Spectroscopic investigations of divertor detachment in TCV

K. Verhaegha,b,∗, B. Lipschultza, B.P. Duvalb, J.R. Harrisonc, H. Reimerdesb, C. Theilerb, B. Labitb, R.Mauriziob, C. Marinib, F. Nespolib, U. Sheikhb, C.K. Tsuid,b, N. Vianelloe, W.A.J. Vijversf, TCV team,

MST1 team

aYork Plasma Institute, Department of Physics, University of York, Heslington, York, YO10 5DD, United KingdombEcole Polytechnique Federale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland

cCCFE, Culham Science Centre, Abingdon, Oxon, OX14 3DB, United KingdomdUniversity of California San Diego (UCSD), San Diego, CA, USA

eCorsorzio RFX, Corso Stati Uniti 4, 35127 Padova, ItalyfFOM Institute DIFFER, 5600 HH Eindhoven, The Netherlands

Abstract

The aim of this work is to provide an understanding of detachment at TCV with emphasis on analysis ofthe Balmer line emission. A new Divertor Spectroscopy System has been developed for this purpose. Furtherdevelopment of Balmer line analysis techniques has allowed detailed information to be extracted on free-freeand three-body recombination.

During density ramps, the plasma at the target detaches as inferred from a drop in density at, and ioncurrent to, the target. At the same time the Balmer 6 → 2 and 7 → 2 line emission near the target isdominated by recombination, indicating that the ionization region has also detached from the target to bereplaced by a recombining region with densities more than a factor 2 higher than at the target. As the coredensity increases further, the density and recombination rate are rising all along the outer leg to the x-pointwhile remaining highest at the target. Even at the highest core densities accessed (Greenwald fraction 0.7)the peaks in recombination and density do not move more than a few cm poloidally away from the target,which is different to other, higher density tokamaks, where both the peak in recombination and densitycontinues to move towards the x-point as the core density is increased. However, the recombining regiondoes expand towards the x-point while still being peaked ∼ 5 cm above the target.

The inferred magnitude of recombination is small compared to the target ion current at the time de-tachment (density and particle flux drop) starts at the target. Later the total recombination does reachlevels similar to the particle flux. There is no clear evidence that recombination is playing a significant rolein reducing the target ion current. However, recombination may be having more localized (to a flux tube)effects which we cannot discern at this time.

Keywords: Detachment; divertor spectroscopy; volumetric recombination, tokamak power exhaust; TCVtokamak; Balmer line spectroscopy.

1. Introduction

For future fusion devices such as ITER, operatingat least in a partially detached state is important forreducing the heat flux incident on the divertor to be-low engineering limits (10 MW/m

2). Modelling for

ITER demonstrates reduction of the peak heat fluxnear the separatrix by factors of up to 100 due toa number of atomic physics processes including line

radiation, charge exchange and recombination. Toaddress the need for further power removal beforeexhaust heat reaches the targets, which is needed fora DEMO fusion reactor and beyond, it behoves usto understand the detachment process better. Thatwill enable better models for predicting ITER andDEMO performance and potentially guide us in en-hancing both detachment power and particle loss as

∗Corresponding authorEmail address: kevin.verhaegh@epfl.ch (K. Verhaegh)

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well as control of detachment.There has been considerable work utilizing spec-

troscopic measurements for understanding detach-ment, where the characteristics of the recombiningregion are extracted from the Balmer series emission[1, 2, 3, 4, 5]. Typically a high density recombinationfront forms at the target and moves rapidly towardsthe x-point as the core plasma density is increased.

The aim of this study is to develop a detailed un-derstanding of the detachment process at TCV wherelow densities should give us insight into how the roleof recombination changes. The TCV tokamak is amedium-sized tokamak (R = 0.89 m, a = 0.25 m,Bt = 1.4 T). For this investigation, a new spectro-scopic diagnostic has been developed for the TCVdivertor and improvements for extracting informa-tion on recombination and electron temperature fromBalmer series spectra have been made. Using spectro-scopic measurements we show that the observed highdensity recombination front at TCV during a densityramp stays near the target even after the target ioncurrent and density drop.

