INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION

Plasma Phys. Control. Fusion 48 (2006) 1425–1435 doi:10.1088/0741-3335/48/9/011

Modelling of radial electric field profile for differentdivertor configurations∗

V Rozhansky1, E Kaveeva1, S Voskoboynikov1, G Counsell2, A Kirk2,H Meyer2, D Coster3, G Conway3, J Schirmer3, R Schneider4 and theASDEX Upgrade Team

1 St Petersburg State Polytechnical University, Polytechnicheskaya 29, 195251 St Petersburg,Russia2 EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon,OX14 3DB, UK3 Max-Planck Institut fur Plasmaphysik, EURATOM Association, D-85748 Garching, Germany4 Max-Planck Institut fur Plasmaphysik, EURATOM Association, D-17491 Greifswald, Germany

Received 7 February 2006, in final form 19 July 2006Published 15 August 2006Online at stacks.iop.org/PPCF/48/1425

AbstractThe impact of divertor configuration on the structure of the radial electric fieldhas been simulated by the B2SOLPS5.0 transport fluid code. It is shown thatthe change in the parallel flows in the scrape-off layer, which are transportedthrough the separatrix due to turbulent viscosity and diffusivity, should result invariation of the radial electric field and toroidal rotation in the separatrix vicinity.The modelling predictions are compared with the measurements of the radialelectric field for the low field side equatorial mid-plane of ASDEX Upgradein lower, upper and double-null (DN) divertor configurations. The parallel(toroidal) flows in the scrape-off layer and mechanisms for their formation areanalysed for different geometries. It is demonstrated that a spike in the electricfield exists at the high field side equatorial mid-plane in the connected DNdivertor configuration. Its origin is connected with different potential dropsbetween the separatrix vicinity and divertor plates in the two disconnectedscrape-off layers, while the separatrix should be at almost the same potential.The spike might be important for additional turbulent suppression.

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

1. Introduction

There are several experiments where the impact of divertor configuration and magnetic fielddirection on the L–H transition threshold have been reported. It was demonstrated that fortokamaks with a single X-point the threshold is lower for the normal direction of the magnetic

∗ This was originally submitted to the special issue on H-mode Physics and Transport Barriers. This special issue maybe accessed online at stacks.iop.org/PPCF/48/i=5A.

0741-3335/06/091425+11$30.00 © 2006 IOP Publishing Ltd Printed in the UK 1425

1426 V Rozhansky et al

field (∇B drift of ions is directed towards X-point) [1, 2]. On MAST [3] for the double-null(DN) divertor configuration access to H-mode is easier for the connected DN case, when twoX-points belong to the same separatrix, compared with the upper single-null (USN) or thelower single-null (LSN) cases. Improved H-mode access for the DN case with respect tothe USN case was observed on Alcator C-Mod [4] and ASDEX Upgrade (AUG). On JET, theL–H transition threshold depends on the plasma shape (triangularity) and the presence of theseptum (real or virtual), which changes the X-point height [5]. The toroidal rotation in the coreregion strongly depends on the distance between the two separatrices in C-Mod [6]. Theseexperimental findings raise the question of how the electric field structure and shear of thepoloidal rotation in the separatrix vicinity depend on these geometrical factors, which mightcontribute to the understanding of the L–H transition threshold dependence.

The impact of the direction of the ∇B drift of ions on the radial electric field profile inthe separatrix vicinity and hence possibly on the L–H transition threshold has been studiedpreviously using the B2SOLPS5.0 transport code [7,8]. The mechanism, which could explainthe observed easier access to H-mode for the normal direction of the magnetic field, has beenput forward. In the present paper the same code is used to investigate the impact of the divertorconfiguration (DN, USN or LSN cases) on the radial electric field structure in the separatrixvicinity both for MAST and AUG. It is demonstrated that a similar mechanism, which isconnected with the radial transport of parallel flows through the separatrix, is responsible forthe radial electric field structure in the separtrix vicinity. A special case is the DN configuration,where a spike in the radial electric field arises at the high field side (HFS).

