimate for radiative power loss and MAR from plasma-moleculeinteractions. If we assume that the molecular contribution of Hα only comes from H +2 and T e ∼ n e ∼ m − at the region where H +2 undergoes interactions with theplasma, we estimate a MAR rate of ∼ Hα photon (figure 9). Multiplyingthis with ”molecular” part of the Hα emission provides a MAR ion sink which is inquantitative agreement with the full analysis chain. A similar quantitative agreementbetween this ’simplified’ estimate and the ’full’ analysis chain is obtained for radiative lossestimates. These estimates appear to be fairly accurate despite the lack of quantitativelyseparating Hα emission from plasma-molecule interactions with H +2 and H − . However,the full analysis chain would be required to estimate the ’molecular’ contributions to themedium-n Balmer line emission - which may be important for the ionisation estimates inthe most strongly detached conditions, which will is investigated [35].Therefore, monitoring Hα and comparing it to its atomic estimate is sufficient to:(i) Show that plasma-atom interactions involving H +2 (and possibly H − ) may occur (inenvironments with low/negligible Lyβ opacity).(ii) Estimate what their influence on the plasma is in terms of particle and power losses.Afterwards, one could consider running the full analysis presented to:(i) Propagate this information to all Balmer lines to get a self-consistent picture whichseparates each hydrogenic line into its individual contributions, similar to figure 14).(ii) Delineate the plasma-molecule contributions from H +2 and H − . pectroscopy inferences of plasma-molecule interactions Previous research on investigating plasma-molecule interactions in the divertorspectroscopically generally focused on monitoring the molecular band emission, such asthe Fulcher band which comes from electronically excited molecules [17, 24, 23]. Suchmeasurements provide important information on collisions between the plasma and H , exciting the molecules rovibronically . Such collisions are different from reactions betweenthe plasma and H +2 and H − , which result in MAR, MAI and excited atoms resulting inatomic line radiation/radiative power loss.MAR rate estimates from reactions with H +2 and H − have been estimated previouslyusing measurements of the Fulcher band to get information on H and its vibrationaldistribution, which is combined with n e , T e estimates and a model or simulations toextrapolate the H density to the H +2 density and its resulting MAR rate [17, 24, 23].This differs from the approach in this work which aims to extract the Balmer lineemission arising directly from the excited atoms after plasma-molecule interactions with H +2 , H − . Therefore, it does not require any assumptions on the H +2 /H ratio neitherdoes it require assuming that the location of the H electronic excitation (e.g. Fulcherband emission) is the same as the location of the MAR reactions along the lines of sight.That latter assumption could be problematic as electronic excitation of H requiresfairly high electron temperatures ( T e > − eV ), whereas MAR can occur at lowertemperatures ( T e = [1 . − eV ). Our measurements indicate, for instance, that the peakBalmer line emission from excited atoms after reactions between the plasma and H +2 (and/or H − ) may occur at a different position than the region with the brightest Fulcherband emission, which is investigated in [35].This analysis chain can be used as an alternative tool to investigate more closelyhow such interactions with H +2 , H − influence the plasma and provide an indirect tool toinvestigate the conditions which promote H +2 , H − creation. It could for instance be usedto investigate the differences in how plasma-molecule interactions with H +2 , H − differbetween carbon and metallic walls (which influences the vibrational state of moleculesreflected from the wall, influencing the creation/destruction mechanisms behind H +2 , H − [51, 32, 52, 53]). One advantage of using Balmer line measurements is that they aremore routinely employed on tokamaks and are often more ’straightforward’ to measuregiven the high spectral resolution and high sensitivity often required for molecularband studies. As such, the discussed analysis technique could also be extended to 2Dmulti-spectral imaging diagnostics [48] and its analysis [54]. However, the presentedtechnique is influenced by opacity and requires high quality collisional radiative modelresults to provide information on how the various plasma-molecule interaction processeslead to atomic line emission from excited hydrogen atoms after such processes [29, 28]. pectroscopy inferences of plasma-molecule interactions One important thing to note is that the discharge analysed experimentally in this work isa deuterium discharge. However, collisional radiative models such as ADAS [36, 37] andYacora (on the Web) [28, 29] are applicable to hydrogen . Isotope effects may, however,play a role [46]. We thus provide this analysis with the caveat that the used collisionalradiative modelling inputs to the analysis are calculated for hydrogen while the analyseddischarge is a deuterium discharge and thus we refer to Hα as opposed to Dα emission.Future improvements in the accessibility of collisional radiative results specifically fordeuterium could be combined with the outlined analysis approach.The isotopes effects of the cross-section for creating H − as well as H +2 are currentlydebated in literature [46]. There is experimental evidence [55] that particularly thecross-sections for creating D − is significantly smaller than H − ; although this likely alsodepends on the vibrational distribution of H . As such we have opted to keep the H − Balmer line