INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION

Plasma Phys. Control. Fusion 43 (2001) R183–R224 www.iop.org/Journals/pp PII: S0741-3335(01)07063-4

REVIEW ARTICLE

Effects of divertor geometry on tokamak plasmas

Alberto Loarte

European Fusion Development Agreement–Close Support Unit Garching, Max-Planck-Institutfur Plasmaphysik, D-85748 Garching bei Munchen, Germany

Received 22 November 2000

AbstractThe design, construction and operation of advanced divertors have been themain topics of tokamak research during the last decade. The design of thesedivertors (carried out with two-dimensional plasma modelling codes) has beenoptimized to provide: a large operating density range for partially detachedplasmas with large radiative losses; satisfactory particle control by efficientdeuterium pumping; and He exhaust capability sufficient to remove fusionashes when extrapolated to next step devices. This article explains the criteriathat have guided this optimization process and then critically reviews theexperimental evidence that confirms or refutes the physics-based design criteriaon which the various existing advanced divertors have been based.

1. Introduction

During the last decade, one of the key drivers for the design and upgrade of the currentgeneration of tokamaks has been the incorporation of advanced divertors (Marmar et al 1999,Gruber et al 1999, Allen et al 1999a, JET Team 1999, Ishida and JT-60U Team 1999). Thedesign of such divertors has been optimized by means of two-dimensional (2D) plasma edgecodes, such as B2-Eirene, EDGE2D-NIMBUS and UEDGE (Braams 1986, Reiter et al 1991,Schneider et al 1992, Simonini et al 1992, 1994, Rognlien et al 1992, Rognlien 1996), in orderto maximize the benefits that can be expected from successful divertor operation:

• access to regimes with low power load onto the divertor target and acceptable divertortarget erosion, by means of large volumetric losses, which are compatible with good coreplasma energy confinement;

• achievement of sufficient divertor particle removal (pumping), which is necessary for coreplasma density control and for removing helium ash in future fusion reactors and next stepexperiments, such as ITER (Parker et al 1997).

Although with less theoretical justification, it was also expected that divertors whichachieved these goals would reduce the ionization source in the core plasma (by reducingneutral escape from the divertor and main chamber neutral density) and this, in turn, wouldimprove energy confinement (as seen in the experiments of ASDEX (Wagner et al 1991)). Thedecrease in main chamber neutral density would reduce the core plasma impurity contaminationby reducing charge-exchange sputtering in the main chamber.

0741-3335/01/060183+42$30.00 © 2001 IOP Publishing Ltd Printed in the UK R183

R184 Review article

Many of the effects associated with changes in divertor geometry are linked to the couplingof plasma transport and neutral and impurity sources at the edge and divertor plasmas. Dueto the very nonlinear coupling between plasma parameters and neutral and impurity sources,2D codes are necessary to model accurately the effects of divertor geometry on tokamakplasmas. Because of the intrinsic difficulties in modelling these nonlinear processes, detailedexperiments have been carried out to test the validity of the 2D code predictions in mostdivertor tokamaks. This review will concentrate on the analysis of the results obtained inthese experiments. The basic concepts of divertor physics will not be discussed in detail inthis review; only those relevant to the studies of divertor geometry will be considered. For anextensive and up-to-date review of experimental divertor physics, the reader is referred to therecent work by Pitcher and Stangeby (1997).

In order to study the regimes with enhanced divertor losses and efficient particle control,most divertor tokamaks (Alcator C-mod, ASDEX-U, DIII-D, JET, JT-60U, JFT-2M, etc) havemodified their divertors and conducted dedicated experimental campaigns to assess whether theexpected beneficial effects of divertor geometry are reproduced in the experiment or not. Thisarticle reviews the main results obtained in the course of this ongoing activity. Figures 1(a)–(e)show some of the divertor geometries which will be considered in this review (Alcator C-mod,ASDEX-U, DIII-D, JET and JT-60U).

In this review, we concern ourselves with tokamak poloidal divertors only. These are,at present, the favoured option to tackle the power-load and particle-control problems in nextstep tokamak devices. The reader is referred to a recent review (Grosman 1999) for the othermain option being considered in relation to these problems, i.e. ergodization of the tokamakedge plasma. Following their success in tokamaks, divertors are also being re-implemented inother magnetic confinement devices such as stellarators. For recent experimental work on thisemerging area of research the reader is referred to (McCormick et al 1999) for results fromW-7AS, and (Komori et al 2000) for results from LHD.

2. Basic effects of the divertor geometry on target power load and ionization sources

2.1. Basic effects of the divertor geometry on target power load

The presence of an X-point at the separatrix in a tokamak plasma introduces some complexitiesthat affect the particle and power fluxes to divertor targets, as compared to limiter discharges.For given upstream SOL plasma parameters, the parallel (to the magnetic field) power andparticle fluxes at the divertor target are determined by the expansion of the flux surfaces at thetarget. This magnetic flux expansion is greatest when the X-point is located very close to thetarget and decreases as the X-point-to-target distance increases. The actual power and particlefluxes deposited on the target are determined not only by the parallel fluxes but also by theangle of incidence of the field line onto the target itself. In the absence of toroidal inclinationof the divertor tiles (which is used in several tokamaks to avoid the exposure of leading edgesdue to tolerances in the alignment of the divertor tiles (JET Team 1995a, Gruber 1999)), thisangle (θ⊥) is determined by the normal component of the poloidal field to the divertor targetand the toroidal field, i.e. sin(θ⊥) = Bθ⊥/Bφ . Because the poloidal field is zero at the X-point,θ⊥ is typically very small, of the order of a few degrees, and increases linearly with distance tothe X-point, in a first-order approximation (Loarte et al 1992a). The combination of magneticflux geometry affecting both the parallel fluxes and their projection onto the divertor targetcan give rise to ‘unexpected’ behaviours of the measured energy and particle target fluxes,as seen in JET (Loarte et al 1992a, Harbour et al 1992). Figures 2(a) and 2(b) (Loarte et al1992a, Loarte 1992b) show the effect of changing the X-point-to-wall distance on the energy

Review article R185

bypass+intrinsicleakage

plenum

0.1 m

G

G

duct

D2

D2

plasmamain chamber

X-point

divertor

Divertor II, LyraDivertor I

(a) (b)

1.0 1.4 1.8 2.2R (m)

Z(m

)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5

(c) (d)

(e)

Figure 1. (a) Diagram of the divertor geometry in Alcator C-mod indicating the location of the by-pass divertor leaks and the location of gauges for neutral pressure measurements (G) (Pitcher et al2000). (b) Diagram of the divertor geometry in ASDEX-U with Div I (open) and the Div II ‘Lyra’(closed). Pumping in Div I is done by turbo-molecular pumps which are connected to the vacuumvessel near the outer divertor through the ports shown in the figure. Besides these turbo-pumps,a cryo-pump has been installed in Div II to provide additional pumping (Gruber et al 1999). (c)Diagram of the divertor geometry in DIII-D with two equivalent magnetic equilibria for the bottom(open) and top (closed) divertors. The position of the divertor cryo-pumps for the bottom andtop divertors is indicated by solid circles (Allen et al 1999a). (d) Diagram of the three divertorgeometries explored in JET. Divertor closure was increased in going from Mk I → Mk IIA → Mk IIGas Box. During the exploration of Mk IIA, the conductance of the by-pass leaks was reduced(these divertor experiments are referred to as Mk IIA/P which stands for Mk IIA with pluggeddivertor leaks). In all geometries, divertor pumping is carried out by a divertor cryo-pump (JETTeam 1999). (e) Diagram of the two divertor geometries explored in JT-60U: (open) divertor andW-shape divertor (closed). Divertor pumping in W-shape divertor takes place through the privateflux region (Asakura et al 1999a).

R186 Review article

c)

(a)

X-point to Target distance Zt (cm)

Γ ⊥m

ax/Γ

⊥m

ax(Z

t=0)

(b)

Figure 2. (a) Calculated divertor flux profiles for typical JET parameters in an X-point-to-targetscan showing: row a) the magnetic flux geometry and the target positions for a range of X-point-to-wall distances from 30 cm to zero; row b) the normalized parallel flux at the target; row c) theangle between the field line and the divertor target; row d) the normalized flux onto the divertortarget. These profiles are skewed Gaussians and present local maxima (at a position independentof X-point-to-wall distance) away from the magnetic strike points (R = ±Zt ), when the X-pointis close to the wall. The effect of diffusion into the private flux region is not taken into account inthese calculations (Loarte et al 1992a). (b) Maximum flux onto the divertor plate versus X-point-to-target distance for the JET configurations of figure 2(a). The fluxes are normalized to the valueobtained when the X-point is onto the divertor target (Zt = 0 cm). The effect of diffusion into theprivate flux region is not taken into account in these calculations (Loarte 1992b).

and particle parallel fluxes and on the fluxes deposited onto the target. With decreasing X-point-to-target distance, parallel fluxes become wider (increasing flux expansion) while thefluxes onto the divertor have their peak value away from the separatrix strike point, for lowX-point-to-target distances. This is due to the very low angle of incidence of the separatrixfield line onto the (flat) divertor target which leads to a small flux onto the target there, despitethe separatrix parallel flux being largest (Loarte et al 1992a). Increasing the X-point-to-walldistance increases the actual maximum flux onto the divertor target due to two factors: the fluxexpansion decreases (increasing the parallel flux density) and the angle of incidence increases(increasing the projected flux density), as shown in figure 2(b). The measured increase of thepower flux onto the divertor target is actually smaller than the one shown in figure 2(b) due tothe effect of diffusion into the private flux region, which is discussed next.

Review article R187

0

0.1

0.2

q div

,out

(MW

/m2 )

0

1

2

3(a)

4.8MW6.8MW

q par

alle

l,mp

(MW

/m2 )

P tot

,div

/Pbe

am

(c)

X-point height (m)0 0.05 0.10 0.15 0.20 0.25 0.30 0.35

High X-point

Low X-point

Figure 3. Outer divertor power load versus X-point-to-target distance in DIII-D ELMy H-modesfor two different additional heating levels: (a) shows the peak heat flux onto the divertor target;(b) shows the maximum parallel power flux mapped to the outer midplane deduced from thesemeasurements; (c) shows the total power to the outer divertor normalized to the input power, whichremains approximately constant during the X-point height scan (Lasnier et al 1998).

A further effect on the divertor fluxes, intrinsic to a diverted configuration, is the diffusioninto the private flux region (PFR) between the two separatrices. Energy and particles enterthis region by perpendicular diffusion from the main divertor SOL. This causes a decrease ofseparatrix power and particle fluxes from the values which would be measured if this diffusiondid not take place (Loarte 1992c). Experiments to quantify the effect on the peak powerdeposited onto the target have been carried out in DIII-D by varying, on a shot-to-shot basis,the distance between the X-point and the divertor target (Hill et al 1993, Lasnier et al 1998).Figure 3 (Lasnier et al 1998) shows the results of such experiments for two input power levels(both correspond to ELMy H-mode conditions). Increasing the X-point-to-target distanceleads to an increase of the peak power onto the target, as explained earlier (see figure 2(b)).However, this increase is significantly smaller than that expected if no diffusion into the PFRwould take place. In fact, due to the diffusion into the PFR, the maximum parallel power fluxmapped to the outer midplane decreases by a factor of two when the X-point-to-target distanceis increased from 0 to 33 cm. If no diffusion into the PFR occurrs, the maximum parallelpower flux mapped to the outer midplane should remain constant; in mapping to the outermidplane the effect of changing flux expansion at the divertor with varying X-point-to-walldistance is taken into account. These experiments were carried out at low densities so thatdivertor radiation would be small and not influenced by divertor geometry changes. Therefore,the measured total power reaching the divertor target remained practically constant when theX-point-to-wall distance was changed. The reduction of the parallel power load by diffusionin the divertor has been evaluated for the ASDEX-Upgrade by modelling with B2-Eirene

R188 Review article

(Schneider et al 1999). Up to a factor of two decrease in the peak load at the divertor (ingoing from Div I to Div II) can be attributed to the change in energy diffusion in the divertorassociated with the change in divertor magnetic configuration. As shown in figure 1(b), Div IIhas a longer PFR as well as a smaller flux expansion compared to Div I. Both effects enhancethe energy diffusion within the divertor reducing the peak parallel power flux at the target.

2.2. Basic effects of the divertor geometry on ionization sources

Although the described effects have noticeable influence on the divertor peak power load, theyare purely related to the divertor magnetic geometry itself and its geometric projection ontothe divertor target. However, even for a fixed divertor magnetic geometry, the shape of thedivertor target can have an even stronger influence on the particle sources/sinks in the divertoritself and at the plasma edge. The physical basis for this strong influence is twofold:

• For typical parameters at the plasma edge, the ionization mean free path of neutralsrecycled at the divertor target is similar (usually shorter) to the typical dimensions of thedivertor plasma (Stangeby 2000). As a consequence, the divertor plasma is not transparentto neutrals and a large proportion of the neutrals re-emitted from the divertor target arere-ionized in the divertor plasma itself, without reaching the SOL nor the core plasma.This is the origin of the name that characterizes this divertor regime as ‘high recyclingdivertor’.