Previously it was demonstrated that the radial electric field at some distance (1–2 cm)inside the separatrix is close to the neoclassical electric field [7, 8]. The neoclassical electricfield is given by the expression

E(NEO) = Ti

e

(1

hy

d ln n

dy+ kT

1

hy

d ln Ti

dy

)− Bx

B〈BVz〉, (1)

where x is the poloidal co-ordinate, y is the radial co-ordinate, z is the toroidal co-ordinate,hx = 1/‖∇x‖, hy = 1/‖∇y‖, hz = 1/‖∇z‖ are metric coefficients, kT is the numericalcoefficient, which depends on collisionality, and Vz is the toroidal rotation velocity. Anexample of a comparison of the simulation results obtained using the fluid code B2SOLPS5.0and the Monte-Carlo code ASCOT with the neoclassical electric field is shown in figure 1 [9].One can see that the radial electric field 1–2 cm inside the separatrix is indeed close to theneoclassical electric field for the two codes (with the same viscosity coefficients). The fact thatthe radial electric field 1–2 cm inside the separatrix is close to the neoclassical electric field isdemonstrated by a large number of numerical simulations [7,8]. To check this result many runswere performed with the B2SOLPS5.0 code for AUG with different densities, temperatures,plasma currents, toroidal magnetic fields, both for Ohmic and for NBI shots with co- andcounter-current rotation (the toroidal rotation profile is determined by turbulent transport and iscalculated in the code). Subsequently the same result was obtained in B2SOLPS5.0 simulationson MAST [8, 10]. The neoclassical character of the radial electric field was also reported inthe simulations using the UEDGE fluid code [11–14]. There are analytic arguments in supportof this result [8, 15]. As observed in the simulations, in the core region (with the exception ofthe dip in the radial electric field profile (viscous layer)) the parallel viscosity averaged overthe flux surface 〈 �B · ∇ · ↔

π ||〉 ≈ 0 is as predicted by neoclassical theory [7, 8].However, just adjacent to the separatrix a viscous layer exists [7, 8], where the radial

electric field deviates significantly from the neoclassical value. Inside this layer the impact ofthe parallel plasma flows in the SOL is important. The parallel flows of the SOL are transportedthrough the separatrix and further to the core due to anomalous viscosity and the anomalous

Modelling of radial electric field profile for different divertor configurations 1427

-3 -2 -1 0 1 2-14

-12-10

-8-6

-4-2

0

2468

10 EB2SOLPS

E(NEO)

EASCOT

EASCOTvis

sepa

ratr

ix

SOLcore

Rad

ial e

lect

ric fi

eld

( kV

/m )

Radial coordinate Y (cm)

Figure 1. Radial electric field at the LFS mid-plane. Simulations by B2SOLPS5.0 and ASCOTfor AUG, the separatrix temperature Ti = 105 eV. The curve EASCOTvis corresponds to the sameanomalous viscosity as in B2SOLPS5.0.

particle flux. The width of the layer is determined by the anomalous viscosity coefficient andcollisionality. Inside the layer the perpendicular viscosity in the parallel momentum balanceequation balances the classical parallel viscosity. As a result 〈 �B · ∇ · ↔

π ||〉 = 0 and a dip in theradial electric field arises, figure 1. The structure of the viscous layer depends on the poloidaldistribution of the parallel fluxes in the SOL. The change in the direction of the ∇B drift of ionsleads to the change in the distribution of the parallel flows in the SOL and, as a result, through theviscous coupling through the separatrix to the change in the parallel flows inside the separatrix.The simulations [7] show that the dip is larger for the normal magnetic field direction. The shearof the radial electric field is also larger for the normal direction of the magnetic field, which isconsistent with the observed easier access to H-mode for the normal magnetic field direction.

In spite of the existence of a dip in the radial electric field, the general neoclassical trendmight contribute to the explanation of the parametric dependence of the L–H transition thresh-old. In accordance with equation (1) for the given density and temperature and toroidal rotationprofile the shear of poloidal �E × �B drift depends on the parameter Ti/B. If it is assumed thatL–H transition takes place at some prescribed shear value of the order of (3–5)×105 s−1 (for thediscussion see results of gyrokinetic simulations [16] for a given shear layer) at some referencepoint near the separatrix, then it would be natural to expect the threshold to be dependent onthe local value of Ti/B. Such a linear dependence was reported in the JET experiments [17].Moreover, simulations performed by B2SOLPS5.0 for AUG [7] and by ASCOT for JET [18]demonstrated that to reach this prescribed poloidal rotation shear value one has to increase theheating power linearly with the average density and toroidal magnetic field P ∼ nB, whichwould also keep the local value of Ti/B constant near the separatrix. This is consistent withthe ITER scaling [19].

