A comparison of experimental measurements and code results ...pitts/pitts/erents_ppcf_46_1757_2004.pdf · INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION Plasma

INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION

Plasma Phys. Control. Fusion 46 (2004) 1757–1780 PII: S0741-3335(04)80664-X

A comparison of experimental measurements andcode results to determine flows in the JET SOL

S K Erents1, R A Pitts2, W Fundamenski1, J P Gunn3 and G F Matthews1

1 EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire,OX14 3DB, UK2 Centre de Recherches en Physique des Plasmas, Association EURATOM-Confederation Suisse,Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland3 Association CEA-EURATOM sur la fusion controlee, 13108 Saint Paul Lez Durance, France

Received 14 May 2004, in final form 28 July 2004Published 14 September 2004Online at stacks.iop.org/PPCF/46/1757doi:10.1088/0741-3335/46/11/006

AbstractTwo reciprocating probe systems, at the same poloidal position at the top of theJET torus but toroidally separated by 180˚, have been used to measure parallelflow in the scrape-off layer (SOL) of lower single-null, diverted plasmas. Onesystem uses the entrance slit plates of a retarding field analyser to recordupstream and downstream flux densities, whilst the second employs two pins ofa nine-pin turbulent transport probe. Measurements have been made for bothforward and reversed toroidal field directions. The results from both probesystems are similar.

In the forward field direction, that is with the ion B × ∇ �B drift directiondownwards towards the divertor, a strong parallel flow is measured at the topof the machine in the direction from the outer to the inner divertor. The flowgenerally has a low value, Mach number M ∼ 0.2, close to the separatrix, butrises in the region of high magnetic shear close to the separatrix to a maximumof M ∼ 0.5 some 20 mm outside the separatrix. In contrast, for a reversedfield, the measured flow is small (close to zero) throughout much of the SOLbut rises near the separatrix to a value equal in both magnitude and direction tothat observed in the forward field. There is thus some symmetry in the flow withrespect to field reversal but with a symmetry axis given by a positive offset ofaround M ∼ 0.2. This paper presents simulations using the EDGE2D/Nimbuscode, which predicts very low values of parallel flow Mach number near theprobe position. The possibility of impurities released from the probe surfacesincreasing the flow velocity is explored using the code.

(Some figures in this article are in colour only in the electronic version)

0741-3335/04/111757+24$30.00 © 2004 IOP Publishing Ltd Printed in the UK 1757

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1758 S K Erents et al

1. Introduction

Measurements of strong parallel flow of plasma ions with Mach numbers M ∼ 0.5 in thedirection from the outer to the inner divertor in JET have been reported in [1] for forwardtoroidal fields, BT. This flow has been suggested as a possible cause of the large accumulationof carbon (and trapped tritium) at the inner divertor louvres by frictional coupling between thehydrogenic ions and the carbon impurities sputtered from the outer divertor target plates [2].However, these high measured values of flow are not as yet understood and are generally notincluded in two-dimensional code modelling of scrape-off layer (SOL) transport. The effectsof SOL flow on, for example, divertor power asymmetries, impurity migration and the mainplasma itself are important topics that need to be addressed for designing next generationmachines using codes in a self-consistent manner [3].

Preliminary simulations using the EDGE2D/Nimbus code package with drifts includedhave also been reported in [1] and suggest that the flow changes direction almost symmetricallyabout zero when the field direction is reversed. The code yielded flow values significantlylower than experimental observations. In this new work, these code simulations have beenpursued and improved such that they represent more closely the real experimental situation.Although, as before, the new code results do produce radial Mach number profiles, M(r),similar to experimental observations, the predicted absolute values remain much lower thanexperimentally observed. Whilst the cause of this disagreement cannot be unambiguouslyidentified, this paper will demonstrate that the probe itself may be exhibiting an influence onthe magnitude of the measured SOL flow.

New measurements in the JET SOL have shown that there is experimental evidencefor a dynamical coupling between cross-field turbulent transport and parallel flows [4]. Ithas been suggested that this mechanism is responsible for driving at least part of the highflows, particularly in view of the fact that invoking classical drifts alone cannot explain themagnitude of the flow. Further evidence that the strong flow really exists, i.e. is not just dueto wrong interpretation of the ion flux measurements on the upstream and downstream sidesof the probe, comes from the ion temperature, Ti(r), on each side [5]. These are found to bevery different—a situation that is theoretically expected to occur in the presence of a strongflow [6].

Mechanisms such as the Pfirsch–Schluter flow and an enhanced, ballooning like transportat the outer mid-plane have been proposed in [1] as driving forces for the flow in JET. Codemodelling using the EDGE2D/Nimbus package at JET including �E × �B, ∇ �B and centrifugaldrifts has failed to match the magnitude of the strong measured flows at the probe location [7].The code was able, however, to qualitatively match the observed Mach number profile in theforward field, which was invariably found to exhibit a maximum in the SOL at a radius ofr ∼ 10–25 mm from the separatrix in mid-plane co-ordinates. (Interestingly, a similar profileshape is also found in C-Mod [8], though the maximum occurs much closer (∼2 mm) to theseparatrix than in JET.) In contrast, when BT was reversed in JET, an important finding was thatthe flow reversed but with a much smaller velocity (|M| ∼ 0.1). In addition, a minimum, ratherthan a maximum, appeared in the flow profile. This was not reproduced by the model, whichsuggested that the flow should reverse but have a similar absolute value of Mach number,especially close to the separatrix. The simulations thus predicted that if one takes the averageof forward and reversed field parallel flow Mach numbers, the result should be close to zero,within 25 mm of the separatrix—if field dependent forces, e.g. drifts, are mainly responsiblefor the flow. (It should be pointed out here that EDGE2D modelling as reported in [1] assumedvery high temperature, low density plasmas—we will show here that the result is somewhatdifferent when ‘real’ edge parameters are used.)

Determination of flows in the JET SOL 1759

Numerical simulations of ion orbit losses [9] have also suggested that these may beresponsible for flows in the SOL, through momentum transfer from orbit lost ions to backgroundions in the separatrix region. Using momentum sources predicted in [9], attempts have beenmade to model the large (M ∼ 0.6) flows observed in JET using EDGE2D. However, themomentum source is insufficient and can only produce a flow with M < 0.1 [10]. So,although the direction of momentum transfer was correct, it was concluded that this mechanismwas probably not the primary cause of the large flows observed in the SOL, which occur atr ∼ 20 mm, rather than close to the separatrix (3–5 mm), where orbit loss momentum istransferred.