2. Experimental setup

2.1. TCV’s Divertor Spectroscopy System (DSS)

The primary measurements of the recombinationcharacteristics are made using a new spectrometerwith views of the divertor, which we refer to as theDSS. The viewing optics provide a poloidal, line-integrated, view of the divertor, yielding 32 lines ofsight (figure 1B). The fibres of each system are cou-pled to a Princeton Instruments Isoplane SCT 320spectrometer coupled to an Andor iXon Ultra 888EMCCD camera with a 1024 x 1024 pixel sensor.A 1800 l/mm grating was used to allow ne mea-surements through Stark broadening of the n=6,7Balmer series lines with a measured FWHM resolu-tion of 0.06 nm. The system has been absolutelycalibrated in intensity (∼10% inaccuracy) and wave-length (< 0.1nm), taking stray light contributionsinto account.

A dark frame is acquired before and after theplasma discharge, which is subtracted from the mea-surements. Due to the relatively low frame transfertime, the the measurements are susceptible to read-out smear of the CCD [6]. At least 90% of the smear-ing is removed by post-processing using a numericalmatrix-based algorithm.

For the results analysed in this work, the mea-sured spectra have been re-sampled by averaging

frames and/or multiple chordal signals over the entiredischarge, greatly improving S/N ratio which leads toimproved determination of ne from line fitting (sec-tion 2.3).

Figure 1A shows that the observed intensity ofmedium-n Balmer lines (n = 6, 7) increases stronglyduring the density ramp. The observed spectra corre-sponds to the view line close to the target highlightedin figure 1B (red), where the locations of the primarydiagnostics used in this work are shown.

398 402 406 410Wavelength (nm)

1

0

ne/nGW = 0.38 (x 10)

ne/nGW = 0.68

6

7

Nor

mal

ised

cou

nts

B

Bolometry LangmuirProbes

DSS

A

396

Figure 1: A) Example Balmer line spectra # 52065, averagedover 100 ms, measured by DSS near the target at two differentcore densities. B) Primary diagnostic locations used in thiswork

2.2. Extracting information on recombination fromBalmer lines using a collisional-radiative model

The brightness (Bn→2 in [photons m−2s−1]) ofa hydrogen Balmer line with quantum number ncan be modelled using the Photon Emissivity Co-efficients (PECrec,exc

n→2 ) [photons m 3s −1], obtainedfrom the ADAS collisional-radiative model [7], forrecombination and excitation as indicated in equa-tion 1. Bn→2 consists of a recombination and ex-citation part: Brec,exc

n→2 . It is assumed that all lineemission comes from a region with width ∆L withhomogeneous electron density ne, electron tempera-ture Te and neutral density no. The effect of theseassumptions are discussed in section 2.4. Additionalassumptions are that hydrogen collisional radiativemodel results are valid for deuterium and that thecontribution of charge exchange and molecular reac-tions (which might be significant for detachment inlow density plasmas [8]) to the emission of a certainBalmer line are negligible.

For further discussion we define Frec as the frac-tion of total Balmer line radiation due to recombina-tion (Frec(n) = Brec

n→2/Bn→2). We also define F76 asthe ratio of brightness of the 7→ 2 and 6→ 2 Balmer

2

lines (F76 = B7→2/B6→2). We define RL as the vol-umetric recombination rate line integrated along aparticular chord [rec / s m2]. Although the analy-sis in this section is mainly focused on the n = 6, 7Balmer lines, the analysis strategy is general and canbe applied to other Balmer lines.

Bn→2 = ∆Ln2ePECrecn−>2(ne, Te)︸ ︷︷ ︸

Brecn→2

+ ∆LnonePECexcn−>2(ne, Te)︸ ︷︷ ︸

Bexcn→2

(1)

2.2.1. Using Balmer line ratios to obtain the fractionof Balmer line emission due to recombination

We have developed a method for separating therecombination and excitation part from the Balmerline emission, which can be particularly important foranalysing medium-n n = 6, 7 Balmer lines.

