A study of the influence of plasma-molecule interactions on particle balance during detachment
K Verhaegh, B Lipschultz, J R Harrison, B P Duval, C Bowman, A Fil, D S Gahle, D Moulton, O Myatra, A Perek, C Theiler, M Wensing
AA study of the influence of plasma-molecule interactions on particle balanceduring detachment
Kevin Verhaegh a,b,c , Bruce Lipschultz b , James Harrison a , Basil Duval c , Chris Bowman b , Alexandre Fil b,a , DaljeetSingh Gahle d,a , David Moulton a , Omkar Myatra b,a , Artur Perek e , Christian Theiler c , Mirko Wensing c , MST1 team g ,TCV team f a Culham Centre for Fusion Energy, Culham, United Kingdom b York Plasma Institute, University of York, United Kingdom c Swiss Plasma Centre, ´Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland d SUPA, University of Strathclyde, Glasgow, United Kingdom e DIFFER, Eindhoven, The Netherlands f See author list of ”S. Coda et al 2019 Nucl. Fusion 59 112023” g See author list of ”B. Labit et al 2019 Nucl. Fusion 59 086020”
Abstract
In this work we provide experimental insights into the impact of plasma-molecule interactions on the target ion fluxdecrease during divertor detachment achieved through a core density ramp in the TCV tokamak. Our improved analysisof the hydrogen Balmer series shows that plasma-molecule processes are strongly contributing to the Balmer seriesintensities and substantially alter the divertor detachment particle balance.We find that Molecular Activated Recombination (MAR) ion sinks from H + and / or H − are a factor ∼ ff ecting power balance in the divertor. Asthose enhancements vary spatially in the divertor and are di ff erent for di ff erent transitions, they are expected to resultin a separation of the Ly β and Ly α emission regions. This may have implications for the treatment and diagnosis ofdivertor opacity.The demonstrated enhancement of the Balmer series through plasma-molecule processes potentially poses a challengeto using the Balmer series for understanding and diagnosing detachment based only on atom-plasma processes. Keywords:
Tokamak divertor; Molecules; Plasma; Plasma spectroscopy; Particle balance; Detachment
1. Introduction
Divertor detachment is expected to be a crucial aspectfor handling the power exhaust of future fusion devices,such as ITER and DEMO [1]. During detachment, arange of atomic and molecular processes result in simul-taneous power, particle and momentum losses from theplasma to neutral species or to photons (e.g. radiativepower loss). This results in a simultaneous reduction ofthe target plasma temperature ( T t ) and the ion target flux Γ t . Such changes in the plasma facilitate large reductionsin the target heat flux ( q t ) as shown in equation 1 where γ is the sheath transmission coe ffi cient and (cid:15) is the surface Email address: [email protected] (Kevin Verhaegh) recombination energy that is deposited when an H + ion converts to an atom (13.6 eV) and afterwards to amolecule ( + . q t = Γ t ( γ T t + (cid:15) ) (1)This simultaneous reduction of the ion target flux ( Γ t )and the target temperature requires target pressure ( p t )loss according to the sheath-target conditions (equation2). That target pressure loss can be facilitated through In this work we use H for hydrogen as the available reactionrates / emission coe ffi cients are only available for hydrogen. The dis-charge discussed in this work is, however, a deuterium discharge. Theimpact of such assumptions are further discussed in [2]. Preprint submitted to Elsevier August 4, 2020 a r X i v : . [ phy s i c s . p l a s m - ph ] A ug olumetric momentum losses [4, 5] and may involve anupstream pressure loss as indicated in previous researchon TCV [6]. Γ t ∝ p t / T / t (2)The importance of detachment for reducing the targetheat flux is illustrated by asking how much power losscan occur during attached plasmas where p t is constant.As T t drops, Γ t (equation 2) increases while q t drops -but not very much: assuming T t drops from 100 eV to 1eV, one would have a reduction of q t of only a factor 2 . γ = (cid:15) = . how the ion flux drops, we have toinvestigate the particle balance in the divertor - equation3. Here, Γ i ( Γ r ) is the divertor ion source (sink) and Γ u is a net ion flow from upstream towards (positive) / away from (negative) the target. Γ t is generally thoughtto be much larger than Γ u : Γ t (cid:28) Γ u → Γ t ≈ Γ i − Γ r :high recycling conditions ([5–9] and figure 2). In theseconditions, a reduction in the ion target flux requireseither a reduction of the divertor ion source Γ i and / or anincrease of the divertor ion sink Γ r . Γ t = Γ i − Γ r + Γ u (3)The divertor ion source ( Γ i ) is strongly connected topower balance as each ionisation event requires a certainamount of energy ( E ion ) [5–9]. The ionisation source ( Γ i )can become limited by the power flux flowing into therecycling / ionisation region ( q recl ) if the power flux lossdue to ionisation ( Γ i E ion ) becomes comparable (within afactor of two [6]) to q recl . Impurity radiation is often (oneof) the main power dissipation processes reducing thepower crossing the SOL ( q S OL ) before the power entersthe recycling region ( q recl ). Particle, power and momen-tum balance are thus all connected through equations 2,3 and 1 (where q t = q recl − E ion Γ i ). All