Recent EDGE2D simulations at JET have been performed to investigate the effect ofan anomalous pinch term in the radial particle transport, which might correspond to rapidconvective or ‘blobby’ transport [11]. This approach postulates an outward pinch at the lowfield side (LFS) and an inward pinch on the high field side (HFS) and has produced (withoutswitching on classical drift terms) high Mach number flows at the probe location, consistentwith the experimental measurements described here for the forward field. It is not clear,however, how this relates to the reversed field situation, in which the same arguments wouldhave to impose an inward pinch on the LFS and an outward flux on the HFS.

Finally, in the absence of any strong physics understanding of how the large flows aregenerated, EDGE2D modelling of JET carbon screening experiments including flow are beingperformed for the forward and reversed field by imposing an ad hoc external momentum sourcein the SOL [12]. This source is prescribed along a specific poloidal extent of the SOL in sucha way as to match the experimentally measured flows.

In this paper, the preliminary results of [1] are expanded by presenting further, moredetailed measurements of parallel flow in JET for closely matched forward and reversedfield discharges. Throughout, forward field refers to the negative BT direction for which theion B ×∇ �B drift direction is downwards, towards the X-point of lower single null discharges.This is the normal operating mode of JET and most other tokamaks. In JET, when BT isreversed, the plasma current, Ip, must also be reversed to preserve helicity (the divertor targettiles are arranged in a ‘roof-top’ design to avoid overheating on leading edges). The resultsare compared from two fast reciprocating probe systems, a retarding field analyser (RFA) anda turbulent transport (fluctuation) probe (TTP) inserted at the same poloidal position at the topof the torus but toroidally separated by 180˚. In particular, the effect of the magnitude of BT

on the measured parallel flow is examined. Some results are also presented showing the flowdependence on line averaged plasma density, ne and increasing neutral beam power in L-modedischarges. Finally, modelling results (EDGE2D with drifts) will be discussed in which bothfield directions and puff rates of deuterium and impurities (carbon) have been studied usingseparate grids constructed for each specific experimental discharge. These results will beused to show that a strong candidate explanation for the observed high measured flows is theinfluence on the local plasma of the probe itself as it reciprocates through the SOL.

2. The probe systems used for parallel flow Mach number measurements

A detailed description of the JET RFA can be found in [13]. This system is positioned at thetop of the torus just outboard of the plasma centre line at a major radius of 3.25 m. It canreciprocate vertically to the separatrix region from a distance of 100 mm above the plasma ina time period of 200 ms. When used as a Mach probe, entrance slit plates positioned at rightangles to the field lines on either side of the probe body are biased at ∼−150 V to collect ionsaturation currents, Jsato and Jsati, along field lines in the directions facing the outer divertorand inner divertor, respectively. These slit plates, made of a titanium–zirconium–molybdenum


alloy that will withstand high heat loads, are positioned behind openings in a boron nitridehousing that defines a rectangular collection area of 24 mm2.

Details of the TTP design may be found in [14], whilst details of a number of experimentsperformed with the probe are reported in [15]. It comprises nine cylindrical graphite pins usedas Langmuir probes, with five pins positioned on the top of a 5 mm high boron nitride dividepositioned at right angles to the field lines. These, together with three more behind one sideof the divide have a 1 mm diameter. A single pin positioned on the other side of the divide hasa 2.5 mm diameter and faces the outer divertor in the forward field configuration. For parallelflow measurements, the pins on each side of the divide are biased at −200 V to collect Jsato

and Jsati. Any pin may be floated to record the floating potential, Vf . It is normal to record Vf

on at least one of the pins on top of the divide during flow measurements, giving informationon the probe position relative to the separatrix, i.e. the radial field distribution, Er(r).

Each probe has a boron nitride body with overall diameter 40 mm, to which is applieda thin carbon coating. The carbon layer is applied to avoid sputtering of the boron nitride,which can lead to coating, by an insulating layer, of the TTP pins and RFA slit plates. Aswill be discussed later, this carbon coating may have important consequences for the flowmeasurements.

Two systems of data acquisition are used, a slow system with a 10 kHz collection rate anda fast system that uses 500 kHz digitizers. Both are used with the TTP, but only the slow systemis used with the RFA. In addition to the normal mode of operation with a fixed negative biason the Mach probe elements, a voltage sweep at 100 Hz may also be applied to the TTP pins ina separate discharge, permitting the acquisition of Langmuir I/V characteristics. From these,electron temperature profiles, Te(r), may be derived. Ion temperature profiles are measuredusing the RFA.

3. Experimental measurements of parallel flow

3.1. Comparison between parallel flow measurements using different probes

The RFA and TTP probe systems have been used to measure parallel flow in the steady stateregion of both ohmic and neutral beam heated discharges in which the density was stepped upduring the discharge and in discharges with a slow ramp in the toroidal field (0.06 T s−1). Upto four probe reciprocations are made at 2 s intervals during each discharge.

Typical measurements of Jsat on each side of the probe are presented in figure 2. Thisexample is for an Ip = 2 MA, BT = 2 T forward field Ohmic discharge with a central densityramp from ne = 1.6 × 1019 to 3.4 × 1019 m−3. Although measurements are made with theprobe moving vertically into the plasma at R = 3.25 m (see figure 1), all SOL profile resultsin this paper are mapped to the outside mid-plane and are presented in terms of distances fromthe magnetic separatrix. As with all measurements of this type, there is an uncertainty in theabsolute position of the separatrix and of the probe itself with respect to the torus. It is difficultto estimate with any precision the magnitude of this uncertainty, but it is believed that errorsin the magnetic equilibrium reconstruction (EFIT) can be large (as much as 20 mid-plane mm)at probe locations where magnetic pick up coils are sparse. The electron pressure balancebetween the reciprocating probe and divertor target Langmuir probe data at a low densitywhen the divertor plasma is attached has been used to derive an approximate correction of22 mm at the outside mid-plane, which is used henceforth in all radial profile plots.