emission pathway as a free parameter in our analysis model. As our analysisdetects the Balmer line emission arising from H − recombining with H + (as opposed tothe creation process of H − ), it does not depend on the reaction rates for creating H − .Potentially, this analysis could provide clarity on the presence of H − - but that requiresfurther investigation. Additionally could provide clarity on the isotope dependencies ofthe creation of H +2 as well.There are several uncertainties related to the molecular modelling, some of whichinvolve specifically the H +2 creation rate through charge exchange ( H + + H → H + H +2 )[46]. That impacts our analysis as we utilise this rate to distinguish between H +2 beingcreated by molecular charge exchange or H ionisation ( e − + H → e − + H +2 ) - equation13 which directly impacts our calculated ”MAI/MAR rate per Hα photon ratios” for H +2 (equation 14). In particular, the molecular charge exchange rate is expected to beisotope dependent and depends strongly on the vibrational distribution of H .We study these uncertainties on our analysis by calculating the fraction of H +2 creation by molecular charge exchange ( f H +2 fromCX ( n e , T e ) (figure 17 b) and its impacton the ”MAI/MAR rate per Hα photon ratios” for H +2 (equation ?? ) (figure 17 a) forthree different molecular charge exchange rates: 1 - the default rates from AMJUEL forhydrogen; 2 - the default rates from AMJUEL where the rates are shifted by dividing theelectron temperature by two to model the deuterium rate (which is the default in Eirene);3 - an alternative rate for deuterium investigated in [46]. In the Eirene formulationof these rates, the vibrational distribution is counted for by modelling it based on a H temperature. This H temperature has been varied in the Monte Carlo uncertaintyprocessing throughout the entire validity regime of the data.We find in figure 17 that the impact of the various rates on the calculated ”MAI/MARrate per Hα photon ratios” for H +2 is small. Therefore, our analysis seems to be robustagainst these uncertainties. The reason for the impact of the different rates being thatsmall (despite the rates themselves having orders-of-magnitude variation in the T e regimewhere most molecules exist in the divertor) is that for all rates for T e < − pectroscopy inferences of plasma-molecule interactions H ionisation (figure 17b). Figure 17.
A more detailed version of figure 9. We show the ”MAR/MAI per Hα ”ratios for various molecular charge exchange reaction rates for the creation of H +2 asfunction of T e at two different electron densities. In addition we show the calculatedratio between the molecular charge exchange reaction rate and the total H +2 creationrate for the various reaction rates used. In this work we have applied an analysis technique to separate the Balmer line emissionfrom its various atomic and molecular channels; after which the power losses due to eachindividual channel as well as the ion sources and sinks can be estimated. Experimentalresults of this from TCV have been shown and its workings have been demonstratedanalysing synthetic diagnostic results obtained from SOLPS simulations of both TCVand MAST-U. Emission characteristics differ, however, between TCV, MAST-U andhigher power, higher density machines, such as ASDEX-Upgrade and JET. This raisesthe question how generally applicable our presented analysis techniques are. pectroscopy inferences of plasma-molecule interactions Hα with the total measured Hα , which only depends on the atomic analysis part of theanalysis and should be generally applicable to other devices.The same is true, in principle, for the full version of the analysis. However,as illustrated in this work, inferring information from plasma-molecule interactionsimultaneously with the ionisation rate complicates extracting the ionisation rate instrongly detached conditions unless temperature ’constraints’ are employed. Althoughthe temperature constraints employed here may only be applicable to specific situationsor specific devices, constraints based on other measurements and conventions on othermachines can be employed as well. Ultimately, all that is required is estimating that atemperature at a certain location of the divertor during a certain divertor state is ’likelypossible’ or ’unlikely’.However, this analysis relies on the lower-n Balmer lines and as such is susceptibleto opacity. In devices where Lyβ opacity is significant, which can be monitored usingVUV spectroscopy based on the measured
Lyβ/Hα ratio, such as JET [16] and C-Mod[33], modifications to this analysis have to be employed to separate the Hα increase dueto molecular processes and due to opacity.Ultimately, the entire analysis technique can be improved through the inclusion ofmultiple diagnostics in a consistent statistical framework. This could be achieved byexpanding the Integrated Diagnostic Analysis (IDA) framework developed in [54]. Sucha technique would use ’2D spectroscopy’ using filtered camera imaging, which has beenenabled recently through extensive diagnostic development [48]. This could be furtherimproved by complementing the Balmer line measurements with impurity lines, suchas He-I lines, providing more information on temperature and density. Using imagingspectroscopy would also enable a more precise localisation of all the different processesinvolved both along and across the field lines. This (partially) resolves the difficulty of’line integration’ effects and facilitates the separation of the various processes - since theyare already spatially separated. Additionally, such a 2D variety of the analysis couldenable estimating 2D maps of the H +2 and H − densities, which is not feasible otherwise.