• On average, recycled neutrals and molecules are emitted perpendicularly to the recyclingsurfaces (i.e. divertor targets) (Pitcher and Stangeby 1997). Hence, the target orientationdetermines where in the divertor plasma the neutrals will be ionized. A schematic viewof such effect is shown in figure 4 for a horizontal and a vertical divertor, taking as anexample the JET-Mk IIA divertor. Contrary to a horizontal divertor, the vertical divertorconcentrates the ionization sources in the region of largest power flux (separatrix).

The optimization in the design of divertors has been focused towards the achievement ofconditions with large re-ionization fractions in the divertor over the widest possible range ofbulk operating plasma conditions (i.e. separatrix temperature and density). The benefits ofoperating the divertor in this regime are clear from the standpoint of divertor power load andpossibly divertor erosion. A divertor where intense neutral (and impurity) re-ionization takesplace produces large volumetric energy losses (ionization and radiative losses), which decreasethe power load onto the divertor plate. Furthermore, these losses contribute to the reduction ofthe plasma temperature at the divertor target which can, in turn, reduce the physical sputteringof the target. Trying to investigate and profit from these effects in existing experiments has ledto the design and construction of divertors with increased ‘closure’ in most divertor tokamaks.

Power FluxPower Flux

Horizontal DivertorHorizontal DivertorVertical Divertorertical Divertor

Recycled NeutralsRecycled Neutrals

(V(Vertical)Recycled NeutralsRecycled Neutrals

(Horizontal)(Horizontal)

Power FluxPower Flux

Figure 4. Schematic representation of the neutralre-ionization pattern associated with a horizontaldivertor (shown at the outer divertor) and for a verticaldivertor (shown at the inner divertor). For verticaldivertors, neutrals are recycled towards the separatrixwhere the power flux is maximum. For horizontaldivertors, neutrals produced at the separatrix strikepoint are recycled in the outer part of the SOL.

Review article R189

The term ‘closure’ refers to the degree in which neutrals recycled from the divertor target canescape the divertor region. The larger the closure, the smaller the neutral escape from thedivertor. In general, the expected benefits of a closed divertor are (Horton et al 1999a):

• to provide easier access (over a larger range of plasma densities/input powers) to regimeswith high volumetric losses in the divertor;

• to increase divertor neutral pressure, hence improving divertor particle removal bypumping;

• to reduce deuterium neutral density in the main chamber which reduces main chambersputtering and may improve confinement.

The closure of a divertor depends on divertor plasma parameters and magnetic geometry aswell as on the geometry of the divertor components. In the first place, to achieve good closure,the divertor support structure itself has to have a very low conductance for neutral back flowinto the main chamber. The problem of neutral leakage from the divertor support structure (notescape from the divertor plasma) has been identified and tackled in several divertor experiments(Horton et al 1999a, Pitcher et al 2000). Its influence on plasma behaviour is still an area ofactive research and will be discussed in more detail in section 6.

In general, a divertor whose target and baffle structure tightly fits the magnetic geometrywill also be more closed to neutral escape, as the neutrals cannot escape the divertor exceptthrough the plasma where they can be ionized. This is particularly important for divertorswith horizontal targets where the neutrals can escape sideways from the divertor and notthrough the divertor plasma. Therefore, in order to increase the degree of closure of horizontaldivertors, baffle structures have been introduced that are designed to minimize this sidewaysescape (see figure 4). The position and shape of these side baffles have to be optimized suchthat they are close enough to the separatrix to prevent the sideways neutral escape but not soclose that they receive a significant particle flux, which will immediately escape the divertor(reducing its closure). A typical optimum criterion for the side baffles is to position them at adistance corresponding to the field line at ∼2–3 λn (midplane scrape-off density width) fromthe separatrix. For vertical targets, the recycled neutrals are launched towards the PFR (seefigure 4). In this case, two criteria must be taken into account to optimize the closure of thedivertor (ITER Expert Groups 1999):

• The divertor target must be designed such that most of the flux arriving at the target isre-emitted towards the divertor region itself. This means, in practice, that the normal tothe intersection point between the field line at a distance of 2–3 λn (midplane scrape-offdensity width) from the separatrix and the vertical target should point in a direction lowerthan the X-point itself.

• A baffle structure is introduced in the PFR which prevents neutrals from escaping back intothe bulk and SOL plasma through the PFR. This baffle structure is particularly importantto improve pumping through the PFR.

The exact application of these ‘design principles’ has to be carried out by means of 2Dplasma edge modelling codes, as the divertor plasma parameters are influenced by the geometryof the divertor components, for given upstream SOL plasma parameters. These codes, suchas EDGE2D-NIMBUS (Simonini et al 1992, 1994), B2-EIRENE (Braams 1986, Reiter et al1991, Schneider et al 1992) and UEDGE (Rognlien et al 1992, Rognlien 1996), solve theplasma and neutral species conservation equations taking into account the real geometry ofthe divertor, as well as of the pumping structures. An example of the calculated closure of theJET-Mk I and Mk IIA (figure 1(d)) divertors (for horizontal and vertical target discharges, seefigure 4) for typical conditions in JET is shown in figure 5 (Taroni et al 1994). The reduction in

R190 Review article

0

0.05

0.1

0.15

0.2

0.25

0.5 1 1.5 2 2.5

Mk IMk IIA Horizontal

1 9 - 3Separatrix Density (10 m )

SS

OL

+C

ore

/STo

tal

Mk IIA Vertical

Figure 5. Proportion of the calculated ionization source outside the divertor (with respect to thetotal ionization source) versus separatrix density for several JET divertor geometries. More closeddivertor configurations correspond to smaller ionization sources outside the divertor (Taroni et al1994).

the ionization source outside the divertor (i.e. neutral escape) from Mk I to Mk IIA horizontaltarget discharges comes from the introduction of the two tightly fitting side plates (also used asdivertor targets) preventing sideways neutral escape. The further increase in divertor closurefor Mk IIA vertical target discharges is a direct consequence of the neutrals being re-emittedperpendicular to the target and, hence, towards the PFR and not the main SOL (+ core plasma)for vertical target divertors.

An example of optimization calculations performed for the positioning of side baffles inhorizontal divertors is shown in figure 6 for the DIII-D advanced divertor (a modification of

Figure 6. Calculated core ionization source(normalized to that of an open divertor) for severalside baffle configurations for the DIII-D divertor. Theposition of the baffle is determined by the distancefrom the baffle to the separatrix mapped to the outermidplane (W-baffle width) (Allen et al 1999b).

Review article R191

0

0.5

1

1.5

2

2 3 4 5 6 7 8

PFR BaffleNo PFR Baffle

Pum

ped

Par

ticle

Flu

x (1

0 22 s

-1 )

Separatrix Density (10 19 m-3 )

Figure 7. Calculated pumped particle flux versus separatrix density for typical conditions inASDEX-U for two configurations of the Div II, with and without baffle in the private flux region(Schneider et al 1997a).

the upper divertor in figure 1(c)) (Allen et al 1999b). In this figure, the calculated reduction incore plasma ionization (normalized to that of a divertor without side baffles) is plotted versusthe position of the baffle with respect to the separatrix mapped to the midplane. The resultsclearly show that there is an optimum distance for the position of this baffle around 1.5–2 cm.Positioning the baffle at larger distances does not prevent neutral escape directly from thedivertor to the main chamber through the tenuous plasma in the outer SOL regions. However,positioning the baffle too close to the separatrix leads to a large ion flux being deposited ontothe baffle itself, which is poorly screened by the SOL plasma, thus contributing to a large coreionization source and poor divertor closure.

For vertical targets, besides the optimization of the target shape, there is the possibility ofadding a structure that prevents neutral escape through the PFR, increasing the PFR neutralpressure which favours divertor pumping. This PFR baffle must be optimized in such a waythat it is ‘open’ enough to allow neutrals reaching the divertor pumping system but ‘closed’enough so as to impede their escape back into the plasma. An example of the calculated effecton pumping of the PFR baffle for the ASDEX-U Divertor II is shown in figure 7 (Schneider et al1997a). In this figure, the calculated pumped particle flux is compared for two divertorconfigurations of Div II, one with PFR baffle (as in figure 1(b)) and one without (identicalto the one in figure 1(b) but without the PFR baffle). The effect of the baffle in increasing thepumped particle flux is more than a factor of two even at the lowest densities, demonstratingthe need to optimize this component when designing vertical plate divertors. Obviously, thesize of this effect is linked to the relative size of the ionization mean free path and the physicaldimensions of the divertor plasma. Therefore, its importance and the baffle dimensions willbe different for different devices/operating regimes.

All of the above considerations are related to edge plasmas in stationary conditions.Transient phenomena such as edge-localized modes (ELMs), which are typical of H-modes,add further complications to the design of the divertor. ELMs cause transient particle andpower loads which reach locations in the divertor where the normal (in-between ELM) fluxis usually negligible. This is due to either a broadening of the scrape-off layer during theELM and/or movements of the strike points associated with the ELMs (Hill 1997). As aconsequence, ELMs tend to produce large recycling particle sources away from the strikepoints, as shown in figure 8 for a JET Mk IIA discharge on the horizontal target (JET Team1997). It is difficult to optimize the divertor closure with respect to these ELM transient particle

R192 Review article

Figure 8. Measured particle ion flux ontothe JET-Mk IIA divertor during an ELMfor a discharge with the strike points onthe horizontal target. During the ELMs,very large ion fluxes can be measured upthe vertical target at considerable distances(>20 cm) from the in-between ELM positionsof maximum ion flux (strike points) (JETTeam 1997).

loads. In general, with increasing geometrical closure, the transient particle recycling occursat larger distances away from the divertor strike points. Depending on the relative magnitudeof the ELM particle fluxes to the in-between ELM fluxes (which varies from experiment toexperiment), the geometrical closure of the divertor, usually optimized for in-between ELMplasmas, has to be decreased. In this way, a larger proportion of the ELM particle fluxes canreach the divertor target and not be intercepted by surrounding baffle structures.

The rest of this review is focused on a detailed assessment of the various areas in which thedivertor geometry has been predicted to affect the plasma parameters and to which extent theexpectations have been confirmed in the experiment. From this assessment we will concludewhat is a good physics basis on which to carry out the optimization of a divertor design.

3. Divertor geometry effects on detachment and divertor radiated power

3.1. Divertor geometry effects on detachment

The initial drive in optimizing divertor designs was the need to solve the power-load problemin next step tokamaks (Parker et al 1997). In order to achieve an acceptable peak power loadon the divertor of a tokamak such as ITER, it is required that a large proportion of the powerflow into the plasma edge (typically ∼60%) is lost in the divertor via volumetric processes,such as hydrogen and impurity radiation, before reaching the divertor target. These lossescan only be achieved in a low-temperature/high-density divertor close to plasma detachment(Loarte 1997a, Kukushkin et al 1999, 2001). Achieving divertor detachment has the additionaladvantage that not only the power flux onto the target is reduced but also the ion flux via plasmarecombination which, in turn, leads to a reduced erosion of the divertor target (Lumma et al1997, McCracken et al 1998, Whyte et al 2000).

The area of the divertor which is subject to the largest power fluxes is the separatrix strikepoint and, therefore, divertor designs have been optimized to maximize the volumetric lossesnear the separatrix. In order to study this problem, 2D codes have been used to determinethe divertor design which most favours this effect. This corresponds to a vertical divertor

Review article R193

1

10

Te,

plat

e (e

V)

32.521.510.5ne (1020 m-3 )

vertical-plate

flat-plate

Te,SOL(eV)

detached divertor

Figure 9. Electron temperature at thedivertor strike point for similar dischargesin Alcator C-mod run on the horizontal(flat-plate) and vertical (vertical-plate)parts of the divertor. Open symbolscorrespond to attached divertor plasmasand full symbols to partially detacheddivertor plasmas. The measured mainSOL separatrix temperature is shown forreference; no influence of the divertorconfiguration on the SOL temperature ismeasured (Lipschultz et al 1997).

(Vlases 1993, Taroni et al 1994, JET Team 1995b, Schneider et al 1997a). In a verticaldivertor, the recycling neutrals are emitted towards the separatrix, which becomes a region ofpreferential ionization, decreasing the temperature and increasing the density in its vicinity.This concentration of recycling neutrals promotes separatrix detachment at lower main plasmadensities and increases volumetric energy and particle (recombination) losses in the separatrixregion. Such typical vertical divertor behaviour was originally seen in Alcator C-mod, whichwas the first tokamak to routinely operate with a vertical divertor (Hutchinson et al 1994).Figure 9 (Lipschultz et al 1997) shows the measured difference in main plasma density requiredto achieve divertor separatrix detachment in Alcator C-mod for discharges with the strike pointon the horizontal and vertical parts of the divertor target. Discharges on the vertical target reachdivertor detachment at densities typically 40% smaller than those required for horizontal targetdischarges (Lipschultz et al 1997). Initial experiments in JET with the Mk I divertor showedsimilar effects, in particular when the plasma was located in the lower part of the vertical plate(Loarte et al 1995, Loarte et al 1998). Positioning the strike point in this area of the JET-Mk Idivertor target leads to enhanced neutral baffling and easier access to plasma detachment (lowermain plasma density) compared to positioning the strike point either in the upper part of thevertical target or in the horizontal target. However, the complex three-dimensional structureof the JET-Mk I divertor target (with toroidal gaps to allow better divertor pumping) producedquite a complicated ionization picture that masked some of the geometry effects (Loarte et al1995, Loarte 1997a).

