INSTITUT OF PHYSICS PUBLISHING and INTRNATIONAL ATOMIC NRGY AGNCY NUCLAR FUSION Nucl. Fusion () 63 7 doi:.88/9-//3/ Helium exhaust experiments on JT wi Type I LMs in H-mode and wi Type III LMs in ITB discharges K.-D. Zastrow, S.J. Cox, M.G. von Hellermann, M.G. O Mullane 3, D. Stork, M. Brix, C.D. Challis, I.H. Coffey, R. Dux 6, K.H. Finken, C. Giroud, D. Hillis 7, J.T. Hogan 7, K.D. Lawson, T. Loarer 8, A.G. Meigs, P.D. Morgan, M.F. Stamp, A.D. Whiteford 3 and JT FDA Contributors a uratom/ukaa Fusion Association, Culham Science Centre, Abingdon, UK FOM Instituut voor Plasmaphysica, Associatie uratom, Nieuwegein, The Neerlands 3 Department of Physics, University of Straclyde, Glasgow, UK Forschungszentrum Jülich GmbH, IPP, uratom Association, Jülich, Germany Department of Physics, Queens University, Belfast, UK 6 Max-Planck-Institut für Plasmaphysik, uratom Association, Garching, Germany 7 Oak Ridge National Laboratory, P.O. Box 8, Oak Ridge, USA 8 Association URATOM-CA sur la Fusion, CA Cadarache, St Paul-lez Durance, France Received 3 April 3, accepted for publication December Published February Online at stacks.iop.org/nf//63 Abstract An analysis of helium exhaust experiments on JT in e MkII-GB divertor configuration is presented. Helium is pumped by applying an argon frost layer on e divertor cryo pump. Measurement of e helium retention time, τhe, is performed in two ways: by e introduction of helium in gas puffs and measurement of e subsequent decay time constant of e helium content, τhe d ; and by helium beam injection and measurement of e helium replacement time, τhe r d. In LMy H-mode, wi plasma configuration optimized for pumping, τhe 7. τ is achieved, where τ is e ermal energy replacement time. For quasi-steady internal transport barrier (ITB) discharges, e achieved τhe r. τ is significantly lower. The achieved helium recycling coefficient, confirmed by an independent measurement to be R eff.9, is e same in bo scenarios. None of e discharges are dominated by core confinement. The difference in τhe is instead due to e confinement properties of e edge plasma, which is characterized by Type I LMs for e H-mode discharges studied, and Type III LMs for e quasi-steady ITB discharges. This difference is quantified by an independent measurement of e ratio of e helium replacement time wi a helium edge source to e energy confinement time. PACS numbers:..fa,..pi,..rk,..fi,..vy. Introduction Control of helium ash produced in D T reactions is one of e key issues affecting e performance and possibly e achievable burn time of a fusion reactor. The removal of helium is determined by a combination of e intrinsic transport of helium in e plasma, especially across internal and edge transport barriers, e enrichment and compression of helium in e sub-divertor region, and e pumping and refuelling efficiency for helium. Thus, e task is one of system integration and is only partially determined by plasma physics. The overall engineering requirement is a See annex of J. Pamela et al Fusion nergy ; Proc. 9. Int. Conf. (Lyon ) (Vienna: IAA). best stated [] in terms of e ratio of e helium retention time, τhe, to e ermal energy confinement time, τ, since effective α particle heating is essential in a burning fusion plasma. If small levels of additional impurities are present, e requirement is τhe to obtain steady-state burn conditions. Wi additional impurities, e requirement becomes more strict, e.g. τhe would be required if carbon concentrations were of order 3%. The target for e pumping arrangement is specified in terms of e helium enrichment factor, η, i.e. e ratio of e partial pressures of helium and deuterium in e sub-divertor region (at e pump roat) to e ratio of He + to D + in e plasma core, which needs to be larger an. for stationary operation of ITR []. 9-//363+3$3. IAA, Vienna Printed in e UK 63
K.-D. Zastrow et al A recent review of e research on helium transport and exhaust has been written by Hogan [3]. In most experiments, helium is introduced by gas puffs and e decay time constant of e helium content, τhe d, is studied. On DIII-D and JT-6U, helium neutral beam injection (NBI) was used to provide a central source [ 7] so at e replacement time, τhe r, can be measured. In L-mode and LMy H-modes it was always found at e helium exhaust rate is limited by e pumping efficiency and not by e helium transport in e plasma edge, let alone e plasma core. The achieved ratio τhe (measured by eier of e two techniques) has been low enough and it has been shown at helium can be pumped at a satisfactory rate by divertor pumping, which is e meod used in e majority of experiments, and also wi pumped limiters [8]. Improved core confinement by e formation and sustainment of internal transport barriers (ITBs) is seen as a possible route to steady-state tokamak operation because of e potential of is regime for full non-inductive current drive. However, helium removal from e region confined by e ITB might not be fast enough and would us limit e burn time. Results from experiments in JT-6U ITB discharges indicate increased helium retention in e region confined by e ITB by factors of between two and ree [6], and due to reduced diffusivity by a factor of five to six [9]. Also, ere is concern at, since ITB discharges to date tend to be characterized by lower edge density an LMy H- mode plasmas, e potential for pumping of helium might be reduced. To investigate bo issues, a series of experiments was conducted on JT during helium plasma operation. For comparison, we also report re-analysed results in LMy H- modes from earlier experiments in is paper. In [], two characteristic times have been introduced to quantify retention, e replacement time for a central source, S, defined as τ = N He /S and e replacement time for an edge source, S edge, defined as τ edge = N He /S edge. N He is e plasma helium content at is sustained by e source in each case. In is context, e edge is a region of closed flux surfaces close to e plasma boundary and should not be confused wi e Scrape-Off Layer (SOL), which is a region of open field lines. Note at in is paper we use symbols different from ose in [], namely an index at refers to e location of e source ( and edge ). The definition is e same. In a numerical model bo τ and τ edge can be readily calculated, whereas in experiments only τ edge can be measured. This is because e effect of helium recycling cannot completely be removed, so an experiment wi only a central source cannot be