CHAPTER 6SCRAPE-OFF LAYER TRANSPORT ON JET
W. FUNDAMENSKI* Euratom0UKAEA Fusion Association
Culham Science Centre, Abingdon OX14 3DB, United Kingdom
Received June 25, 2007
Accepted for Publication October 5, 2007

The tokamak plasma boundary, which is typically
identified with the area of open field lines known as the
scrape-off layer (SOL), determines the degree of plasmawall interaction. SOL physics, much of which is concerned with the exhaust (removal) of particles and energy
from the plasma, has been one of the major topics investigated on JET during the past two decades. In thischapter, SOL transport/exhaust studies on JET are reviewed. The discussion proceeds chronologically, beginning with the limiter SOL and treating in turn the
successive divertors (Mk0, MkI, MkIIA, and MkIIGB)
with which JET was equipped in subsequent years. Whenappropriate, old results are reinterpreted in the light ofrecent improvements in our understanding of edge/SOL
turbulence and edge-localized modes (ELMs). Althoughemphasis is placed on deuterium transport in the SOL,
impurity transport is briefly considered. In particular,
the effect of divertor closure, of L-mode versus H-mode,and of inter-ELM versus ELM erosion on plasma purity(Z eff ), radiation ( f rad ), and confinement ( tE ) isbriefly discussed. The chapter concludes with a summary of empirical scaling expressions for SOL profile
widths (radial e-folding lengths) in both limiter anddivertor configurations.

Contents—Chapter 6

I. INTRODUCTION

I. INTRODUCTION
II. BASIC CONCEPTS OF SOL PHYSICS
II.A. Perpendicular ~Radial! Transport
II.B. Diamagnetic Transport
II.C. Parallel Transport
II.D. Plasma Turbulence in the SOL
II.E. Effects of the H-Mode and ELMs on the SOL
III. LIMITER SOL
III.A. Carbon Limiters
III.A.1. Ohmically Heated Discharges
III.A.2. NBI-Heated Discharges
III.A.3. ICRH Discharges
III.B. Beryllium Limiters
III.C. SOL Turbulence and the H-Mode in Limiter Plasmas
IV. DIVERTOR SOL
IV.A. Mk0 ~1986 to 1992!
IV.B. MkI ~1994 to 1995!
IV.C. MkIIA ~1996 to 1998!
IV.D. MkIIGB ~1994 to 2004!
IV.E. Effect of Divertor SOL on Plasma Purity, Radiation, andConfinement: MkI to MkIIGB
V. CONCLUSIONSREFERENCES

In confined plasmas, the term scrape-off layer ~SOL!
refers to the region of open field lines between the lastclosed flux surface ~LCFS!, or the magnetic separatrix~sep!, and the vessel wall. It was famously labeled as
the domain of kitchen physics,1 in which the interactionof ions and electrons with molecules, atoms, sheaths,
and solid surfaces can dominate the overall plasma behavior. For many fusion physicists, accustomed to a
fully ionized, collisionless, hydrogenic plasma occupying a succession of nested toroidal flux surfaces andobeying the single-fluid ideal-magnetohydrodynamic~MHD! equations, the SOL, where the stellar world of
hot plasmas meets the earthly world of cold solids, i.e.,
the real world of our everyday experience, represents
novel and often unfamiliar territory. For the same reasons, the SOL is of particular interest to the fusion
engineer, whose primary interest lies in the design andexploitation of a fusion reactor, and who struggles withsuch problems as
1. the exhaust of fusion power without undue damage to the vessel walls*E-mail: wojtek.fundamenski@jet.uk
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KEYWORDS: scrape-off layer, edge plasma, plasma-surface
interaction
Note: Some figures in this paper are in color only in the electronic
version.

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2. the removal of fusion ash ~helium! and other impurities from the core plasma
3. recovery of fusion fuel and prevention of tritium retention ~codeposition! in plasma-facing
components
4. control of material erosion and migration within
the vacuum vessel.
These issues are clearly of critical importance for theplanned ITER experiment.
Throughout its long history, JET has made pivotal
contributions to the understanding of SOL physics andhas provided invaluable information to tackle the statedfusion technology issues.1–160 In what follows, these contributions will be briefly reviewed, focusing on thosewith highest importance to ITER. After a modern introduction to the basic concepts of SOL transport theory,
which are introduced principally using JET results, inSec. II, JET SOL transport studies in limiter and divertor
configurations are examined in Secs. III and IV, respectively; the latter is divided into two subsections, dealing
separately with ohmic and L-mode, and ELMy H-mode
SOLs, which are further divided into subsections dealing
with carbon and beryllium limiters; ohmic, neutral beam
injection ~NBI!, and ion cyclotron resonance heating~ICRH!; and successive divertors ~Mk0, MkI, MkIIA,
and MkIIGB! operating on JET. The chapter concludes
with a brief summary of the empirical scaling expressions for SOL profile widths.

II. BASIC CONCEPTS OF SOL PHYSICSAs the name suggests, the last closed flux surface
represents the transition between the region of closed andopen magnetic field lines. This surface can be createdeither by inserting a solid object, known as the limiter,
into the plasma,a or by shaping the poloidal magnetic
field with external current-carrying coils to create a poloidal field null, or X point, and a magnetic separatrix,
and thus to divert the SOL plasma into a specificallydesigned structure, known as the divertor.b The two methods, shown for JET in Fig. 1 ~also see Figs. 1 and 18 in
Ref. 2! produce distinct SOL geometries: the limiter SOL
generally resembles the closed flux surfaces, whereas thedivertor SOL expands poloidally in the vicinity of the X
point, such that its footprint on the solid targets is typically a factor of 3 to 5 times broader than its width at theouter midplane. This broadening, commonly referred toas poloidal flux expansion, is illustrated in Fig. 1 foraHistorically, this is the earlier technique. There are four typesof limiters: poloidal, toroidal ~belt!, vertical ~rail!, and discrete ~mushroom!.
bThis is a comparatively recent innovation; there are two typesof divertors, toroidal and poloidal, with the latter being by far
the most common.
1024

three JET divertor designs, MkI, MkIIA, and MkIIGB~gas box!. Another consequence of the poloidal field nullis the near-linear decrease of the field line angle between
the field line and divertor target, u4 , in the vicinity of the
X point and the associated increase in the radial gradientof the safety factor q, i.e., of the magnetic shear s ⫽rdq0dr. Assuming that upstream profiles of thermodynamic variables decay exponentially with radius, one
finds that as the distance between the X point and thetarget is gradually reduced, the particle and heat fluxes
normal to the tile surface are reduced at the strike point
location and tend to peak away from the LCFS, as shownin Fig. 2.
Aside from poloidal flux expansion, the main difference between the limiter and divertor SOLs lies in the
distribution of particle ~plasma! sources. The limitermethod leads to a relatively simple SOL ~fueled by radial
particle transport from the core region!, whereas the divertor method, in which the SOL is generally more complex, both geometrically and physically, is dominated byplasma recycling in the divertor volume. In both cases,
the source of energy can be firmly located inside the
LCFS, where it is deposited by plasma heating or generated by fusion reactions. Some of this thermal energy
may be radiated in the edge plasma, including the SOL,
with the remainder conveyed by parallel transport to thelimiter or divertor tiles, where it is removed, e.g., by heatexchange with an active cooling loop. The sources andsinks of energy are thus well separated, with the SOL
acting as the medium for energy flow and power exhaust.
In contrast, the sources and sinks of particles in the SOL
cannot be easily separated due to the recombination ofions and electrons at the limiter0divertor tiles. The recombined plasma species leave the surface as molecules,
dissociate into atoms, and then ionize at some distancefrom the solid surface. This distance, known as the neutral transport mean-free-path, l 0 , is determined by the
relative strength of the ion-neutral charge-exchange andatomic ionization processes 5 :l 0 ⫽ ~s0 ne !⫺1
and
s02 ⫽

^siz v&~^siz v& ⫹ ^sCX v&!
Ti 0m i,~1!

where s0 is the average neutral transport cross section.
In the limiter SOL, most of the neutrals penetrate
the LCFS, ionize in the edge plasma, and distribute ~asions! roughly uniformly on each closed flux surface.
They return to the SOL via an ambipolar ~chargeconserving! radial plasma advection0diffusion c drivencAdvection refers to transport of mass due to fluid flow, whereas
diffusion refers to transport of mass due to interparticle collisions. The related terms for transport of heat are convection
and conduction.