three balancesplay an important role in detachment [4, 6, 10]. Moststudies of detachment have focussed on the target ioncurrent in detachment and how plasma-atom interactionsa ff ect power, momentum and particle balance, leading Γ t to drop.Plasma-molecule interactions can also impact all threeof these balances significantly [10–14]. To investigatethis further, we must distinguish between two di ff erent’types’ of plasma-molecule interactions: (’elastic’) colli-sions between the plasma and H and reactions from theplasma chemistry of H . A schematic overview of such reactions and collisions are shown in figure 1. Collisions between the plasma and H lead to rovibronic excitation[11, 12, 14–18] (figure 1 a).Reactions between the plasma and H can lead to H dissociation and to the formation of H + and H − [11, 12,19] as illustrated in 1 b: H + is formed by Molecularcharge exchange ( H + + H → H + + H ); dissociativeattachment of H ( H + e − → H − + H ) results in theformation of H − . These ”creation” reactions for H + and H − are summarised in table 1.1. Figure 1: Schematic overview of important plasma-molecule andplasma-atom collisions (in orange) and reactions (in magenta) dis-cussed in this work. a) Collisions between the plasma and H excite themolecule rovibronically (meaning electronically - resulting in Fulcherband emission, vibrationally - H ( ν ) and rotationally); b) Reactionsbetween the plasma and H ( ν ) result in the ”creation” of H + and H − (see reactions in table 1.1), which is enhanced by vibrationally excited H ( ν ); c) Reactions ”destroying” H + and / or H − (see reactions in table1.1), which can result in Molecular Activated Recombination / Molec-ular Activated Ionisation (MAR / MAI) and excited neutral atoms ( H ∗ ),resulting in Balmer line emission; d) Collisions between electronsand H excite H ∗ , resulting in Balmer line emission; e) Electron-ionrecombination reactions with H + resulting in excited H ∗ and Balmerline emission. Dissociative attachment as well as molecular chargeexchange (step b in figure 1, which involves the ”cre-ation” reactions for H + and H − listed in table 1.1) canbe greatly enhanced by the population of higher vi-brationally excited states ( ν ) which can be populatedthrough plasma-molecule collisions [11] (figure 1a). H + and H − can react with the plasma (figure 1c), ”destroy-ing” H + and H − (see the rates in table 1.1). For instance: H + can undergo dissociative recombination with an elec-tron H + + e − → H + H ∗ ; and H − can undergo mutualneutralisation with an ion H − + H + → H + H ∗ . Many ofsuch reactions ultimately result in neutral (often excited ∗ ) atoms, which emit atomic hydrogen line emissionthrough the various series such as Balmer and Lyman[2, 15, 19, 20] - see figure 1c. ff ect of plasma-molecule interactions on parti-cle, energy and momentum balance Plasma-molecule reactions can impact particle bal-ance of the plasma. For instance, the reactions abovewhich create H + and then destroy it through dissociative2 Creation’ reaction T e (eV) ’Destruction’ reaction T e (eV) Type H ( ν ) + H + → H + + H Molecular charge exchange 1.5-4 e − + H + → e − + H + + H + >
15 MAI e − + H + → H + H < e − + H → e − + H + H ionisation > e − + H + → e − + H + + H + >
15 MAI (x2) e − + H + → e − + H + + H > . e − + H ( ν ) → H − + H Dissociative attachment 0.7-2.5 H + + H − → H + H > . Table 1: Table highlighting plasma-molecule reaction chains havingan impact on particle balance through Molecular Activated Ionisation / Recombination (MAI / MAR). The ’creation’ reactions are part ofprocess ’b’ in figure 1 and the ’destruction’ reactions are part of process’c’ in figure 1 recombination, can start o ff with molecular charge ex-change H + H + and end with H + H + H ∗ - so a molecularreaction ’activated’ the recombination of a plasma ion:Molecular Activated Recombination - MAR. However , if electrons have su ffi cient energy ( > eV ),they could ionise H directly to form H + : e − + H → e − + H + . Such higher energy electrons can also reactwith H + and the resulting species from that could be twoions instead of two neutrals (e.g. e − + H + → H + + H + + e − ) or one ion and one neutral. In that case we havestarted with H (in the case of H ionisation) and endedwith H + + H + - so a molecular reaction ’activated’ theionisation of (two) plasma neutrals: Molecular ActivatedIonisation - MAI. Plasma reactions with H and H + can result in MAI while reactions with H − and H + canresult in MAR. All MAR and MAI reactions and reactionchains are summarised in figure 1 together with theirrelevant electron temperature ranges.Both plasma-molecule collisions and reactions canalso impact the power balance of the plasma. Collisionsbetween the plasma and the molecules can transfer ki-netic energy from the plasma to the molecular cloud[21–23]. Some of the energy gained by H can be dis-sipated through radiation from molecular ( H ) bands,however the radiative losses from such processes areexperimentally estimated to be relatively small, whichis supported by EDGE2D-Eirene modelling [14]. Re-actions between the plasma and the molecules can alsoresult in excited atoms which contribute to atomic lineradiation [2, 19, 20] (step c in figure 1).Plasma-molecule collisions can transfer momentumfrom the plasma to the