performed. The relationship of e observed retention time to refuelling efficiency, f, and recycling is given by equations (.6) and (.) from [], which we reproduce here: τ R eff = τ + τ edge, () R eff R eff = R ret f, () ( f)r ret where R ret is e fraction of helium returning from e wall and divertor and R eff = Ɣ ion /Ɣ out is e fraction of e helium outflux, Ɣ out, at is returning to e confined plasma as an edge influx, Ɣ ion, of helium ions. The prediction of R eff for ITR cannot be e subject of experimental studies on existing devices since R ret depends on divertor geometry and e helium pumping speed, and f depends on e details of e SOL plasma. Bo of ese are likely to be very different, and require modelling [] to be assessed. The goal we have set ourselves in is study is to determine e contribution of τ edge to τhe for each operational regime, which can potentially be scaled to ITR. In all experiments reported in is paper we make use of e helium pumping capability of e JT pumped divertor. Details on e pumping arrangement and calibration of e pumping speed for helium are given in section. The results on helium retention in LMy H-mode discharges are presented briefly in section 3. Helium ash simulation experiments in quasi-steady ITB discharges are presented in detail in section and e results from all regimes are compared in section by independent measurements of R eff and τ edge. We have used two different techniques to study helium retention, measurement of e time constant of e decay of e total helium content, τhe d, and measurement of e replacement time for e total helium content, τhe r. A comparison of ese techniques, from a model point of view, is presented in appendix A and a discussion of statistical and systematic errors in e experiments in appendix B.. Helium pumping scheme in e JT MkII-GB divertor All experiments presented in is paper were performed during campaigns wi e JT divertor in e MkII-GB configuration []. Helium can be pumped by applying a layer of argon frost on e divertor cryo pump (ArFCP). The pumping speed for helium on e vessel, S V (He), has been characterized as a function of various argon frost coatings using sequential helium and deuterium gas pulses. The calibration established e systematic behaviour of e pumping speed as a function of e ratio of e D + He gas condensed on e supercritical helium cooled panels to e amount of argon frost condensed, i.e. N(D +He)/N(Ar), termed saturation. This ratio is a function of time into each discharge and has to be evaluated to obtain e rate of helium removal during e experiment. The pumping speed for helium is a universal function of e amount of argon laid down in e most recent frosting; specifically it does not depend on e ickness of e argon layer and a refresh layer restores S V (He) to its original value. The maximum values at could be achieved were S V (He) = 8 9 m 3 s. For comparison, e pumping speed of e divertor cryo pump for deuterium on e JT vessel is S V (D ) = m 3 s []. The helium pumping speed on e vessel was measured to be S V (He) = m 3 s after a JT discharge using puffs of helium gas into e torus. These results are shown in figure. The effect of loading on e argon layer did not have quite e same effect as in e earlier gas-only calibration runs, showing at e effect is dependent on e way deuterium is introduced. Specifically, e pumping speed for e same level of calculated saturation was higher after a plasma discharge an after gas-only deposition. However, no difference is seen depending on e way helium was introduced in e discharge preceding e calibration pulse, i.e. wheer by gas puff or by beams. 6
S (m 3 / s) 8 6 After He gas After He NBI Before Discharge Helium exhaust experiments on JT Finally, we note at e mean helium removal rate of e JT ArFCP wi strike points in e corner configuration is S Div (He) p Div (He) m 3 s 3. 3 Pa.8 Pa m 3 s. () Thus, e ratio of e removal rate to plasma volume (S Div (He) p Div (He)/V P wi V P 8 m 3 for JT) is similar to e design basis ratio for ITR, i.e..3 3 Pa s for JT compared to.8 3 Pa s for ITR []. 3. Rate of decay of helium content in Type I LMy H-mode N (D +He) / N (Ar) (%) Figure. Pumping speed for e argon frosted divertor cryo pump on e vessel, as a function of e saturation of e argon frost layer wi deuterium and helium. The pumping speed is measured using helium gas puffs into e vessel after e discharge. N(D +He) is calculated from a measurement of e sub-divertor pressures for helium and deuterium and e pumping speed of e divertor cryo pump on e sub-divertor region. N(Ar) is e amount of argon applied in e most recent frost. After a discharge, e pumping speed can be restored by repeated argon frosting until a total of 6 Pa m 3 of argon has been deposited on e pumps. At higher deposition values argon may be released, which degrades e plasma purity, and carries e risk of causing disruptions. In figure e saturation is calculated from e amount of argon applied in e most recent frost (typically 3 Pa m 3 in e first frost and Pa m 3 for refresh layers), and by integrating in time e amount of helium and deuterium at was condensed on e pump. The calculation uses e time resolved measurement of e partial pressures p of helium and deuterium in e sub-divertor region, obtained from Penning gauge spectroscopy [3, ], and e pumping speeds S Div on e sub-divertor region for e two species: N(D +He) = (p(d ) S Div (D ) kt +p(he) S Div (He)) dt. (3) The saturation is dominated by e amount of deuterium, since is is e majority species and because e pumping speed for deuterium is higher and not dependent on e saturation of e cryo pump. The pumping speed for helium is self-consistently calculated using e saturation as a function of time and interpolated using a cubic spline fit to e data in figure (shown as a solid line) for e pumping speed itself. We use S Div (D ) = m 3 s [] and assume S Div (He)/S V (He) = / at all times. All measurements for partial pressures and pumping speed, as well as for e amount of argon used in e frost, are referred to room temperature []. JG3.6-c All LMy H-mode discharges were performed at.9 T,.9 MA and wi MW of NBI heating. The configuration chosen had an elongation of.68.7, and a triangularity of.6.3. The discharges had Type I LMs and achieved a ermal confinement enhancement factor as given by e IPB(98(y,)) scaling law [6], of..3. The discharges had low Z eff based on e local measurements of impurity densities (He, Be and C) wi little sign of argon. A