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Fig. 1. MHD equilibria for JET limiter ~top left! and various divertor configurations: Mk0 ~top right!, MkI ~middle left!, MkIIA~middle right!, and MkIIGB ~bottom!. In limiter equilibria, the LCFS is formed on either the lower or upper toroidal ~belt!
limiters or, occasionally, on the inner wall. The earliest ~Mk0! divertor configuration involved forming the X point in thevicinity of the upper or lower dump plates, shown in the middle left frame, and using these as divertor targets. The threesubsequent divertors represent increasing geometrical closure: Mk0 r MkI r MkIIA r MkIIGB. Reproduced withpermission from Refs. 3, 57, and 58.

by thermodynamic and magnetic gradients and flow toward the limiter tiles along the magnetic field lines; theresulting flow increases linearly from the stagnation point
located roughly halfway between the bounding limiter
plates to sonic or supersonic velocities in front of thelimiters as required by the Bohm criterion ~see Sec. II.C!.
The closed cycle, involving a recirculation of plasma
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species and their recombination at some plasma-solidinterface, is commonly known as plasma recycling.dd It is worth noting that the limiter SOL, because of its prox-

imity to the LCFS and the associated high electron temperature and low electron collisionality, ne* ⬍ 10, is normallyfound in the sheath-limited regime ~see Sec. II.C!.
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Fig. 2. A scan in the distance between the X point and the divertor target ~top!, typical of the horizontal target configurations suchas those used in Mk0, MkI, and MkIIA divertors, showing the resulting plasma flux profiles, both along the field lines~second from top! and normal to the divertor target ~bottom!; the angle between the field line and divertor target scales
linearly with the X-point distance to the target ~second from bottom!. Reproduced with permission from Ref. 4.

In the divertor configuration, where the poloidal distance between the divertor tiles and the X point is typically larger then l 0 , plasma recycling is localized to thedivertor volume and, as a result, influences the plasma
flow only in the vicinity of the divertor tiles ~the recycling region!. As the upstream density nu increases, thelarge particle source in the divertor augments the parallel
plasma flow to the targets, Gt , an effect known as flow
amplification; this flow increases as the square of the
upstream density, Gt @ nu2 , whereas the target density
increases as its cube, nt @ nu3.e In the recycling region, thestrong convective flow of energy reduces the paralleltemperature gradients, whereas line radiation associatedwith excitation of neutral hydrogen effectively cools thedivertor plasma, Fig. 3. At sufficiently low temperatures~typically below 5 eV!, the loss of parallel plasma momentum due to charge exchange with background neutrals reduces the plasma flux to the divertor tiles, evenas the upstream density is increased, an effect known
as plasma flux rollover, as seen in the example from
JET, Fig. 4. It corresponds to plasma detachment fromthe divertor plates and the detached regime of SOL
transport, Gt @ nu⫺a and nt @ nu⫺b , where a, b ⬎ 0 ~seeSec. II.C!. At still lower temperatures ~typically below
1 eV! and sufficiently high densities, plasma detachment
is further enhanced by volumetric recombination, which
can extinguish the plasma flame entirely, preventing any
plasma-surface contact.
The effectiveness with which the divertor structure
traps neutral particles, an essential requirement for efe That is, SOL transport follows the conduction-limited regime~see Sec. II.C!.
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fective pumping of both hydrogenic and impurity species, is quantified in terms of the fraction of neutrals thationize outside the divertor volume and is commonly referred to as divertor closure.f Thus, divertor closure is acomplicated function of both divertor target geometry,magnetic geometry, and divertor plasma parameters. However, it can be roughly approximated as the geometricalclosure, i.e., the angle subtended by the separatrix andthe divertor targets, with the strike point as the pivot
location. For more than a decade, JET has operated withthree divertors of increasing closure: Mk0 r MkI r
MkIIA r MkIIGB ~Fig. 1!. Not surprisingly, subdivertor neutral pressures and neutral compression ~ratio ofdivertor to main chamber pressures! increase with divertor closure ~Fig. 5!. As the divertor plasma detaches, theionization front moves away from the target, effectively
reducing the closure of the divertor structure and thus
degrading its ability to trap neutral particles. This effectis manifest in the rollover of neutral compression in adensity scan, as seen in Fig. 5.
Despite the toroidal symmetry g inherent in the tokamak concept and its primary consequence, namely, theexistence of nested toroidal flux surfaces, one should notlose sight of the three-dimensional nature of magnetizedplasma transport. This is particularly true in the region off A closed divertor traps a larger fraction of neutrals than anopen divertor.
g We forget for the moment about the toroidal field asymmetry

due to a finite number of coils, localized heating by rf antennas and neutral beams, localized cooling by gas and pellets
injection, and localized recycling from poloidal limiters andother nonuniformities in the vessel wall.
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Fig. 3. Left: Schematic representation of density n and temperature T profiles along the SOL magnetic field lines x, illustrating
both the conduction and convection ~recycling! dominated regions; here u denotes the upstream location halfway between
two solid targets, t denotes the target, and r the beginning of the recycling region, L ⫺ L r ⬇ l 0 , where l 0 is the neutraltransport mean-free-path ~note that this region has been greatly expanded for the sake of clarity!. Right: Schematic
representation of the recycling pattern in the MkIIA divertor, comparing the effect of operating with strike points on thevertical targets ~solid lines! and horizontal targets ~dashed lines!. In both cases, the average velocity of the recycled neutrals
is normal to the solid surface, but in the former case they enter, they travel toward the near-SOL, and in the latter casetoward the far-SOL regions. The first case is favorable, since it increases divertor closure and cools the hot, near-SOL
plasma; the second is unfavorable, since it allows neutrals to escape and thus fuel the upstream SOL region. In addition,
the ionization cloud is more radially extended with a horizontal target, resulting in a broader upstream density profile.
Reproduced with permission from Refs. 3 and 6.