An analysis of the type of turbulence is necessary in order to specify the critical shear. Apossible candidate is drift-Alfven turbulence. The critical shear can also depend on the plasmaparameters; see for example [20]. However, at least for the parameters of the simulations thisdependence is not very strong.

1428 V Rozhansky et al

Turbulence suppression should result in the reduction of transport coefficients and theformation of the edge transport barrier. This stage is not considered in this paper; simulationsare performed for Ohmic shots before the L–H transition.

The possible impact of the divertor geometry (similar to the impact of ion ∇Bdriftdirection) on the structure of the dip of electric field makes the situation more complicated andis the subject of the present study.

Reported below are results of a detailed modelling of the radial electric field in theseparatrix vicinity for three divertor configurations: USN, LSN and connected DN using theB2SOLPS5.0 transport code. Simulations were performed for MAST and AUG and comparedwith the observations on these tokamaks. It is shown that the geometrical factors changemainly the distribution of the parallel flows in the SOL and through the anomalous viscositychange the parallel flows inside the viscous layer. To keep the divergence of the fluxes equalto the ionization sources an additional radial electric field arises, which produces an additionalpoloidal �E × �B drift. This is the key issue in the suggested understanding of the impact ofgeometrical factors on the radial electric field structure at the low field side (LFS). A verynarrow dip of the negative electric field is observed in the simulations for the DN cases at theHFS near the separatrix. Its origin is connected with the different potential drops in the twodisconnected SOLs in the DN case. The possible mechanisms for the impact of the divertorconfiguration on the L–H transition threshold are discussed.

2. Simulation results

Simulations were performed with the B2SOLPS5.0 transport fluid code. As in similar codesthe set of modified Braginski equations was solved [21]. The following perpendicular transportcoefficients are replaced by the anomalous values: diffusion coefficient of charged particles,electron and ion heat conductivity and ion perpendicular viscosity coefficient. The philosophyof B2SOLPS5.0 (and other codes) is that the values of perpendicular transport coefficients arechosen to fit the experimentally observed density and temperature radial profiles and densitiesand temperatures near the divertor plates. So the parametric dependence of the transport coeffi-cients is present indirectly, since the chosen values are different for different plasma parameters.

In the simulations presented below constant, radially and poloidally independent, valuesof transport coefficients have been used. The fact that constant values of transport coefficientsproperly chosen in the codes can reproduce experimentally observed profiles has been checkedand reported in many publications, see, for example, [22]. In [22] the following calculated andexperimentally observed quantities for AUG were compared: radial density profile, electronand ion temperature profiles, saturation current and electron temperature profiles along thedivertor plates, electron temperature and saturation current measured by a reciprocating probebelow the X-point and the radial electric field profile. For all the quantities good agreementbetween simulation and experiment has been reported. Moreover, the shot used in [22] hasalso been simulated by the turbulent code DALF3 [23], where transport coefficients similar tothose used in B2SOLPS5.0 (including viscosity coefficients) were obtained. DALF3 is a fullturbulent code based on the set of Braginski type equations, where particle and heat fluxes areobtained from first principles.

Special efforts were made to understand the possible role that the poloidal dependenceof the transport coefficients could have on the results. Many simulations both for MASTand AUG were performed with various poloidal dependences of the ballooning type. It wasfound that changing the poloidal dependence of the transport coefficients by up to an orderof magnitude from the LFS to the HFS has no significant influence on the radial electric fieldprofile. This was done for all three geometries considered in this paper, both for AUG and

Modelling of radial electric field profile for different divertor configurations 1429

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

inne

rse

para

trix

SOLcore

7656 LSN 7669 USN 7666 DN

Rad

ial e

lect

ric

fiel

d (k

V/m

)

Radial coordinate Y, (cm)

Figure 2. Calculated radial electric fields at the LFS mid-plane for three different MASTconfigurations.

MAST. This can be understood since even for poloidally independent transport coefficientsmost of the energy and the particle flux pass through the LFS of the tokamak to the SOL dueto the smaller distances between flux surfaces at the LFS and the larger surface area. Since theradial electric field was more or less the same for all poloidal dependences the simplest variantof constant coefficients has been chosen for the results presented in this paper.