6. Summary
We have developed a new quantitative analysis technique for using the consistencybetween the medium-n (
Hγ, Hδ ) Balmer lines, which are less sensitive to plasma-molecule interactions; and the lower-n Balmer lines (
Hα, Hβ ) to dissect the emission ofall Balmer lines into its various atomic and molecular pathways. The workings of thistechnique have been demonstrated using a synthetic diagnostic approach of TCV andMAST-U SOLPS-ITER simulations. This techniques enables: pectroscopy inferences of plasma-molecule interactions • Inferring the contribution of plasma-molecule interactions (of H +2 and H − ) to eachBalmer line. • Estimating the particle sources/sinks through plasma-atom (ionisation, recombi-nation) and plasma-molecule (Molecular Activated Recombination / Ionisation -MAR/MAI). • Estimating the radiative loss from excited atoms arising from plasma-atom andplasma-molecule interactions.Experimental results from TCV indicate a bifurcation between the measured Hα and the atomic estimate of Hα at the detachment onset stage. This is suggestive ofreactions between the plasma and H +2 (and possibly H − ). Our experimental illustrationshows that such reactions can lead to significant modifications to the entire hydrogenicline series (and thus also hydrogenic line radiation) and can lead to significant ion lossesthrough molecular activated recombination - MAR.
7. Acknowledgements
This work has received support from EPSRC Grant EP/T012250/1 and has been carriedout within the framework of the EUROfusion Consortium and has received funding fromthe Euratom research and training programme 2014-2018 and 2019-2020 under grantagreement No 633053. The views and opinions expressed herein do not necessarily reflectthose of the European Commission.
Appendix A. Detailed information on the iterative scheme and convergence
The analysis scheme uses an Euler iterative scheme in order to obtain self-consistentresults between the various atomic and molecular contributions of the Balmer lines.The convergence of this relative change in the estimated molecular contribution tothe medium-n Balmer line is tracked per each iteration until it is ’converged’. Theconvergence criteria for this are listed below and are applied to the statistical outputsample (which is determined from all the various input distributions) for this relativechange:(i) At least 16 % of the output sample should have a negative change in the estimatedmolecular contribution (to make sure the analysis result is not ’drifting’ towards apositive change).(ii) At least 16 % of the output sample should have a positive change in the estimatedmolecular contribution (to make sure the analysis result is not ’drifting’ towards apositive change).(iii) The median of the change of the output sample should be between -0.2 and +0.2 %(assuming the median is a proxy for the maximum likelihood, this makes sure thatthe analysis estimates are converged). pectroscopy inferences of plasma-molecule interactions
Appendix B. Improving the analysis through temperature constraints
We introduce here two possible temperature constraints which can improve the analysisoutput estimates: one based on the excitation temperature near the target and one basedon the observation of the CIII front. The goal of these ’constraints’ is to provide some’probability’ for having a certain temperature at a certain location of the divertor. Othertemperature constraints could be employed in a similar fashion.