Fig. 4. Illustration of rollover in ion fluxes to JET divertor inner and outer targets during a density ramp, indicating divertor
plasma detachment: MkI ohmic discharge ~left! and MkIIGB L-mode discharge ~right!. The MkI case shows both
integrated and peak ions fluxes, as well as EDGE2D0NIMBUS modeling predictions, which are in fair agreement withthe observed trends. The MkIIGB case compares the results of three gas puffing locations ~inner divertor, outer divertor,and main chamber!, showing that localized gas puffing assists in plasma detachment. Reproduced with permission from
Refs. 3 and 7.
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Fig. 5. Neutral pressure at the divertor cryopump for similar JET L-mode discharges in different divertor geometries is found toincrease with both the line-average ~core plasma! density and divertor closure, MkI r MkIIA r MkIIGB ~left!; note thatchanging the strike point location from horizontal to vertical targets in the MkIIA divertor does not affect the neutralpressure but increases the density limit by ;10%. Neutral compression ~ratio of divertor to main chamber pressures!
increases with divertor closure ~right!. The rollover in neutral compression indicates divertor plasma detachment, which
degrades neutral trapping in the divertor volume, i.e., the effective closure. Reproduced with permission from Ref. 3.

open magnetic field lines that define the SOL. In thefollowing sections we consider the properties of plasmatransport in the three magnetic directions: parallel to themagnetic field, denoted by the symbol 7; normal to themagnetic field and yet confined to the magnetic flux
surface, known as the diamagnetic direction and denotedby the symbol ∧; and normal to the magnetic flux surface, know variously as the radial or perpendicular direction and denoted by the symbol ⬜.

G∧ ⬎⬎ G4 . This fact underlies the thin, elongated, boundary layer aspect of the SOL, whose radial extent is determined by competition between parallel and radial
fluxes. Neglecting volumetric sources, the radial e-folding
lengths of the parallel particle flux density G5 and theparallel heat flux density q5a , which are defined as l G [G5 0¹4 G5 and l qa [ q5a 0¹4 q5a , may be estimated as¹{G ⯝ 0 ]II.A. Perpendicular (Radial) Transport
Classical, collisional transport theory predicts that ina confined plasma, the projections of heat flux density of
species a, denoted by qa , in these directions must beordered as follows:
q5 a : q∧ a : q4a ⬇ 1 : D a : D2a ,D a ⫽ ~vca ta !⫺1 ,~2!

where vca ⫽ ea B0m a is the gyrofrequency and ta is thecollisional time of species a; flux densities of particles,
Ga , are ordered similar to electron heat flow qe . Since vca⬎⬎ ta⫺1 ~D a ⬍⬍ 1! is one of the conditions that define amagnetized plasma, the other being da [ ra 0L4 ⬍⬍ 1,
where ra is the gyroradius and L4 is the transverse gradient scale length of the electromagnetic fields, one generally finds a strong scale separation in the magnitudes ofthe parallel, diamagnetic, and radial fluxes, with G5 ⬎⬎
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lG
L5

;

G4
G5

; D2e ⬍⬍ 1

~3!

and
¹{q a ⯝ 0 ]

l qa
L5

;

q4a
q5 a

; D2a ⬍⬍ 1 ,~4!

where L 5 is half the magnetic connection length between
the divertor or limiter targets. The corresponding lengths
for particle density, l n [ n0¹4 n, temperature, l Ta [ Ta 0
¹4 Ta , and pressure, l pa [ pa 0¹4 pa , are related to l G andl qa as follows:
⫺1
⫺1
l⫺1
G ⫽ l n ⫹ ~2l T !

and
⫺1
⫺1
⫺1
⫺1
l⫺1
q ⫽ l G ⫹ l T ⫽ l n ⫹ 1.5l T ,FUSION SCIENCE AND TECHNOLOGY

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Fundamenski⫺1⫺1and l⫺1pa ⫽ l n ⫹ l Ta . The estimates of Eqs. ~3! and ~4!
are highly idealized, since unlike parallel and diamagnetic fluxes, which are typically well understood, radial
fluxes in the SOL are governed by turbulent advection
and can exceed the classical values by two to three ordersof magnitude; we return to this point in Sec. II.D. As aresult, the SOL is generally much broader than predicted
by Eqs. ~3! and ~4!, with typical values of l n ; l Te ;l pe ; 0.01r0 , where r0 is the minor radius of the torus.
It is conventional to divide the SOL into two radial
regions: the near SOL, defined as the region of highplasma potential, w ⬇ 3Te,LCFS , strong radial electric fields,
E4 ⬇ ¹4 w ⬇ 3Te, LCFS 0l Te , LCFS , and poloidal flow shear,¹4 vE ⬇ ~E4 0Bl Te , LCFS !, which extends ;l Te , LCFS beyond the LCFS, and the far SOL, which refers to theremaining region of the SOL extending toward the vessel
wall. The near SOL is of particular importance to power
deposition on divertor0limiter tiles, whereas the far SOL
determines the degree of plasma interaction with the mainchamber wall.
If the radial turbulent fluxes of particles and heat are
expressed in terms of effective radial velocities, v⬜n ⫽G4 0n and v⬜T ⫽ q4 0 _52 nT, or diffusivities, D4 ⫽ G4 0¹n andx4 ⫽ q4 0n¹T, these may be inferred from the measured
e-folding lengths as follows:l G ⬇ v⬜n t5 n ,SCRAPE-OFF LAYER TRANSPORT ON JET

l G ; l T ; l p ; l q , such that D4 and x4 can be approximated as
l n ; l G ; t5 n D4

Mandl T ; l q ; t5 T x4 .

In all the above expressions, the volumetric sourcesin the SOL were assumed to be negligible, which is reasonable for the simple SOL but not for the complex SOL,
as defined in Sec. II. The influence of volumetric sourcesof particles Sn and heat Sq may be estimated by includingthese in Eqs. ~3! and ~4!. For simplicity, let us consider
the particle conservation equation, ¹G ⯝ Sn ⬇ Siz ⫺ Srec ,where Siz and Srec are the ionization and recombination
densities ~typically, Sn ⬇ Siz ⬎⬎ Srec !, which may be written aslG ⫽G4Siz ⫹ G5 0Liz5

and
Liz5 [

冕L5

Siz s5 ds50l n l G ⬇ D4 t5 n ,t5 n ⬇

L5

~6!

cs

l q ⬇ v⬜T t5 T ,l T l q ⬇ x4 t5 T ,
L25
x5 e

,

~7!

where cs ⫽ @~Te ⫹ Ti !0m i # 102 is the plasma sound speed
and x5e is the parallel electron heat diffusivity, which islarger than the ion diffusivity by the square root of themass ratio, hence x5e ⬎⬎ x5i .h On JET, under typicalohmic and L-mode conditions, the effective velocities
and diffusivities are found in the range ;10 to 100 m0s
and ;0.1 to 1 m 20s, respectively.
Simple models of the SOL suggest that all the above
radial e-folding lengths are linearly proportional, l n ;h Note that Eq. ~7! presupposes the conduction-limited regime,

L5

Siz ds5 .

~9!

0

1. The connection length L 5 is replaced by theionization-weighted, parallel distance away from thetarget, Liz5 , which corresponds to the beginning of
the recycling region L r in Fig. 3; since Liz5 ⬍ L 5 , theparallel density removal time is thereby reduced, t5izn ⫽Liz5 0cs ⬍ t5n .
2. An additional ~source! term appears in the denominator and tends to reduce l G when Sn ⫽ Siz ⫺ Srec is
positive and comparable to G5 0Liz5 ⬇ n0t5izn.
Evidently, both of these effects act to increase the radial
density gradient ~reduce l n ; l G !. This is most clearlyobserved by rewriting the advective0diffusive expressions for l n and l G , Eq. ~6!, in terms of Eq. ~9!, whichyieldslG ⬇

ln lG ⬇

10 ⬍ ne* ⬍ 100 ~see Sec. II.C!, i.e., that parallel energy trans-

port is dominated by electron conduction; in the sheathlimited regime, ne* ⬍ 10, parallel convection dominates, andt5T ⬇ t5n .
FUSION SCIENCE AND TECHNOLOGY冒冕This expression differs from Eq. ~3! in two respects:

andt5 T ⬇

~8!