The re-ionization pattern produced by the divertor affects not only the values close to theseparatrix but also the shape of the temperature and density profiles across the divertor target.For vertical divertors, the density profiles tend to be more peaked towards the separatrix and,correspondingly, the temperature profiles tend to have low values close to the separatrix andto be very flat away from it. These ‘inverted’ divertor temperature profiles were some of thefirst predicted evidence for the effect of the divertor geometry (Vlases 1993, JET Team 1995a)and have been found in most tokamaks operating with vertical divertors (see, for instance,(La Bombard et al 1995, Schneider et al 1999, Asakura et al 1999a)) confirming the modellingpredictions. Examples of temperature and density profiles at the divertor and in the main SOLfor the open (horizontal) JT-60U divertor and the closed (vertical) JT-60U W-shape divertorare shown in figure 10 (Asakura et al 1999b).

An outwards inclined horizontal divertor (such as JET-Mk IIA, or the outer target of Div Iin ASDEX-U) produces the completely opposite effect to that described above for a verticaldivertor. In this case, the recycling neutrals are concentrated far away from the separatrix.

R194 Review article

at outer divertor target

Distance from separatrix (mm)

Te

(eV

)di

v0

10

20

30

40

50

-10 0 10 20 30 40 50

0

1

2

3

4

5

m-3

)n

ediv (

1019

(mapped at midplane radius)

W-shaped divertor

open divertor

ne=2.3-2.4x1019m-3

0

1

2n

e (

1019

m-3

)m

id

L-mode:

Distance from separatrix (mm)

at outer midplane

(a) (c)

(d)ne=2.3-2.4x1019m-3

ne=2.7x1019m-3

-10 0 10 20 30 40 5020

cm

10 cm

(b)

Te,sep=61eVmid

(W-shape)

(Open)

Te,sep=68eVmid

Figure 10. Comparison of the measured SOL (ne) and divertor profiles (ne and Te) for similardischarges in JT-60U open (horizontal) and W-shape (vertical) divertors. As predicted by modelling,the density profiles at the divertor are more peaked for the vertical divertor and, correspondingly,the temperature profiles are flatter, with much lower values at the separatrix itself (Asakura et al1999b).

Particle Neutral Losses (m-3s -1)

2.2 2.4 2.6 2.8 3.0 3.2

R(m)

-0.8

-1.0

-1.2

-1.4

-1.6

-1.8

Z(m

)

0.0

-2.5 1021

-1.0 1022

-2.5 1022

-5.0 1022

-7.5 1022

-1.0 1023

-2.5 1023

-7.5 1021

-5.0 1021

0.0

-2.5 1021

-1.0 1022

-2.5 1022

-5.0 1022

-7.5 1022

-1.0 1023

-2.5 1023

-7.5 1021

-5.0 1021

2.2 2.4 2.6 2.8 3.0 3.2

R(m)

-0.8

-1.0

-1.2

-1.4

-1.6

-1.8

Z(m

)

Particle Neutral Losses (m-3s -1)

(a) (b)

Figure 11. (a) B2-Eirene divertor particles losses (recombination) for typical L-mode conditionsin a vertical divertor JET-Mk IIA discharge showing the largest recombination sink at the innerdivertor separatrix (Borrass 1998). (b) B2-Eirene divertor particles losses (recombination) fortypical L-mode conditions in a horizontal divertor JET-Mk IIA discharge showing the largestrecombination sink at the inner divertor corner away from the separatrix (Borrass 1998).

This neutral re-ionization pattern leads to detachment starting away from the separatrix(Borrass et al 1997a) rather than close to it, as is more usual (Loarte 1997a, Loarte et al 1998).The different detachment behaviour associated with these two extreme divertor geometrieswas predicted with B2-Eirene for the JET-Mk IIA divertor (Borrass et al 1997a) and foundexperimentally (Monk et al 1997). Figures 11(a) and 11(b) (Borrass 1998) show the predicted

Review article R195

Horizontal

JET Pulses Nos. 36862,

0cm 1.6cm 6.1cm 11.9cm

10

1

100

DivertorMARFE

Distance from Separatrix

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

Line Average Density (1019m–3)

D.O

.D. (

Inne

r)

10

1

100

DivertorMARFE

Distance from SeparatrixVertical

0cm 2.0cm 4.9cm

D.O

.D. (

Inne

r)

37154

Early Onset ofDetachment

Figure 12. Degree of detachment for the inner divertor plasma at various distances from theseparatrix for two JET-Mk IIA L-mode density scans. The upper figure shows the early onset ofdetachment for the plasma starting away from the separatrix for horizontal divertor discharges. Thelower figure shows the detachment starting progressively from the separatrix outwards in the SOLfor vertical divertor discharges (Monk et al 1997).

recombination strengths for two similar B2-Eirene runs in JET-Mk IIA vertical and horizontaltargets displaying the behaviour outlined above. For the vertical divertor, the enhancedseparatrix recycling leads to detachment (characterized in these simulations by the onset ofplasma recombination) starting close to the separatrix. In contrast, for the horizontal divertor,neutral recycling is enhanced far away from the separatrix (in this case at the corner betweenthe horizontal and vertical plates) and plasma detachment (characterized by the onset of plasmarecombination) starts away from the separatrix. In the JET experiments, upstream density andtemperature profiles, as well as profile resolved information on plasma recombination, are notroutinely available. Therefore, divertor detachment is usually characterized by the degree ofdetachment (DoD) (Loarte et al 1998). The DoD provides a normalization criterion for theincrease of the ion flux with upstream plasma density, at constant power flux into the edgeplasma, compared to the high recycling scaling (ion flux ∼ 〈ne〉2). In this way, experimentalvalues of DoD > 1 indicate that the divertor plasma is detached. Figure 12 (Monk et al 1997)shows the inner divertor experimental detachment behaviour for two comparable density scanson the JET-Mk IIA horizontal and vertical targets. The vertical divertor shows the detachmentstarting at the separatrix and progressing smoothly across the SOL with increasing density,typical of the evolution from partial to total detachment (Loarte et al 1998). The horizontaldivertor shows the plasma detaching away from the separatrix (6–12 cm distance from the

R196 Review article

sepa

ratr

ix p

artic

le fl

ux d

ensi

tyInner DivI

Outer DivI

Inner DivII

Outer DivII

inte

grat

ed p

artic

le fl

ux

(10

m

s

)

22

-2-1

0

4

8

Outer DivI

0 1 2 3 4separatrix density (10 m )19 -3

0

0.5

1.0

1.5

(10

s

)

23-1

Inner DivII

Outer DivI Inner DivI

Outer DivII Figure 13. Inner and outer divertor ion flux (separatrixand integrated) for two density scans in ASDEX-Umodelled with B2-Eirene for Div I (horizontal) andDiv II (vertical). The upper figure shows the reductionin density required to achieve separatrix detachment inDiv II compared to Div I. The lower figure shows theintegrated ion flux to inner and outer divertor both forDiv I and Div II displaying much smaller differences withrespect to total detachment (Schneider et al 1999).

separatrix at the divertor target), with the separatrix plasma itself remaining attached until theformation of a divertor MARFE, in agreement with modelling predictions (Borrass 1998).

The achievement of partial detachment at lower densities for a vertical divertor does notnecessarily lead to a lower L-mode density limit. The L-mode density limit is very wellcorrelated with the onset of strong recombination and total divertor detachment (Borrass et al1997b, Schneider et al 1999, Coster et al 1999a, Maggi et al 1999a). Modelling with B2-Eierene for ASDEX-U Div I and Div II has demonstrated that the onset of large divertorrecombination is relatively insensitive to the geometry of the divertor target, contrary to theresults for partial detachment (Schneider et al 1999). Modelling results show (see figure 13(Schneider et al 1999)) that the range of densities in which separatrix detachment can beobtained is much larger in Div II (vertical) than in Div I (horizontal). However, this doesnot imply a smaller range of operating densities in terms of total divertor detachment, asshown in figure 13 by the drop of the integrated ion flux. The reason for such behaviourcomes from the typically ‘inverted’ temperature profiles characteristic of vertical divertors(figure 10). Even if the divertor plasma close to separatrix can reach the very low temperaturesrequired for detachment in vertical divertors, the outer SOL remains at higher temperaturesand, therefore, attached. Figure 14 (Loarte 2001) shows the detailed experimental confirmationof this modelling prediction for JET-Mk IIA L-mode discharges. In figure 14, the degree oftotal divertor detachment at the inner divertor is shown for the same discharges in figure 12.Despite the very different ways in which detachment proceeds across the SOL for these twodivertor geometries (see figure 12), total detachment is reached in a very similar way for bothdivertor geometries. In this case, a difference of less than 10% in plasma density correspondsto the same degree of total detachment in both divertor geometries.

One of the problems in the achievement of detached divertor plasmas is the asymmetrybetween inner and outer divertors. This asymmetry is usually not due to divertor geometryeffects but to plasma drifts (Chankin et al 1994). For the normal direction of the toroidal field(for lower X-point divertors this is clockwise when seen from the top), the power flux to theouter divertor is largest, which makes the inner divertor reach detachment at lower densities thanthe outer divertor (Hutchinson et al 1995). Despite this intrinsic in/out divertor asymmetry, the

Review article R197

Figure 14. Total degree of detachment forthe inner divertor plasma for two JET-Mk IIAdensity scans in the horizontal and verticaldivertors (those in figure 12). Despite the verydifferent behaviours in the approach to partialdetachment in these two divertor geometries (seefigure 12), the approach to total detachment issimilar (Loarte 2001).

geometry of the divertor can influence the way in which both divertors approach the detachedstate (Maggi et al 1999b, Pitts et al 2000). For instance, physically separating the inner and theouter divertors allows some control of the detachment asymmetry by separately fuelling bothdivertors. Experiments of this type have been carried out in the JET-Mk II Gas Box divertor inL-mode and ELMy H-mode discharges (Maggi et al 1999b). The JET-Mk II Gas Box divertor(see figure 1(d)) has a septum that separates the inner and outer divertors with a gas injectionsystem that can fuel both strike zones independently. Figure 15 (Maggi et al 1999b) shows theresults of such an L-mode density scan experiment in which gas was fed separately to eitherdivertor, together with a scheme of the JET-Mk II Gas Box geometry and the position of the gasinlets. When the discharge is fed by gas puffing in the inner divertor, it is possible to reach thedensity limit with a strongly detached inner divertor (low ion flux) and a fully attached outerdivertor (large ion flux). However, when the discharge is fed from the outer divertor, the ionflux to both divertors behaves in a much more symmetric way in the approach to detachment.Feeding the gas at the main chamber (midplane) produces an intermediate result. However, itmust be pointed out that the most symmetric behaviour that can be achieved in the JET-Mk IIGas Box divertor is similar to that observed with the JET-Mk I and JET-Mk IIA divertors(no structure in PFR), for which the location of the gas feed had no effect on the detachmentasymmetry (Loarte et al 1998, Monk et al 1997). When the strike points are located high onthe Mk II Gas Box divertor vertical target, the septum does not significantly restrict the pathfor neutrals to travel between the two divertors. In this case, the effects of the gas puff locationon detachment asymmetry are much weaker even in JET-Mk II Gas Box, and detachmentbecomes more symmetric with little influence of the gas feed location (Maggi et al 1999b).

Similar experiments carried out in JET-Mk II Gas Box ELMy H-mode discharges did notshow such a clear evidence for a relation between gas puff location and the achieved divertorparameters (Maggi et al 1999b). Although this issue is still the object of research, presentanalysis indicates that the limitations in obtaining high divertor densities in JET ELMy H-modes are related to confinement deterioration at high pedestal densities (and low pedestaltemperatures) rather than to detachment in the divertor (Saibene et al 1999). Because of this,H-mode confinement is seriously deteriorated before any clear sign of strong detachment can be

R198 Review article

0

1

2

3

4

0

1

2

3

4

1.5 2 2.5 3 3.5

InnerOuterMain

Line Average Density (1019 m-3)

Inte

grat

ed Io

n F

lux

(102

2 s-

1 )Inner Divertor

Outer Divertor

Figure 15. Inner and outer divertor integrated ion fluxes versus line average density for severalL-mode density scans in the JET-Mk II Gas Box divertor with different gas fuelling locations (innerdivertor, outer divertor, main chamber). Fuelling the discharge by gas puffing in the outer divertorleads to more symmetric detachment (simultaneous decrease of the ion flux with density at bothdivertors) before the density limit is reached. A scheme of the magnetic configuration used in theseexperiments with the JET-Mk II Gas Box divertor, as well as the location of the divertor gas inlets,is shown for reference (Maggi et al 1999b).

identified in the JET divertor plasma (Monk et al 1997, Saibene et al 1997, Maggi et al 1999b).This confinement deterioration limits the achievable edge plasma density, which seems to betoo small to bring the divertor into a regime in which the location of the gas feed can affectdetachment asymmetry.