The ratio of two Balmer lines (e.g. F76) changesas function of Frec (figure 2) and is thus useful toinfer the dominance of recombination in the totalemission of a particular Balmer line. This relation-ship depends only weakly on ne and no/ne. Divertorpressure measurements with an absolutely calibratedbaratron gauge have been used to estimate no and in-dicate no/ne rises from order 10−3 to order 10−1 as Tedrops, which is supported by OSM-Eirene modelling[9] and SOLPS-Eirene modelling [10] of the TCV di-vertor. In this range, Frec changes by < 0.1. In therange of ne = [1019 − 1020] m−3, typical for TCVdivertor densities, Frec changes by < 0.5%. Wheninferring Te and RL from either 6, 7→ 2 lines (usingFrec(n = 6, 7)), the result differs by < 3%.

Therefore, by measuring F76 we can obtainFrec(n), where we use the ne obtained from Starkbroadening and we assume no/ne = 0.1, which isappropriate considering both modelling and pressuremeasurements. By multiplying the measured B6,7→2

with Frec(n = 6, 7), determined from the measuredF76, we obtain Brec

6,7→2.

0.8

0.6

0.4

0.2

n = 6n = 7n = 9

0

1.0

F rec (n

)

0.2 0.3 0.4 0.5 0.6F76

no/ne = 10-2

no/ne = 1

Figure 2: Relation between F76 and Frec(n = 6, 7, 9).

2.2.2. Obtaining RL from absolute Balmer line in-tensities

We have developed a method for calculating RL,which has the advantage over previous work [11] thatno direct temperature estimate is required in the cal-culation.

We start by obtaining the number of recombina-tions per photon as in [11] for a particular Balmerline, which is (assuming the plasma is optically thin)the ratio of the ADAS effective recombination ratecoefficient (ACD(ne, Te)), which takes into accountboth radiative and three body recombination, and theADAS PECrec

n→2(ne, Te). By multiplying the numberof recombinations per emitted photon with Brec

n→2, weobtain RL(ne, Te,∆L) [rec /m2s].

With fixed ne and ∆L, a unique relation is ob-tained between RL(Te) and Brec

n→2(Te) (figure 3),which only depends weakly on ne and ∆L. Usingthis relation, RL can be obtained using ne (Starkbroadening), ∆L, and Brec

n→2 (obtained from Bn→2

and Frec(n)). The measurement inaccuracy of RL is∼ 30 % and is insensitive to profile effects (section2.4). A similar approach as described here could beused to obtain excitation rates and track the excita-tion region.

Using ne (Stark broadening), ∆L, and Brecn→2

(obtained from Bn→2 and Frec(n)) one canalso extract a line averaged Te from Brec

n→2 =∆Ln2ePEC

recn→2(ne, Te), which has the advantage that

less spectral information is needed to obtain Te thanfor other methods [1, 11]. However, this method isonly applicable when Frec(n) ∼ 1; is sensitive to in-accuracies in ∆L and is susceptible to profile effects(section 2.4). Hence, Te derived in this way shouldbe used as an indicator for trends in Te, instead of anabsolute Te measurement.

We define ∆L as the full-width 1/e fall-off lengthof the ne profile at the target measured by Lang-muir probes in the attached phase, which is mappedalong the flux surfaces to determine ∆L for each pointwhere the DSS view line intersects with the separa-trix. We assume ∆L does not change during the dis-charge, although camera data suggests such a changemight occur [9].

2.3. Obtaining ne from Stark broadening

Spectral lines emitted by plasmas are affected byStark broadening. Our chordal measurement providea density weighted integral of contributions to the lineshape and thus of the electron density [4] (nStark

e ).

3

1012 1014 1016 1018 1020

1017

R L (rec

/m2 s

)ΔL = 1 cm; ne = 5 . 1019 m-3

ΔL = 2 cm; ne = 5 . 1019 m-3

ΔL = 5 cm; ne = 5 . 1019 m-3

ΔL = 2 cm; ne = 1 . 1019 m-3

ΔL = 2 cm; ne = 1 . 1020 m-3

B7->2rec (ph / m2 s)

1019

1021

1023

Figure 3: Modelled relation between the RL and Brec7→2 for a

range of different ne and ∆L.