M

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t5izn ⬇

v⬜n t5izn
1 ⫹ aizD4 t5izn
1 ⫹ aiz
Liz5
cs

,

,

,
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SCRAPE-OFF LAYER TRANSPORT ON JET

andII.C. Parallel Transport
aiz ⫽Siz t5izn
n

.

~10!

Note that these complex SOL expressions reduce to thesimple SOL expressions, Eq. ~6!, when Siz ⬍⬍ n0t5izn , inwhich case aiz r 0, Liz5 r L 5 and t5izn r t5n .
Similar expressions may be derived for l Ta and l qa ,starting with the heat conservation equation, ¹qa ⯝ Sq ⬇
Sheat ⫺ Srad , where Sheat and Srad are the volumetric densities of heating and radiation. Since Srad is typicallylarger than Sheat in the SOL, Sq is generally negative andrepresents a net sink of heat. Thus, in contrast to theparticle sources in the SOL, which are generally positive
and thus tend to reduce l G and l n , energy sources are
typically negative and thus tend to increase l qa and l Ta ,i.e., to broaden the temperature profiles.
II.B. Diamagnetic Transport
In the presence of strong radial gradients, as is thecase in the near SOL, the magnetization condition da ⫽ra 0l a ⬍⬍ 1 and the associated scale separation, Eq. ~2!,
are less pronounced, such that diamagnetic flux densitiesG∧ and q∧a can become comparable to parallel flux densities G5 and q5a and must be retained when calculating the
net transport within the flux surface; i.e., the net poloidal
flux densities Gu and qua should replace G5 and q5a in theestimate of the SOL radial extent in Eqs. ~3! and ~4!. The
poloidal projection of the leading diamagnetic flows in adivertor SOL configuration ~see Sec. IV! is shown schematically in Fig. 10 in Ref. 8, with a normal direction of
the toroidal magnetic field ~B ⫻ ¹B toward the divertor!.
Since diamagnetic flows depend on the direction of themagnetic field ~or, rather, the direction of B ⫻ ¹B!, all
single arrows appearing in that figure would reverse when
this direction is changed. For this reason, they have asignificant effect on the time-average asymmetries in particle and power deposition on inner versus outer limiteror divertor plates ~Sec. IV!. More important, transientdiamagnetic flows, which have opposite directions forions and electrons, give rise to local charge separationand thus to fluctuating radial velocities, v4 ⫽ E ⫻ b0B{e∧ ⫽E∧ 0B. When phase shifted with respect to local density
fluctuations nI and combined with a radial density gradient, these result in net radial particle outflow. Such phaseshift can be produced by parallel resistivity or by unfavorable magnetic curvature, both of which lead tointerchange-like motion of localized plasma structures. It
is now widely accepted that this interchange mechanism,
which naturally explains the ballooning nature of theobserved radial fluxes—with outflow on the outboard
side of the torus, on which the magnetic curvature isunfavorable—is the origin of plasma turbulence in theedge SOL region ~see Sec. II.D!.
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Plasma transport along the magnetic field is, at least
to first order, unaffected by the magnetic field and thus
bears close resemblance to neutral gas dynamics, whether
in their kinetic or fluid description. Nonetheless, it differs from gas dynamics in at least two major respects.
The first is the formation of the magnetic presheath at
the plasma-solid interface due to the mass difference
between ions and electrons and their recombination at
the solid surface. The main consequence of the sheathis the Bohm criterion, which states that the plasma
enters the magnetic presheath with a fluid velocity noless than the local plasma sound speed, i.e., thatthe local parallel Mach number must exceed unity, M5 ⫽v5 0cs ⱖ 1. The second is the strong variation of x5e
with plasma temperature and density, arising fromthe fact that collisions impede parallel free streamingof heat and that the Coulomb collision cross section
between charged particles decreases as the cube of theirrelative velocity. One thus obtains the Spitzer-Harm
expression,9–11 x5e ⫽ 3.2vte l e @ L 5 vte 0ne* @ Te502 0n,
where vte is the electron thermal velocity, l e ⫽ vte te is
the electron-ion collisional mean-free-path, and ne* ⫽L 5 0l e @ L 5 nTe⫺2 is the electron collisionality.i Whencollisionality approaches unity, Spitzer-Harm diffusion
reduces to parallel free-streaming of electron heat atsome fraction of vte , q5e ⫽ ae vte nTe , where ae is known
as the flux-limiting factor; heat flux limiting in SOL
parallel transport is reviewed in Ref. 12. Combining
these results with conservation equations of particles,
momentum, and energy reveals three regimes of parallel plasma transport in the SOL ~Ref. 13!:
1. the sheath-limited0low recycling regime, relevant to low collisionality, ne* ⬍ 10, in which both temperature and pressure are roughly uniform along themagnetic field ~Te 0¹5 Te ⬇ p0¹5 p ⬇ L 5 ! and parallel transport is dominated by the kinetic features of the plasmasurface interface, i.e., by the electrostatic sheath. Denoting
the upstream, main SOL quantities by subscript u andsolid target quantities by subscript t, the above constraints, which may be written as Tu ⯝ Tt and q5u ⯝ q5t ⫽gnt Tt cst , together with total pressure conservation, nu Tu ⯝~1 ⫹ Mt !nt Tt ⯝ 2nt Tt , define the sheath-limited regime
and imply the following relations: G5t @ G0t @ nt @ nu andTu ⯝ Tt @ nu⫺203 , where G0t is the flux of neutrals to thetarget.13
2. the conduction-limited0high-recycling regime relevant to moderate collisionality, ne* ;10 to 100, in whichpressure remains uniform but parallel heat conduction is
sufficiently impeded by collisions to support significant
parallel temperature gradients in the region upstream of
the near-target recycling flow, Te 0¹5 Te ⬍⬍ p0¹5 p ; L 5 ,i This Spitzer-Harm expression is valid only under collisional

conditions, ne* ⬎⬎ 1.