Modelling for the JET-Mk II Gas Box divertor with EDGE2D-NIMBUS (Maggi et al1999b) has demonstrated that the calculated insulating effect of the septum for neutralscan explain the observed differences in detachment symmetry. The role of the septum ondetachment symmetry has been quantitatively assessed by calculations carried out for theJET-Mk II Gas Box divertor with and without septum. Figures 16(a) and 16(b) (Maggi et al1999b) show the results of these calculations which closely resemble the experimental findings:discharges with inner side puffing and a divertor with a septum display a very large asymmetrybetween the two divertors, with the whole inner divertor temperature under 5 eV while theouter divertor remains fully attached (Te > 10 eV). Removing the septum, while keepingeverything else the same in the calculations, leads to a much more balanced situation with thetwo divertors reaching low temperatures and detachment much more symmetrically. The exactdegree of the modelled in/out detachment asymmetry is related to the in/out divertor power-loadasymmetry. Modelling of the experimentally observed in/out power-load asymmetry and itsrelation to drifts is an issue of present research with 2D codes (Coster et al 1998, Chankin et al2000).

Review article R199

(a)

(b)

Figure 16. (a) Electron temperature contours from EDGE2D-NIMBUS modelling of gas fuellingexperiments (inner divertor) in the JET-Mk II Gas Box divertor. In the simulations, the innerdivertor can reach total detachment (Te < 5 eV) while the outer divertor remains fully attached(Te > 10 eV) (Maggi et al 1999b). (b) Electron temperature contours from EDGE2D-NIMBUSmodelling of gas fuelling experiments (inner divertor) in JET-Mk II Gas Box divertor without theseptum. These simulations demonstrate the influence of insulating the inner/outer divertor via aseptum on detachment asymmetry. When the septum is removed, both divertors reach detachmentin a much more symmetric way (Maggi et al 1999b).

R200 Review article

3.2. Divertor geometry effects on divertor radiated power

Besides allowing an easier access to separatrix detachment at the target, a vertical divertorcreates an extended region of low electron temperature along the separatrix, which favours theformation of large radiating volumes (Schneider et al 1999). Hence, the divertor can radiatea large fraction of the power flowing out of the bulk plasma, as required for next step devices(Parker et al 1997). Such extended radiation patterns have been measured in ASDEX-UDiv II and are in very good agreement with B2-Eirene modelling predictions (see figure 17(Schneider et al 1999)). As a consequence, the total divertor power load in ASDEX-U hasdecreased typically by a factor of two to three in Div II as compared to Div I (Herrmann et al1999). Simulations with B2-Eirene have been carried out to understand in detail the reductionin the divertor power load between Div I and Div II (Schneider et al 1999, Kallenbach et al1999a) whose results are shown in figure 18 (Schneider et al 1999).

In the first place, it has been recognized that the change of energy diffusion within thedivertor (see section 2.1) can, by itself, explain a reduction of the peak power flux by about afactor of two in going from Div I to Div II for similar main plasma conditions, in agreement withprevious evidence (Loarte 1992c, Hill et al 1993, Lasnier et al 1998). However, the enhanceddivertor diffusion does not change the total power load to the divertor (Loarte 1992c); thisreduction can only take place through an increase in the divertor radiative losses. Recentstudies of the nature and size of this divertor radiation in ASDEX-U (Coster et al 1999b) havedemonstrated that the Div II divertor geometry leads to these large radiated fractions throughthe following chain of effects. The divertor geometry of Div II causes the formation of anextended region along the separatrix with high density/low temperature for lower separatrixdensities than in Div I (see figure 19(a)). Once a low-temperature divertor is achieved, the exactsize of the divertor radiation is then determined by the size of the carbon source (i.e. chemicalsputtering yield, because Te is low), as shown in figure 19(b). However, if the divertor doesnot reach a low-temperature regime (Te 10 eV), which is driven by the re-ionization ofdeuterium, increasing the chemical sputtering yield leads only to very modest increases of thedivertor radiated power (figure 19(b)). This means that for typical ASDEX-U edge powerflow/separatrix density, with the change from Div I to Div II the proportion of the edgepower flux that reaches the divertor target has decreased from 60% to 30%, in agreementwith modelling (Kallenbach et al 1999a, Coster et al 1999b). Detailed experiments have beencarried out to verify this point by using the roof baffle of Div II as a flat target for the outerdivertor. These experiments have found that, for similar main plasma conditions, the parallelpower flux to the outer divertor is a factor of two larger for the flat divertor than for the normalvertical divertor configurations (see figure 20 (Herrmann et al 1999, Kallenbach et al 1999a)).This is in good agreement with the arguments above, as the roof baffle geometry approximatelyresembles that of the Div I divertor target. In section 5.1, it will be further shown that the divertorflows established by Div II help to increase carbon radiation by enhancing non-coronal effects.

Despite being a similar divertor to Div II, ELMy H-mode discharges in JET with theMk IIA divertor have not shown such a large fraction of total divertor radiated power as inASDEX-U (Horton et al 1999a, Matthews et al 1999). This experimental result is consistentwith the fact that the outer divertor in JET does not reach low electron temperatures (<10 eV)for ELMy H-mode discharges, as shown for a gas puff scan in figure 21 (Monk et al 1997).Trying to increase the edge plasma density (reducing the divertor temperature) by gas puffingin ELMy H-modes at JET leads to a deterioration of energy and particle confinement and theloss of the H-mode regime (Saibene et al 1997, 1999). If the separatrix density in JET couldbe high enough in H-mode such that the outer divertor reaches low temperatures, modellingpredicts similar levels of radiation in JET-Mk IIA to those of Div II in ASDEX-U (Taroni et al

Review article R201

2.0

4.6

7.2

9.8

12.4

15

Radiation losses [MW/m-3]

Experiment

B2-Eirene

Figure 17. Measured and B2-Eirene modelledradiation profiles in ASDEX-U Div II showingthe extended region of radiation close to theseparatrix. The absence of this feature in themeasurements for the outer divertor is due tothe lack of bolometer channels in this area(Schneider et al 1999).

Experiment Modelling

2 MW input power, density ramp

outer divertorDiv I

Div Iinner divertor

0.8

0.0

0.4

1.2

pow

er d

ensi

ty /

MW

/m2

0.8

0.0

0.4

1.2

pow

er d

ensi

ty /

MW

/m2

0.00 0.04 0.08

distance from separatrix / m

0.00 0.04 0.08

distance from separatrix / m

Div II

Div II

P_heat = 1.5 MW NBI, Ý = 5e19 1/m**3

0.8

0.0

0.4

1.2

pow

er d

ensi

ty /

MW

/m2

outer divertor

Div I

Div II

0.00 0.04 0.08

distance from separatrix / m

pow

er d

ensi

ty /

MW

/m2

inner divertor

Div I

Div II

0.00 0.04 0.08

distance from separatrix / m

0.8

0.0

0.4

1.2

Figure 18. Measured and B2-Eirene calculated power flux to the inner and outer divertors inASDEX-U with Div I (solid curves) and Div II (dashed curves). The calculations are performedfor a density scan in both divertor configurations and show a much lower divertor power flux inDiv II due to the large divertor radiated power (figure 17). The calculated power fluxes in bothdivertors decrease with increasing density (Schneider et al 1999).

R202 Review article

Div

. sep

. Te

(eV

)0.010.1

110

1001000

0 2e+19 4e+19 6e+19 8e+19 1e+20

midplane separatrix density (m-3)

Outer target DivI 2MWDivII 2MWDivI 8MWDivII 8MW

(a)

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100

Fra

ctio

n of

pow

er r

each

ing

targ

et

Target temperature (eV)

1%3%5%

0

0.2

0.4

0.6

0.8

1

0.001 0.01 0.1

C chemical sputter yield

T=1eVT=3eVT=5eV

(b)

Figure 19. (a) B2-Eirene modelled separatrix divertor temperature for ASDEX-U Div I and Div IIin simulations which do not include carbon impurities for two levels of edge power flux (2 MW,8 MW). The divertor geometry in Div II leads to enhanced separatrix ionization and lower separatrixtemperatures over a larger density range compared to Div I (Coster et al 1999b). (b) Top: fraction ofpower reaching the divertor target in ASDEX-U Div II from B2-Eirene simulations versus divertortemperature, for various values of the carbon chemical sputtering yield (1, 3 and 5%). Bottom:fraction of power reaching the divertor target in ASDEX-U Div II from B2-Eirene simulationsversus chemical sputtering yield, for various values of the divertor temperature (1, 3 and 5 eV)(Coster et al 1999b).

1994), as is indeed the case experimentally for the inner divertor in both devices. Figure 22(Kallenbach et al 1999b) shows the measured radiation profiles in two similar ELMy H-mode discharges (in terms of Pinput/R) in JET and ASDEX-U with very comparable radiationlevels for the inner divertor, but much lower values for the outer divertor in JET. At present,it is not clear if this difference is due to a larger in/out divertor power asymmetry in JETthan in ASDEX-U or to the inaccessibility of larger separatrix densities in ELMy H-modesin JET. The typical ratio of separatrix to line average density in ELMy H-modes with goodconfinement in JET is ∼0.15–0.30 (Davies et al 1999) while it is 0.50–0.60 in ASDEX-UDiv II (Schweinzer et al 1999). This difference is large enough to explain the colder moreradiating divertor in ASDEX-U Div II compared to JET-Mk IIA.

Review article R203

0.995 1.000 1.005 1.010 1.015normalized poloidal flux

0

20

40

60

80

100pa

ralle

l hea

t flu

x [M

W/m

]

2 7.5 MW NI; ELM averaged Figure 20. Measured outer divertor parallelpower flux in ASDEX-U Div II versus normalizedpoloidal flux (which is proportional to distancefrom the separatrix at the midplane) for ELMyH-mode discharges with the strike point on thehorizontal roof baffle (full lines) and the verticaltarget (dashed line). A decrease of a factor oftwo of the measured deposited power for verticaldivertor discharges is measured, which is dueto enhanced radiative losses in vertical divertorconfigurations. In these configurations, a 0.01distance in normalized poloidal flux correspondsto∼5 cm distance along the vertical divertor target(Herrmann et al 1999, Kallenbach et al 1999a).

Figure 21. Top: separatrix ion flux (between ELMs) for the inner and outer divertors in JET-Mk IIAELMy H-mode discharges versus gas fuelling rate. Bottom: separatrix electron temperature (in-between ELMs) for the inner and outer divertor in JET-Mk IIA ELMy H-mode discharges versusgas fuelling rate. The outer divertor in JET-Mk IIA does not reach temperatures cold enough(Te < 5 eV) for detachment and large radiative losses to take place, even at the highest fuellingrates. Increasing the gas fuelling rate beyond 3.0 × 1022 el s−1 in these experiments leads to theloss of H-mode confinement in the discharge (Monk et al 1997).

R204 Review article

2 2.5 3 3.5

-1.5

-1

R (m)

Z (

m)

JG99.157/1c

JETdischarge39609

t=19.44s 4

3

2

1

0

ASDEXUpgrade: Pheat= 5 MW, Praddiv=3MWJET: Pheat= 11 MW, Praddiv=3 MW

0

2

4

6

8

10

[MW/m³]

1.1 1.9

#109823.2s

-1.2

-0.4

ASDEX Upgrade

R (m)

[MW/m³]

JET-Mk IIA/P

Figure 22. Bolometric reconstructions of the radiation emission profiles for two ELMy H-modedischarges in ASDEX-U (with Div II) and JET with (Mk IIA) at similar levels of Pinput/R. Notethe larger in/out asymmetry of the divertor radiation (consistent with the divertor parameters infigure 21) in the JET-Mk IIA discharge, in comparison with the one in the ASDEX-U Div IIdivertor (Kallenbach et al 1999b).

Achieving a high radiated fraction in the divertor does not automatically lead to a lowpower load on the divertor target. If the divertor plasma is not detached enough, most of theradiation is re-emitted very close to the target and a large fraction is immediately re-depositedin a highly localized area of the target. In the case of closed divertors, this fraction is usuallylarge due to the geometrical divertor closure. Observations in ASDEX-U Div II (figure 23(Kaufmann et al 1999)) show that under normal operating conditions most of the measuredpower flux at the inner target is due to the radiative power load and not to power depositedby the plasma itself (Kaufmann et al 1999). While this effect is of no concern in presentexperiments, for next step devices, such as ITER, it is one of the main drivers in the designand optimization of the divertor and of its reference operating regime. Divertor designs andoperating regimes which do not provide a distributed enough radiation lead to unacceptablepower loads on the ITER divertor target, even when the radiated power fraction in the divertoris large (∼60%) (Kukushkin et al 2000).

Review article R205

inner divertor outer divertorroof baffle

0

1

2Total heat flux from thermographyRadiative heat flux

# 10982

Figure 23. Measured power flux to the divertor target in a typical ELMy H-mode in ASDEX-Uwith Div II. The full curve is the measurement of the power flux by IR thermography. The dashedcurve is the calculated power flux onto the divertor from the measured radiated power emission(Kaufmann et al 1999).