molecules, e ff ectively acting as amomentum sink [10, 13, 21–23]. Apart from collisions,the molecular charge exchange reaction ( H + H + → H + + H ) can also result in momentum losses [13, 22]. Most experimental investigations into the impact ofmolecules on plasma-edge physics in tokamaks have uti-lized H Fulcher band (590-640 nm) emission measure-ments [11, 16] which arise from electronic excitation of H due to plasma-molecule collisions (step a in figure 1).Those measurements directly show that that the plasmais interacting with the molecules resulting in rovibronicexcitation [11, 12, 16]. That information, combined withmodel or simulation results, has been used in studies toinfer information on reactions between the plasma andmolecules [11, 16] which directly lead to such e ff ects asdissociation, MAR and MAI.The ultimate e ff ect of plasma molecule reactions onatomic line emission (e.g. Balmer and Lyman series) hasbeen discussed and it is suspected from DIII-D and JETstudies [16, 24] that the H α emission in the divertor maybe enhanced by plasma-molecule interactions. However,the impact of plasma-molecule interactions on Balmerline emission (see figure 1) has not yet been studiedquantitatively on tokamak divertors. More importantly,there has not been any study or technique described toutilize the Balmer series to extract information aboutplasma-molecule interactions. That is the subject of thispaper. ff ort to utilze the Balmeremission from divertor plasmas to quantify the roleof plasma-molecule reactions in detachment In our previous research [6, 25] we have investigatedthe power / particle and momentum balance of the di-vertor plasma during detachment that are the result ofonly plasma-atom processes . In this work, we expandthis investigation by expanding our analysis to includeplasma-molecule reactions involving H + and H − andthe resultant hydrogenic (Balmer) line emission duringdetachment [2].Our results indicate H + and / or H − can strongly in-crease hydrogenic line emission as well as modify par-ticle balance significantly during detachment comparedto plasma-atom processes alone. Our analysis separatesthe molecular contributions to the Balmer line emissionspectra ( n = −
6) which are then used to infer themagnitude and location of MAI / MAR ion sources / sinksaccounting for the possible H + and H − reactions. Ourresults indicate that plasma-molecule reactions involving H + (and / or H − ) lead to significant levels of both MARand MAI. MAI starts to contribute to the ion target flux ataround the detachment onset. For the TCV case studied,MAR is ∼ H Fulcher emission3egion tracks the ionisation region; suggesting that dif-ferent plasma-molecule interactions occur at di ff erentlocations of the TCV divertor; 2) are indicative of in-creases of the Lyman series, which could potentiallya ff ect power balance in the divertor; 3) could have im-plications for divertor opacity e ff ects as it expected toresult in a spatial separation between the Ly α and Ly β emission regions.
2. Spectral analysis techniques of inferring infor-mation on plasma-molecule interaction from theBalmer spectra
In this section we present a short summary of theanalysis technique ’Balmer Spectroscopy of Plasma-Molecular Interactions’ - ’BaSPMI’ [2] used to investi-gate the spectroscopic data in this work. For simplicitywe define Balmer line emission from electron-impact ex-citation of H and EIR of H + as ”atomic” contributionsto the Balmer line emission while we define Balmerline emission arising from excited atoms after plasmainteractions with H , H + and H − as contributions to theBalmer line emission arising from ”plasma-moleculeinteractions” . The total atomic line emission is then thesum of the ”atomic” ( H , H + ) and ”plasma-molecule in-teraction” ( H , H + , H − ) contributions [2]. This analysistechnique utilizes chordal-integrated brightness measure-ments of H α, H β , as well as two other medium-n Balmerlines (e.g. n = / sinks and Balmer line emission” [2]. This buildsupon previous atomic analysis technique developed bythe authors in [29]. This works on the principle thatplasma-molecule reactions can lead to excited atoms emitting atomic line emission , which is more dominantfor lower-n Balmer lines ( H α, H β ) than higher-n ones.The analysis scheme can be summarised as follows:1. The analysis applies the technique in [29] and sep-arates the ”atomic” emission of medium-n Balmerlines into its electron impact excitation (of H ) andEIR (of H + ) components assuming that medium-nBalmer line emission is due to ”atomic” interac-tions only. This provides us with ionisation andrecombination estimates. Characteristic tempera-ture estimates of the excitation and recombinationregions are inferred using the respective excitation and recombination brightnesses limited by possibleranges (obtained from SOLPS-ITER simulations)of the neutral fraction and path-length (see [29] formore information). Electron density estimates areobtained from a Stark broadening fitting analysis ofmedium-n Balmer lines [30].2. This information is used to estimate the ”atomic ex-citation” (e.g. electron-impact excitation of H ) andrecombination (of H + ) contributions to the entirehydrogenic line series, in particular the ”atomic”component of the H α and H β emission. The di ff er-ence