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while the recycling region is dominated by parallel convection ~Fig. 3!. Expressing the parallel heat flux density
as q5 ⫽ nx5e¹5 Te ⫽ k0e Te502¹5 Te leads to the following
relation between upstream and target temperatures:
Tu702 ⫽ Tt702 ⫹ 7q5 L 5 02k0e . Using this relation in place ofTu ⫽ Tt , it is easily shown 13 that Gt @ nu2 , G0 @ nt @ nu3 ,Tt @ nu⫺2 , and Tu @ nu0. The experimental evidence for thetransition from the low to the high recycling regime as nu
is increased is shown in Fig. 6 for a JET L-mode, diverted discharge in which a density scan was performed.15 Note the predicted change from Te @ nu⫺1 forlow density to Te @ nu0 for high density and the fact thations are warmer than electrons, Tiu 0Teu ⬇ 2, consistent
with x5e 0x5i ; 60 and Tiu 0Teu @ ~k0e 0k0i ! 207 ; 3.
3. the detached regime, relevant to high collisionality, ne* ⬎ 100, in which parallel plasma momentum isprogressively removed by charge exchange collisions withneutrals ~effective below Tet ⬇ 5 eV on JET!, thus generating significant parallel pressure gradients, Te 0¹5 Te ;p0¹5 p ⬍⬍ L 5 ~see Fig. 7!. As a result, the plasma flux tothe target and the target density decrease with upstream
density, Gt @ nu⫺a and nt @ nu⫺b , where a, b ⬎ 0, while the

SCRAPE-OFF LAYER TRANSPORT ON JET

target neutral flux continues to increase with nu ~Figs. 4
and 5!. If volumetric recombination becomes significant~typically below Tet ⬇ 1 eV on JET!, the target density
tends toward zero and the plasma enters a strongly detached regime.
One might expect the upstream plasma to be virtually stagnant in a complex SOL due to the localized plasma
recycling in the divertor volume, irrespective of the SOLtransport regime. On the contrary, strong parallel flows,with Mach number of order unity, are observed over muchof the SOL when the B ⫻ ¹B direction points toward the
X point ~the flows are smaller and toward the outer target
when B ⫻ ¹B direction is reversed!.17–20 Systematic studies of parallel SOL flow on JET were first performed in
MkIIGB divertor SOL plasmas.19,20 The upstream SOL
particle flux and parallel Mach number profiles for typical MkIIGB ohmic plasmas are shown in Fig. 8. The
parallel SOL flows are believed to originate due to a
combination of Pfirsch-Schlütter return flows 21,22 andballooning return flows caused by the turbulent outfluxof plasma on the low-field side of the tokamak 23,24 ~seeSec. II.D!.
II.D. Plasma Turbulence in the SOL

Fig. 6. Variation of inner Tetinner and outer Tetouter divertor target temperatures and of upstream electron Teu and ion
Tiu temperatures with the outer target density ntouter.
The data were taken during a JET NBI-heated ~Lmode!, MkI diverted discharge in which the density
was gradually increased by an additional gas puff.
Electron temperatures were measured using fastscanning, reciprocating probes,14 whereas ion temperatures were inferred from the widths of the CIII
emission line. Reproduced with permission from
Ref. 15.
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Since the SOL plasma is both tenuous and cold compared to the core or edge ~pedestal! plasmas, it is often
neglected, or rather approximated as a vacuum envelope,
when considering the global stability against fast MHD
motions. This omission, although clearly reasonable, israrely taken to its logical conclusion, namely, that the
SOL plasma is not in MHD equilibrium. This is not to saythat nested magnetic flux surfaces are necessarily destroyed in the open field line region, but rather that their
origin lies almost exclusively in currents external to the
SOL—the toroidal field being generated due to external
poloidal coils, the poloidal field due to toroidal currents
inside the LCFS, including any edge-localized bootstrap
current—such that the SOL plasma carries only a small
toroidal current in response to the toroidal inductive electric field ~EMF! in a pulsed tokamak. The cause of thisbehavior is twofold: First, the SOL plasma is cold andthus electrically resistive j ; second, the presence of open
field lines, which terminate at either end with electrostatic sheaths at solid targets, likewise impedes charge
flow and gives rise to a sheath resistivity h5sh. The large
effective SOL resistivity, h5SOL ⫽ h5coll ⫹ h5sh , invalidates
the cornerstone assumption of ideal MHD, E ' ⫽ E ⫹ V ⫻B ⫽ h5 j ⫽ 0, known as the ideal MHD Ohm’s law, alongwith such results as the frozen-in property of the magnetic flux and the Grad-Shafranov equation of twodimensional ~2-D! MHD equilibrium. Consequently, thej Recall that low T and high n * imply high resistivity, h coll @ee5n0nei @ Te⫺302.

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Fig. 7. Radial profiles of electron pressure ~top!, density ~middle!, and temperature ~bottom! in the upstream SOL and at the outer
divertor target of an MkI L-mode discharge. The three columns represent a density scan by additional gas puffing: ~left!
high recycling regime, ~middle! the plasma flux “rollover,” and ~right! partial detachment. Reproduced with permission
from Ref. 16.

SOL cannot be in equilibrium in the sense of ideal MHD k
and is thus inherently unstable to a range of dynamical
instabilities, first among which are the already mentioned interchange motions.
Parallel electrical resistivity has an equally strong
effect on the dynamical evolution of the SOL plasma,
which is clearly unable to follow the fast, electromagnetic ~EM!, MHD ordering and evolves instead according with the slower, electrostatic ~ES!, drift ordering.
The two orderings, which are discussed extensively in
Ref. 1, are defined in terms of the speed of transverse
plasma motions compared to the plasma sound speed,i.e., in terms of the transverse Mach number M4 , with
M4 ; 1 in the MHD ordering and M4 ⬍⬍ 1 in the driftkThis is because the parallel return currents required to balance
the thermal and Lorentz forces, ¹p ⫽ j ⫻ B, are impeded by
the large h5SOL.

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ordering. The two ordering schemes lead to a different
relation between magnetic flux tubes and plasma filaments: in MHD ordering the two terms are practicallysynonymous, with the plasma filament frozen into themagnetic flux tube, whereas in drift ordering, the filament drifts across a succession of nearly stationary flux
tubes.25
Based on these observations, one would expect tofind quite intense ES turbulent activity in the SOL but
only moderate levels of EM turbulence, typically identified with magnetic flutter. The radial flux densities associated with each type of turbulence may be estimated as
G4ES [ ^nv4 & ⫽

ES
q4a
[

3
2

^ nI EE ∧ &B^nTa v4 & ⯝3
2,

Ta G4ES ⫹FUSION SCIENCE AND TECHNOLOGY

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SCRAPE-OFF LAYER TRANSPORT ON JET

Fig. 8. Ion saturation current ~left! and parallel Mach number ~right! profiles measured by a reciprocating Mach probe located near
the top of the JET vessel, in normal ~B ⫻ ¹B toward the X point! and reversed ~B ⫻ ¹B away from the X point! field
directions in JET MkIIGB divertor ohmic plasmas. The average value represents the B ⫻ ¹B–independent part of the flow,which shows a clear ballooning character ~positive values indicate flow toward the inner divertor!. Reproduced withpermission from Ref. 20.

and
G4EM ⯝

EM
q4e
⯝

^ nc
I s BD 4 &
B
5
2

,

Te G4EM ⫺ q5 e

冓 冔
BD 42

B

2

L5
l Te

,

~12!