If toroidal symmetry is assumed, then in principle both probe systems should yield similarprofiles of Jsato and Jsati. At first sight, the agreement between the two sets of measurementsin figure 2 is surprisingly poor, but the principal reason for the discrepancy is understood. It is


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RFAandTTP

B (Forward field)B×

Figure 1. Poloidal view of the JET torus showing the Mach probe position. Both RFA and TTPprobes are at the same poloidal position but are separated 180˚ toroidally. The grid shown in thefigure is a typical example of that used in the EDGE2D modelling described later.

due to the relatively thick walls (∼7 mm) presented to the incoming ion flow by the window inthe RFA boron nitride housing described in section 2. The large ion Larmor radius comparedwith that of the electrons leads to ions being scraped off preferentially and to the subsequentdevelopment of a strong radial electric field gradient, which demagnetizes the ion gyro-orbits.Ions are ripped from their guiding centre trajectories and further drawn to the wall, subsequentlydecreasing the ion flux to the RFA slit plate compared with that which would be measured inthe absence of the thick walls. This ‘tunnel’ effect has been described in detail with respect toan application with a dedicated probe [16], where it is modelled using the object oriented PICcode XOOPIC [17]. The code has also been applied to the specific geometry of the RFA probeentrance slits, and ion flux attenuation factors in the range 3–4 have been found for plasmaconditions appropriate to those for which the data in figure 2 were obtained [18]. It shouldalso be noted that to obtain the profiles in figure 2, the separatrix position estimated from theTTP data was displaced relative to that of the RFA in order to match the observed change ine-folding length for the flux—the break between the ‘near’ and ‘far’ SOLs typically observedat ∼20 mid-plane mm on JET (see also figure 15 in section 4 and figure 17 in section 5).

Using the ion particle fluxes in figure 2 from the two probe systems and the TTPmeasured Te profile, probe density profiles are compared in figure 3 with data derived from twoother independent (and non-perturbative) edge diagnostics (lithium beam and edge LIDAR).


105

104

103

102

10 20 30 40 50 600

J sat

(A.m

-2 )

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Distance from Separatrix (Mid-plane mm)

Pulse No: 56891 Density ramp

RFA Jsato <ne> = 1.6 (1019m-3) RFA Jsati <ne> = 1.6 (1019m-3)

TTP Jsati <ne> = 1.6 (1019m-3)

TTP Jsati <ne> = 3.4 (1019m-3)

RFA Jsati <ne> = 3.4 (1019m-3)RFA Jsato <ne> = 3.4 (1019m-3)

TTPJsato <ne> = 3.4 (1019m-3)

TTP Jsato <ne> = 1.6 (1019m-3)

Figure 2. Ion flux densities, Jsato and Jsati, as measured on the upstream and downstream sides ofthe RFA and TTP acting as Mach probes for two different plasma densities.

The lithium beam measures along a chord at the same poloidal location as the two reciprocatingprobe systems and the edge LIDAR along a horizontal chord just above the mid-plane. Thedensity as derived from the TTP is systematically about a factor 2 lower than that from theLithium beam and the few points from the edge LIDAR. Such disagreement is not unreasonable,considering uncertainties in the effective particle collection areas for the TTP (due to ion Larmorradii effects) and positional uncertainties in both diagnostics.

For the RFA, the tunnel effect appears unable to account for all the large discrepancy(a factor of 6–10). An issue to which section 5 will return in the context of a possible probeinfluence on the measurement is the absence in the lithium beam profiles of any sign of thenear and far SOL breaks at r ∼ 20 mm referred to earlier.

In this paper, as in [1], parallel flow Mach numbers are calculated from the ion saturationcurrent densities using Hutchinson’s formula [19]:

M(r) = 0.4 ln

(Jsato

Jsati

), (1)

where the value of the pre-logarithmic constant is very close to that used by other authorsfor Mach measurements (see, e.g. [8, 20–22]). This constant is a function of the plasmaviscosity in the SOL and falls as viscosity increases [19] and so could possibly be somewhat inerror (lower) if, for example, the SOL has a high carbon concentration (assuming that such aplasma has a higher viscosity than its pure hydrogenic counterpart). This is largely conjecture,however, since so little is known about the viscosity of the hydrogenic plasma, let alone that of


1016

1017

1018

1019

1020

0 10 20 30 40 50 60

Den

sity

(m-

3 )


Pulse No: 56891

RFA 1.6 1019 m-3

RFA 2.6 1019 m-3

RFA 3.4 1019 m-3

TTP 1.6 1019 m-3

TTP 2.6 1019 m-3

TTP 3.4 1019 m-3

Li-beam 1.6 1019 m-3

Li-beam 2.6 1019 m-3

Li-beam 3.4 1019 m-3

Edge Lidar 1.6 1019 m-3

Edge Lidar 2.6 1019 m-3

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Figure 3. Density profiles as calculated from RFA Jsato and TTP Te compared with those measuredby other diagnostics.

one containing carbon impurities. In any case, Hutchinson suggests that the pre-logarithmicconstant is not a strong function of viscosity.

Parallel flow Mach number profiles in forward field, derived from the measurementspresented in figure 2 for both the RFA and TTP probes, are shown in figure 4. The results areshown separately for clarity—the profile shapes from each probe system are similar, with theabsolute magnitude slightly higher for the RFA. Otherwise, the agreement is good (remarkable,in fact, considering the uncertainties in estimating the flux to the two probes). A positive Machnumber in this figure and all others in this paper denotes a flow in the direction from the outerto the inner divertor. Since the RFA data are derived from direct measurement of the currentto the slit plates, no error bars are included in figure 4. In contrast, for this example the TTPdata have been obtained through voltage scanning of the probe pins, and the error bars depictthe error resulting from the Langmuir probe fits. Note that in this particular case the TTP doesnot reciprocate as far into the SOL as the RFA. Note further the shift (clear in the RFA data butless evident for the TTP, which did not travel as far towards the separatrix) in the maximumof the flow velocity to larger radii as the density increases.