between this and the total measured measuredbrightnesses is attributed to ”plasma-molecule in-teractions” involving H + and H − .3. We find that most of the molecular contributions to H α emission contributions are from H + (and / or H − [2]) as as opposed to H contributions which makeup less than a percent of the measured Balmer lineemissions in the (detached) conditions at which weapply the analysis - see [2] for more details. The H + and H − H α contributions are separated usingthe H β/ H α (of H + , H − ) line ratio.4. The H α emission has now been separated intothe contributions due to H , H + , H + , H − , H . Thefollowing sub-steps are taken in order to deter-mine a consistent description of the molecular andatomic contributions to all Balmer lines: a) Themakeup of atomic and molecrular contributions tothe H α brightness measurements are used to es-timate the ”plasma-molecule interaction” compo-nents of the medium-n Balmer lines; b) These aresubtracted from the measured medium-n Balmerline brightnesses to get the ”atomic” componentof the medium-n Balmer line emission; c) Withthis, the above steps 1 through 4 are iterated untila self-consistent description of the contributions tothe various emission pathways of H α , H β and themedium-n Balmer lines is obtained.5. The separated contributions to H α brightnesses areused to estimate the integral of MAR ( H − , H + ) andMAI particle sinks / sources ( H , H + ) along a par-ticular spectrometer viewing chord using ’reactionto emission coe ffi cient’ ratios and the temperaturesand densities obtained in step 1.In the above analysis uncertainties are propagated us-ing a Monte Carlo scheme [2, 6]; a series of random sam-ples are generated from all input parameters within theirestimated uncertainties. These are analysed individuallyto obtain a sample of values for each output parameter;which is processed to obtain the most probable valuesfor desired parameters (e.g. MAR, MAI, etc.) as well4s their uncertainty (probability distribution function).Additional probability constraints on the characteristictemperature of the ”atomic” excitation emission are em-ployed based on power balance and the location / extentof the CIII emission region (see [2] for more details).The profile of the various emission contributions varycontinuously along the line of sight. However, the anal-ysis technique (see [2]) simplifies the emission profilesas a ’dual slab’ model (with a hot and cold temperature)along the line of sight. That approach has been veri-fied using SOLPS-ITER simulations for both TCV andMAST-U, where the full profiles of the various emissioncontributions along the line of sight were calculated (see[2]). In those simulations, there is indeed a strong spatialseparation of the various emission and reaction regions.However, the analysis of the chordal-integrated bright-nesses still provide similar estimates of the chordal-integrated atomic and molecular ion sources / sinks asis obtained when summing those sources / sinks from thesimulation directly along the line of sight. The analysis(for those tested conditions) seems fairly resilient to theactual variation of plasma-profiles along the line of sight.More discussion can be found in [2, 29].Throughout this analysis we have bundled the con-tributions of H , H + and H − together in terms of theirBalmer line emission and MAR / MAI ion sinks / sources.
3. Experimental results on TCV
In the following we apply the above analysis chain(BaSPMI) to a representative discharge in TCV todemonstrate the role of plasma-molecule interactionson particle balance. The TCV discharge used for thisstudy ( I p = kA dischargein reversed field (i.e. ion grad-B drift away from theprimary x-point) without additional impurity seeding (al-though intrinsic carbon impurities are present and are animportant power loss process [6]). This discharge hasbeen repeated multiple times with di ff erent spectroscopysettings to obtain su ffi cient spectroscopic coverage toobtain the Balmer line brightnesses of H α, H β, H γ, H δ and H (cid:15) , the latter being used for Stark broadening esti-mates [29]. In addition, several of the repeat dischargeswere used to obtain Fulcher band measurements. Thereproducibility of these discharges has been investigated[6] and has been found to be adequate for this purpose. Figure 2: Inferred particle balance only considering plasma-atom in-teractions. a) Particle balance (ion target current) shown together withestimated atomic ion source, electron-ion recombination (EIR) sink. b)Measured total H α in the divertor together with the estimated atomicpart of the H α emission. c) Target temperature estimates (based onthe spectroscopically inferred excitation temperature - T Ee and a tem-perature estimate obtained from power balance, adopted from [6]. d)Magnetic equilibrium of the investigated discharge with spectroscopicline of sight coverage (two chords are highlighted which are used infigure 3. First we investigate particle balance of this discharge(2) based on a spectroscopic analysis [29] which assignsall medium-n Balmer line emission to atomic interac-tions only . Under TCV attached conditions we observea linear increase of the ion target current (figure 2 a).Such a linear increase is predicted by analytical models,due partially to the reduction of