where the tilde denotes a fluctuating quantity, AD ⫽ A ⫺^A&, the angle brackets represent a temporal average, andq4a are written as the sum of the convective and conductive terms. Measurements on a number of tokamaks, including JET, indicate that the relative fluctuations of
E !, and electric potential
density ~ n0n!,I
temperature ~ T0T~ew0T
J e ! approach unity in the SOL, whereas magnetic
fluctuations are always much smaller than one, typically
B0B
D; 10⫺4 . Recalling the earlier discussion, we may
conclude that SOL turbulence is dominated by ES, driftordered dynamics.26,27 It is worth noting that since fluctuations in SOL quantities are comparable to ambient
values, their dynamics cannot be described by standard
quasi-linear turbulence theories and require instead a fully
nonlinear treatment. In fact, as one moves away from the
LCFS, n0n,I
TEe 0Te , and ew0T
J e increase above unity andexhibit bursty, intermittent time signatures. This SOL
intermittency can be interpreted as quasi-periodic ejection and radial movement of isolated, field-aligned structures, variously known as blobs or filaments, which advect
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particles, momentum, and energy into the far SOL~Refs. 28 through 33!. When averaged over all scales,
this radial advection is the origin of the enhanced, or
anomalous, radial transport in the SOL. It is worth notingthat the large radial electric fields in the near SOL and theassociated poloidal velocity shear ~zonal flow! play anactive and self-regulating role in edge SOL turbulence bydecorrelating ~effectively ripping apart! coherent structures, thus reducing radial turbulent fluxes; this mechanism has been demonstrated in numerical simulations of
SOL turbulence ~e.g., Ref. 34!. To conclude, the theoretical framework of SOL turbulence thus appears to bewell established and capable of explaining the observed
phenomenology.
II.E. Effect of the H-Mode and ELMs on the SOL
For a brief and accessible introduction to the highconfinement regime ~H-mode! in tokamaks and the related topic of edge-localized modes ~ELMs!, Ref. 35 ishighly recommended. There are also several fine reviewsof these subjects in the topical literature.36– 47 For more
information on ELM transport in the SOL, the reader isreferred to a recent topical review 48 ; the key results ofrelevance to ITER are summarized in Refs. 49 and 50.
From the point of view of the SOL, ELMs can beviewed as semiperiodic eruptions of hot, dense plasma
from the edge ~pedestal! region, which on JET expel up
to 10% of the plasma stored energy. There is now ample
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SCRAPE-OFF LAYER TRANSPORT ON JET

evidence from many machines to suggest that this ejection is not uniform in space but occurs preferentially on
the low-field side of the torus, i.e., exhibits ballooning
character, and is localized in field-aligned, filamentary
structures. The highly intermittent nature of these eruptions ~typical inter-ELM time ;10 to 100 ms; typical
ELM duration ,1 ms! motivates the division of SOL
transport into the inter-ELM and ELM phases. For some
applications, e.g., power loading on the target plates, one
may also speak of ELM-averaged transport, which represents transport processes averaged over timescales much
longer than the inter-ELM time.
Soon after the H-mode regime was first establishedon JET in the Mk0 divertor configuration, it was observed that following the L r H transition, the SOL
density profiles became significantly steeper, and hence
narrower, than the L-mode profiles.51 Averaged over the
SOL, the degree of steepening varied from as little as
50% to more than a factor 2 ~Ref. 51!, but in the nearSOL region the H-mode profiles were up to 10 times
steeper. Such an increase in the radial gradients is consistent with the reduction in edge turbulence ~formationof the edge transport barrier! and hence the reduction ofradial edge transport coefficients in the H-mode regime.
Lower transport ~improved confinement! produced a transient reduction in the particle flux crossing the LCFS andthus reaching the divertor; the particle confinement time,
calculated based on the exponential recovery of the particle flux, was estimated as tp*H ⬇ 0.5 s in the H-mode
phase, which was a factor of 3 larger than in the L-mode
phase, tp*L ⬇ 0.15 s.

III. LIMITER SOL
Before the installation of the MkI divertor, JET was
operated initially with discrete poloidal limiters, followed by two toroidal belt limiters, initially made fromgraphite, then replaced by beryllium. The belt limiters
were removed during the installation of the MkI divertor
and replaced by a dozen or so poloidal graphite limiters,
which aside from occasional tile replacement are still on
the machine today. Thus, JET offers a wealth of data on
limiter SOL behavior, including the effect of limiter material, wall conditioning, and heating methods. The database of LCFS quantities and SOL profiles in JET limiter
discharges was compiled in Refs. 52, 53, and 54 and its
implications discussed in Refs. 55 and 56. With somemodification these results are presented here and summarized in Table I.
III.A. Carbon Limiters
III.A.1. Ohmically Heated Discharges
During its “limiter” period ~up to 1993!, the standard
mode of JET operation involved forming the LCFS on
the outboard ~poloidal or toroidal! limiters, although occasionally the LCFS was also formed on the inner wall.
Radial profiles of jsat ⫽ G0e, Te , and ne in the SOL in theselimiter plasmas have been measured using a fast scanning Langmuir probe, reciprocating into the SOL near
the top of the torus; plasma diagnosis by electrical, including Langmuir, probes is reviewed in Ref. 14.

TABLE I
Summary of Empirical Scalings of SOL Density and Temperature on the LCFS and Their Radial E-Folding Lengths
in the SOL in JET Limiter and Divertor Discharges*
Configuration ~Mode!
Limiter discharges
C, ohmic ~V!
C, NBI ~L!
C, ICRH ~L!
Be, ~L!
Divertor discharges
Mk0, horizontal, Be ~V, L!
Mk0, horizontal, C ~V, L!
MkI, horizontal, C ~V, L!
MkI, vertical, C ~V, L!
MkI, C ~V, L!
MkIIA, NBI ~L!
MkIIGB, NBI ~L!
MkIIGB, NBI ~H !

neLCFS @TeLCFS @ln, lG @l Te , l pe , l q @~ nS e !1 to ~ nS e ! 2——~ nS e !1 to ~ nS e ! 3~ nS e !⫺2 to ~ nS e ! ⫺3——
~ nS e !⫺0 to ~ nS e !⫺2

Ip⫺10
Ip⫺1.2 PNBI
0.3
Ip⫺1.2 PICRHnS e

nS e Ip⫺1.3
0.4
Ip⫺1.2 PNBI
0.5
PICRH
nS e

~ nS e ! 2—~ nS e ! 2———~TeLCFS ! 2—~ nS e !⫺0 to ~ nS e !⫺1—~ nS e ! 0———~neLCFS ! 102—~ nS e ! 0 to ~ nS e !1
~ nS e ! 0.3
0.25
0.75
~ nS e ! 0.4 to ~ nS e ! 0.5 ⫻ Ptot
to Ptot~ nS e ! 0
0.4 0.3~ nS e 0nGW ! 0.4 q95
Ptot⫺0.8 1.3
0.1 ⫺0.4
Bf q95 ~ nS e ! PSOL
@ lq
—

nS e
—
0
1
~ nS e ! 0.75 to ~ nS e ! 1 ⫻ Ptot
to Ptot—
0.4 0.45~TeLCFS !⫺1.35 q95
Ptot⫺0.8 1.3
0.7 ⫺0.5
Bf q95 ~ nS e ! PSOL
q95 PSOL ~neLCFS !⫺1.2
0.41 ⫺0.48 0.15
l q @ A a Z b Bf⫺0.93 q95
Pt
neu*The auxillary heating method ~NBI, ICRH!, type of target material ~C, Be!, divertor targets used ~horizontal or vertical!, andmode of plasma operation ~ohmic, L-mode, or H-mode! are also indicated in the configuration column. Note that in the final row,a ⫹ b ⫽ 1.1.
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It is instructive to begin the discussion by comparing the inboard-, or high-field-side- ~HFS-!, limited andthe outboard-, or low-field-side- ~LFS-!, limited SOLs.
Such a comparison is possible because of a carefully
controlled study of two phases of a single ohmic discharge, the first limited on the inner wall ~IW ⫽ HFS!,
the second on the lower belt ~LB ⫽ LFS! limiter.57 Thechange from the HFS-limited to the LFS-limited phase
was accomplished by moving the plasma outward as arigid body by '5 cm. The core plasma parameters were
nearly identical during the two phases ~Ip ⫽ 3.1 MA,
Bf ⫽ 2.9 T, nS e ⯝ 2.5 ⫻ 10 19 m⫺3, PSOL ⯝ 1.7 MW, andZ eff ; 4!, and helium was used as the background species to minimize effects of flow amplification due toionization in the SOL.
Typical radial SOL profiles, plotted versus the radial
distance at the probe location, are shown in Fig. 9 for the
LFS phase ~left! and the HFS phase ~right!. It is immediately obvious that the HFS phase profiles are muchbroader. Defining the enhancement factors of HFS phasecompared to LFS phase quantities as E~A! [ A HFS 0
A LFS, one finds that radial e-folding lengths of density,
particle flow, and power flow are enhanced by a factor of'3, and the temperature by a factor of '1.5:

SCRAPE-OFF LAYER TRANSPORT ON JET

E~l n ! ⬇ 55017 ⯝ 3.2 ,E~l T ! ⬇ 100076 ⯝ 1.3 ,~13!