3.2. Measurements in forward and reverse fields

Whilst offering evidence for good agreement in the Mach number profile and magnitudebetween the two diagnostics, the data in figure 4 suffer from insufficient coverage in thecritical region near the separatrix. A separate set of measurements obtained with the RFA


RFA ne = 1.6 1019m-3

RFA ne = 2.6 1019m-3

RFA ne = 3.4 1019m-3

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

010 20 30 40 50 600

Mac

h N

umbe

r

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

010 20 30 40 50 600

Mac

h N

umbe

r

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TTP ne = 1.6 1019m-3

TTP ne = 2.6 1019m-3

TTP ne = 3.4 1019m-3

Pulse No: 56891

Figure 4. Parallel flow Mach numbers derived from the data presented in figure 2 for RFA andTTP probe systems and for three different densities during a density ramp.

only have been obtained for deeper probe penetration in plasmas with fixed plasma currentIp = 2.0 MA and density (ne = 1.8 × 1019 m−3) but varying BT and thus varying the safetyfactor, represented here by its value, q95, at the 95% poloidal flux surface. These measurementshave been repeated in closely matched forward and reversed field discharges in a density rangefor which the divertor plasma remains always attached. The average Jsat (average on bothsides of the RFA) for the two field directions is plotted in figure 5, and the resulting Machnumbers in figure 6. It is clear from the latter that there is no change in parallel flow Machnumber as the toroidal field is increased from 1.6 to 1.9 T. More importantly, it is also evidentthat the flow remains almost always in the same direction, independent of the field direction,although it is virtually stagnant in the reverse field in the region where the forward field flowis a maximum. The curve at M(r) ∼ 0.2 is the difference (smoothed) between the forwardand reverse field measurements. The poloidal position of the flow measurement is important,


-10 0 10 20 30 40 50

Ave

rage

Jsa

t (A

.m-

2 )


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104

103

102

56723 Normal Field q95 = 2.9359737 Reverse Field q95 = 3.0056723 Normal Field q95 = 2.7559737 Reverse Field q95 = 2.8456723 Normal Field q95 = 2.5459737 Reverse Field q95 = 2.67

Figure 5. Average flux density profiles in the SOL measured using the RFA in matched dischargeswith forward and reversed fields, for different values of q95.

Figure 6. Parallel flow Mach number profiles in the SOL measured using the RFA in closelymatched discharges with forward and reverse fields, for different values of q95. The average M(r)

from the two field directions is also shown as the full curve at M(r) ∼ 0.2.


Figure 7. Parallel flow Mach number profiles in the SOL measured using the RFA in dischargeswith forward and reversed fields, for different values of central density, ne.

however. In recent forward field measurements just above the HFS X-point in JT-60U [22]the flow is observed to reverse direction in the separatrix vicinity, being directed towards theouter target in this region and to the inner target deeper in the SOL. In JET, the flow measuredat the top of the torus close to where one might intuitively expect a stagnation point is alwaystowards the inner target for both field directions.

3.3. The effect of density on parallel flow Mach numbers in the SOL

Discharges in which the central density was increased in four steps, coming into equilibriumin <2 s after each increase in D2 gas puff rate, were used to record parallel flow as a functionof density. All measurements shown in figure 7 are for 2 MA, 1.76 T Ohmic discharges. In theprocess of this particular experiment, it was observed that parallel flow Mach numbers obtainedin similar discharges later in the series differed slightly from the earlier measurements, an effectlikely due to the effects of wall conditioning. The general trend in figure 7, namely an increasein Mach number in reversed field and a slight decrease in forward field with increasing densitywas nevertheless preserved.

It is often assumed that Ti ∼ 2Te in the SOL (with Ti,e respectively the ion and electrontemperatures), an assumption typically confirmed both by onion-skin modelling [23] and bymeasurements made using the RFA itself [3]. Unfortunately, however, good RFA Ti dataare difficult to obtain in all but the lowest density plasmas or, equivalently, at relativelylarge separatrix distances under higher density conditions [13]. Moreover, to obtain Te

measurements, the TTP must be operated with a voltage sweep on the pins, a bias configurationincompatible with turbulent transport measurements. Given the extremely limited number of


Figure 8. The relationship between Te and Vf (measured with respect to torus potential) obtainedusing the TTP in a number of JET discharges, Ohmic, L- and H-modes. The solid line is theory,equation (2), for various Ti/Te ratios and different secondary electron emission coefficients.

discharges possible in JET for these dedicated probe measurements, simultaneous data forSOL temperature and parallel flow are difficult to obtain. This means that the electron density,calculated from Jsat and Te, cannot be routinely obtained. This measurement is needed forcomparison with other diagnostics, e.g. the lithium beam. However, one quantity, the localfloating potential, Vf , is routinely measured using the TTP. On JET it is found that for manydischarge conditions, including H-mode, Vf is closely related to Te. This relationship, betweenVf and the average Te of both sides of the TTP in scanning mode, is shown in figure 8.

The solid lines are the theoretical floating potentials (Vfth)—given by Stangeby [24]—together with a constant offset of Vc = 17 V,

Vfth = 0.5Te ln

(me

mi(Ti/Te)(1 − δ)−2

)+ 0.5Te + Vc, (2)

where δ is the secondary electron emission coefficient. For Ti/Te = 2, the best fit to thedata is found for δ = 0.3, though experimental scatter means that the range 1 < Ti/Te < 5approximately bounds the data. Since the theoretical expression [24] is derived with respect tothe plasma potential, the constant offset of ∼17 V implies a relatively constant plasma potentialfor all discharges. An equivalent result was found in [25] for the DITE tokamak, where thedirectly measured sheath potential, plotted as a function of the measured Te, was in very goodagreement with the simple sheath theory from which equation (2) is derived.

Although equation (2) is not accurate to better than about a factor 2 in Te across the SOL,the fact that Te appears only as a square root in the ion sound speed, cs (an important parameterin discussing the magnitude of parallel flow—see below) indicates the relationship is generallyuseful for calculating densities in the SOL: ne = 2jsat/cs.

For the same density ramp, forward field discharge of figure 2, Te profiles from the ionand electron sides of the TTP operating in scanning mode are shown in figure 9. At the lowestdensities Te is similar on each side, but is somewhat lower on the side facing the outer divertor


Figure 9. Electron temperatures measured on probes facing the outer divertor, Teo, and innerdivertor, Tei, of the TTP probe in scanning mode (points with error bars). The squares are fromequation (2) and the solid lines are fits to the data.

at the higher densities. The calculated profiles from equation (2) are in good agreement withthe data from the pin facing the outer divertor.

It is useful, for comparison with data from other tokamaks to establish the collisionalityregime appropriate to the discharges described here. Precise evaluation of the density in theSOL from the probe measurements is difficult, but the lithium beam data, figure 3, are correct atleast to within a factor of 2. At the separatrix, for the lowest density discharges presented here,the normalized SOL collisionality, ν∗ = Lc/λee ≈ 20, and for the highest density dischargesν∗ ≈ 10. Here Lc is the connection length from target to target around the SOL, and λee is theelectron–electron mean free path. ν∗ rises rapidly with radial distance in the SOL: ν∗ ≈ 67 at10 mm from the separatrix at a low density and ν∗ ≈ 46 for the highest density case.