The Stark broadened line shape of a n → 2 linecan be expressed as a modified Lorentzian [4] as func-tion of ne and Te, which is a parametrisation ofthe Microfield Model Method [12]. The spectrom-eter induces additional instrumental broadening tothe emitted spectral line, which is parametrized usinga modified asymmetric Lorentzian whose parametersare obtained as function of wavelength and viewingchord.

The experimentally observed Balmer line shape isfitted using a numerical algorithm based on Gradi-ent Expansion Algorithm [13]. The fitting functionused is the convolution of Stark broadening, Dopplerbroadening (depends on Ti) [14] and the instrumen-tal line shape. Magnetic effects are neglected. Tolower the amount of fitting parameters it is assumedTe = Ti = 3 eV. For Te between [0.2 − 15] eV, thevariations in nStark

e are < 0.1%. For Ti between[0.2− 15] eV the variations in nStark

e are < 10%.The main parameter leading to measurement un-

certainty in nStarke is the signal/noise level. By fit-

ting synthetic spectra with a level of random noise,we have determined the measurement uncertainty ofnStarke as function of ne, S/N level and viewing chord.

We have used the 7→ 2 line for determining nStarke ,

since higher-n Balmer lines lead to wider Stark broad-ening.

2.4. Investigating profile effects on nStarke , Te and re-

combination measurements

The sensitivity of the nStarke , Te and recombina-

tion measurements to profile effects has been investi-gated by using various a priori ne, Te and no profiles,including hollow, flat and peaked (Gaussian) profileswith a width varying from 0.5 - 7 cm. For peakedprofiles, peak densities ne,0 = [3, 5, 10].1019 m−3 andcorresponding peak temperatures Te,0 = [15, 3, 1] eV

have been assumed. A flat neutral density profile us-ing no = [1018, 1019] m−3 has been assumed.

Using these profiles, the Balmer line emission ismodelled at every point of the profile and the cor-responding Stark line shape is calculated. The Starkline shapes, weighted by the Balmer line emission, aresummed over all points of the profile and the nStark

e ,RL and Te are inferred using the methods describedin sections 2.2 and 2.3.

Assuming peaked ne profiles, nStarke is in between65 - 100 % of ne,0. RL obtained from the syntheticspectrum deviates < 5% from RL obtained by inte-grating the local recombination rate over the profile,except for cases with a strongly hollow ne. For peakedTe profiles with sufficiently low peak (Te,0 < 2 eV)the Te obtained from the synthetic spectrum is inbetween 50 - 100 % of Te,0.

3. Experimental results

In this section we will use the DSS data and analy-sis techniques described in section 2 to illustrate howdivertor conditions vary as detachment proceeds inTCV. Connections will be made to other diagnosticmeasurements to form a more complete picture of thedetachment process. Our observation is that some ofthe characteristics of detachment on TCV are simi-lar to that found at other, higher density, tokamaks.However, detachment in TCV does not lead to a largemovement of the recombination region.

3.1. Onset, evolution and dynamics of detachment

A reference plasma discharge is utilized for illus-trating the process of detachment in TCV (#52065).It has a single null magnetic divertor geometry with aplasma current of 340 kA and a reversed toroidal fielddirection (∇B away from the x-point). The spectro-scopic data has been acquired at 200 Hz and has beenaveraged over 2 viewing chords and a number of timeframes to improve S/N level, as indicated in the leg-ends in figure 4. The line colour and line style shownin figure 4A-H correspond to the diagnostic locationsshown in figure 1B. Similar detachment characteris-tics as observed for #52065 have been found for ∼ 20other density ramp discharges, with slight variationin timing of changes (e.g. drop in target density) andmagnitude (e.g. the total recombination).

Bolometry and spectral features consistently in-dicate an expansion of a cold plasma region from thetarget towards the x-point during a density ramp.