detailed study on helium enrichment on JT, which includes some of ese discharges, has previously been published by Gro et al [3]. Therefore, we only discuss e results for rate of decay of e total helium content following short ms gas puffs, τhe d, in is section. The achievable helium removal rate is affected by e location of e divertor strike points due to changes in e conductance for neutrals between e main chamber and e sub-divertor region [3]. To illustrate is, a comparison of a corner strike zone (C) discharge wi a vertical target strike zone (VT) discharge is shown in figure. The measured decay time constant of e helium content, τhe d, is much lower in e corner configuration, due to e enhanced pumping of helium arising from e higher pressure at e pump roat. At is elevated exhausted flux, a value of τhe d 7. was achieved, well wiin e range required by a reactor. The decay time of e helium density was similar at all radii wiin e plasma. The helium profile us relaxed in a self-similar manner wi n He /n He remaining approximately constant. We find at τhe d is independent, of heating power over e limited range tested. Strong deuterium gas puffing from e midplane tends to cause τhe d to increase by about %, but is is mainly because τ declines as e electron density increases in e gas puff discharges, where e electron density reaches about 7% of e Greenwald density. We did not try deuterium gas puffing from e divertor during ese experiments. We note at is has been found on JT-6U [7] to enhance e helium pumping rate. The results are reproducible even across long periods of plasma operation, i.e. under different vessel conditions. We repeated discharge #636 in e beginning of e experiments on helium ash simulation as discharge #36, more an two years later, and obtained e same τhe d. This reproducibility is robust to e apparent difference in LM behaviour. For #636 e amplitude of e Dα signal was noticeably increased following e He puff and remained so during e helium decay (see figure ). For #36 e LM amplitude did not change (see figure 6). This illustrates at some edge perturbation can be tolerated in gas puff experiments, as long as e confinement regime itself is not changed. 6
K.-D. Zastrow et al (MW) ( 9 / m ) ( 9 ) (s) 6 <n e > D Helium Content Decay Time 6 P NBI Pulse No: 636 (C) Pulse No: 69 (VT) (.9 T,.9 MA) 6 8 Figure. Comparison of e decay of e helium content for two LMy H-mode discharges (.9 T,.9 MA) at constant input power for two different strike point configurations. The discharge wi e strike points in e corner ( and ) exhibits a faster helium removal rate an e one wi e strike points on e vertical target (----and+).. Helium ash simulation experiments in ITB discharges On JT it is found at impurities accumulate in e region confined by e ITB in discharges wi large values of β N (strong ITBs) at high magnetic field (see [7] and references erein) wi higher Z impurities exhibiting e strongest peaking. This has been explained by a reduction of e turbulence driven diffusion coefficient, D, in e presence of inward convection, v, where e latter was found to be in agreement wi neo-classical predictions. As shown in figure 3, helium is also subject to is accumulation. The helium density in e region confined by e ITB (shown at R = 3. and 3.3 m) increases while it decreases outside e ITB footpoint (shown at R = 3.7 and 3.8 m). While is is interesting in its own right, it does not answer e question of what e ratio of helium replacement time to ermal energy confinement time, τhe r, would be wi a central source under ese conditions. The reduced diffusion, which acts on e gradient, can easily result in strongly peaked density profiles wi a central source (see appendix A), but en again e same reduction in turbulence will be responsible for e improved energy confinement time, and it is only e ratio of ese at we are concerned wi. If e peaking is mainly due to inward convection, is may not be very efficient at retaining a central source since it acts on e density (see appendix A). The more radial structure ere is in e transport coefficients, e more important it becomes to conduct experiments at measure e replacement time wi a central source raer an e decay time of e helium content after a puff (see appendix A). In addition, ITB discharges on JT rely on a low edge density, and erefore we find at, when helium JG3.6-c ( 8 /m 3 ) (MW) ( 6 /s) Pulse No: 378 (3. T,. MA) Neutrons LH Helium β N NBI Puff RF 3. m 3.3 m 3.7 m 3.8 m 3 6 7 8 9 Figure 3. Helium is slowly introduced by gas puff into a discharge wi reversed q-profile prior to ITB formation. Helium is not pumped (but ere is good potential for pumping, i.e. η =.79 ±.3). The observed changes in e helium density profile reveal changes in v/d, as shown in e bottom part of e figure (two chords wi radii enclosed by e ITB and two chords wi radii outside e ITB footpoint are shown). ITBs are first formed on e reversed q profile region (t =. s). The first strong ITB is located at q = 3(t = 6. s). To avoid e β limit, e power is stepped down (t = 6.9 s), e subsequent loss of e ITB results in a redistribution of helium. The second strong ITB is located at q = (t = 8. s). is puffed in e same way as in LMy H-mode discharges (see section 3), a back transition is triggered due to e increased edge electron density. The helium retention time in ITB discharges was, erefore, studied using helium neutral beams to provide a central source, to simulate e production of helium ash in a burning core. To is end, one of e two JT beam systems was converted to helium beams wi an injection energy of 7 kev. For e discharges in is study, 6% of e helium is deposited wiin r/a., i.e. wiin e region enclosed by core ITBs. For is paper we chose to study two different ITB scenarios, as illustrated in figures 6, at.63 T/. MA and at 3. T/. MA. The latter is a quasi-steady-state ITB scenario where lower hybrid current drive and heating (LHCD) was used to slow down e current profile evolution. Bo make use of a LHCD prelude phase to create a reversed q-profile at e onset time of e main heating [8]. Since helium beams have a larger shine rough, it was necessary to develop scenarios wi higher line average density an is normally e case on JT. The observed dynamics are very similar, and ere are no fundamental differences between ese discharges and more typical ITB discharges. Weak ITBs are formed in e region of e reversed q-profile for all ese discharges, and in addition stronger ITBs are formed when e minimum in e q-profile reaches rational values, but ese collapse quickly as e q-profile continues to evolve (see figure 6). At least MW of beam power is required for strong wide ITBs, as shown in figure 3, and ey were erefore not accessible (see [9] JG3.6-3c 66