Using the TTP measured Vf(r) and Te(r), the radial electric field is estimated in the usualway as

Er = − ∂

∂r(Vf + 2.5Te) (3)

with the factor 2.5 accounting for the magnitude of the sheath potential fall for a deuteriumplasma. Results for the inner and outer divertor facing sides of the probe are shown in figure 10for the lowest and highest plasma densities in figure 9. Unfortunately, only in forward fielddoes the data quality permit the radial derivative in equation (3) to be estimated. The resultindicates that Er increases more rapidly at the higher density, approaching values of 3 kV m−1

near the separatrix. It also illustrates the apparent tendency for the electric field to increase atany given radius as the density increases.

If one assumes that the magnetic equilibrium reconstruction code (EFIT) at least predictsthe relative position, if not the absolute position of the separatrix, correctly as the density isincreased, then Er at the position of maximum flow (r ∼ 20 mm) roughly doubles in value asthe density doubles. Yet the effect of switching on �E × �B drifts is to increase the flow towards


Eri 3.4 × 1019 m-3

Ero 1.6 × 1019 m-3

Eri 1.6 × 1019 m-3

Ero 3.4 ×10 19 m-3

0

1000

2000

3000

4000

0 10 20 30 40

Er (

V.m

-1 )


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Figure 10. Mid-plane mapped radial electric field profiles on TTP pins facing the outer divertor,Ero, and inner divertor, Eri, from TTP, deduced from equation (3). Forward magnetic field only.

the inner divertor in forward field at the probe position, as shown in [1]. So an increase in Er

would be expected to produce an increase in flow. This is at variance with figure 10, as theexperimentally measured flow does not increase rapidly close to the separatrix as does Er ; infact, it falls! Figure 7 also shows that the measured flow in forward field does not increase withdensity. These observations suggest that the radial electric field is not an important parameterin the flow as measured with the reciprocating probe on JET.

It is useful at this point to distinguish between the Mach number, which is related to theparallel flow velocity v‖ = csM , and the total flow of particles, which may, for example,be responsible for the transport of carbon from the outer to the inner divertor by frictionalcoupling. The parallel flow velocity is perhaps a more physically meaningful parameter thanthe Mach number, but its derivation at first sight requires knowledge of both Ti and Te:

cs =√

e(Te + Ti)

mi. (4)

The parallel flow of particles is defined by

�‖ = necsM, (5)

where ne is the local density, but this is unnecessary for the calculation of �‖ since

2jsat = enecs, (6)

so that �‖ can be computed directly from the results of figure 2:

�‖ = 2jsatM

e. (7)

Examples of the parallel flow of particles across the SOL are plotted in figure 11 for matchedforward and reversed field cases.

3.4. The effect of neutral beam power on parallel flow Mach numbers in the SOL of L- andH-modes discharges

To study the effect of input power on the parallel flow, neutral beam injection (NBI) fromOhmic (1 MW) up to >5 MW was used in four steps during matched forward and reversed


Figure 11. Parallel flow of particles in the SOL measured using the RFA in discharges with forwardand reverse fields, for different values of central density, ne. The solid symbols are for forwardfield, the open symbols for reversed field.

field discharges. The reciprocating probes are inserted towards the end of each step whensteady state conditions have been obtained (dW/dt ∼ 0, with W the total plasma storedenergy). Plasmas are generally L-mode, with Ip = 2 MA, BT = 2.4 T. In the parallel flowMach number profiles shown in figure 12, the highest total input power (5.1 MW) shown forforward field is just sufficient for access to H-mode characterized by low frequency ELMs(which do not occur in the time period of the reciprocation). In reversed field, for the highesttotal power (5.3 MW), the plasma remains in L-mode. The rapid rise in Mach number forr > 40 mid-plane mm corresponds to low levels of Jsat, and as such must be treated withcaution. Note that although the aim of this experiment is to examine the effect of power onparallel flow, ne also increases as a result of the neutral beam heating, as shown in figure 12.A clear conclusion from the RFA data is that there is little change in M(r) with increasingpower, both in forward and reversed field configurations.

4. EDGE2D code simulations of the parallel flow measurements

Some preliminary EDGE2D modelling with �E× �B, ∇ �B and centrifugal drifts has been reportedin [1]. However, to match the experimentally observed values of M(r) as high as ∼±0.2, shownin figure 8 of [1], required that very high divertor target temperatures (i.e. a very hot, low densityplasma) be assumed. Simulations with drifts made using the UEDGE fluid code [21] on JETand other machines [22, 26] also consistently find predicted Mach numbers in the LFS SOL tobe much smaller than those measured experimentally. Here we will try to match the divertortarget densities and temperatures, net(r) and Tet(r), predicted by EDGE2D to those measuredby divertor tile embedded Langmuir probes. If a reasonable match between code predictionand experiment is obtained for these downstream (target) parameters, then the upstream (SOL)


Figure 12. The effect of increasing plasma input power on parallel flow Mach number in theSOL. With an increase in neutral beam power, ne also increases as shown. The full red diamondscorrespond to an H-mode flow profile.

profiles, neu(r) and Teu(r), as measured by the reciprocating probes, are usually also wellmatched [27].

The simplest situation of an ohmic plasma is modelled, but varying density is allowed,so that this exercise reduces to an attempt to reproduce the Mach number profiles presentedin figure 6. Separate simulation grids are generated for each of the forward and reversed fielddischarges (figure 1 illustrates one example of the typical grids employed). Deuterium puffingfrom the top of the torus is used in the code, as in the experiment, to control the density andis fixed at the same rate for any particular discharge for both forward and reversed fields, alsoas in experiments. Whilst experimental puff rates were up to 1022 D2 s−1, the code typicallyrequires a factor of 3–4 less, (2–3)×1021 s−1. Although wall pumping is a possible cause, thisdiscrepancy is a feature when modelling discharges obtained during vertical target operation.When the strike points are positioned on the horizontal targets, puff rates of up to 1022 D2 s−1

are indeed required by the code. Of the 1.6 MW total input power in these discharges, thesimulations assume that 1 MW and 0.6 MW are, respectively, carried in the ion and electronchannels. All important particle drifts are activated for both deuterium and impurity (carbon)species including radial, parallel and transverse components. Carbon chemical sputtering wasincluded according to the experimental measurements made by Haasz [28].