4

C: H: Frec (n = 7) - DSS (tavg = 100 ms)

H: Te [eV] - DSS (tavg = 100 ms, B7 -> 2) LP - Sep (I-V �t) LP - Sep (Jsat + ne-DSS)

G: RL [1020 rec. / m2 s] - DSS (tavg = 100 ms)

A: Greenwald fraction <ne>/nG - FIR

0.3

0.4

0.5

0.7

0.6

40

60

80

D: ne [1019 m-3] - DSS- Stark (n = 7, tavg =100 ms) LP - Seperatrix

1

3

5

7

0.8

0.6

0.4

0.2

2

4

6

8

10

F: Particle �ux [1021 part./s] LP - Toroidally integrated DSS (tavg = 10 ms) RV (x 10)

ne2

x 10

Time (s)0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

Time (s)0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

2

6

10

14

18

4

8

12

16

B: B7 -> 2 [ph / m2 sr s] - DSS, tavg = 100 ms

1016

1017

E: Line integrated emissivity[kW/m2] - (bolometry)

Figure 4: Temporal evolution of several quantities measured by DSS and derived using DSS data for three view lines during asingle null density ramp shot (52065). In addition, data obtained from Langmuir probes (LP) and bolometry is shown. Thecolours of the plot indicate the measurement locations shown in figure 1B.

During a considerable increase in Greenwald frac-tion from ne/nG = 0.4 to ne/nG = 0.6 (figure 4A,F76 increases resulting in an increase in Frec(n = 7)from ∼ 0 to ∼ 1 (figure 4C). Significant increasesin Frec first occur near the target and later the re-gion of enhanced Frec expands towards the x-point,indicating an expansion of the recombining region.The radiation front as measured by bolometry (figure4E), which is representative of higher temperaturesthan those at which recombination occurs [9, 15],also moves from the target towards the x-point andprecedes the expansion of the recombining region(Frec > 0.5).

All the various spectral features are consistentwith a strong recombining region near the target.Those features include a strong increase in B6,7→2

(figure 4B) which, combined with a rising Frec(n =7), implies that RL (figure 4G) is strongly increasing.

Similar to trends in Frec, the onset of this non-linearincrease starts first close to the target and later in-creases closer to the x-point. The increase in B7→2

during the density ramp is both due to the ne in-crease (figure 4D) and Te decrease (obtained fromB7→2 when Frec(n = 7) > 0.5 - figure 4H).

Our results suggest that recombination is insuf-ficient to effectively reduce particle flux and densityclose to the target. After Frec(n = 7) → 1, B6,7→2,RL and nStark

e keep increasing until the end of thedischarge while remaining highest at the lowest DSSchord 5 cm above the target. At first glance this andbolometric measurements (figure 4E) would seem toindicate that while ionization and impurity radiationhave detached from the target, the high density re-gion has not. But clearly the density has dropped atthe target (figure 2D).

It is possible that the inferred RL is an under-

5

estimate, since the closest target DSS view line in-tersects the separatrix 5 cm above the strike point.If the RL spatial profile is extrapolated to the tar-get, RL at the target is three times higher than atthe DSS chord closest to the target. However, targetprobe measurements (figure 4D) indicate ne dropsin this non-observed region, which would lower RL.The high-density recombination front is located inthe region between the target and the lowest DSSchord. Detachment in TCV has so far never reachedthe level where the density and recombination regionpeak moves to points above the lowest DSS chord.

The total recombination rate in the divertor RV

[rec./s] is determined by integrating RL toroidallyand poloidally across the chords. RV increasesstrongly during the last phase of the discharge (fig-ure 4F), and reaches values of up to RV = (9.0 ±0.35).1021 rec/s, which is ∼ 20% of the total particleflux measured by Langmuir probes at that time.

Although the particle flux measured by the Lang-muir probes drops at 1.0 s, RV at that time is rela-tively low, which indicates that recombination lossesare not the main contributor to the initial particleflux drop. However, at later times, RV could poten-tially contribute to the particle flux drop.

3.2. Recombination signatures compared with Lang-muir probe data

Combining data from the DSS and divertor tar-get Langmuir probe data is informative about thedevelopment of detachment. The peak target elec-tron density determined from Langmuir probe (LP)I-V characteristics is in agreement with nStark

e nearthe target until 0.9 s (figure 4D), which is close to thetime when B6,7→2 starts increasing strongly.