Helium exhaust experiments on JT (m 9 /m ) ( 9 ) (MW) D-NBI LH Helium Content dge <n e > 3 β N He-NBI (.63 T,. MA) RF 6 7 8 9 Figure. Comparison of ree ITB discharges wi identical current profile evolution and heating power (LH and RF heating are only shown once for clarity; ). Wi 8 MW of D beams and MW of helium beams, but wiout helium pumping (- - - -), e edge density is increased compared to e D only reference pulse ( ). Wi helium pumping ( ), e edge density is controlled, and a reduction of e helium core concentration from % to 6% is achieved. The discharge does not reach e same value of β N as e reference pulse, because of e larger shine rough of helium beams compared to deuterium beams. for a detailed discussion of e requirements on JT for ITB formation on e one hand and access to high performance ITBs on e oer). Quasi-steady-state helium exhaust is provided by e ArFCP for e whole time, alough e reduction of e helium pumping speed becomes noticeable towards e end of e heating phase, and as a consequence e derived helium replacement time increases (illustrated in figure by e rising helium density in e core). In addition, e use of e ArFCP provides effective edge density control by reducing e helium recycling flux, as shown in figure, for up to s wi MW of helium beam power, and up to 3 s wi 3 MW. The discharges exhibit Type III LMs roughout e helium beam injection phase. For e two discharges wi helium beams in figure, e helium enrichment factor η is.8 ±.8 wiout e ArFCP, and. ±. wi ArFCP. These values demonstrate at e low edge and SOL density of ITB discharges does not impede helium removal. The discharge in figure wi ArFCP has e best value for τhe r = at was obtained at.63 T/. MA, because of its improved energy confinement as indicated by its value of β N =.. The results obtained in a scan of e helium source rate at oerwise constant time evolution in e two ITB scenarios (as shown in figures and, respectively) is shown in figure 7. /τ /τ The figure shows τhe r, e achieved helium enrichment and, for reference, e corresponding values of β N, averaged during e phase when e helium content was in steady state. The helium source rate was varied by using one, two or ree helium sources (positive ion neutral injectors; PINIs), respectively. JG3.6-c ( 8 /m 3 ) (kev) (MW) ( /s) Pulse No: 39 (3. T,. MA) Neutrons. LH T i Helium RF NBI 3.m 3.8m 3.7m 3.m 3.8m 3.7m 6 8 Figure. ITB discharge wi identical current profile evolution and heating power as e discharge shown in figure 3 up to =.8 s. Wi MW of helium beams (black bar), e edge density (not shown) is controlled for s, while e pumping speed for helium decreases during is time as indicated by e slight increase of e helium density in e core. The formation of e q = 3 ITB at t =.6 s and e q = ITB at t =. s and eir collapse can be clearly observed in e neutron yield, central ion temperature and helium density profile. In between ese events, ITBs form and collapse rapidly in e region of e plasma where e q-profile is reversed, which is e reason for e observed fluctuations on neutron yield, central ion temperature and to some extent central helium content. Radial profiles for is discharge are shown in figure 6. The highest helium source rate (.3 s ) is equivalent to at produced by 3 MW of α heating, i.e. a total fusion power of 66 MW.. Comparison of helium retention in LMy H-mode and ITB discharges The database for e regime comparison consists of discharges wi bo experimental techniques (τhe d for LMy H-modes, τhe r for ITB discharges). The systematic differences expected for ese two meods in identical plasma conditions is discussed in appendix A. We expect τhe d <τr He. This means at, if τhe d r was lower in LMy H-mode an τhe in ITB discharges, e difference could be due to e experimental technique. In contrast, we find at e lowest τhe d at was achieved in LMy H-mode discharges is significantly larger an e lowest τhe r <τr He in ITB discharges. Note at from here on we will only refer to e helium retention time τhe for simplicity. The results are shown in figure 8 where τhe and e helium enrichment factor are plotted against edge plasma density for all discharges, including variation in ICRH and helium beam heating power beyond e range selected for figure 7. The figure contains only discharges wi an optimized strike point configuration for pumping, i.e. a corner configuration. LMy H-mode discharges in e vertical target JG3.6-c 67
K.-D. Zastrow et al ( 8 /m 3 ) ( 9 /m 3 ) (kev) ( /s) Pulse No: 39 (3. T,. MA) Neutrons n e T i 6 8 T e. Helium 3. 3. 3. 3.6 3.8 R (m) Figure 6. Radial profiles of electron and ion temperature, as well as electron and helium density, for e discharge shown in figure. The ITB is located in e core ( 3.3 m) and does not expand to large radii. The magnetic axis is at R = 3. m for is shot. The panel at e top is reproduced from figure to indicate e time of e profiles relative to e time evolution of e discharge. configuration have been excluded. ITB discharges were only performed in e corner configuration. Also shown in figure 8 is e ermal confinement enhancement factor as given by e IPB(98(y,)) scaling law [6]. This demonstrates at e low edge confinement in ese particular ITB discharges is not offset by an increased core confinement. In equation () ere are ree terms at could potentially differ between ese regimes, namely e retention time for a central source τ, e retention time for an edge source τ edge, and e effective recycling coefficient R eff. We cannot measure τ directly, but we can measure e oer two terms, which we elaborate in e following. First, taking a time t < t before e helium puff or before e start of helium beam injection when e total helium content,n He, is in steady state (see appendix B), we can determine e total helium influx under e assumption of toroidal and poloidal symmetry from τ edge = N He Ɣ edge, () ( ) S Ɣ edge = πa P I 3.. (6) XB He +,3. Here I 3. is e line of sight integrated intensity, measured by a vacuum UV spectrometer wi a line of sight located in e geometric midplane of e vessel, of e He + line at λ = 3. nm, absolutely calibrated in ph/(m sr s). A P is e plasma surface area and S/XB is e measure of ionizations per photon [] for is spectral line. The coefficient is evaluated for each discharge using atomic data taken from JG3.6-6c... τ He / τ *. 