The same transport coefficients were used for the three different geometries in accordancewith the experimental observations that the radial density and electron temperature profileswere practically the same in all three cases. For MAST three Ohmic shots No7656 (LSN),No7666 (DN) and No7669 (USN) with similar radial profiles of temperature and densityin the core but different geometry of the separatrices were simulated. The parameters ofthese discharges are central density 4 × 1019 m−3 and electron temperature 500 eV, plasmacurrent 3.5 × 105 A and toroidal magnetic field 0.9 T. For AUG Ohmic shot No19415 wassimulated in which the equilibrium changes in time from LSN through DN to USN. Theparameters of this discharge are average density 4 × 1019 m−3 and electron temperature2 keV, plasma current 7.6 × 105 A and toroidal magnetic field 2.2 T. The following modellingparameters were chosen. (i) MAST: plasma density at the inner boundary (6.3 cm inside theinner separatrix at the LFS mid-plane) ne|core = 2 · 1019 m−3, electron and ion temperaturesTe|core = 100 eV, Ti |core = 100 eV, turbulent diffusion coefficient D = 1 m2 s−1, electron andion heat conductivity χe = 2.5 m2 s−1, χi = 1.5 m2 s−1. (ii) AUG: plasma density at the innerboundary (7 cm inside the inner separatrix at the LFS mid-plane) ne|core = 2.85 · 1019 m−3,Te|core = 275 eV, Ti |core = 275 eV, D = 0.5 m2 s−1, χe,i = 0.7 m2 s−1. The perpendicularviscosity coefficient was chosen according to η = nmiD. The simulated radial electric fieldsat LFS mid-plane for the three configurations in MAST are shown in figure 2. The simulationsfor AUG and a comparison with the experimental profiles are shown in figure 3.

For MAST the LFS radial electric fields in the peripheral region inside the separatrix inall three cases are negative and comparable. For AUG the DN and LSN electric fields arecomparable while the USN electric field is significantly smaller in absolute value. On AUGmeasurements were performed using Doppler reflectometry diagnostics [24]. As can be seen,

1430 V Rozhansky et al

-8 -6 -4 -2 0 2 4-6

-4

-2

0

2

4

6

8

Rad

ial e

lect

ric

fiel

d (k

V/m

)

Radial coordinate Y, (cm)

CDND UDND LDND

LSN USN DN

Figure 3. Calculated and experimental radial electric fields at the LFS mid-plane for differentAUG configurations.

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

inner

separatrix

SOLcore

7656 LSN

7669 USN

7666 DN

Rad

ial

elec

tric

fie

ld (

kV

/m)

Radial coordinate Y, (cm)

Figure 4. Calculated radial electric fields at the HFS mid-plane for three different MASTconfigurations.

the tendency obtained in the simulations is similar to that observed in the experiment: theradial electric field for the USN configuration is more positive than for the two other cases.Various simulations performed for Ohmic shots with other parameters both for MAST andAUG do not add anything essentially new.

The radial electric field profiles at the HFS mid-plane are shown in figures 4 and 5. Onecan see strong spikes at the separatrix in the DN radial electric field profiles for both the AUGand MAST shots. These spikes disappear in the LSN and USN configurations. The existenceof the HFS spike is a robust feature typical for DN simulations. The generality of this featureis confirmed by various simulations for Ohmic shots with other parameters both for MASTand AUG. The amplitude of the spike depends on the difference in potential drop between theplates and the equatorial mid-planes in the HFS and LFS SOL. The amplitude of the spikemight be controlled by changing the LFS or HFS SOL parameters. For example, in the test

Modelling of radial electric field profile for different divertor configurations 1431

-6 -4 -2 0 2 4-6

-5

-4

-3

-2

-1

0

1

2

3

4

inne

rse

para

trix

SOLcore

LSN USN DN

Rad

ial e

lect

ric

fiel

d (k

V/m

)

Radial coordinate Y, (cm)

Figure 5. Calculated radial electric fields at the HFS mid-plane for three different AUGconfigurations.