Across many tokamaks it has been found that thetemperature derived from Langmuir probes is over-estimated for Te < 5 eV, [16, 17]. Assuming this isalso true for TCV, we utilize Jsat and nStark

e (5 cmfrom the target) to calculate Tmod

e (figure 4H). Tmode

decreases during the density ramp in agreement withthe Balmer line derived Te up until 0.9 s when thetarget particle flux starts dropping. Past that timeTmode is lower than the Balmer-derived Te, most likely

because the density in the two locations (DSS chordand probe) differs.

After 0.9 s also ne (LP) start to drop, while nstarke

5 cm away poloidally continues to increase. Alterna-tively, we can use Jsat and the Balmer-line derivedTe to determine nmod

e . nmode has the same time be-

haviour as the Langmuir-derived ne, but has a largervalue.

4. Discussion

The onset of detachment observed spectroscopi-cally at TCV is generally similar to the dynamicspreviously observed at higher density machines, butthere are also significant differences.

As the core density is increased in L-mode plas-mas, the target density increases and the tempera-ture decreases, which are general characteristics of ahigh-recycling divertor. However, the ion current tothe target does not increase ∝< ne >

2 as expectedfrom the two point model (assuming ne,up ∝< ne >)[15] (figure 4G). This difference to other, high den-sity machines and the 2-point model may be due tothe fact that the ionization mean free path in TCV(λioniz ∼ 5− 10 cm) is larger compared to the widthof the divertor plasma (dfan ∼ a few cm) near thetarget [10]. Together with the open nature of thedivertor, neutrals are not well-confined, thus leadingto less ionization and a slower rise in divertor den-sity. That slows down the rise in charge exchangeand recombination processes, thus slowing down thedetachment process.

Once the detachment process starts with the dropin divertor target density and the rise in recombi-nation signatures (Frec and RL, figures 4C and 4H)the process of detachment proceeds slowly. Insteadof a swift movement of the recombination and high-density regions, observed at other higher density ma-chines [1, 5], the recombining region and peak densitystays near the target at TCV while recombinationsignatures extend towards the x-point. At the high-est core and divertor densities in the TCV plasmasstudied so far, the drop in target density (figure 4D)concurrent with the continued increase in the DSS-inferred density indicates that the detachment region(in the sense of both low density and low tempera-ture) has moved off the target slightly, less than the5 cm corresponding to the lowest DSS chord. How-ever, that movement is very slow given that the Stark-derived density continues to rise throughout the re-mainder of the discharge.

The inference of recombination rates through theDSS data analysis also provide some insight intothe role of recombination in removing ions from theplasma and causing a density drop. As discussed ear-lier, recombination remains highest near the targetthroughout the discharge, with the total amount ofrecombination rising rapidly to levels at the end of thedischarge comparable to the target ion flux. Giventhat the target density drops earlier in the pulse andthat the total recombination rate is less than 1% of

6

the particle flux at the point the particle flux startsdropping, the question is whether recombination isplaying an important role at this time. The two pos-sibilities are that the ion source upstream could startdropping at the same time as the target density falls.Or, that the recombination local to the flux tube ofthe peak ion flux is removing significant ion flux. Wedo not have enough spatial information at this timeto comment further on the relative important of thetwo effects.

5. Summary

The physics of the TCV divertor, including the de-tached regime, has been investigated at TCV, using anewly developed divertor spectroscopy system (DSS),together with advancements in techniques for extract-ing information from the Balmer spectrum. Analysisof the DSS data has been instrumental in character-izing the behaviour of detachment in TCV. We findthat the detachment process develops slowly: the ra-diation first peaks near the divertor and then movestowards the x-point. The rise in the dominance ofrecombination signatures over excitation follows themovement of the radiation peak, while the strongestlevel of density and recombination remains close tothe target. Even as the plasma density above thetarget continues to increase, the density at, and ioncurrent to, the target drop, implying that the de-tached, low pressure and density region has movedoff the target. But within the density range studiedon TCV, the detachment front moves no further.

The role of recombination in ion loss has been in-vestigated. We find that there is no clear connectionbetween the ion current drop at the target and thelevel of recombination and further studies are needed.

6. Acknowledgements

This work has been carried out within the frame-work of the EUROfusion Consortium and has re-ceived funding from the Euratom research and train-ing programme 2014-2018 under grant agreement No633053. The views and opinions expressed herein donot necessarily reflect those of the European Com-mission.

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