E~l G ! ⬇ 44014.5 ⯝ 3.0 ,E~l q ! ⬇ 30012 ⯝ 2.5 ,
~14!

and
E~nl G ! ⬇ 1.7 ⫻ 3.1 ⯝ 5.3 ,E~nTe l q ! ⬇ 1.7 ⫻ 1.2 ⫻ 2.5 ⯝ 5.1 .

~15!

These are averages of ion and electron side quantities.
The last two items, which represent enhancement factorsof integrated fluxes of particles and power, are more than
twice larger than expected based on plasma flow along amagnetic flux tube whose cross-sectional area scales inversely with toroidal magnetic field ~due to magnetic
flux conservation!; i.e., nl G @ nTe l q @ Bf ~R! @ R ⫺1such that E~nl G ! ⫽ E~nTe l q ! ⫽ 2.2. The origin of theadditional enhancement of ⬇5.202.2 ⬇ 2.4 has not been
resolved. The authors in Ref. 57 suggest subsonic flow
into the inner-wall sheath, which they justify by the highly

Fig. 9. Radial SOL profiles of jsat ⫽ G0e, n, and Te for LFS- ~left! and HFS- ~right! limited phases of JET pulse 27513. Horizontal
axis is the radial distance at the position of the probe ~which is 2.5 times larger than the radial distance at the outer
midplane!. Mapped to the outer midplane, the LFS phase e-folding lengths are found to be l n ' 7 mm, l T ' 30 mm, andl q ' 5 mm. Reproduced with permission from Ref. 57.
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SCRAPE-OFF LAYER TRANSPORT ON JET

grazing angle of incidence there ~'0.12 deg!, for which
the Bohm criterion could potentially be violated. Morelikely, the enhancement is caused by ballooning transport, which would tend to produce E~L 5 ! ⬇ 2m ⫺ 1,
where u ⫽ p0m is the poloidal angle ~from outer midplane! measuring the extent of uniform radial outflow.
Since according to Eq. ~6!, E~l n ! ⯝ E~L 5 !102 , we canestimate the required E~L 5 ! as 2.4 2 ⬇ 5.8 or u ⬇ p03.4 ⬇
50 deg. For comparison, to account for the observed E~l n !
by ballooning transport alone requires E~L 5 ! ⬇ 3.2 2 ⬇10
or u ⬇ p010 ⬇ 20 deg. This range of values is comparable
to those inferred in similar experiments on the Tore Supra,59 where ballooning transport was established as themain cause of the observed profile broadening. However,unlike the Tore Supra experiments, where strong parallel
flow ~required by ballooning transport! was measured at
the probe location during the HFS phase, JET experiments indicate only weak or moderate parallel flows at
the probe location.
Since LFS-limited plasmas offer a larger plasma volume and limiter wetted area, they were historically thepreferred choice for plasma operation. As a result, LFSlimited SOL profiles have been characterized more extensively than their HFS-limited counterparts. The resultsof one such systematic study, consisting of a scan inmagnetic field Bf , plasma current Ip , and line averagedensity nS e for JET ohmic discharges using the earlier,poloidal limiters, are shown in Figs. 10 and 11.
We first consider the variation of electron density
neLCFS and temperature TeLCFS on the LCFS with nS e and Ip~or ohmic heating power PV , which is related roughly
linearly to the plasma current PV ⬇ 0.7Ip1.15 !, with powerin MW and current in MA ~Fig. 10!. At fixed Ip ~PV !,one finds
neLCFS @ ~ nS e ! 1 to ~ nS e ! 2 ,TeLCFS @ ~ nS e !⫺2 to ~ nS e !⫺3 ,and
G5LCFS @ ne Te102 @ ~ nS e ! 0 to ~ nS e ! 102 .

~16!

Note that peLCFS @ ~ nS e !⫺1 across this entire range. As
Ip ~PV ! increases, so do neLCFS , TeLCFS , G5LCFS , and peLCFS~Fig. 10!; the latter is consistent with the linear increaseof tE @ nTe0Pheat with Ip , and its decrease as the squareroot of Pheat , as described by most empirical scalings,⫺102@ Ip102e.g., the Goldstone L-mode scaling, tE @ Ip Pheat
for Pheat @ PV @ Ip . Similarly, the approximate dependence inferred from Fig. 10 ~right frame!,
TeLCFS @ Ip ~ nS e !⫺2 @ PV ~ nS e !⫺2 ,~17!

Fig. 10. Variation of the density and electron temperature at the LCFS with line average density in JET limiter ohmic discharges.
Solid squares, 1 MA, 2.1 T; solid circles, 2 MA, 2.1 T; open circles, 3 MA, 3.4 T; crosses, 4 MA, 3.4 T; and solid triangles,
5 MA, 3.4 T. The solid line in the left figure represents Eq. ~18!, neLCFS @ ~ nS e ! 2 , with neutral penetration velocity of v0 ⫽30 km0s. The solid lines in the right figure are fits to the data, and the dashed lines are predictions of a basic model TeLCFS @Ip203 ~ nS e !⫺403 ; much better agreement is found using the model based on empirical particle confinement time, which yields
TeLCFS @ Ip ~ nS e !⫺1.8 . Reproduced with permission from Ref. 60.
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Fig. 11. Variation of radial e-folding lengths of SOL density and temperature with line average density in JET limiter ohmic
discharges. The notation is the same as in Fig. 10. Reproduced with permission from Ref. 5.

is consistent with the empirical particle confinement timescaling tp @ ~ nS e !⫺0.8 , which leads to the prediction
TeLCFS @ PV ~ nS e !⫺1.8 ; note that, as expected, peLCFS @ PV .
The same model predicts neLCFS @ PV⫺102 ~ nS e ! 2.7 , which isin fair agreement with the Ip scan data in Fig. 10 ~leftframe! but overestimates the density dependence for any
given value of Ip .
The above behavior of neLCFS and TeLCFS with nS e may
be understood in terms of a simple, one-dimensional modelof particle balance in which the plasma is fueled by radial
influx of neutrals and is depleted by a diffusive, ambipolar outflux of ions and electrons. Equating these two
fluxes yields the following relation for the LCFS plasma
density:ped

niLCFS ⬇

l n nil0⬇

~ nS i ! 2 l n s0
2⬇

~ nS i ! 2 l n ^siz v&
2v0

,
~18!