-5 0 5 10 15-24

-20

-16

-12

-8

-4

0

separatrix

SOLcore

7656 LSN 7669 USN 7666 DN

Para

llel v

eloc

ity (

km/s

)

Radial coordinate Y, (cm) Radial coordinate Y, (cm)-10 -5 0 5

-4

0

4

8

12

separatrix

SOLcore

7656 LSN 7669 USN 7666 DN

Para

llel v

eloc

ity (

km/s

)

(a) (b)

Figure 6. (a) Calculated parallel velocity profiles at the LFS mid-plane for three different MASTconfigurations. (b) Calculated parallel velocity profiles at the HFS mid-plane for three differentMAST configurations.

runs changes in the parallel ion heat conductivity can reduce the spike amplitude for the AUGcase by almost a factor of two. In figures 4 and 5 one can also see a spike in the electric fieldnear the second unmatched outer separatrix; however, it is located too far from the closed fieldlines to contribute to turbulence suppression and edge barrier formation.

The parallel velocity at the LFS mid-plane is shown in figure 6(a) for three MAST shots. Inthe DN case the parallel velocity at the LFS near the separatrix is a few km s−1 less negative (the

1432 V Rozhansky et al

-6 -4 -2 0 2

-12

-10

-8

-6

inne

rse

para

trix

SOLcore

LSN

USN

DN

Par

alle

l vel

oci

ty (

km

/s)

Radial coordinate Y, (cm)

-10 -5 0 5-10

-5

0

5

10

15

20

25

inne

rse

para

trix

SOLcore

LSN

USN

DN

Par

alle

l vel

oci

ty (

km

/s)

Radial coordinate Y, (cm)(a) (b)

Figure 7. (a) Calculated parallel velocity profiles at the LFS mid-plane for three different AUGconfigurations. (b) Calculated parallel velocity profiles at the HFS mid-plane for three differentAUG configurations.

negative sign corresponds to the co-current direction and to the upward direction in figure 9(a))at the core boundary. This is consistent with observations on MAST [3], where less negativetoroidal velocity was observed in the DN case with respect to the LSN case. The same effecthas been reported for C-Mod [4]. However, on C-Mod the toroidal velocity in the USN casewas reported to be even more positive than in the DN case in contrast to the MAST simulationresults (there are no similar data for MAST). This difference might be due to the fact that inMAST most of the unbalanced parallel particle flux caused by the radial flux from the coregoes to the outer plates. The strong counter-current parallel velocity at the HFS in the DNcase, figure 6(b), corresponds to the counter-current Pfirsch–Schlueter (PS) flux observed onC-Mod [4]. The HFS parallel velocity is positive in the USN case and negative in the LSNcase, which is consistent with C-Mod measurements. The parallel velocity profiles at themid-planes obtained in modelling for AUG, figures 7(a) and (b), are qualitatively similar to theMAST profiles. The parallel velocity at the LFS mid-plane is less negative for the DN AUGcase. The parallel velocity in the SOL region at the HFS mid-plane for AUG is counter-currentdirected in all cases. However, the magnitude of parallel velocity is largest in the USN caseand is smallest in the LSN case.

3. Discussion

In order to understand the impact of geometry on the LFS radial electric field one should startwith the analysis of the parallel fluxes in the SOL. It is possible to trace three contributions tothese fluxes, figure 8. The first one is the PS flux, which arises to close the vertical ∇B driftof ions. The expression for the PS velocity, with the assumption of poloidally independentpressure (for a more sophisticated expression see [7]), is

V P.S.| | =

(1

enhy

∂pi

∂y+

1

hy

∂ϕ

∂y

)Bz

BxB

(1 − B2

〈B2〉)

. (2)

Modelling of radial electric field profile for different divertor configurations 1433

Figure 8. Scheme of parallel fluxes in the SOL for the LSN case. (a) Normal magnetic field, (b)reversed magnetic field.

Since the radial electric field in the SOL is positive and the ion pressure is decreasing withradius, the PS flux is negative at the outer and positive at the inner equatorial mid-plane andis zero at the top and bottom. The second contribution is the flux compensating the �E × �Bdrift in the radial electric field which keeps the same poloidal flux in the presence of drifts aswithout drifts. The corresponding value is

V E|| = 1

Bx

∂ϕ

hy∂y. (3)

The final contribution is a parallel unbalanced flux, which is not connected with drifts andis directed towards the plates in the divertor regions. In the SOL this flux is often (e.g.for AUG for LSN and USN cases) directed from the outer to the inner plates due to thelarger radial flux through the outer part of the torus and temperature asymmetries at theplates (hotter outer plates). This pattern is supported by the results of simulations. Dueto viscosity coupling, these parallel fluxes are transported through the separatrix and thus asimilar parallel flow pattern is created in the core as in the separatrix vicinity (inside the viscouslayer).