4. Divertor geometry effects on deuterium and impurity pumping

4.1. Divertor geometry effects on deuterium pumping

One of the main goals of an optimized divertor is to provide sufficient neutral pumping.This is required both to obtain good density control in existing experiments as well as toremove the helium ash in next step devices. Increasing the closure of the divertor reducesthe escape probability of recycled neutral atoms/molecules reaching the bulk plasma and,therefore, increases the divertor neutral pressure and consequently divertor pumping. Thisbehaviour has been observed in most divertor experiments and is in good agreement withmodelling predictions (Bosch et al 1999a, Horton et al 1999a). Figure 24 (JET Team 1999)shows the increase in divertor neutral pressure for similar L-mode plasmas with increasingdivertor closure from JET-Mk I through JET-Mk IIA to the JET-Mk II Gas Box divertor.

Beyond this expected result, many other effects of the divertor geometry on pumpinghave been determined since the first pumping experiments carried out in DIII-D (Klepper et al1993). The probability of a recycled neutral being pumped depends on the probability ofthe neutral reaching the pumping plenum with respect to that of being ionized in the plasma.The initial results from DIII-D had shown a very strong dependence of divertor deuteriumpumping on the geometry itself, in particular on the distance between the strike point andthe entrance of the pumping plenum (Klepper et al 1993). In contrast, other experimentshave not found such strong dependence for deuterium pumping on the strike point positionbut a much smoother one (Saibene et al 1995, Loarte et al 1997b, Bosch et al 1997, 1999b,Niemczewski et al 1997, Tamai et al 1999). The reason for such a difference was identifiedin (Loarte et al 1997b) by means of analytical models and 2D modelling with EDGE2D-NIMBUS for Alcator C-mod, DIII-D and JET. In (Loarte et al 1997b) it was found thatdivertor pumping depends strongly on the exact position of the plasma with respect to thepumping plenum entrance only when the transport of neutrals to the plenum is dominatedby the first flight neutral contribution. Otherwise, when the neutral transport to the plenum isdominated by multiple scattering (charge-exchange and multiple collisions with divertor/vesselwalls), the transport process is diffusive and presents a naturally weaker dependence on theneutral source location. Figure 25(a) (Loarte et al 1997b) shows a comparison betweenmodelling results from EDGE2D-NIMBUS and experimental measurements from JET-Mk IIAdischarges, demonstrating the weak dependence of the pumped particle flux on the strike point

R206 Review article

JG98

.583

/2c

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Div

erto

rne

utra

l pre

ssur

e(1

0–3m

bar)

2.0 2.5 3.0Line averaged density (1019 m–3)

3.5 4.0

Horiz.

Mark I

Vertical

Horiz.

Mark IIA

VerticalMark IIGB

Figure 24. Measured neutral pressure at the divertor cryo-pump for similar JET L-mode dischargesin various divertor geometries. The divertor closure increases in going from JET-Mk I → JET-Mk IIA → JET-Mk II Gas Box. Correspondingly the measured neutral pressure at the cryo-pumpincreases with divertor closure for the same main plasma density (JET Team 1999).

JET–MkII

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

R (m)

–2.4

–2.2

–2.0

–1.8

–1.6

–1.4

–1.2

–1.0

Z(m

)

JG97.2

30/1

2c

(a) (b)

Figure 25. (a) Experimental and EDGE2D-NIMBUS modelled neutral pressure at the cryopumpfor JET-Mk IIA L-mode experiments, versus distance from the strike point to the plenum entrance(vertical dashed line) (Loarte et al 1997b). (b) Calculated neutral trajectories for typical L-modeconditions in the JET-Mk IIA divertor showing a large concentration of neutrals near the divertorcorner despite the separatrix strike point being located ∼20 cm from these corners (Loarte et al1997b).

Review article R207

position on the horizontal plate. Figure 25(b) (Loarte et al 1997b) shows some of the calculatedneutral trajectories, with a large density of these near the corner between the horizontal andvertical divertors (entrance from the divertor to the pumping plenum), corresponding to a largeneutral pressure. This high neutral pressure at the divertor corner, despite the location ofthe separatrix being far away from this corner, is a consequence of the JET-Mk IIA divertorgeometry. The JET-Mk IIA geometry produces this enhanced divertor corner neutral pressurefor horizontal divertor discharges in the following way: the orientation of the horizontal targetin JET-Mk IIA is such that recycled neutrals (emitted on average normal to the target) traveloutwards/inwards through the divertor plasma where they are ionized or undergo charge-exchange or reach the pump. Most of the neutrals that are able to travel through the divertorplasma without interaction arrive at the vertical divertor target where they are recycled againand re-emitted towards the divertor plasma. This neutral re-circulation pattern leads to ahigh neutral concentration near the divertor corner, weakly dependent of the location of theprimary neutral source, but only if the strike point is on the horizontal plate. This is indeed thesame phenomena which led to detachment starting away from the separatrix in JET-Mk IIAhorizontal discharges, as discussed in section 3.1. When the strike point is located on thevertical plate, this neutral re-circulation pattern disappears and the neutral pressure decreasesrapidly as the strike point moves away from the divertor corner (figure 25(a)).

In contrast, the DIII-D lower divertor pumping geometry (see figure 1(c)) is such that theneutrals that arrive at the pumping plenum come almost uniquely from direct recycling at thehorizontal divertor target. If a neutral misses the pumping slot in its first flight after leaving thetarget, it is very improbable that it will reach the pumping plenum by multiple scattering. It willmost likely escape towards the midplane of the device or will be ionized in the bulk plasma.As a consequence, the pumped particle flux depends critically on the relative position of thestrike point with respect to the pumping slot entrance. The measured dependence of particlepumping on the strike point position in DIII-D can be properly described with 2D codes suchas EDGE2D-NIMBUS (see figure 26 (Loarte et al 1997b)) as well as with analytical models,given the simplicity of the problem (Loarte et al 1997b). Recent experiments in DIII-D(Maingi et al 1999) have tested in detail the explanation put forward in (Loarte et al 1997b)to describe DIII-D divertor pumping and have found it to be in excellent agreement with themeasurements.

0

0.2

0.4

0.6

0.8

1

-5 0 5 10 15

Experiment_Low_neExperiment_High_neEDGE2D-NIMBUS

No

rmal

ised

Neu

tral

Pre

ssu

re @

Pu

mp

Distance from Separatrix to Bias Ring (cm)

Horizontal TargetBias Ring

Figure 26. Experimental and EDGE2D-NIMBUS modelled normalized neutral pressure at thepumping plenum for DIII-D, versus distance from the strike point to the plenum entrance (biasring) (Loarte et al 1997b).

R208 Review article

0.1

1

10

Neutral gas flux density [m s ]-2 -11022 1023

Ne

Helium

Com

pres

sion

fact

or C

i

B2-Eirene modelling

NeHe

Experiments

Figure 27. Experimental and B2-Eierene modelled He and Ne compressions (ndivertor/nedge plasma)versus divertor neutral gas flux for ASDEX Div I discharges. Larger neutral divertor gas fluxdensities correspond to discharges/modelling with larger main plasma densities. He has a longerionization mean free path and escapes more easily the divertor. Therefore, He compression issmaller than Ne compression in the pumping geometry of Div I (Schneider et al 1997b).

4.2. Divertor geometry effects on impurity pumping

The physical neutral transport mechanisms described above apply not only to deuteriumneutrals but also to recycling impurities. In this case, the ballistic component of neutraltransport is particularly important, as the recycling impurity neutrals are not subject to charge-exchange in the experiment (due to their low concentrations). Modelling with B2-Eirenefor ASDEX-U reproduces satisfactorily the relative compression (ndivertor/nedge plasma) of Neand He in the pumping plenum of Div I (Schneider et al 1997b) as well as their increasewith plasma density (neutral pressure), as shown in figure 27 (Schneider et al 1997b). Thepredicted relative changes in He and Ne compression observed in changing from Div I to Div II(Schneider et al 1999) have also been confirmed experimentally (Bosch et al 1999b). For Div I(see figure 1(b)) He and Ne were pumped from the outer side of the SOL in the divertor region.This means that atoms with a shorter mean free path (Ne) are better confined near the pumpingplenum entrance in the divertor. He, which has a longer mean free path, can escape from thedivertor more easily. Therefore, its compression in the pumping plenum was lower, as shownin figure 27 for the measured and calculated He and Ne compressions in ASDEX-U Div I(Schneider et al 1997b). In detail, the effect of the improved Ne retention with respect to He inDiv I reflects itself in the impurity fluxes to the divertor target, shown in figure 28 (Coster et al1997). The maximum Ne flux is located in the outer SOL plasma and close to the pumpingplenum entrance, hence, leading to the observed larger Ne compression. The compressionsfor He and Ne changed in opposite directions, as expected, when the divertor was modifiedto Div II (Bosch et al 1999b). In Div II, pumping takes place through the gaps between thelower part of the vertical target and the PFR dome (figure 1(b)). In this case, the longer meanfree path of He facilitates its enrichment in the pumping plenum (Schneider et al 1999). Suchpredictions have been confirmed experimentally, as seen in figure 29, which shows the increaseof the He removal rate and the decrease of the Ne removal rate in ASDEX-U when comparingsimilar discharges in Div I and Div II (Bosch et al 1999b).

Modelling of similar experiments with EDGE2D-NIMBUS for the JET-Mk II divertorssatisfactorily reproduces the relative He and Ne enrichment, as well as the observed decreaseof He enrichment for discharges at high plasma density (Guo et al 2000). This He enrichment

Review article R209

Distance along Target (m)

Figure 28. ASDEX-U B2-Eierene modelled He and Ne fluxes at the outer Div I target versusdistance to the separatrix. Ne has a shorter ionization mean free path and this leads to its largertrapping in the Div I geometry in the area close to the pumping plenum entrance (∼20 cm fromthe separatrix) and, consequently, to its larger compression in the pumping plenum (Coster et al1997).

Figure 29. Experimental decay rates of He and Ne for pumping experiments in ASDEX-U withboth divertor configurations Div I (horizontal) and Div II (vertical) versus main plasma density. Ingoing from Div I to Div II, He pumping is improved and Ne pumping is deteriorated, in agreementwith modelling predictions (Bosch et al 1999b).

R210 Review article

deterioration at high densities is observed in most divertor tokamaks (Sakasai et al 1999,Groth et al 1999, Pacher et al 1997) and is well reproduced by modelling (Guo et al 2000,Pacher et al 1997). The basic reason for such behaviour is that the neutral mean free pathof He becomes much longer than that of deuterium in conditions of divertor detachment.From this, it must not be concluded that detached divertors perform poorly in terms of Hepumping necessarily. The He enrichment deterioration at high density is a common findingin existing experiments because of the mean free path of He becoming long compared tothe dimensions of the divertor itself. However, in next step devices such as ITER, reachingdivertor detachment is required to have adequate He exhaust (Kukushkin et al 2001). This isdue in part to the divertor pumping geometry (pumping through the PFR) and to the separatrix

R(m)

Z(m

)

(a)

1

2

3

4

5

0.1

0.2

0.3

0.4

0.5

3 3.2 3.4 3.6 3.8 4

PRF Pressure Deuterium He Enrichment

Separatrix Density (101 9 m- 3)

PF

R D

eute

rium

Neu

tral

Pre

ssur

e (P

a) Helium

Enrichm

ent @ P

lasma E

dge

Detachment Inner Divertor

Detachment Outer Divertor

(b)

Figure 30. (a) B2-Eirene modelled contour levels of He concentration (nHe/ne) in the ITERdivertor. The values of the He concentration along several contour levels are given in the figureand show the He concentration peaking away from the separatrix because of the thermal force.Deuterium and He pumping in ITER will be performed from the PFR (Loarte et al 1999a).(b) B2-Eirene modelled deuterium pressure and helium enrichment in the ITER private flux regionversus separatrix density. A stepwise increase in He enrichment is obtained when the inner and theouter divertors reach partial detachment (Loarte et al 1999a).

Review article R211

1 2Subdivertor pressure (10–3 mbar)

He

enric

hmen

t

0

0.4

0.2

0.6

1.0

0.8

1.2JET-Mk IIA L-mode

HorizontalCornerVertical

0 3 4

Figure 31. Measured He enrichment versus sub-divertor neutral pressure for JET-Mk IIA L-modedischarges. For every configuration, increasing sub-divertor pressure corresponds to increasingmain plasma density. The largest He enrichment is found in the corner configuration for which theprobability of He ballistically reaching the pumping plenum (sub-divertor volume) is highest. Thehorizontal line at an enrichment of 0.2 is the ITER reference enrichment (Groth et al 1999).

plasma becoming thick to neutral He atoms in ITER attached divertor plasmas. Because ofthe thermal force, the concentration of He atoms is lowest close to the separatrix, where thethermal force which pushes impurities away from the divertor is largest (Neuhauser et al 1984).Therefore, the largest flux of recycled neutral He coming from the target is peaked away fromthe separatrix. Under attached plasma conditions these neutrals cannot easily penetrate into thePFR, from which pumping is performed in ITER (Kukushkin et al 2001). When the divertorplasma reaches partial detachment, the probability of He neutrals reaching the pumping plenum(PFR) increases and, with it, He enrichment. Figures 30(a) and 30(b) (Loarte et al 1999a)show the divertor geometry for ITER and the He concentration contours, as well as the neutraldeuterium pressure and He enrichment in the PFR, for a density scan study carried out withB2-Eirene (Loarte et al 1999a). A stepwise increase of the He enrichment with separatrixdensity is observed which is correlated with the subsequent achievement of partial detachmentat the inner and outer divertors.