Cross-field diffusion coefficients are often assumed to be radially constant in edge plasmasimulation, but DIVIMP-OSM [29] modelling of plasmas similar to those considered hereindicates that the thermal diffusivity, χ⊥(r), often increases with radial distance in the SOL,reaching a maximum at ∼20 mid-plane mm. This has been confirmed experimentally forthe particle diffusivity, D⊥, by analysis of turbulence measurements obtained with the TTP,which suggest a rise in transport at r ∼ 20 mm in carbon rich discharges [30]. A value ofD⊥ = 0.5 m2 s−1 close to the separatrix rising to 1.5 m2 s−1 at r = 20 mm and then falling backto 0.5 m2 s−1 for r > 30 mm has been chosen for the simulations described here. In addition,


1

10

10 0 10 20 301017

1018

1019

10 0 10 20 30

Te inner divertor Te outer divertor

ne inner divertor ne outer divertor

EDGE2D


Ele

ctro

n te

mpe

ratu

re (

eV)

Den

sity

(m-

3 )

Shot: 56725 1.8×1019 m-3

JG04

.61-

41c

Figure 13. Profiles of density and electron temperature across the inner and outer SOL in forwardfield measured using Langmuir probes embedded in the divertor target tiles. The groups of pointscorrespond to data obtained from the various target probes as the strike point makes a small,deliberately imposed sweep across the target.

χ⊥(r) = 2D⊥(r) has been assumed. Code results do not appear to be too sensitive to changes(factor of 2) in these coefficients.

4.1. Simulation of forward and reverse field measurements

Measurements in reversed field, figure 7, show a clear overall increase in M(r) towards theinner divertor as density increases, with the flow being almost totally in this direction acrossthe entire SOL at the highest density. However, this is not the case in forward field, wherevery little change in M(r) with density is recorded. Figure 13 illustrates the experimentallymeasured and simulated target profiles mapped to the outer mid-plane for the lowest densityforward field case, ne = 1.8 × 1019 m−3.

Agreement with density in the outer divertor main SOL is within a factor of 2 and isconsidered more than acceptable in view of uncertainties in the values of field line anglesand projected surface areas that must be used to compute the experimental probe densities.Likewise, simulation and experiment are well matched in the reversed field case, but require aslightly higher puff rate for the same ne. Generally, the simulation of inner target Te is poor,i.e. much lower than that recorded experimentally—a common feature of edge code simulationresults at JET.


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

FWDB: 1.5x1021s−1

FWDB: 3.0x1021s−1

REVB: 2.0x1021s−1

REVB: 4.0x1021s−1

10 0 10 20 30 40

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

FWDB: 2.0x1021s−1+C sourceREVB: 2.0x1021s−1+C source


Mac

h N

umbe

r

JG04

.61-

46c

Figure 14. EDGE2D simulated Mach number profiles for various densities. These should becompared with their experimental analogues in figure 7. Puff rates in forward field = 1.5 and3×1021 are required for low and high density simulations. 2 and 4×1021 are similar requirementsfor low and high density simulations for reversed field. The lower curves are for a carbon sourceat the probe position (see section 5.2).

Simulated parallel flow Mach numbers are presented in figure 14 and should be comparedwith the measurements in figure 7. Evidently, although the experimental trend with both radiusand density is relatively well reproduced by the model, the predicted Mach number is too lowby a factor in the range 5–10.

Upstream, the unperturbed ion saturation current density to the Mach probes, i.e. correctedfor the measured flow by using Hutchinson’s fluid model [19], can be approximated by a simplefunction that proves to be accurate to better than 0.1% for all M: �0 = �� + 0.1∗ sin(2.3813∗��), where �� = Jsato − Jsati. Figure 15 compares �0 calculated from the RFA data withthe EDGE2D prediction. The RFA Jsat data must be multiplied by a factor of ∼6.5 to match thesimulated profile, but the profile shape is well approximated by the code. Note in particular theclear break in the profile gradient separating the SOL into near and far regions at ∼20 mm as firsthighlighted in section 3.1 with reference to the data in figure 2. The initial gradient is regainedin the far SOL at separatrix distances >30 mm, consistent with the transport falling again inthis region. With regard to the discrepancy between the measured and simulated magnitudes,the strong tunnel effect described in section 3.1 due to the RFA probe head geometry canaccount for a large part, but not all of, the difference [18].


0 10 20 30 40

EDGE2D Puff rate = 4×10 21 s− 1

RFA *6.5 ne = 3.1×1019 m− 3


J sat

(A.m

−2 )

JG04

.61-

43c

104

105

103

Figure 15. A comparison of the Mach number corrected ion saturation current density to the RFAwith the EDGE2D prediction for a high density simulation, ne = 3.1×1019 m−3. The experimentaldata must be multiplied by a factor of 6.5 to match the code prediction but the experimental profileshape is well reproduced. The dotted curve is a sixth order polynomial fit to the experimental data.

5. Discussion

5.1. Ballooning as a possible mechanism for increased M(r)

The experimental parallel flow Mach numbers presented here are different in one significantrespect compared with those presented in [1]. In both forward and reversed fields, M convergesto a common value (M ∼ 0.2) at the separatrix. This is true for both increasing density(figure 7) and increasing neutral beam power up to H-mode (figure 12). In [1] this feature wasnot apparent—the tendency was for a flow value close to zero at the separatrix.

Ballooning transport was proposed in [1] as a possible mechanism for the high Machnumbers measured in the SOL, but then dismissed, given that such a driver for the flow couldexplain neither the peaked structure of M(r) nor the disappearance of flow at the separatrix.Measurements of this type made in the main SOL of the C-Mod [21] and JT-60U [20] tokamaksdo not appear to indicate this field independent offset in Mach number close to the separatrix.In both these cases, however, the reciprocating probes used to obtain the data were inserted inthe vicinity of the outside mid-plane, close to the region of unfavourable field line curvature,where any excess ballooning-like transport would occur. A measurement in this region istherefore unlikely to be sensitive to any parallel flow that is established as a consequence ofthe local pressure increase caused by the excess cross-field transport. This is not the case atJET, where the probes are inserted near the top of the torus (figure 1), far from the ballooningregion. Any flow component due to a supposed ballooning contribution would, of course, befield independent, depending only on the presence of a region of unfavourable curvature.

Assume the total flow, Mt(r), to be composed of two components, one due to drifts anddependent on the field direction, Md(r), and the second independent of field, Mb(r). Then, in


the forward field direction

Mtf(r) = Md(r) + Mb(r) (8)

and in reversed field

Mtr(r) = −Md(r) + Mb(r), (9)

so that, trivially, adding (8) and (9) gives the field independent term,

Mb(r) = Mtf(r) + Mtr(r)

2, (10)

which is nothing more than the average of the two plots, which has already been shownin figure 6 as the full line. It is therefore clear that this ‘extra’ mechanism is, at leastexperimentally, almost independent of the radius.