3. T /.MA.63 T /.MA β N (p He / p D ) / (N He / N e ) He-Beam Source ( 9 /s) Figure 7. Overview of results, averaged during e phase in each discharge when e helium content is in steady state, for τhe r and helium enrichment factor η wi helium pumping for two reversed q-profile scenarios. The best value for τhe r was obtained for e.63 T/. MA discharge shown in figure 3, because of its improved energy confinement as indicated by its value of β N =.. The heating power to form an ITB wi e values of β N at 3. T/. MA as in figure 3 while retaining edge density control was not available due to e conversion of half e beams to helium, and only core ITBs were obtained as shown in figures and 6. JG3.6-7c ADAS [], and turns out to be a weak function of density and temperature, wi an average value of about. for e plasma conditions in e edge of JT. Active pumping of helium is crucial in order to make is measurement, since wiout it e helium level would not be in steady state. In e following, we make e assumption at τ edge does not change after e gas puff or during helium beam injection. In e case of e ITB discharges is assumption is probably incorrect, since e total heating power also increases when e helium beams are injected, see figures 3. For e example of e discharge shown in figure 3, where we can measure τ edge roughout e whole time evolution, we find at τ edge decreases from an initial value of about. (before e formation of e strong barrier) to. at e peak of e neutron yield. As defined in e introduction, R eff = Ɣ ion /Ɣ out is e fraction of e helium outflux, Ɣ out, at is returning to e confined plasma as an edge influx, Ɣ ion, of helium ions. This can be measured independently, since we can make a measurement of Ɣ ion, again based on e intensity of e He + line at 3. nm but is time after e gas puff or during helium beam injection. In addition, we can perform a calculation of e rate at which helium is pumped, Ɣ out, considering two terms representing e wall and e ArFCP, us R eff = Ɣ ion Ɣ out = Ɣ edge Ɣ edge + Ɣ pump = Ɣ edge Ɣ edge (+ε Wall ) + Ɣ ArFCP. (7) 68
Helium exhaust experiments on JT H-Mode ITB 3.T /.MA τ* / τ ITB.63T /.MA H-Mode (C) H-Mode (VT) L-Mode ITB 3.T/.MA ITB.63T/.MA IPB98 (y,). τ* / τ.. (p He / p D ) / (N He / N D ). 3 n e, edge ( 9 m -3 ) Figure 8. Overview of results for τhe and helium enrichment factor as function of edge density. Also shown is e confinement enhancement factor. Up to ree data points are taken in each discharge, and results averaged during. s. The error bar reflects e variation of e data wiin each. s interval. All results are obtained wi plasma configuration optimized for pumping, i.e. strike points in e corner on e horizontal target of e Mark II-GB divertor, but at varying pumping speed due to variations in e saturation of e ArFCP. Table. Constants quantifying e helium exhaust for e four regimes studied in is paper. The solid lines in figure 9 and e x-axis for e data in figure are calculated using ese coefficients. ε Wall L-mode (.9 T/.9 MA).. LMy H-mode (.9 T/.9 MA).7.9 ITB at (.63 T/. MA).. ITB at (3. T/. MA)..8 τ edge /τ The rate Ɣ ArFCP of helium pumped by e ArFCP can be determined from e sub-divertor partial pressure of helium and e pumping speed for helium (see section ). The fraction of helium pumped by e wall, defined here as ε Wall = Ɣ Wall /Ɣ edge, can be estimated from e reference discharges at we performed for each scenario wiout active pumping, i.e. for Ɣ ArFCP =, making e assumption at τ = and using e measurement of τ edge from equation (6). Note at using is definition, ε Wall is related to a measurement of R eff and, erefore, ( ε Wall ) R ret ; see equation (). Specifically, ε Wall is not only a property of e wall, but also includes e properties of e SOL plasma. One consequence of is is at e result differs for each regime studied; see table. The result is not sensitive to e assumption for τ = since e decay or replacement time wiout active pumping is in e range τhe 8. We can now combine all measurements in a single plot of against R eff, and is is shown as figure 9. The solid τ He /τ JG3.6-8c.8.9.9. R eff Figure 9. Overview of results for τhe plotted against e independent estimate of effective recycling coefficient as obtained from a measurement of e influx and a calculation of e pumping rate, including removal by e ArFCP and by wall pumping. The curves represent + τ edge R eff/( R eff ) using e average of e measured τ edge for each of e regimes, see table. H-mode data follow e same curve for corner (C) and vertical target (VT) configuration. Only ITB discharges wi one helium PINI are included in is figure. Data from discharges wi two or more helium PINIs all lie significantly below e corresponding curve and are not shown, as explained in e text. lines represent + τ edge R eff/( R eff ) where τ edge is e ensemble average for each of e four regimes; see table. All curves are made to pivot around e average τ edge for e shot wi wall pumping, which is e one wi e highest value for R eff for each group. The observed trend for LMy H-mode and L-mode discharges wi active pumping is well reproduced by e curve. Specifically for LMy H-mode discharges, data wi corner configuration and vertical target configuration follow e same trend, e difference in helium exhaust between em being explained by e independent measurement of a different R eff. The L-mode discharges (e data are based on a measurement of τhe d e same as for LMy H-mode) were performed in vertical target configuration. During earlier studies in JT wi e Mark I divertor a pair of discharges wi optimized pumping, one in H-mode and one in L-mode, was performed wi τ (H) =.8 τ (L) and τhe d (H) = (L) [3, ] which is in qualitative agreement wi our result at τ edge (H) =.8 τ edge (L). For ITB discharges, e trend is less well reproduced, and only discharges wi just one helium beam source are close to e trend line. Data wi two or more PINIs (not shown in figure 9) lie well below e trend lines. This is probably due 3.8 τ d He to a reduction of τ edge caused by e increase in heating power, raer an an error in e measurement of R eff.ifwe assume at τ edge can be as low as. (as obtained for e discharge shown in figure 3) we could explain all data. Wi is in mind we can conclude at e best ITB discharges have a much lower τhe an e best LMy H-mode discharges JG3.6-9c 69