The longer mean free path of He makes its pumping particularly sensitive to the strikepoint position in some divertor configurations, such as those of the JET-Mk II divertors andASDEX-U Div II. This explains some of the scatter in figure 29 for ASDEX-U Div II whichis due to small uncontrolled displacements of the separatrix affecting strongly the probabilityof He reaching the plenum and much more weakly that of neutral deuterium (Bosch et al1999b). Such divertor geometrical effects on He enrichment can be well reproduced by 2Dplasma modelling and have been studied experimentally in detail at JET (Groth et al 1999).Positioning the divertor strike point near the pumping plenum entrance, both for JET-Mk IIAand JET-Mk II Gas Box divertors, leads not only to an increase of the deuterium pressurein the pumping plenum but also of the He enrichment. The maximum He enrichment is,hence, found when the strike point is at a location such that the probability of He ballisticallyreaching the plenum is highest (Loarte et al 1997b, Groth et al 1999); this is the so-calledcorner configuration. The experimental results obtained in these experiments for JET-Mk IIAL-mode discharges are shown in figure 31 (Groth et al 1999) for several divertor configurations(horizontal, vertical, corner). Because of the same effects discussed above for deuteriumpumping, the vertical configuration is the one with the lowest He enrichment. Results in

R212 Review article

experiments in ELMy H-modes at JET show similar trends but with much larger scatter due tothe ELMs themselves and to the influence of the divertor geometry on the ELM frequency/size(Groth et al 1999). Despite the decrease of He enrichment with increasing plasma density(divertor neutral pressure), the lowest value measured in JET for the Mk IIA and Mk II GasBox divertors in L and ELMy H-modes and in ASDEX-U is equal to or larger than 0.2, whichis the value required for operation in the ITER reference regime (ITER Expert Groups 1999).

5. Divertor geometry effects on the SOL plasma and divertor flows

5.1. Divertor geometry effects on divertor flows

The divertor geometry has a determining influence on the ionization sources in the divertorplasma and, as a consequence, on divertor plasma flows. From the theoretical point of view,a major difficulty in the study of these flows is that edge plasma flows are not only drivenby particle sources/sinks but also by plasma drifts. Presently, new versions of 2D codesare becoming available which will include a proper treatment of the classical drift terms(Chankin et al 2000, Coster et al 1998). The complete picture of the relative importance of thesource-driven and drift flows, both in the SOL and divertor, remains to be evaluated. From anexperimental point of view, the accurate determination of flow patterns is quite complicatedbecause of their intrinsic 2D structure, which requires detailed measurements of flow profilesalong and across the field for all ions in the plasma. Despite this, considerable advances in themeasurements, understanding and modelling of 2D plasma and impurity flows in the divertorplasma have taken place in the last few years (Loarte 1997a, La Bombard et al 1997, Gafert et al1999, Isler et al 1999, Boedo et al 1999, Porter et al 1998, Stotler et al 1999, Asakura et al2000, Chankin et al 2000). At present, it is reasonable to assume that the inclusion of drifts inthe computations will affect mainly absolute values (by an offset of the calculated velocity) ofthe flows. In this way, the relative changes of ion flows due to changes in ionization patternsprovoked by the divertor geometry will be similar with and without drifts, although theirabsolute values will, of course, be different.

The concentration of neutral ionization towards the separatrix, typical of vertical divertors,tends to create a region of deuterium flow reversal in this area (Loarte 1997a, La Bombard et al1997). Flow reversal occurs in a flux tube when the ionization source exceeds the ion lossto the divertor target for that flux tube (Krasheninnikov et al 1992). As a consequence, thedeuterium ion flow is directed away from the divertor in an extended region, which starts atsome distance from the target. This region of flow reversal is extinguished by the diffusion ofparticles and momentum into the neighbouring flux tubes in which the plasma flows forwards(towards the divertor). A typical pattern for the deuterium ion flow in a vertical divertorconfiguration is shown in figure 32 for B2-Eirene modelling of Alcator C-mod (Loarte et al1999b). Alcator C-mod has reported observations of flow reversal close to the divertor entrance(La Bombard et al 1997) but not in the main SOL (Pitcher et al 2001). This indicates thatthis reversed flow is mainly driven by the divertor ionization balance and not by SOL drifts.As shown in figure 32 (Loarte et al 1999b), a region of reversed flow close to the separatrixis found for Alcator C-mod both at the inner and outer divertors which extends beyond thedivertor entrance, where it has been measured in the experiment (La Bombard et al 1997). Thisflow pattern affects not only particle transport but also momentum transport in the divertor. Aninwards diffusion of momentum through the interaction of the forward and reversed flows (byparticle diffusion and perpendicular viscosity) (Loarte 1997a, Stotler et al 1999) takes placeat the plasma edge. This inwards momentum diffusion produces a region of overpressurenear the separatrix strike point, in which the plasma pressure is higher than that derived from

Review article R213

R(m)

Z(m

)

Mach Number

Figure 32. Contours of the Mach number for the plasma flow in Alcator C-mod modelled withB2-Eirene. Normal flow to the inner divertor corresponds to negative values, while normal flowfor the outer divertor corresponds to positive values of the Mach number. In both inner and outerdivertors, a region of reversed flow is located close to the separatrix and extends beyond the divertorentrance, in good agreement with experimental measurements (Loarte et al 1999b).

momentum conservation along the flux tubes and acceleration to Mach 1 at the sheath. Suchdivertor separatrix overpressure has been observed experimentally in Alcator C-mod and giventhe name of ‘Death Ray’ (La Bombard et al 1997). This overpressure is reproduced properlyby modelling with EDGE2D-NIMBUS (Loarte 1997a) and B2-Eirene (Stotler et al 1999,Loarte et al 1999b) that includes the momentum diffusion mechanisms discussed above.

Although more likely in a vertical divertor, reversal of the deuterium ion flow in thedivertor is an intrinsic feature of the 2D divertor ionization balance besides the target geometry.Therefore, divertor flow reversal has also been observed in horizontal divertors such as DIII-Dfor high recycling conditions (Boedo et al 1999), in good agreement with UEDGE predictions.As detachment proceeds, the region of forward flow with Mach number ∼1 (which alwaysexists close to the target) moves away from the divertor. In all the experiments in which aregion of flow reversal close to the separatrix is observed, this flow reversal disappears withdivertor detachment (Boedo et al 1999, Gafert et al 1999). It is also universally seen that thedeuterium ion forward flow decreases between the recombination region and the divertor target(due to the momentum loss processes caused by ion–neutral interactions) in good agreementwith modelling calculations (Schneider et al 1999, Asakura et al 2000, Isler et al 1999).

Reversal of the deuterium flow is not as drastic, in terms of core impurity contamination, asoriginally feared (Loarte 1997a). This is because impurity flow reversal appears usually beforedeuterium flow reversal takes place. This indicates that the thermal force dominates frictionon the parallel impurity transport over a large density range. Impurity flow reversal in DIII-D occurs typically at low–medium densities well before deuterium flow reversal is observed

R214 Review article

1.00 1.28 1.57 1.85R (m)

1.400

Z(m

) 1.200

0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25

experimentUEDGE

Machnumber

∆ Z [m]

(a) (b)

1.2 105

8 104

4 104

0

4 104

1.4 1.5 1.6 1.7

Attached phase

ExperimentUEDGE

u||(C

)[m

/s]

R (m)

(c)

Figure 33. (a) Experimental diagnostic geometry for measurements of deuterium (Mach probe,vertical line) and impurity flows (spectroscopic view) in DIII-D (Porter et al 1998). (b)Experimental and UEDGE modelled Mach number of the deuterium flow in DIII-D along thevertical line covered by the Mach probe, versus height above the divertor floor. The flow measuredat all positions is towards the divertor (M > 0) (Porter et al 1998). (c) Experimental and UEDGEmodelled velocity of the carbon impurity flows in DIII-D (view in (a)) versus radial coordinatealong the divertor floor. A region of reversed flow close to the separatrix (u‖(C) < 0) is clearlyseen both in measurements and simulation (Porter et al 1998).

(Porter et al 1998, Isler et al 1999). The region of impurity flow reversal is concentratedclose to the separatrix where the thermal force is largest. Measurements and UEDGEmodelling of this impurity flow reversal and of the deuterium flow are in good agreement,as shown in figures 33(a)–(c) (Porter et al 1998). The complicated 2D pattern of impurityflows influences the impurity radiated power by enhancing its radiation potential from that ofcoronal equilibrium (Krasheninnikov 1997). Such an effect has been studied experimentally inASDEX-U Div II and modelled with B2-Eirene (Schneider et al 1999). Figure 34 (Gafert et al1999) shows the B2-Eirene calculated carbon flow as well as the measured C2+ velocity witha clear region of flow reversal in the vicinity of the separatrix. In the case of ASDEX-UDiv II, the region of slow/reversed carbon flow close to the separatrix, together with thelow-temperature/high-density plasma there, enhances the carbon radiative losses and leads toan extended radiation pattern in the divertor, as seen in figure 17 (Kallenbach et al 1999a,Coster et al 1999b).

5.2. Divertor geometry effects on the SOL plasma

In the absence of strong parallel flows in the main SOL, the flow pattern created by the divertorwould also influence the upstream density profiles. A horizontal divertor creates a moreradially spread ionization source, while a vertical divertor concentrates the ionization close tothe separatrix. If divertor ionization were the only factor determining the SOL density width,

Review article R215

-0.6

-0.8

-1.0

-1.2

-1.41.4 1.5 1.6 1.7 1.8 1.9

Parallel velocity

R (m)

C2+

0

+20

+40

-20

-40

-50

-30

-10

+10

+30

+50

(km/s)v

z (m

)-0.6

-0.8

-1.0

-1.2

-1.4

Figure 34. B2-Eirene modelled velocity of carbonions in ASDEX-U Div II experiments. The measured(along the viewing line shown) C2+ forward velocityis 21 km s−1 (15 km s−1 from modelling) and themeasured C2+ reversed flow velocity is −24 km s−1

(−21 km s−1 from modelling). The slow/reversedcarbon flow close to the separatrix enhances thecarbon radiated losses in this region by increasingthe residence time of the carbon ions in the divertor(Gafert et al 1999).

the density profiles should be narrower for vertical divertor discharges than for horizontaldivertor discharges (Vlases et al 1992, JET Team 1995a). Most experiments report verysmall differences in the SOL plasma for similar discharges in horizontal and vertical divertors(Lipschultz et al 1997, Asakura et al 1999a, Schweinzer et al 1999). These results reveal thatin these experiments there are other effects which have a greater influence on the SOL densityprofiles than the divertor ionization pattern. The two most obvious of these effects are plasmadrifts in the main SOL and main chamber recycling. Plasma drifts in the main SOL influencethe parallel velocity of the plasma in the SOL and consequently the density width. Driftsin the SOL are not affected by details of the divertor geometry as such. Therefore, if SOLparallel transport is dominated by drifts, no change of density profiles is expected with differentdivertors for the same main plasma conditions. Many experiments observe SOL density profilesin which two decay lengths are present: a shorter one close to the separatrix and a longer onein the outer SOL (La Bombard et al 1995, Schweinzer et al 1997, Asakura et al 1997). Thisis consistent with substantial levels of plasma recycling in the main chamber of these devices.The strong main chamber ionization source is likely to have a large effect on the densityprofiles in the SOL. The experiments which report broad shoulders in the SOL density profilesalso report small changes of the main chamber neutral pressure and main chamber recyclingwith divertor geometry (Pitcher et al 2000, Asakura et al 1999a, Bosch et al 1999b). Thisindicates that these three observations are linked to the same common underlying phenomenon(independent of divertor geometry) which drives the SOL transport and ionization balance inthese experiments. At present, the issue of main chamber neutral pressure/recycling and itsrelation to divertor geometry (and SOL anomalous transport) is an area of active research andsome of its aspects will be discussed in more detail in section 6.

The only experiment where some of the expected changes of SOL density thickness withdivertor geometry have been seen is JET with the Mk I divertor, for Ohmic and L-modedischarges performed with reversed magnetic field (ion grad-B away from the divertor)(Davies et al 1995). Figure 35 (Davies et al 1995) shows the measured density e-foldinglengths for attached discharges on the vertical and horizontal divertor targets. As expected for

R216 Review article

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

JET-Mk I

Horizontal OhmicVertical OhmicHorizontal L-modeVertical L-mode

λ nmid

plan

e(c

m)

<ne> (101 9 m- 3)

Figure 35. Measured SOL density e-foldinglengths in JET-Mk I Ohmic and L-mode discharges(with reversed toroidal field) on the horizontal andvertical targets of the Mk I divertor. Dischargeson the vertical target have narrower SOL densityprofiles in agreement with the ionization/flowpattern established by this divertor geometry(Davies et al 1995).

a vertical divertor (Vlases et al 1992), the e-folding lengths are smaller than for a horizontaldivertor. It is not well understood why the divertor geometry effect on the SOL densityprofiles is seen only under these conditions. The effect itself is not only in qualitative butalso in reasonable quantitative agreement with modelling calculations which do not includedrift effects (Loarte et al 1995). There is experimental evidence showing that for this set ofexperiments the other two effects that may influence the SOL density thickness (drifts andlarge main chamber recycling/neutral pressure) are small. Discharges with reversed field inJET have an almost stagnant plasma parallel flow in the main SOL (Chankin et al 2000). JETseems to be one of the experiments (see section 6 for a more detailed discussion) in whichmain chamber recycling/neutral pressure can be affected by changes in the divertor geometry(JET Team 1999, Horton et al 1999a). This indicates that the measured level of ionization atthe edge of the main plasma is not mainly due to direct interaction between the SOL plasma andthe main chamber wall, as might be the case in other divertor experiments (La Bombard et al2000).