Appendix B.1. Target temperature constraint
Assuming that we have a estimate for a range of possible target temperatures, we can usethis to constrain the analysis. In this, we assume that this target temperature estimateis similar to the excitation emission weighted temperature of the nearest chord at thetarget ( T Et ). For synthetic testing we obtain this estimate directly from the SOLPSoutput (assuming an uncertainty of ± T Et . Given the ’known’ T Et at the target and its uncertainty wecan compute the probability of that sample being true (for this we assume a Gaussianprobability distribution for T Et ). The samples and their probabilities are then mappedto a probability density functions (PDFs) using a weighted Gaussian Kernel densityestimator. From the PDF estimates, the maximum likelihood and shortest intervalcorresponding to 68 % uncertainty can be extracted, representing the estimated outputsand its uncertainty in a similar way as done in [34].This way of implementing constraints also changes how the integrated values shouldbe obtained. Since the uncertainties are assumed to be systematic, the uncertaintiesapplied to each chord per sample are the same - there is thus a correlation betweenthe uncertainties of different chords when calculating integrated values (such as thetotal ionisation source). This could interfere with the way the constraints are built up.For instance, if all the analysis outputs would, hypothetically, be isothermal, then themaximum likelihood values of the temperature profile along the divertor leg would, afterapplying the constraints, not be isothermal (since a probability per point on the poloidalprofile is ascribed). However, the integrated ionisation values would be determined all pectroscopy inferences of plasma-molecule interactions Appendix B.2. CIII temperature ’exclusion’ constraints
The match improves further when a temperature constraint along the viewing chordfan is added; rather than a single point at the target. The front of the CIII (465 nm)emission line is an emission line frequently used in the qualitative characterisation of edgephysics experiments in carbon devices, especially at TCV [57, 47, 58] where it is used asa ’proxy’ for the ’cold front’ taking off the target [58] during detachment experiments.Depending on transport, the expected temperature of such a ’front (1/e fall-off point)’(assuming the carbon concentration does not change dramatically over the field line) is4-8 eV. Whether such a front can be used accurately for detachment characterisation isstill debated since changes in carbon (impurity) transport changes during a/betweendischarge(s) can lead to changes in the corresponding temperature of the front. However,we can make the statement that below the CIII front the electron temperature willlikely not be hotter than 8 eV. Likewise, above the front, the temperature will likelynot be colder than 4 eV: the CIII emission front thus provides us with information tospatially ’exclude’ (e.g. lower the likeliness) certain temperatures. We can thus constrainthe temperature samples further by adding a probability function which represents thisargument - equation B.1.In here z represents the z position of the line of sight intersecting the divertor leg, z f represents the CIII front location estimate and T f,l , T f,h corresponds to the lowest/highest-temperature estimate of the front respectively. In this case, z f is determined analogouslyto [57, 58] as the 1/e fall-off-length of the CIII emission profile, which is determinedby (synthetic) line of sight spectroscopy. The probablity used for each line of sightshown in equation B.1 represents an analytical depiction of the multiplication of twoblock-functions making two clauses likely: below CIII front z f and below temperature T f,h = 8 eV & above CIII front z f and above temperature T f,l = 4 eV. The fall-off lengthof the functions are set to kz = 2 cm and kT = 1 . P ( T e ) = 11 + exp − ( z − z f kz ) 11 + exp − ( T e − T f,l kT ) + (cid:20) −
11 + exp − ( z − z f kz ) (cid:21)(cid:20) −
11 + exp − ( T e − T f,h kT ) (cid:21) (B.1)One drawback of such constraints is that it strongly reduces the ’effective’ Monte pectroscopy inferences of plasma-molecule interactions [1] Pitts R A, Carpentier S, Escourbiac F, Hirai T, Komarov V, Lisgo S, Kukushkin A S, Loarte A,Merola M, Naik A S, Mitteau R, Sugihara M, Bazylev B and Stangeby P C 2013 Journal ofNuclear Materials