K.-D. Zastrow et al τ * / τ H-Mode (C) H-Mode (VT) L-Mode ITB 3.T/.MA ITB.63T/.MA ( τ edge / τ )R eff / (-R eff ) Figure. As figure 8 except e x-axis is e product of e ensemble average τ edge and R eff/( R eff ) instead of R eff. Also shown is one curve to represent unity as well as ree curves wi an offset due to ree assumptions, τ =, and, respectively. JG3.6-c because of e lower value for τ edge at characterizes ese regimes. We can, erefore, take e next step and plot all measurements against τ edge R eff/( R eff ), in figure. The four curves in is figure represent unity, and ree separate curves for different values of τ (e.g., and ). Alough all measurements follow e trend reasonably well, over almost two orders of magnitude, it is not possible to conclude what τ is for each of e regimes because e scatter is too large. Also, it is worwhile recalling at e data for L-mode and LMy H-mode discharges have been obtained from a measurement of e rate of decay of e total helium content and cannot be extrapolated to R eff = even if e scatter was lower, as explained in appendix A. Finally, we note at e agreement between data and prediction using e zero-dimensional model in figures 9 and is only sensitive to errors in e relative calibration between e measurement of e helium content and e pumping rate. Specifically, e absolute calibration of e He + line at λ = 3. nm line cancels. This can be seen when equations () and () to equation (7) are combined τ Ɣ edge = τ + τ edge = τ + N He,t<t Ɣ edge,t>t. (8) Ɣ pump Ɣ pump Ɣ edge,t<t The error in e helium content measurement is of e order of % (see also appendix B) and e error in e pumping rate is of e same order (see section ). When R eff and τ edge are considered separately, e calibration of e influx measurement enters, which is only known to about 3%. Thus, e uncertainty of a prediction of τhe on ITR based on our data is dominated by is measurement because in at case we are only interested in e scaling of τ edge itself. In addition to e error in e calibration, ere is also an uncertainty in e validity of e estimate of e total helium influx from a main chamber, horizontal line of sight, when using equation (6). The approach we have taken can be justified for helium for two reasons. First, e mean free pa of helium atoms of. ev (which corresponds to e vessel temperature) would be cm in a plasma wi conditions as ey exist on top of e edge pedestal in our experiments. Therefore, even e slowest helium atoms are expected to penetrate e SOL and we do not expect a large contribution to e observed emission to originate from e SOL. Second, it has been seen on JT at e poloidal profile of helium emission extends far outside e region close to e divertor, in contrast to at of oer impurities, e.g. carbon [3]. From ese emission profiles we have estimated at e influx derived from a line-of-sight in e geometric midplane is wiin 3% of e true volume integral. If is relationship varied strongly for e discharges in is study, specifically between LMy H-mode and ITB discharges, our approach would not have been able to explain e difference in e measured τ He 6. Summary and outlook /τ between ese regimes. In JT LMy H-modes wi Type I LMs and optimized pumping, e best result we achieved is τhe d 7., where τhe d is e measured decay time of e helium content following short ms gas puffs. The ratio worsens to τhe d /τ wi poorer pumping in e vertical target configuration, because e effective recycling coefficient is increased in is case. The ratio is independent, over e limited range tested, of heating power. The ratio worsens wi strong deuterium gas puffing, principally because τ declines as e Greenwald density is approached. The value of τhe d in L-mode and LMy H-mode is dominated by recycling (i.e. lack of pumping). In JT quasi-steady ITB discharges wi helium beam fuelling, we find <τhe r r <, where τhe is e measured helium replacement time, wi τhe r obtained for e discharge wi e highest value of β N =. wiin e accessible operational space. These results were obtained in quasi-steady-state for a duration of up to τhe r. The value of τhe r in ese discharges is still dominated by edge transport and recycling (i.e. lack of pumping) and none of e discharges exhibit a significant increase of τhe r due to e presence of e ITBs. The helium enrichment factor wi pumping for all ITB scenarios is in e range. <η<.6, which is mainly a reflection of e fact at helium is pumped, noting at wiout pumping, η rises up to.8. We have shown by an independent measurement of R eff at it is possible to explain all observed results for τhe in terms of e differences between e regimes in τ edge, where τ edge is e helium replacement time wi a source at e edge, in contrast to τ, which is e replacement time wi a central source. The largest value τ edge.9 is observed in Type I LMy H-mode discharges, whereas in quasi-steady ITB discharges wi Type III LMs e measurements range between. and.8. This is comparable to L-mode where e one discharge we studied has τ edge.. The properties of e SOL and e sub-divertor make a reduction of R eff to e same value, namely.9, possible in /τ /τ bo regimes, and erefore τhe is lower in e ITBs at we have studied. However, we do not know e contribution to R eff of e two factors at determine it e return coefficient R ret and e fuelling efficiency, f, for helium, in any discharge. 7
Helium exhaust experiments on JT If R eff can be modelled for ITR, our results should allow a prediction of τhe based on a scaling of τ edge between present tokamaks and ITR. Such a scaling is, however, made difficult because, to our knowledge, an independent measurement of R eff and τ edge has not been attempted as part of e helium exhaust experiments on any oer tokamak and so scaling wi machine size is not possible at present. Also, e errors of R eff and of τ edge are quite large (about %), because e measurement relies on e absolute calibration of a vacuum UV spectrometer and e assumption at is measurement is representative for e volume source of helium. Unless inter-machine scaling of τ edge is a very strong function of machine geometry, such a comparison is unlikely to be conclusive. More experiments on JT wi active helium pumping are required to investigate scaling wiin each operating regime of τ edge. The accuracy of such a study is much better (e relative error is about %). Wiin e limited range studied, we have found no clear variation of τ edge for Type I LMy H-modes. ven ough e two ITB regimes wi LH prelude at we