6. Divertor geometry influence on main chamber neutral pressure and plasmaconfinement

Besides increasing divertor neutral pressure (thereby improving pumping) a closed divertorcould, in principle, decrease the main chamber neutral pressure as well. Initial results in PDX(Kaye et al 1984) and ASDEX (Wagner et al 1991) had shown that reducing the conductanceof by-passes for divertor neutrals back into the main chamber improved the access to H-mode (lower power threshold) as well as the H-mode energy confinement enhancement. Onthis basis, it was expected that with more closed divertors it could be possible to lower themain chamber neutral pressure with beneficial effects for H-mode confinement. Reductionof the main chamber neutral pressure/recycling could also contribute to the decrease ofimpurity production due to charge-exchange sputtering by energetic atoms on the main chamberwalls. Understanding the relation between the divertor neutral pressure, main chamber neutralpressure and main chamber recycling is still an area of active research. In what follows, wewill describe our present understanding of the processes that control this relation, but this maychange as more detailed studies become available.

Review article R217

A priori, it is not straightforward that installing a closed divertor in a device will lead to alower main chamber neutral pressure. In first place, there is abundant experimental evidence fordirect plasma recycling onto main chamber walls due to the appearance of broad ‘shoulders’ inthe SOL density profiles (La Bombard et al 1995, Schweinzer et al 1997, Asakura et al 1997).Such direct recycling may dominate the main chamber neutral pressure and is independentof divertor geometry. Furthermore, a more closed divertor leads to an increased divertorneutral pressure which, in turn, increases the flow of neutrals leaking back from the divertorto the main chamber through by-passes in the divertor structure. If the divertor structureis not tight enough to neutral back-leakage, the main chamber neutral pressure can indeedremain unchanged, even if a more closed divertor is installed in the device. Observations inAlcator C-mod (Pitcher et al 2000) and ASDEX-U (Bosch et al 1999b) indeed show that amore closed divertor produces larger divertor neutral pressures but without affecting the mainchamber neutral pressure. Therefore, the neutral compression (ratio of divertor to main plasmapressure) increases with a more closed divertor by the increase of the divertor pressure andnot by the decrease of the main chamber pressure. In particular, the role of by-pass leaksfrom the divertor into the main chamber has been experimentally studied in Alcator C-modby installing a system that allows changes in the conductance of the divertor by-pass leaksduring a shot (Pitcher et al 2000). The results obtained indicate that in Alcator C-mod theneutral escape from the divertor back into the main chamber through the divertor leaks is a ‘flux

Figure 36. Midplane neutral pressure (a), divertor neutral pressure (b) and neutral compression(c) versus line averaged density in Alcator C-mod experiments: crosses correspond to experimentswith the divertor by-pass leaks closed, and triangles to similar experiments with the by-pass leaksopen. The largest change with opening/closing the by-passes occurs in the divertor neutral pressure,which is strongly reduced with the by-pass leaks open. Consequently, the neutral compression ismuch smaller with the open by-pass leaks (Pitcher et al 2000).

R218 Review article

limited’ phenomenon (Pitcher et al 2001). Therefore, increasing the conductance of these leaksreduces the divertor pressure, so that the neutral flux escaping the divertor through the leaksis the same, leaving the main chamber neutral pressure unchanged (see figure 36). Therefore,in experiments such as ASDEX-U and Alcator C-mod, the main chamber neutral pressure hasremained unchanged with the incorporation of more closed divertors. Consequently, no majorchanges in main plasma confinement properties or main plasma impurity contamination havebeen observed (Pitcher et al 2000, Gruber et al 1999).

The observations in JFT-2M (Kawashima et al 1999), DIII-D (Allen et al 1999a) and,chiefly, JET (Horton et al 1999a, JET Team 1999) seem to be more in line with the idealbehaviour of a closed divertor with respect to main chamber neutral pressure. In theseexperiments, the increase of divertor closure has been accompanied by a decrease in mainchamber neutral pressure. In the case of JET, the decrease of divertor by-pass conductances,for an otherwise unchanged divertor geometry (JET-Mk IIA), has led to a reduction in mainchamber neutral pressure by almost a factor of two with no change in divertor neutral pressure(Horton et al 1999a). Increasing the divertor closure further going from the JET-Mk IIAto the JET-Mk II Gas Box divertor (with the by-pass conductances as in JET-Mk IIA withplugged leaks) has further increased the divertor pressure, while maintaining a similar orslightly lower main chamber neutral pressure (JET Team 1999). These results indicate thatin JET (after closing the neutral by-pass leaks) and possibly also in JFT-2M and DIII-D, theneutral pressure in the main chamber is more related to neutral escape from the divertor plasmaitself rather than through leaks in the divertor structure. Figure 37 (JET Team 1999) showsmeasurements of neutral compression (ratio of divertor to main chamber neutral pressures) inJET Mk IIA, Mk IIA/P (Mk IIA with plugged leaks) and JET Mk II Gas Box divertors forthe same discharges in figure 24. Contrary to the results from ASDEX-U and Alcator C-mod,

40

50

60

70

80

90

100

30

Neu

tral

com

pres

sion

1.6Line averaged density (1019 m–3)

3.22.82.42.0

Mark IIAP

Mark IIA

Mark IIGB

JG98

.589

/1c

Figure 37. Neutral compression (Pdivertor/Pmain chamber) in JET L-mode discharges versus lineaveraged density for several divertors with increasing degree of closure Mk IIA → Mk IIA/P(Mk IIA with closed by-pass leaks) → Mk II Gas Box. With increasing divertor closure the neutralcompression increases. The rollover on the neutral compression is due to the onset of divertordetachment, which deteriorates neutral retention in the divertor. No calibrated midplane neutralpressure measurements were available for the JET most open divertor (Mk I) (JET Team 1999).

Review article R219

the neutral compression in JET has been increased by: decreasing the conductances of theby-pass leaks in going from Mk IIA to Mk IIA/P without changing the divertor pressure and(at constant leak conductance) by increasing the divertor neutral pressure with a more closeddivertor in going from Mk IIA/P to Mk II Gas Box (JET Team 1999).

Despite the changes in neutral compression and the reduction of the main chamber neutralpressure, no large effects have been observed in H-mode confinement at JET (Horton et al1999a). An example of two otherwise identical discharges in JET, but for the reduction indivertor by-pass leakage, is shown in figure 38 (Horton et al 1999a) illustrating this point.The present understanding of these JET results is based on the existence of H-mode regimeswith temperature profiles with stiff and non-stiff behaviour rather than on a direct role of theneutral density in the main chamber, as previously thought. The observation of confinementdegradation at high main chamber neutral pressures is, therefore, caused by the associated lowvalues of the temperature in edge transport barrier (and by their influence in central confinementthrough profile stiffness) rather than to the neutral pressure itself (Horton et al 1999b). Withthe increase of divertor closure, a reduction of the H-mode power threshold has been observedin JET (Horton et al 1999a) and JT-60U (Tsuchiya et al 2000). At present, it is not clear ifthis is an effect of the neutral density itself or of the change of plasma parameters at the edge

2

Pulse No: 38293 (MkIIA), 39628 (MkIIAP)

1

H97

ne

Ppump

Pmid

Dα (hor)

0

1

φD2

0

6

22

1

04

2

03210

16 18 20 22 24 26

Time (s)

(a.u

.)(1

0–5m

bar)

(10–3

mba

r)(1

019 m

–3)

(1022

)

JG98

.145

/14c

Figure 38. Overview of two ELMy H-mode discharges in JET before and after the pluggingof the by-pass leaks in the JET-Mk IIA divertor: full curves, Mk IIA; dashed curves, Mk IIA/P.�D2 is the gas fuelling rate in el s−1, H97 is the energy enhancement factor with respect to theITER-H97 scaling law, ne is the line average density, Ppump is the neutral pressure at the divertorcryo-pump, Pmid is the main chamber neutral pressure, Dα (hor) is a measurement of the Dα

emission along a horizontal chord along the minor radius of the discharge. Contrary to the resultsin other experiments (see, for instance, figure 36) closing the by-pass leaks in JET decreases themain chamber pressure (Pmid) without affecting the divertor pressure (Ppump). This is independentlyconfirmed with measurements of the main chamber recycling levels by Dα emission (Dα (hor)).Despite this change the plasma density (ne), required fuelling (�D2) and energy confinement remainunchanged (Horton et al 1999a).

R220 Review article

Mk IIA/pMk II Gas Box

1.0 1.5 2.0 2.5 3.0 3.5

1.0

1

.5

2.0

2

.5Z

eff

<ne>(1019 m-3)

Figure 39. Plasma Zeff versus line averagedensity for similar L-mode density scans in JET-Mk IIA/P and JET-Mk II Gas Box divertors.The more closed divertor (JET-Mk II Gas Box)improves the purity of the plasma, therebyincreasing the density limit in L-mode discharges.For ELMy H-modes in JET, no difference in Zeffhas been found between Mk IIA/P and Mk II GasBox (Guo et al 2000).

caused by the divertor modifications. The latter has been found in ASDEX-U (Bosch et al1999a) in which an increase of the H-mode power threshold with the installation of the moreclosed Div II has been observed. The issue of the influence of divertor closure on H-modethreshold is particularly complicated because not only the closure but also the distance betweenthe divertor target and the X-point seems to play a role in determining the H-mode threshold(Righi et al 2000) and it is still the subject of active research.

The levels of main plasma intrinsic impurity contamination seem to depend little ondivertor closure (McCracken et al 1999, Gruber et al 1999), despite the larger SOL flowswhich are induced by the larger divertor pumping. Some reduction in the carbon impurityconcentration has been observed in JT-60U with the more closed W-shape divertor in ELMyH-mode discharges with forced SOL flow (Ishida and JT-60U Team 1999). In general, however,the intrinsic SOL flows caused by plasma drifts are much larger than those that can be inducedby the larger divertor pumping with more closed divertors (Asakura et al 2000). The reductionin main chamber neutral pressure can indeed reduce the contamination of the plasma dueto impurities from the wall sputtered by energetic charge-exchange neutrals. In the changefrom JET-Mk IIA to Mk IIA/P (plugged divertor leaks) the main chamber neutral pressurewas decreased. Unfortunately, the carbon coverage of the inner wall was also increased whenthe divertor by-pass leaks were closed and, as a consequence, no changes in main plasmaintrinsic impurity levels were observed (Horton et al 1999a, McCracken et al 1999). With theinstallation of the more closed JET-Mk II Gas Box divertor, an improvement in plasma purity forL-mode discharges has been observed (Guo et al 2000) (see figure 39). This is consistent withthe increased neutral compression and the larger divertor pumping in JET-Mk II Gas Box (atpresent there is no conclusive evidence for the dominance of either of these). However, it mustbe pointed out that this improved plasma purity in JET-Mk II Gas Box is only seen in L-modedischarges. ELMy H-mode discharges have similar levels of intrinsic impurities as those of themore open JET-Mk IIA divertor. The explanation put forward to account for this observationis based on the fact that, for more closed divertors, ion impact during an ELM can lead tostronger impurity sputtering at the components forming the narrow entrance of the divertor,as shown in figure 8. These impurities can more efficiently contaminate the bulk plasma thanthose produced at the divertor target (Guo et al 2000), offsetting possible improvements byreduction of main chamber sputtering that more closed divertors may produce.

7. Conclusions

In this review, we have summarized the results obtained in the area of divertor geometryoptimization carried out mainly in the last five to ten years with intensive use of 2D modelling

Review article R221

codes. Many of the expected effects, on which the divertor optimization procedure was based,have been proven by the experiments:

• influence of the divertor magnetic geometry in energy diffusion within the divertor itself;• influence of divertor geometry on achieving easier detachment without affecting the

density limit—the divertor geometry can be used as well to modify the in/out asymmetryof divertor detachment;

• enhancement of the divertor radiation by divertor geometry effects;• enhanced deuterium pumping with divertor closure—the divertor geometry optimization

provides a degree of freedom to adjust the achieved deuterium pumping to therequirements;

• enhanced recycling impurity pumping for optimized divertor geometry—the divertorgeometry optimization can be used to achieve selective impurity pumping.

Other effects of the divertor geometry have been confirmed as well by experiment but theirinfluence on the divertor and/or main plasma and their extrapolability to next step devices aremore questionable:

• influence of the divertor geometry on plasma flow patterns. The divertor geometry is seento influence plasma flows within the divertor and the SOL through the modification ofionization sources. Reasonable descriptions of the experimental deuterium and impurityion flows can be obtained with 2D modelling codes. However, the relative size of thedivertor-induced flows and of the drift flows remains to be quantified. As a consequenceit is not possible to assess quantitatively the role of divertor geometry on impuritycontamination of the bulk plasma.