Assuming that ballooning is responsible for the flow offset nevertheless leads to a problemof internal consistency. If there are no ionization sources in the SOL and no return flux tothe core, then the total particle flux leaving the core in the steady state must be equal to thatflowing past the reciprocating probe and eventually reaching the inner divertor. Under theseconditions, it is easy to verify whether or not the core efflux calculated by EDGE2D is sufficientto account for the measured probe flux (see figure 11). Considering the forward field, highdensity case (ne = 3.1×1019 m−3), the code predicts a total outflux, �T = 8.8×1019 m−2 s−1,corresponding to a predicted Dα photon flux of 7×1013 photons s−1 cm−2 sr−1. Experimentally,the Dα photon flux measured along a horizontal chord on the tokamak mid-plane amounts to9 × 1013 photons s−1 cm−2 sr−1. In view of the fact that some poloidal asymmetry mightbe expected (less outflux on the HFS), simulation and experiment are therefore in goodagreement.

Integrating the particle flux profile in figure 11 across the SOL for the highest densityforward field discharge gives a loss rate due to the flow of 6.9 × 1020 m−2 s−1. This is almostan order of magnitude higher than is possible from the code prediction (and experiment), evenassuming that the entirety of the core efflux passes the probe position! So the experimental Dα

photon flux and code predictions agree, but the probe result from the flow does not. It is notdifficult to imagine a situation in which the measured flux would be smaller (the flux is, afterall, integrated along the flux tube), but not much higher than the core efflux. The inconsistencywould be resolved if the ‘true’ Mach number were really that predicted by EDGE2D, namelyM ∼ 0.04 for forward field (see figure 14). This is strong evidence that the flows calculatedfrom the probe measurements are too high. Nevertheless, even with the additional mechanismto be proposed below by which the probe may, by its very presence, amplify the backgroundflow, the explanation for the constant positive Mach Number offset which persists for bothfield directions remains unclear.

5.2. Does carbon radiation affect flow?

The code simulations predict (figure 14) that the Mach flow in forward field from the outerto the inner divertor is essentially insensitive to density, at least for the density range and lowinput power plasmas considered here. Figure 7 shows that this insensitivity to density is exactlywhat is seen in experiments in forward field. Furthermore, the EDGE2D predicted poloidaldistribution of flow velocity shows that the flow is always in this direction, extending around theSOL from locations just above the X-point on the HFS and LFS. In contrast, in reversed field,the flow towards the outer divertor is from a stagnation point located, by coincidence, close tothe poloidal location of the reciprocating probe [3]. The code Mach numbers (figure 14) reducewith increasing density, again as observed in experiment (figure 7). This poloidal distribution


could partially explain why carbon is transported from the outer divertor region right roundtowards the inner divertor region in forward field discharges, but preferentially towards theouter divertor in reverse field discharges. There remains, however, a clear discrepancy betweenthe magnitude of the experimentally measured Mach number in forward field and the codeprediction.

Local pressure differences can be caused by carbon sputtered from the probe body itself,radiating and cooling the plasma and leading to the formation of a local temperature gradient.Experimentally, this radiation is seen on every probe reciprocation as a bright white carbon‘plume’ in visible CCD camera images. These plumes are often brighter than the plasma–divertor interaction, with greenish-blue tails, possibly from dissociation of boron nitride, thebasic material from which the carbon coated probe housing is manufactured (see section 2).

Using published data for carbon ionization cross-sections [31], the mean free path, λ, fora carbon atom sputtered from the probe surface in the vicinity of the separatrix (Teu ∼ 30 eV,neu = 6×1018 m−3) in these discharges is ∼8 mm. Deeper in the SOL, at the peak of the M(r)

profile (Teu ∼ 14 eV, neu ∼ 1 × 1018 m−3), λ ∼ 75 mm. Experimentally, the bright region ofthe plume extends about 100 mm from the probe position in the approximate direction of thetotal magnetic field.

By introducing a carbon source of varying magnitude at the poloidal position of the probeon the simulation grid, a crude attempt has been made to model this carbon radiation dueto the probe using EDGE2D. The same carbon density has been used in both forward andreversed fields. If the plume is due to carbon sputtering, then carbon atoms will be emittedapproximately in a cosine squared distribution prior to ionization. This three-dimensionalsituation cannot be exactly reproduced using a two-dimensional code such as EDGE2D, andso accurate numerical simulation is difficult. A simple uniform source, Si(r), has thereforebeen used from the separatrix (the position of maximum insertion) out to r = 30 mm. It turnsout, however, that the simulation results regarding the local generation of parallel flow arerather insensitive to the shape of Si(r) in that a simulation using an exponentially decreasingradial source distribution (as might be caused by deuterium sputtering) yields similar results.However, differences between the measured Mach number and the code simulations withcarbon, close to the separatrix, could be caused by desorption and loss of hydrocarbons fromthe surface before reaching the separatrix. The lower panel of figure 14 demonstrates howthe inclusion of a carbon source affects the Mach number at the probe location for bothfield directions. In forward field, the Mach number increases by a large amount to a valueM(r) > 0.2 at r ∼ 20 mm. In contrast, there is little effect on the flow in reversed field. Inboth magnitude and behaviour with field direction, these predicted flows are now much moresimilar to what is seen experimentally. Ratios of carbon to electron densities in the range8–33% are obtained, depending on the original carbon source strength and the radial positionin the SOL, the 33% corresponding to larger radii. These numbers are consistent with a carbonsputtering yield of ∼0.1 near the separatrix, which is about a factor of 4 too high for purephysical sputtering. Chemical and self-sputtering, or even dissociation of the boron nitrideitself, may, however, also be playing a role.

So what is driving the flow to such high values in the probe vicinity when the carbonsource is introduced? Some, but not all, forces on ions may be extracted from EDGE2D ona cell-by-cell basis, to give an idea of the force balance. Doing so reveals that the pressuregradient, thermoelectric, E-field and frictional forces all increase considerably in the vicinityof the probe when carbon is introduced. In forward field, the first three forces accelerate theions towards the inner target, whilst the frictional force opposes the motion. All forces are ofsimilar magnitude, and so the net force is towards the inner target. In reverse field, the forcesare in the opposite direction and the increase is smaller.