upstream temperatureduring the ramp of the upstream density [6]. The totalion target current, Γ t , stops rising linearly at around aGreenwald fraction of 0.33 (detachment onset) and rolls-over around a Greenwald fraction of 0.4. We observethat the atomic electron-ion recombination sink only be-comes relevant at latest phase of the discharge (wherethe target temperature T t ∼ T t ∼ ffi cientionisation - ’power limitation’ [2].A bifurcation starts to occur between the measuredand estimated ”atomic extrapolated” H α emission at thedetachment onset ( T t ∼ T t < n = H α emission is based on the analysis of the medium-nBalmer lines (step 1 of the BaSPM analysis) [2, 29],assuming the higher-n Balmer lines are only populatedby ”atomic” interactions [29].While the expected H densities from SOLPS-ITERsimulations under these density / temperature conditions(e.g. detached T t < n e ∼ m − )contribute less than 1% of the measured H α emission[2], plasma-molecule interactions involving H + and H − could explain the additional H α brightness after detach-ment [2]. Such plasma-molecule interactions lead tolosses (sinks) for ions in the plasma through MolecularActivated Recombination (MAR). Other possible addi-tional sources of n = Ly β opac-ity and plasma-molecule interactions with hydrocarbons,are estimated to only increase the H α emission by a fewpercent for these TCV conditions [2]. Therefore, weassume that the additional H α emission is due to plasma-molecule interaction, which is a starting point for theanalysis outlined in BaPSM - step 2 (section 2).The enhancement of H α after detachment is qualita-tively consistent with measurements from both DIII-D[16] and JET [24] where inconsistencies between themeasured and expected H α emission was suspected,which will be discussed in more detail in section 4.4. We will now investigate the influence of plasma-molecule interactions on the Balmer lines more quantita-tively by applying the full self-consistent BaSPM atomicand molecular spectroscopic analysis chain. First, westudy the influence of this on three measured Balmerlines measured during this discharge. Initially only elec-tron impact excitation (of H ) emission plays a role forall three Balmer lines (figure 3).As the target temperature drops, first plasma-moleculeinteractions and later electron-ion recombination forman increasingly larger part of the Balmer line emission(figure 3). Near the detachment onset ( ∼ . s ), elec-tron impact excitation ’detaches’ from the target (seefigure 3 6 cm above the target), leaving a region whereenhanced Balmer line emission from H + and / or H − aswell as EIR occur. This region expands as the divertorbecomes colder, following behind the movement of theelectron-impact excitation region. At the latest phase ofthe discharge (t = emission fractions (figure 3)(not the actual brightnesses - see figure 4) from plasma-molecule interactions are higher at 25 cm above the targetas the temperatures are higher there ( ∼ [2 . −
4] eV) than near the target, which are still su ffi ciently low for plasma-molecule interactions but are too high for EIR. In thecold region, ”plasma-molecule interactions” are the dom-inant excitation process for H α and H β emissions, whilesignificant for H γ and H δ (not shown) where Balmerline emission from EIR is dominant. Figure 3: Time traces of the H α, H β, H γ self-consistent emissionfractions for two di ff erent chords (figure 2) in terms of ”atomic” con-tributions (electron impact excitation (of H ) and EIR (of H + ) and”plasma-molecule interaction” related contributions. Using the BaSPM analysis technique discussed in sec-tion 2 [2], we obtain information from plasma-moleculeinteractions by analysing the excited atoms arising pre-dominantly from plasma reactions with H + and H − .However, there are also collisions between the plasmaand the H , which transfer power and momentum fromthe plasma to the molecules and excite the molecularcloud . When electrons have su ffi cient energy for thesecollisions to result in excited H electronic states, thisresults in H Fulcher band emission, which is brightestat high molecular densities combined with high electrontemperatures.To provide some insight into the evolution of di ff erentkinds of plasma-molecule interactions during detach-ment, we compare the brightness profile ( line-integrated along the divertor leg and therefore also intersecting theprivate flux and common flux regions) of a part of the H Fulcher band emission (600-614 nm) with that of thevarious H α excitation sources in figure 4. A first obser-vation is that the Fulcher emission penetrates throughoutthe divertor leg in the attached phase.A second observation is that the Fulcher emission pro-file spatially follows the electron impact excitation (of H ) emission profile and thus the ionisation profile. Incontrast, the Balmer line emission from excited atoms6fter reactions with H + and / or H − occurs below theFulcher emission region and remains peaked near the tar-get throughout the discharge; this suggests that there is aspatial and temperature ordering of the various molec-ular processes. Those two observations will be furtherdiscussed in section 4.1. Figure 4: Spatial profiles at three di ff erent times (of the same dischargeas shown throughout the paper) of normalised (to the maximum) H α atomic excitation emission, H α combined emission due to plasmamolecule interactions ( H + , H − , H ) and summed Fulcher emissionbetween 600 and 614 nm (which has the brightest Fulcher emissionlines) with impurity emission lines removed from the spectra. The evidence presented in the previous section sug-gests plasma-molecule interactions can impact hydro-genic atomic line emission significantly. This has im-plications for particle balance in two ways: 1) Whenthe hydrogenic Balmer spectra is attributed to be solelyfrom ”atomic” interactions (as in [25]), any Balmer lineemission from plasma-molecule interactions will be at-tributed to ”atomic processes”; that ’inflates’ the atomicion source / sink estimates. 