• influence of the divertor geometry on main chamber neutral pressure and main plasmaconfinement. In this area the experimental results are divided into two groups ofexperiments. Alcator C-mod and ASDEX-U report no change of main chamber pressureand consequently little change in the main plasma due to the divertor geometry. JET,JFT-2M and DIII-D report a decrease of the main chamber pressure with increasingdivertor closure. Divertor geometry seems to affect, directly or indirectly, the L–H powerthreshold (in JET and JT-60U decreasing it and in ASDEX-U increasing it) but has littleeffect on H-mode confinement. The interaction between anomalous SOL transport, mainchamber recycling and divertor neutral leakage is certainly a complex one and will requirea substantial experimental effort to understand the differences/similarities observed in theexisting experiments.

The experimental results obtained in the optimization process of divertors for the presentgenerations of tokamaks have been used to refine the 2D modelling codes which are employed inthe design of the next generation of divertors. In this way, only the tested divertor optimizationcriteria are considered in the design process of the most challenging future divertor project,the ITER divertor (Kukushkin et al 2000).

Acknowledgments

This review has been made possible with the help and contributions of those working inthe area of divertor research. The author is particularly grateful to the following people fortheir contributions, encouragement and helpful comments: N Asakura, K Borrass, S Bosch,D Campbell, A Chankin, S Clement, D Coster, G Corrigan, S Davies, J Gafert, M Groth,H Guo, P Harbour, L Horton, N Hosogane, I Hutchinson, Y Igitkhanov, G Janeschitz,A Kallenbach, S Krasheninnikov, A Kukushkin, B La Bombard, J Lingertat, B Lipschultz,

R222 Review article

C Maggi, J R Martın-Solıs, G Matthews, G McCracken, R Monk, J Neuhauser, S Pitcher,R Pitts, G Porter, D Reiter, T Rognlien, G Saibene, R Sartori, R Schneider, R Simonini,P Stangeby, D Stotler, A Taroni and G Vlases. Figures 1(a) and 36 are reproduced in this articleby kind permission of the American Institute of Physics. Figures 1(b), 1(c) and 1(d), 2(a), 3, 8,9, 10, 20, 24, 27, 37, 38 and 39 are reproduced by kind permission of the International AtomicEnergy Agency. Figures 1(e), 6, 7, 13, 14, 17, 18, 28, 29, 32 and 34 are reproduced by kindpermission of Elsevier Science. Figures 11(a) and 11(b) are reproduced by kind permissionof the Czechoslovak Journal of Physics and figure 5 by kind permission of Wiley-VCH VerlagBerlin GmbH.

Dedication

This review article is dedicated to the memory of Mario Soler Lopez who introduced the authorto the study of plasma physics.

References

Allen S L et al 1999a Nucl. Fusion 39 2023Allen S L et al 1999b J. Nucl. Mater. 266–9 168.Asakura N et al 1997 J. Nucl. Mater. 241–3 559Asakura N et al 1999a J. Nucl. Mater. 266–9 182Asakura N et al 1999b Nucl. Fusion 39 1983Asakura N et al 2000 Phys. Rev. Lett. 84 3093Boedo J et al 1999 Plasma Physics Division Meeting (American Physical Society, Seattle, USA)Borrass K et al 1997a Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part IV

(Geneva: European Physical Society) p 1461Borrass K et al 1997b J. Nucl. Mater. 241–3 250Borrass K 1998 Czech. J. Phys. 48/S2 113Bosch H-S et al 1997 Plasma Phys. Control. Fusion 39 1771Bosch H-S et al 1999a Plasma Phys. Control. Fusion 41 A401Bosch H-S et al 1999b J. Nucl. Mater. 266–9 462Braams B J 1986 Computational studies in tokamak equilibrium and transport PhD Thesis University of UtrechtChankin A et al 1994 Plasma Phys. Control. Fusion 36 1853Chankin A et al 2000 Contrib. Plasma Phys. 40 288Coster D et al 1997 J. Nucl. Mater. 241–3 691Coster D et al 1998 Czech. J. Phys. 48/S2 327Coster D et al 1999a J. Nucl. Mater. 266–9 804Coster D et al 1999b Controlled Fusion and Plasma Physics, Proc. 26th Eur. Conf. (Maastricht) vol 23J (Geneva:

European Physical Society) p 1571Davies S et al 1995 Controlled Fusion and Plasma Physics, Proc. 22nd Eur. Conf. (Bournemouth) vol 19C, part III

(Geneva: European Physical Society) p 257Davies S et al 1999 J. Nucl. Mater. 266–9 1028Gafert J et al 1999 J. Nucl. Mater. 266–9 365Grosman A 1999 Plasma Phys. Control. Fusion 41 A185Groth M et al 1999 Proc. 4th Int. IEA Workshop on Helium Transport and Exhaust in Fusion Devices p 409Gruber O et al 1999 Nucl. Fusion 39 1321Guo H et al 2000 Nucl. Fusion 40 379Harbour P et al 1992 J. Nucl. Mater. 196–8 386Herrmann A et al 1999 Controlled Fusion and Plasma Physics, Proc. 26th Eur. Conf. (Maastricht) vol 23J (Geneva:

European Physical Society) p 1505Hill D N et al 1993 Controlled Fusion and Plasma Physics, Proc. 2nd Eur. Conf. (Lisboa) vol 17C, part 2 (Geneva:

European Physical Socierty) p 643Hill D N 1997 J. Nucl. Mater. 241–3 182Horton L et al 1999a Nucl. Fusion 39 1Horton L et al 1999b Plasma Phys. Control. Fusion 41 B329Hutchinson I et al 1994 Phys. Plasmas 1 1511

Review article R223

Hutchinson I et al 1995 Plasma Phys. Control. Fusion 37 1389Ishida S and JT-60U Team 1999 Fusion Energy 1998, Proc. 17th Int. Conf. (Yokohama, 1998) vol 1 (Vienna: IAEA)

p 13Isler R et al 1999 Phys. Plasmas 6 541ITER Expert Groups 1999 Nucl. Fusion 39 2137JET Team (presented by D Campbell) 1995a Plasma Phys. Control. Nucl. Fusion Res., Proc. 16th Int. Conf. (Seville,

1994) vol 1 (Vienna: IAEA) p 527JET Team (presented by D Stork) 1995b Plasma Phys. Control. Nucl. Fusion Res., Proc. 16th Int. Conf. (Seville,

1994) vol 1 (Vienna: IAEA) p 51JET Team (presented by G Vlases) 1997 Fusion Energy 1996, Proc. 16th Int. Conf. (Montreal, 1996) vol 1 (Vienna:

IAEA) p 371JET Team (prepared by R Monk) 1999 Nucl. Fusion 39 1751Kallenbach A et al 1999a Nucl. Fusion 39 901Kallenbach A et al 1999b Plasma Phys. Control. Fusion 41 B177Kaufmann M et al 1999 Fusion Energy 1998, Proc. 17th Int. Conf. (Yokohama, 1998) vol 1 (Vienna: IAEA) p 317Kawashima H et al 1999 Nucl. Fusion 39 1679Kaye S et al 1984 J. Nucl. Mater. 121 115Klepper C C et al 1993 Nucl. Fusion 33 533Komori A et al 2000 Plasma Phys. Control. Fusion 42 1165Krasheninnikov S et al 1992 Nucl. Fusion 32 1927Krasheninnikov S 1997 Phys. Plasmas 4 3741Kukushkin A et al 1999 Fusion Energy 1998, Proc. 17th Int. Conf. (Yokohama, 1998) vol 3 (Vienna: IAEA) p 1013Kukushkin A et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/ITER/2-ITERP/10, to be publishedKukushkin A et al 2001 J. Nucl. Mater. 290–3 887La Bombard B et al 1995 Phys. Plasmas 2 2242La Bombard B et al 1997 J. Nucl. Mater. 241–3 149La Bombard B et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/EX5/6, to be publishedLasnier C et al 1998 Nucl. Fusion 38 1225Lipschultz B et al 1997 Fusion Energy 1996, Proc. 16th Int. Conf. (Montreal, 1996) vol 1 (Vienna: IAEA) p 425Loarte A et al 1992a Nucl. Fusion 32 681Loarte A 1992b Estudio de los flujos de energıa y partıculas en el borde del plasma del Tokamak JET PhD Thesis

Universidad Complutense de MadridLoarte A 1992c Contrib. Plasma Phys. 32 468Loarte A et al 1995 Controlled Fusion and Plasma Physics, Proc. 22nd Eur. Conf. (Bournemouth) vol 19C, part III

(Geneva: European Physical Society) p 305Loarte A 1997a J. Nucl. Mater. 241–3 118Loarte A et al 1997b Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part III

(Geneva: European Physical Society) p 1049Loarte A et al 1998 Nucl. Fusion 38 331Loarte A et al 1999a Proc. 4th Int. IEA Workshop on Helium Transport and Exhaust in Fusion Devices p 297Loarte A et al 1999b J. Nucl. Mater. 266–9 1123Loarte A 2001 J. Nucl. Mater. 290–3 805Lumma D et al 1997 Phys. Plasmas 4 2555Maggi C A et al 1999a Nucl. Fusion 39 979Maggi C et al 1999b Controlled Fusion and Plasma Physics, Proc. 26th Eur. Conf. (Maastricht) vol 23J (Geneva:

European Physical Society) p 201Maingi R et al 1999 Nucl. Fusion 39 1187Marmar E et al 1999 Fusion Energy 1998, Proc. 17th Int. Conf. (Yokohama, 1998) vol 1, (Vienna: IAEA) p 71Matthews G et al 1999 Nucl. Fusion 39 19McCracken G et al 1998 Nucl. Fusion 38 619McCracken G et al 1999 Nucl. Fusion 39 41McCormick K et al 1999 Plasma Phys. Control. Fusion 41 B285Monk R et al 1997 Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part I

(Geneva: European Physical Society) p 117Niemczewski A et al 1997 Nucl. Fusion 37 151Neuhauser J et al 1984 Nucl. Fusion 24 39Pacher G et al 1997 Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part I

(Geneva: European Physical Society) p 297

R224 Review article

Parker R et al 1997 J. Nucl. Mater. 241–3 1Pitcher C S and Stangeby P C 1997 Plasma Phys. Control. Fusion 39 779Pitcher C S et al 2000 Phys. Plasmas 7 1894Pitcher C S et al 2001 J. Nucl. Mater. 290–3 812Pitts R et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/EXP4/23, to be publishedPorter G et al 1998 Controlled Fusion and Plasma Physics, Proc. 25th Eur. Conf. (Prague) vol 22C (Geneva: European

Physical Society) p 1994Reiter D et al 1991 Plasma Phys. Control. Fusion 33 1579Righi E et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/EXP5/31, to be publishedRognlien T D et al 1992 J. Nucl. Mater. 196–8 347Rognlien T D 1996 Contrib. Plasma Phys. 36 105Saibene G et al 1995 Controlled Fusion and Plasma Physics, Proc. 21th Eur. Conf. (Bournemouth) vol 19C, part II

(Geneva: European Physical Society) p 121Saibene G et al 1997 Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part I

(Geneva: European Physical Society) p 49Saibene G et al 1999 Nucl. Fusion 39 1133Sakasai A et al 1999 J. Nucl. Mater. 266–9 312Schneider R et al 1992 Contrib. Plasma Phys. 32 450Schneider R et al 1997a J. Nucl. Mater. 241–3 701Schneider R et al 1997b Fusion Energy 1996, Proc. 16th Int. Conf. (Montreal, 1996) vol 2 (Vienna: IAEA) p 465Schneider R et al 1999 J. Nucl. Mater. 266–9 175Schweinzer J et al 1997 Controlled Fusion and Plasma Physics, Proc. 24th Eur. Conf. (Berchtesgaden) vol 21A, part I

(Geneva: European Physical Society) p 1449Schweinzer J et al 1999 J. Nucl. Mater. 266–9 934Simonini R et al 1992 J. Nucl. Mater. 196–8 369Simonini R et al 1994 Contrib. Plasma Phys. 34 368Stangeby P C 2000 The Plasma Boundary of Magnetic Fusion Devices (Bristol: Institute of Physics Publishing)Stotler D et al 1999 J. Nucl. Mater. 266–9 947Tamai H et al 1999 J. Nucl. Mater. 266–9 1219Taroni A et al 1994 Contrib. Plasma Phys. 34 448Taylor T and DIII-D Team 1999 Fusion Energy 1998, Proc. 17th Int. Conf. (Yokohama, 1998) vol 1 (Vienna: IAEA)

p 49Tsuchiya K et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/EXP5/26, to be publishedVlases G et al 1992 J. Nucl. Mater. 196–198 392Vlases G 1993 Plasma Phys. Control. Fusion 35 B67Vlases G et al 1999 J. Nucl. Mater. 266–269 160Wagner F et al 1991 Plasma Phys. Control. Nucl. Fusion Res. 1990, Proc. 13th Int. Conf. (Washington, 1990) vol 1

(Vienna: IAEA) p 277Whyte D et al 2000 Proc. 18th Int. IAEA Conf. (Sorrento, 2000) IAEA-CN-77/EXP4/25, to be published