Figure 16. EDGE2D simulation of the effect on parallel flow Mach number of injecting carbonclose to the separatrix in reverse field discharges. When observing at the inner mid-plane, carbonis injected into this position (upper plots). The lower plots show the effect of flow at the outermid-plane with and without carbon injected into this position.

The somewhat unfortunate location of the probe close to a ‘natural’ stagnation point in thepredicted poloidal distribution of parallel flow in reversed field means that the ‘amplification’of the background flow due to the artificial carbon source is difficult to identify (the flowchanges direction at the probe position). To investigate further, a carbon source (representing,as before, the reciprocating probe) is introduced instead at both the inner and the outer mid-plane locations. At these positions, the predicted reversed field flow pattern is for a strongflow towards the outer target at the outer mid-plane and towards the inner target at the innermid-plane.

Results of these code runs are shown in figure 16. In each case, the flow increases dueto carbon injection. The effect changes direction with the direction of the flow and so is an‘amplification’ process. Investigations at different poloidal locations indicate further that this‘amplification’ occurs throughout the region of carbon injection—not just downstream of it.This therefore confirms the earlier statement—being close to the predicted stagnation pointin reversed field, the hypothetical probe finds itself in a region of low parallel flow. Anyamplification due to carbon release will thus also yield a low Mach number.

Further evidence for the influence of carbon on the probe measurements is exemplified inthe lithium beam data of figure 3. In discharges with low carbon content, the lithium beamrecords density profiles having only a ‘single’ SOL, i.e. no flattening at around r ∼ 20 mm.However, in pulses in which CD4 has been deliberately introduced by gas puffing, the lithiumbeam measures a ‘double SOL’, the break again being at r ∼ 20 mm. This effect is shown moreclearly in figure 17, where measured Li-beam profiles are compiled for a discharge into whichCD4 is puffed into the SOL, followed 2 s later by a D2 gas puff (so that there will be a smallamount of carbon still present). Also included in this figure are the density profiles predicted byEDGE2D for both D⊥(r) and χ⊥(r) peaking at r = 20 mm, as required to match experimentand for constant transport (D⊥(r) = 0.5 m−2 s−1 and χ⊥(r) = 1.0 m−2 s−1). The choice ofconstant D⊥(r) and χ⊥(r) has little effect on the EDGE2D prediction of M(r).

Since the majority of probe measurements exhibit this ‘double SOL’, with a break at thesame radius as measured by the lithium beam when carbon is deliberately introduced, thisconstitutes strong evidence that carbon is influencing the probe measurements. Such ‘double


Figure 17. The effect of the introduction of carbon (CD4) into the plasma on density profiles asmeasured by the lithium beam and simulated in EDGE2D by transport peaking at r = 20 mmrequired to match the probe data (e.g. figure 15).

SOLs’ are also seen on C-MOD [32], though in this case the ‘kink’ in the density profile ismuch closer to the separatrix than observed on JET (∼5 mm), a result that could be due tothe smaller ρ∗ on C-MOD (due to operation at higher toroidal field), rather than an impuritycontamination effect.

As discussed in section 2, a number of possible effects have been suggested by whichthe anomalously high measured SOL flows on JET might be generated. None satisfactorilyaccounts for all aspects of the observations. The new mechanism proposed here, namelya strong influence of the probe itself on the flow measurement, can account for both theapproximate radial profile shape and the behaviour with BT direction (namely that the reversedfield flows are essentially stagnant in the SOL in reversed field but strong throughout the SOLin forward field). It cannot account for the positive offset seen in the flow when comparing theresults from both field directions. If present in JET, this impurity release effect is likely alsoto influence measurements made elsewhere (i.e. the majority) using the same technique. Tounambiguously decide whether or not the probe amplification effect is occurring will requirean alternative, non-perturbing measurement of the parallel SOL flow.

6. Conclusion

This paper has presented new and more detailed recent experimental data on plasma flowsin the JET SOL with forward and reversed toroidal fields. SOL parameters for key pairs of


discharges with the only difference being the direction of toroidal field and plasma currenthave been simulated using the EDGE2D/Nimbus code with neo-classical drifts included andtransport parameters adjusted to give a best match to experimental profiles.

Two mechanisms are proposed as an explanation for the anomalously high experimentallymeasured flows in the SOL (peak values of M(r) ∼ 0.6 in forward field largely independentof plasma parameters). The first is a field independent mechanism, which from the differencebetween forward and reverse field measurements appears nearly constant at M ∼ 0.2 acrossthe SOL. The second is field dependent and exhibits a reversal of the flow with reversal of thedrift direction. Ballooning has been suggested as a possible field independent mechanism, anidea strengthened by the observation that this component increases with increasing density.

Unfortunately, EDGE2D with classical drifts alone predicts Mach numbers of up to anorder of magnitude less than the measured values. Alternatives to classical drifts are discussed,and none appear to offer a consistent explanation for the high values of parallel Mach numbermeasured. An explanation for the relative invariance of M(r) with all plasma parameters inforward field is challenging. Although EDGE2D does suggest a qualitative independence offlow with density in forward field, the considerable short fall in magnitude compared withexperiment presents a serious difficulty.

Using EDGE2D modelling, this paper has explored the possibility that the high Machnumbers are an artefact due to impurities generated at the probe by plasma–surface interactionduring the measurement itself. The intense radiation plumes accompanying each reciprocationinto the SOL make it reasonable to postulate that the measurements may be affected in someway. By introducing a local carbon source into the code, simulations show that the main forcesdriving the flow all increase, such that the flow is ‘amplified’. If this idea is correct, thenMach probes, at least in JET, can be trusted only for determining the direction of the flow andnot its magnitude. Since such measurements are also performed routinely in the same wayelsewhere, the proposed mechanism might well be responsible for the general observation inthe tokamak SOL that experimental Mach numbers are always higher than can be accountedfor theoretically. However, due to the lack of a suitable three-dimensional code, the crudemanner in which the carbon source has been included for the analysis in this paper is opento question and the conclusions drawn still somewhat speculative. It is equally possible thatthere is some important physical process missing from EDGE2D and other similar edge fluidcodes—a rigorous code-to-code benchmarking of drift effects remains a priority. Independentexperimental validation of the probe measurements of flow using a non-perturbing method isa clear experimental priority but is difficult to achieve in the region of the JET edge plasmacurrently also accessible to the Mach probes.

Acknowledgments

This work was partly funded by EURATOM and the UK Department of Trade and Industry.

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