2) When plasma-molecule in-teractions contribute to, and are properly accounted for,in the Balmer line emission, that indicates the presenceof an additional ion sink through Molecular ActivatedRecombination (MAR) and / or ion source through Molec-ular Activated Ionisation (MAI). As will be shown next,both MAR and MAI are important in the particle balanceof discharge studied.Particle balance is shown from the perspective of bothatomic and plasma-molecule interactions in figure 5 forthe discharge discussed throughout this paper. The dif-ference in the ionisation estimate between figure 5 andfigure 2 is due to the self-consistent consideration of bothplasma-atom ( H and H + ) and plasma-molecule interac-tions (involving H , H + and H − ) leading to excited atomsin figure 5. Both the ionisation estimates provide similar results until the detachment onset point (Core Greenwaldfraction 0.33, t ∼ . Figure 5: Inferred particle balance considering plasma-atom andplasma-molecule interactions. This modifies the estimated plasma-atom interaction processes (as it accounts for emission from plasma-molecule interactions in the spectroscopic analysis). a) Particle balance(ion target current) shown together with estimated atomic ion source,the sum of the atomic and MAI ( H + and H ) ion source, EIR sinkand total ( H + and H − ) MAR sink. We have added a linear fit in theattached phase (dotted lines) to the total ion source and ion target flux .b) Ion losses of the ion target flux, ion sources and through EIR andMAR. During detachment, plasma-molecule interactionsstart to contribute to H γ, H δ (larger impact for lower n → n → ff ects leads to an underesti-mate of the ’atomic’ H δ/ H γ ratio (e.g. higher-n / lower-nratio), which makes Balmer line emission ’appear’ tobe more excitation rather than recombination dominated[29], leading to a potentially significant ionisation over-estimate. We can conclude that a self-consistent consider-ation of plasma-atom and plasma-molecule interactionscan be important for inferring information on electronimpact excitation (of H ) emission (and thus ionisation,characteristic excitation temperature and radiated powerfrom atomic excitation).The analysis shown in figure 5 indicates that MARis significant at the detached roll-over phase. The onsetof MAR occurs between the onset of power limitation(detachment onset) and the onset of EIR ion sinks. Theinferred magnitude of MAR for this discharge is ∼ H γ, H δ (figure 3) beingEIR dominated.In this particular case, the MAR ion sink (magentasymbols in figure 5a) represents a significant fraction ofthe ion target flux (green symbols in figure 5a) (51 ±
15 %)and are thus important to account for to get an accuratepicture of the particle balance in the divertor.Plasma-molecule interactions can also increase theion target flux through MAI. The MAI rate calculatedfor this case is significant and starts to occur around thedetachment onset. The MAI ion source in the detachedphase is smaller than the MAR ion sink. These MAIestimates have larger uncertainties and are more sensitiveto chordal integration e ff ects as the MAI / H α photonratio depends on the relative strength between molecularcharge exchange and H ionisation (see table 1.1), whichis strongly temperature dependent - see [2] for moreinformation. To minimise the e ff ects on this on figure 5the MAI and atomic ion sources have been combined asthe individual uncertainties in those are anti-correlated.Most MAI in this case arises from H + ions (createdfrom H ionisation) in a fairly high temperature regime( T e = [4 −
9] eV as opposed to T e = [1 . −
4] eV forMAR) near the electron-impact excitation and Fulcheremission regions, which will be discussed in section 4.1.To obtain a more quantitative comparison of the mag-nitude of ion losses through ion sinks, the reduction ofthe ion source and the reduction of the target ion flux, the’ion losses’ for these di ff erent processes are estimated,analogously to [6], and are shown in figure 5b. We ob-serve that ion source losses start to occur around thedetachment onset and increase from that point onwards.The impact of the total ion source losses (e.g. includingMAI) seems to be the earliest and strongest (togetherwith MAR) contributor to the ion target flux drop duringdetachment. The ion source drop is followed by furtherMAR and ultimately EIR ion sinks. The magnitude ofion loss due to MAR and the observed ion loss at thetarget are similar. The sum of the ion source and sinklosses exceeds the estimated ion target flux loss (figure5), which will be discussed in section 4.3.