Let us first compare the radial electric fields for the normal magnetic field direction (∇B

drift of ions directed towards the lower X-point). Inside the separatrix the divergence of thevertical ∇B drift is to some extent compensated by the divergence of the parallel flux. In thecomplete absence of parallel fluxes, the divergence of the ∇B drift should be compensated bythe divergence of �E × �B drift. The resulting radial electric field is negative:

Ey = ∂pi

enhy∂y. (4)

This electric field is larger than the neoclassical electric field since the neoclassical electricfield has a contribution from toroidal rotation. It is also larger than the real electric field inthe viscous layer since the ∇B drift is partially compensated by the parallel fluxes transportedfrom the SOL. The divergence of the parallel flux is subtracted from the divergence of the ∇B

flux. For the case of the normal magnetic field this subtraction leads to a reduction in the radialelectric field with respect to equation (4).

Switching from the LSN to the DN configuration causes the redistribution of the parallelflux in the SOL. Part of the parallel flux starts to flow to the outer upper divertor, figure 9(a).As a result the parallel flux might become more poloidally homogeneous in the outer SOLsince the reduction of the PS flux in the upper part is compensated by the plasma acceleration

1434 V Rozhansky et al

(a) (b)

Figure 9. (a) Scheme of parallel fluxes in the SOL for the DN case, b for the USN case.

towards the outer upper plate. The divergence of the parallel flux in the DN case might bereduced with respect to the LSN case and hence the divergence of the �E × �B drift might belarger. The radial electric field and its shear should also be larger. This effect depends on theplasma shape. The simulations demonstrated that this effect is not very strong and is morepronounced for MAST than for AUG. Therefore, it is difficult to explain the easer access tothe H-regime in DN configuration solely by this effect.

In the USN case the unbalanced parallel flux is shown in figure 9(b). Its combination withthe PS flux increases the divergence of the parallel flux, the latter becomes more poloidallydependent. The difference between the divergences of the vertical ∇B drift flux and parallelfluxes is smaller than in the DN and LSN cases. The divergence of the radial electric fielditself and its shear are hence smaller than for the DN and LSN cases. This is observed both inthe simulations and in the experiment for AUG, Figure 3. For MAST the effect is smaller. Inaddition the variation of particle sources might also change the parallel flux and through thedescribed mechanism influence the radial electric field.

One more issue specific to the DN case is connected with the electric field at the HFS.Special attention should be paid to the electric field in the HFS SOL just at the separatrix.The potential difference between the divertor plates and the equatorial mid-plane close to theseparatrix is determined mainly by the parallel momentum balance equation for electrons. Theseparatrix potential is close to the potential difference in the LFS SOL between the plates andthe mid-plane. However, the potential difference along magnetic field in the HFS SOL, whichis isolated from the LFS SOL, is different. Hence, the only way to reach the same separatrixpotential is to get a sharp potential jump at the HFS near the separatrix. It is possible thatthe corresponding shear at the HFS might contribute to the turbulence suppression at the LFSthus reducing the L–H transition power threshold. Another possibility is the reduction of theturbulence level itself by the approach of the second X-point to the inner separatrix.

Modelling of radial electric field profile for different divertor configurations 1435

4. Conclusions

1. The impact of geometrical factors on the radial electric field structure at the LFS mid-plane is connected with the change in the parallel flows in the scrape-off layer, which aretransported through the separatrix due to turbulent viscosity.

2. For MAST the LFS electric fields are comparable for the DN and USN cases, and the LSNelectric field is less negative. For AUG the DN and LSN electric fields are comparable,while the USN electric field is less negative. It is difficult to explain the experimentallyobserved change in the L–H transition threshold only by the variation of the shear ofelectric field at the LFS mid-plane.

3. A spike in the electric field exists at the HFS equatorial mid-plane in the DN case. Itsorigin is connected with the different potential drops between the separatrix vicinity anddivertor plates in the two disconnected SOLs, while the separatrix should be at almost thesame potential. The spike might be important for the additional turbulent suppression inthe DN case.

Acknowledgments

The work was supported by grants RFFI 06-02-16494-a and 06-02-08014-ofi.

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