studied (strong ITBs at.63 T/. MA and core ITBs at 3. T/. MA wi LHCD roughout e main heating phase) are characterized by different τ edge, ere are too many parameters at differ between ese regimes to identify a scaling. One furer question still open is, how τhe would behave for very high values of β N at high magnetic field, i.e. for discharges like e one shown in figure 3. We have shown at e low edge density in ese scenarios is not a problem, i.e. sufficient pumping can be achieved, and our results at high values of β N and low magnetic field indicate at e improvement in τ combined wi e intrinsically low τ edge (we have measured values in e range.. for e discharge shown in figure 3) of is type of discharge might offset any increase in τ. Acknowledgments This paper is an extended version of a contribution to e 9 PS Conference on Plasma Physics and Controlled Fusion held in (Montreux, Switzerland, June ). It includes reanalysed material from a paper by D Stork et al from e 6 PS Conference on Controlled Fusion and Plasma Physics (Maastricht, The Neerlands, June 999) and a paper by K H Finken et al from e 8 PS Conference on Controlled Fusion and Plasma Physics (Madeira, Portugal, June ). This work was performed partially wiin e framework of e JT Joint Undertaking and partially under e uropean Fusion Development Agreement. It was funded in part by URATOM, e UK Department of Trade and Industry, and e US Department of nergy under Contract No D-AC- OR7. Appendix A. On retention, replacement and decay time, refuelling efficiency and predictions using zero-dimensional models In is appendix we address e relationship between e particle retention time, τ, in e case of vanishing return flux, and τ at finite return flux for particles. We will show at e N tot (s)..8.6...8.6.. -3 N / (S-dN/dt) N / S - - (N-N ss ) / (dn/dt) 3 Figure. The upper half of e figure shows e calculated time evolution of e total number of particles, N tot, in a cylindrical plasma of m radius (wi transport coefficients D and v as given in figure and R ret =.) wi a phase of central deposition as indicated by e shaded area (t <) followed by a phase of decay (t >). The lower figure shows e time evolution of various characteristic time constants at could be derived from N tot in an experiment, as explained in e text, i.e. decay or rise time constant of e total helium content τ d = N N ss /(dn/dt) ( ), replacement time τ r = N/S ( ) and a variant of e latter correcting for e time evolution τ c = N/(S dn/dt) (- - - -). details of is relationship depend on e type of experiment at was conducted to determine τ. Since ese results are valid for any species, we omit e index for helium in is section. In e first type of experiment, e decay of e total particle content, N, is observed once an external source of particles is turned off, and τ is identified as e rate of decay as τ d = (N N ss )/(dn/dt) where N ss is e steady-state density at t. In e second type of experiment, particles are continuously introduced in e plasma centre, and e replacement time is calculated as τ r = N/S, where S is e total particle source rate. While e steady-state solution develops, it is also possible to try to correct for e retention of particles by calculating τ c = N/(S dn/dt). However, is correction is incomplete, and in identical plasmas e result will be τ d τ r τ c during is transient phase, because e density profile shape is necessarily different. The actual values of τ also depend on e shape of e radial profile of e central and edge source, but is effect will not be discussed in is section. To demonstrate is difference, we show e results of a simple calculation assuming cylindrical geometry and a plasma radius of m in figures and. In is example, ions are introduced in e centre wi a source rate S for t <. The source is en turned off for t >, and e density is allowed to decay. We include an edge source (recycling flux) S edge = R ret Ɣ out, where R ret is e return coefficient. The recycling flux is modelled by introducing ions inside e last closed flux surface near e plasma boundary. This allows us JG3.6-c 7
K.-D. Zastrow et al τ * (s) f.. Steady-state Decay Steady-state Decay D (m /s) n (decay) n (steady-state) R =.99 R =.8 R =. R =.99 R =.8 R =. JG3.6-c v (m/s) τ* (s) f.. Steady-state Decay Steady-state Decay D (m /s) n (decay) n (steady-state) R =.99 R =.8 R =. R =.99 R =.8 R =. JG3.6-3c v (m/s). -...6.8...8. R ret r (m) Figure. The right half of e figure shows (from top to bottom) e profile shape adopted in steady state and during exponential decay for various values of particle return coefficient, R ret, and e transport coefficients used in e model calculation. The central source is located in e shaded area. The top left half of e figure shows two possible results for τ, e replacement time in steady state and e time constant for exponential decay, as a function of R ret. A fuelling efficiency, f, is derived from bo results for τ and is shown in e bottom left half of e figure. The result is e expected value of unity only for e case of e steady-state replacement time. to ignore all physics relating to e introduction by neutrals. Specifically, e fuelling efficiency for is type of artificial edge source is unity, as is e fuelling efficiency for e central source, us R eff = R ret (see equation ()). In e calculation e radial density profile is obtained from particle conservation as dn dt = r ( ( r D n )) r r vn + s n, (9) τ where a time constant for parallel losses, τ, is introduced in e SOL. This ansatz for e particle flux represents a diffusive term plus a convective term, i.e. a flux driven by gradients in oer plasma quantities but e density itself. It can be seen in figure at e calculated τ r = N/S, once steady state has been reached, is always larger an τ d = N/(dN/dt) noting at e helium content does not at first decay exponentially while e density profile shape relaxes (figure ). It is interesting to note at e time constant for decay (e solid line just after t = in figure ) starts off wi a value equal to e steady-state result (e dashed and dashdotted lines just before t = in figure ). xperimentally, is will be very difficult to determine, because e time window when is is e case is very short and too few data points are available to analyse. Figure also illustrates at it is necessary to wait until steady state has been reached, since considering τ c = N/(S dn/dt)results in a time dependent result. The overshoot in τ c occurs as long as e density