S48–S56 ISSN 0022-3115[2] Loarte A, Lipschultz B, Kukushkin A S, Matthews G F, Stangeby P C, Asakura N, Counsell G F,Federici G, Kallenbach A, Krieger K, Mahdavi A, Philipps V, Reiter D, Roth J, Strachan J,Whyte D, Doerner R, Eich T, Fundamenski W, Herrmann A, Fenstermacher M, Ghendrih P,Groth M, Kirschner A, Konoshima S, LaBombard B, Lang P, Leonard A W, Monier-Garbet P,Neu R, Pacher H, Pegourie B, Pitts R A, Takamura S, Terry J, Tsitrone E and Phy I S o L D2007
Nuclear Fusion S203–S263 ISSN 0029-5515[3] Pitcher C S and Stangeby P C 1997
Plasma Physics and Controlled Fusion Nuclear Fusion The Plasma Boundary of Magnetic Fusion Devices. Series: Series in PlasmaPhysics, ISBN: 978-0-7503-0559-4. Taylor & Francis, Edited by Peter Stangeby, vol. 7 [6] Stangeby P C 2018 Plasma Physics and Controlled Fusion Nuclear Fusion [8] Fil A M D, Dudson B D, Lipschultz B, Moulton D, Verhaegh K H A, Fevrier O and Wensing M2017 Contributions to plasma physics ISSN 0863-1042[9] Lipschultz B, Terry J L, Boswell C, Hubbard A, LaBombard B and Pappas D A 1998
PhysicalReview Letters Journal of Plasma Physics Nuclear Materials and Energy Nuclear Fusion Nuclear Materials and Energy Plasma Physics andControlled Fusion Spectroscopic Investigations of detachment on TCV
Thesis URL http://etheses.whiterose.ac.uk/22523/ [16] Lomanowski B, Groth M, Coffey I H, Karhunen J, Maggi C F, Meigs A, Menmuir S and O’MullaneM 2020
Plasma Physics and Controlled Fusion [17] Fantz U 2002
Contributions to Plasma Physics Journal of Nuclear Materials
337 – 342 ISSN 0022-3115[19] Ohno N, Ezumi N, Takamura S, Krasheninnikov S I and Pigarov A Y 1998
Phys. Rev. Lett. (4)818–821[20] Sakamoto M, Terakado A, Nojiri K, Ezumi N, Nakashima Y, Sawada K, Ichimura K, Fukumoto M,Oki K, Shimizu K, Ohno N, Masuzaki S, Togo S, Kohagura J and Yoshikawa M 2017 Nuclear pectroscopy inferences of plasma-molecule interactions Materials and Energy Nuclear Materials and Energy Nuclear Materialsand Energy Plasma Physics and Controlled Fusion Journal of Nuclear Materials
Plasma Physics and Controlled Fusion Physics of Plasmas Nuclear Materials and Energy Atoms ISSN 2218-2004[29] W¨underlich D, Giacomin M, Ritz R and Fantz U 2020
Journal of Quantitative Spectroscopy andRadiative Transfer
Plasma Surface Interactions [31] Park J S, Groth M, Pitts R, Bak J G, Thatipamula S, Juhn J W, Hong S H and Choe W 2018
Nuclear Fusion https://doi.org/10.1088%2F1741-4326%2Faae865 [32] Wischmeier M, Pitts R A, Alfier A, Andrebe Y, Behn R, Coster D, Horacek J, Nielsen P, PasqualottoR, Reiter D and Zabolotsky A 2004 Contributions to Plasma Physics Physics of Plasmas Plasma Phys.Control. Fusion [35] Verhaegh K, Lipschultz B, Harrison J R, Duval B P, Bowman C, Fil A, Gahle D S, Moulton D,Myatra O, Perek A, Theiler C and Wensing M Nuclear Materials and Energy, submitted
URL https://doi.org/10.13140/RG.2.2.28699.49441 [36] Summers H P, Dickson W J, O’Mullane M G, Badnell N R, Whiteford A D, Brooks D H, LangJ, Loch S D and Griffin D C 2006
Plasma Physics and Controlled Fusion [38] Hinkley D V 1969 Biometrika et al. [41] Reiter D, Baelmans M and Brner P 2005 Fusion Science and Technology https://doi.org/10.13182/FST47-172 [42] Fil A, Lipschultz B, Moulton D, Dudson B D, F´evrier O, Myatra O, Theiler C, Verhaegh K,Wensing M and and 2020 Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion [44] McLean A 2019 Understanding plasma divertor detachment in fusion power reactors Tech. rep.Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States) pectroscopy inferences of plasma-molecule interactions [45] Sawada K and Fujimoto T 1995 Journal of applied physics Contributions to Plasma Physics Nuclear Fusion
URL https://doi.org/10.1088%2F1741-4326%2Fab8183 [48] Perek A, Vijvers W A J, Andrebe Y, Classen I G J, Duval B P, Galperti C, Harrison J R, LinehanB L, Ravensbergen T, Verhaegh K and de Baar M R 2019
Review of Scientific Instruments Atomic Data and Nuclear Data Tables
147 –204 ISSN 0092-640X[50] Behringer K and Fantz U 2000
New Journal of Physics Simulating divertor detachment in the TCV and JET tokamaks
Thesis[52] Cadez I, Markelj S and Milosavljevic A R 2011
Nuclear Engineering and Design [53] Miyamoto K, Hatayama A, Ishii Y, Miyamoto T and Fukano A 2003
Journal of Nuclear Materials
Plasma Physics and Controlled Fusion Phys. Rev. Lett. (24) 243201URL https://link.aps.org/doi/10.1103/PhysRevLett.106.243201 [56] Cowles M K 2013
Applied Bayesian statistics: with R and OpenBUGS examples vol 98 (SpringerScience & Business Media) ISBN 1461456967[57] Theiler C, Lipschultz B, Harrison J, Labit B, Reimerdes H, Tsui C, Vijvers W A J, Boedo J A,Duval B P, Elmore S, Innocente P, Kruezi U, Lunt T, Maurizio R, Nespoli F, Sheikh U, ThorntonA J, van Limpt S H M, Verhaegh K, Vianello N, Team T and Team E M 2017
Nuclear Fusion Nuclear Materials and Energy12