4. Discussion
In figure 1 we made the distinction between collisions of the plasma and H , exciting H rovibronically and reactions between the plasma and H + and / or H − leadingto excited atoms and Balmer line emission. The resultsfrom section 3.1 indicated that the Balmer line emission due to plasma-molecule interactions and Fulcher bandemission emit at di ff erent locations and evolve di ff erentlyduring detachment. This suggests that there is a largevolume in TCV of significant H density extending overa range in T e . Di ff erent kinds of plasma-molecule inter-actions dominate at di ff erent positions in this volume.Fulcher band emission occurs when electrons havesu ffi cient energy to electronically excite H ( T e > [4 − H isboth dissociated ( e + H → e + H + H ) as well as ionised( e + H → H + + e ) [16]. Therefore, Fulcher band emis-sion should be fairly well localised around the hot partof the separatrix. It is thus surprising that Fulcher bandemission occurs throughout the ionisation region giventhat the H primary source is at / near the target and meanfree paths at the target in attached conditions are a fewcentimetres according to simulations [31]. This suggeststhat molecules enter the divertor leg radially throughoutthe ionisation region, which could be attributed to theopen, unba ffl ed divertor structure at the time. Accordingto our analysis, those molecules making it to the ioni-sation region are responsible for the significant levelsof MAI inferred (figure 5), which is spatially correlatedwith both the Fulcher emission and atomic ionisationregions.In comparison to the primary location of Fulcher bandemission, most Balmer line emission from H + and / or H − (and thus the MAR ion sink as well as the H + and / or H − densities) remains peaked near the target (where the H + densities seem higher) and extends up until the ionisationregion. Near the target during detachment ( T e = [1 − ffi cient energy to promote H ionisation. However, vibrationally excited molecules canpromote the creation of H + through molecular charge ex-change ( H + + H → H + + H ) significantly. In other words,at the location where MAR occurs and most Balmer lineemission due to H chemistry is observed ( T e = [1 . − vibrationally excited molecules are likely respon-sible for the creation of H + (through molecular chargeexchange) and / or H − , whereas at the Fulcher band emis-sion region H is electronically excited , dissociated andionised into H + resulting in MAI.If there is no longer su ffi cient energy ( T e < [4 − H ,this would result in strongly reduced Fulcher band emis-sion. Our results indeed indicate that the Fulcher bandemission is particularly dim below the ionisation regionwhere most molecules (as well as MAR) are expectedto be present. This may have implications for the appli-cability of using only Fulcher band analysis to diagnoseMAR.Although the mean-free-paths between the target and he ionisation region for H are fairly large in detachedconditions due to the lower electron temperatures, the ex-pected mean free paths of H + and H − , are much smaller.Potentially, transport of vibrationally excited moleculesbetween the target and the ionisation front (and theirinteraction with the wall [11]) may play a role in achiev-ing the higher vibrationally excited states near the tar-get. Additionally, if electron impact collisions with H have no longer enough energy to electronically exciteH ( T e < [4 −
5] eV) a larger proportion of the energytransfer during those collisions could go into raising the vibrational levels in the electronic ground state, whichis consistent with measurements and (vibrational-stateresolved) simulations [12].Further investigations are required to investigate theindividual roles of plasma-molecule collisions and re-actions and what their implications are for detachmentphysics.
Plasma-molecule interactions involving H + and / or H − particularly influence H α , which may have implicationsfor the diagnosis and understanding of (photon) opac-ity. Although the photon opacity is expected to be in-significant for the TCV case studied here, based on post-processing TCV simulation data [2], opacity could playa stronger role in other devices, such as MAST-U wherethe photons can traverse an integrated neutral densityhigher than 10 m − [24, 32, 33] along their path-lengthaccording to MAST-U SOLPS simulations [22]. As thespectroscopic technique we utilise for inferring infor-mation from plasma-molecule interactions [2] relies ondetecting additional excitation of the H α emission line,it can be influenced by Ly β opacity [2]. Figure 6: Schematic overview of Ly α and Ly β absorption / emissionbased on ray-tracing obtained from post-processing a SOLPS-ITERsimulation of a deeply detached MAST-U discharge without externalseeding. Plasma-molecule interactions involving H + and / or H − predominantly lead to Balmer series emission near thetarget while the ionisation region, which coincides withelectron impact excitation of H leading to emission, has already ’detached’ from the target during detachment.Plasma-molecule interactions (involving H + and / or H − )influence H α ( n =
3) much more than Ly α ( n = H α ( / Ly β ) and Ly α emission regions. This is found to be the case for MAST-U based on SOLPS simulations [22] which have beenpost-processed to estimate the impact of H , H + and H − on the hydrogenic Lyman line series similarly to thepost-processing for synthetic testing of the Balmer seriesemployed in [2]. The result is illustrated schematicallyin figure 6.The strong spatial separation of Ly α and Ly β emis-sion can result in Ly β emitting in a region where opac-ity is (relatively) more dominant than for Ly α . This isschematically indicated in figure 6 where the SOLPS hy-drogenic line emissions are further post-processed usingray-tracing to estimate where the emission gets absorbeddue to opacity. This is because the Ly β emission occursin a region below the ionisation region where the neu-tral density and the photon pathlengths are significantlylarger given the MAST-U divertor shape.The existence of plasma-molecule interactions involv-ing H + and / or H − may also have implications for thediagnosis of opacity. Experimentally one can mea-sure opacity of Ly β by comparing the line-integrated H α brightness to the line-integrated Ly β brightness[24, 32, 33]. One can then predict the opacity for Ly α and the rest of the Lyman series assuming that Ly α and Ly β emit at the same location spatially throughcollisional-radiative modelling [24, 33]. However, asin the case shown in figure 6, the emission patterns for Ly α