profile is not yet in steady state because e particle flux rough all....6.8...8. - R ret r (m) Figure 3. As figure except a region of increased convective transport is introduced for r<. m. The profile of v is chosen to give e same steady-state profile shape wiout central source as e case illustrated in figure, which has reduced diffusive transport instead. flux surfaces, including e last closed flux surface, is still increasing and is not yet equal to e central source rate. Using equations () and () we can calculate, as a consistency check, e actual refuelling efficiency, f, from e solutions obtained by our calculations as f = R ret τ τ. () R ret τ edge In figure, we also show e result of is equation using e results for τ d and τ r from e analysis of steady state and decay. When e steady-state replacement is used we obtain f = independent of R ret as expected. When e decay time is used, f can become larger an unity, and will depend on R ret. The reason for is unphysical behaviour is at e radial profile in e steady-state case is a linear combination of two functions, e solution wi central source only and e solution wi edge source only. A solution during e decay phase, on e oer hand, is not. Therefore, a linear ansatz fails. For high values of R ret e difference between τ d and τ r is reduced (figure ). Most of e changes occur for R ret >.8, alough is particular value reflects e particular ratio of τ /τ edge 3, which in turn is determined by e profiles of D and v at we have chosen, in is example. To study e sensitivity to variations in core transport coefficients, we have performed e same calculation wi e transport terms modified in e centre by an additional inward drift and wi a reduced diffusion coefficient. The results are shown in figures 3 and. These two enhanced core confinement cases have been chosen to have e same solution in a source free region, which is given by n n r = v D. () These two calculations illustrate at e two transport coefficients have a different effect on e resulting retention 7
3% % 6% % Helium exhaust experiments on JT τ* (s) f.. Steady-state Decay Steady-state Decay D (m /s) n (decay) n (steady-state). -...6.8...8. R ret r (m) JG3.6-c R =.99 R =.8 R =. R =.99 R =.8 R =. Figure. As figure except a region of reduced diffusive transport is introduced for r<. m. The profile of D is chosen to give e same steady-state profile shape wiout a central source as e case illustrated in figure 3, which has increased convective transport instead. time in e presence of a central source. The reduced diffusion, which acts on e gradient, can result in strongly peaked density profiles, accompanied by a significant increase in τ d and τ r (figure ). If e same peaking wiout a central source is mainly due to inward convection, is is not very efficient at retaining a central source since it acts on e density, and τ d and τ r are not strongly modified. The second aspect is calculation illustrates is at e effect of reduced central diffusion on τ r is more pronounced an on τ d. As a numerical example, for R ret =.8, e replacement time τ r increases from.97 to. s in e case wi increased inward convection and to. s wi reduced diffusion. The decay time τ d increases from.87 s to.9 s and. s, respectively. A ird point wor noting is at e failure of e linear ansatz for e refuelling efficiency is larger in e case of reduced central diffusion an in e oer two cases. In summary, e steady-state replacement time τ r is always longer an e decay time τ d for e same plasma conditions. Only e true steady-state replacement time can be used to predict results at one specific value of R ret from ose at a different value of R ret using a zero-dimensional ansatz. To do is based on experimental data, it is necessary to estimate e replacement time for an edge source, τ edge. Reduced central diffusion is more effective at retaining particles an increased inward convection for e same ratio of v/d in e absence of a central source, wi e effect more pronounced for e steady-state replacement time. Appendix B. On measurement of e decay time constant and e replacement time In is appendix we discuss e assumptions made and e statistical and systematic errors of e techniques adopted in v (m/s) N / N N / N Contours of 8 6 8 6 7% % τ / τ (τ / t =, n / n = %) % 7% 3% % 3 t / τ % Background Known % Background Fitted Figure. Contours of errors in derived decay time constant, τ,as function of observed duration of decay, t/τ, and amplitude over background, N/N. The time resolution t of e signal in is example provides time points per decay time wi a % accuracy per data point. This corresponds to e actual JT experiments for τ = s. When e background level is known, it is sufficient to observe e decay for of a decay time to achieve % 3 accuracy, provided N/N >. If e background level needs to be fitted, almost ree decay times need to be observed. is paper to measure e decay time constant of e helium content and e replacement time of helium. Two parameters control e accuracy of a decay time analysis, e time period during which e decay is observed and e magnitude, N, of e puff. In figure is is illustrated for two cases: one where e background level, N, is known, and one where e background level itself has to be extracted from e experiment. For e first case we need to perform a two parameter fit, for e second case a ree parameter fit, to e measurement. The contours of constant error in figure have been derived from generating exponential decay data, and en analysing em. Time resolution and random noise have been chosen to be representative of e JT helium diagnostic. If e background is known, a % accuracy for τ d is achieved after about 3 of a decay time (% after one decay time). If e background needs to be extracted as well,. decay times have to be included, and observation during five decay times is required to achieve % accuracy. Since e discharge duration is limited by technical constraints, and e puff should be applied only after steady-state conditions have been achieved, it is not possible to observe e decay for long enough to perform a ree parameter fit. Therefore, it is necessary to make an assumption about e helium background. The residual helium in e experiment is due to wall storage from previous discharges []. In e example shown in figure 6 we can see at e helium in e plasma builds up to a steady-state level following e application of NBI heating. The heat and particle flux to e divertor and wall surfaces % JG3.6-c 73