and Ly β emission are significantly di ff erent. Suchan approach may thus not be feasible and somethingmore sophisticated is likely required; the developmentof spatially resolved Ly α , Ly β (as well as the Balmerseries) diagnostics on tokamak divertors may be required.Divertor plasma simulations could be used to explorevarious diagnotics configurations. More detailed opacitysimulations as well as VUV opacity measurements onMAST-U are planned for when it is operational [34]. Our results indicate that plasma-molecule interactionsinvolving H + and / or H − significantly modify both thehydrogenic Balmer line series as well as particle balancethrough molecular activated recombination. Such an im-pact on the hydrogenic Balmer (and thus Lyman) lineseries also implies that these interactions can result insignificant hydrogenic radiation and likely play an im-9ortant role in power as well as particle balance. Thiswill be investigated in more detail in future work.When we compare figure 5 with equation 3 depictingparticle balance, we find that ’high recycling conditions’( Γ t = Γ i − Γ r ) apply in the attached phase but no longerapply in the detached phase as MAR raises Γ r such that Γ i − Γ r < Γ t , which is indicative of a net ion flow to thetarget. This is in contrast to the findings in [6] whereonly atomic reactions were considered. This net ion flowcould arise from ionisation occurring above the spec-trometer’s divertor chordal view range (figure 2d). Sucha behaviour is qualitatively consistent with SOLPS-ITERsimulations for TCV [31, 35, 36] and will be investigatedin future work. This work highlights the importance of includingplasma-molecule interactions in divertor plasma physicsstudies. The fact that this analysis was performed on onTCV data raises a concern as to the importance of plasmamolecule interactions for detachment in other devices.First, we expect divertor molecular densities to behigh in any divertor at low T e . Our research shows thatplasma-molecule interactions lead to MAR and a ff ectparticle balance during detached conditions ( T t < . T e couldstay above 2.5 eV (but still T t < ∼ H + and / or H − do not play a strong role.We will investigate this further in future studies of otherTCV detached discharges.We do believe that variations in the divertor geometry(e.g. ba ffl ed vs non-ba ffl ed, divertor chamber walls tightaround the divertor leg) could a ff ect the role of plasma-molecule interactions. That concern was expressed insections 3.1 and 4.1 to provide an explanation of how H was able to reach high temperature regions whereatom-plasma excitation / ionisation occur and thus MAI.The wall material can also play a role in a ff ecting thestrength of plasma-molecule interactions as the vibra-tional density distributions are found to be influenceddi ff erently by metallic walls than carbon walls [11].The transport of molecules (and what T e regions areaccessed) will also be a ff ected by changes in the meanfree paths for molecular reactions driven by increasesin either or both plasma density and heat fluxes. Forexample, at higher electron densities we expect that thebalance of dominance between plasma-molecule andplasma-atom processes could change and the distance amolecule in any form will survive will shorten, poten-tially impacting the level of MAR. Tokamaks with higher electron densities than for TCVcould modify the relative balance of MAR and EIR. Theelectron density on TCV during detachment is relativelylow ( ∼ m − ) compared to tokamaks like C-Mod andAUG, not to mention future tokamaks approaching reac-tor conditions. Electron-ion recombination scales withthe power 2-3 of the electron density [25, 32] while theplasma-molecule processes influencing MAR and MAIincrease less quickly with electron density. Furthermore,the ratio MAR / EIR likely drops in T t < ff ects, at least on H α are signif-icant. At DIII-D [16], the measured H α/ H β line ratioswere more than a factor 5 higher than that expected basedon atomic interactions, in agreement with figure 2c. Thiscould be explained by an additional n = H α brightnesses as-suming that all H α emission was due to electron-impactexcitation. This was in agreement with the ion targetcurrent up until the detachment onset where the H α ion source increased strongly while the ion target cur-rent rolled-over. That rise of H α could not be fully ex-plained with electron-ion recombination or Ly β opacityand could have been caused by MAR.The experimental results presented here generallyillustrate that plasma-molecule interactions involvingMAR are likely to occur in other devices at a significantlevel.
5. Summary
In this work we have applied new spectroscopic anal-ysis techniques [2] to investigate the detachment processin TCV during core density ramp discharges. We findthat plasma-molecule interactions can play strong rolesin particle balance during the detachment process andcan enhance the hydrogen Balmer spectra significantly.While it is well known that at and after detachmentonset the entire Balmer series intensities and relativeintensities are modified through atom-plasma interac-tions, we have found that plasma-molecule interactionscan also lead to strong modifications. Those plasma-molecule contributions are part of a multi-step plasma-molecule interaction process of producing charged (andexcited) molecules followed by the breakup of thosespecies which can lead to both Molecular Activated Re-combination (MAR) as well as Molecular Activated Ion-isation (MAI). Those reactions result in excited atoms,leading to enhancements of the Balmer series emission.10or the TCV conditions studied both MAI and MARhave an important impact on divertor particle balance.MAR results in ∼ < Balmer line emission attributed to H chemistry re-mains peaked at the target while H Fulcher emission ’detaches’ from the target, following the ionisation re-gion, as detachment proceeds. This suggests that there isa spatial separation between the various plasma-moleculeinteractions.The strong enhancement of Balmer line emission nearthe target attributed to plasma-molecule interactions indi-cates enhancements in the Lyman series, potentially im-pacting power losses. These enhancements are expectedto result in a separation of the Ly α and Ly β emissionregions which would likely lead to changes of the e ff ectsand location of opacity.It appears that attributing the enhancements to Balmerseries emission during detachment just to plasma-atominteractions can lead to an inaccurate description of di-vertor particle balance.
6. Acknowledgements
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