ped

where the ni refers to the density at the pedestal location, i.e., rped ⬇ rLCFS ⫺ l 0 , s0 is given by Eq. ~1!, and theeffective neutral penetration velocity is defined as v0 ⫽ped^siz v&0s0 . Since l 0 scales inversely with ni , the model
predicts that the LCFS density will increase as ~ nS e ! 2 , inagreement with the Ip scan data. The reduction of TeLCFS
as the square-cube of nS e is then a direct consequence ofthe compression of the edge plasma, which requires lessenergy per ion-electron pair leaving the core. It is significant that the ~ nS i ! 2 dependence predicted by Eq. ~18!, andobserved at high densities, is due to a diffusive plasma
outflux, G4 ; D4¹4 n ; D4 n0l n ; in contrast, an advective
outflux, G4 ; nv⬜n , results in a linear density scaling, as
observed at lower densities. This suggests that radial outflux in the edge, or pedestal, region is advective at low
densities and diffusive at higher densities, for any given
value of Ip .
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We next turn to consider the variation of radial
e-folding lengths in the SOL. An early study 61 indicatedtypical values of l n ' 30 to 60 mm and l Te ' 50 to
100 mm, measured at the probe, for plasma currents ranging from 1 to 3 MA. Later,60,62 an inverse dependence on
plasma current was established ~see Fig. 11!, which may
be approximated aslVG ⬇ 30Ip⫺1 ,lVTe ⬇ 3 ⫻ 10⫺18 nS e Ip⫺1.3 ,~19!

where the line average density is in units of m⫺3, theplasma current in MA, and the e-folding lengths in mm;these are once again defined in terms of vertical distanceat the probe location and must be reduced by a factor of'2 to 2.5 when mapped to the outer midplane. At low
density, l n decreases slowly, and l q increases slowly,
with nS e , whereas at high density ~⬎3 ⫻ 10 19 m⫺3 !, l n
and l q are independent of nS e . Note that at low density
l n 0l Te ⬎ 1, whereas at higher density l n r l G so thatl n 0l Te r 10 19 Ip0.3 0nS e ⬍ 1. Similar results were obtainedwith toroidal belt limiters,63 although the absolute valueof l n was found to be roughly 25% smaller, consistent
with shorter connection lengths in the belt-limiter configuration. In addition, both l n and l T were found toscale as Ip⫺1.
For constant toroidal field, which is the case for mostof the data points in Fig. 11, Ip is linearly proportional tothe poloidal magnetic field Bu is inversely proportional
to the safety factor at the 95% flux surface q95 and to theparallel connection length L 5 ⬇ pRq95 , and is nearlylinearly related to the ohmic heating power and LCFS
pressure:⫺1
0.85
Ip @ Bu @ q95@ L⫺1@ ~ peLCFS ! 0.85 .
5 @ PV~20!

Using Eqs. ~17! and ~20!, one may thus rewrite Eq. ~19!
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lVn ⬇ lVG @ L 5 ,0.7
LCFS ⫺102
lVTe @ L1.3!
.
5 nS e @ L 5 ~Te~21!
Note that the effect of the toroidal field Bf is difficult to
extract from the data since Bf was varied for only one setof discharges. Combining Eqs. ~6! and ~21!, one obtains
the effective particle velocity and diffusivity as
LCFS
vV@ ~TeLCFS ! 102 ,⬜n @ cs

D4V @ L 5 csLCFS @ L 5 ~TeLCFS ! 102 ,~22!

with typical values of D4 ; 0.1 to 1 m 20s and v4 ; 10
to 100 m0s. Note that Eq. ~17! implies that D4 scales
inversely with both line average density and the squareroot of the plasma current; the inverse scaling with nS e
was already derived in Ref. 64. This result can also be
obtained by recalling Eq. ~8! and subsequent discussion, which suggest that the SOL density profile is most
simply explained in terms of radial advection withv⬜n 0csLCFS @ constant, for which Eq. ~8! yields l n 0L 5 @constant, in agreement with Eq. ~21!.l The derived scaling of Eq. ~22! is consistent with theories of interchange~curvature-! driven SOL turbulence, which predict plasma
filaments to move radially with a velocity proportional
to the plasma sound speed.34
Assuming sheath-limited parallel transport ~generally applicable to limiter SOL on JET!, the effective velocity and diffusivity of heat transport may be derived
using Eqs. ~7! and ~21!:Vv⬜T@ L⫺0.3@ ~ peLCFS ! 0.25
5~23!

x4V @ L⫺0.6@ ~ peLCFS ! 0.5 .
5~24!

III.A.2. NBI-Heated Discharges
When additional power is coupled to the plasma, theabove expressions are modified depending on the type ofheating method, which can be generally divided into NBI
and rf heating.
NBI heating is more straightforward to consider, since
it transfers most of the injected power directly to the coreplasma. This can be inferred from the rise time of SOL
quantities following the beginning of NBI heating, whichchange on the timescale of the global energy confinement time, typically ;0.5 s. Thus, NBI does not directly
heat the SOL, but rather, NBI power is conveyed to the
SOL by radial convection and conduction across the LCFS.
It should be noted that suprathermal particles are promptly
observed in the SOL following the start of NBI heating
and can be attributed to shine-through losses, beamplasma charge exchange, and loss of fast ions on large
banana orbits and those trapped in toroidal ripple magnetic wells. However, these fast particles, which represent a high-energy tail of the velocity distribution andthus only a small fraction of the total SOL population, do
not affect the bulk, thermal population.
For pure NBI-heated plasmas,62,65 the particle flux
e-folding length shows little, if any, dependence on the
NBI heating power and decreases somewhat stronger thanlinearly with the plasma current, l G @ Ip⫺1.2 , in fair agreement with the ohmic scaling of Eq. ~19!; the density
e-folding length, shown in Fig. 12, exhibits a similar scaling, l n @ Ip⫺1.2. The temperature e-folding length increases slowly with input power, Ptot ⫽ PV ⫹ PNBI , mainly

andWith conduction-limited parallel transport, these expressions for v⬜T and x4 have to be divided by ne,* LCFS
and ne,*2LCFS , respectively. Note that both coefficients in
Eq. ~23! increase moderately with plasma current, ohmic@
heating power, and LCFS pressure; e.g., v⬜T @ L⫺0.3
5
Ip0.3 @ PV0.25 @ ~ peLCFS ! 0.25 .
To summarize, in ohmically heated JET limiter
discharges, radial transport in the edge, or pedestal, region appears to be dominantly advective0convective at
low density and dominantly diffusive0conductive at highdensity. Radial transport in the SOL appears to be dominantly advective0convective, with SOL transport coefficients most easily represented in terms of effective
radial velocities, v⬜n @ cs and v⬜T @ L⫺0.3.
5
diffusive transport based on radial profile scaling alone, there
is ample evidence from a number of tokamaks to suggest that
SOL particle transport is indeed dominated by radial motion offield-aligned filaments or blobs, i.e., by radial advection of mass.

Fig. 12. Variation of radial e-folding length ~in mm! of SOL
density with total input power in JET limiter ohmic~open symbols without vertical bars! and NBI-heated~open symbols with bars! discharges for several values of plasma current from 1 to 5 MA ~from top tobottom in descending order! for a toroidal field of
3.4 T. Reproduced with permission from Ref. 65.

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due to the observed increase of nS e with Ptot , which according to Eq. ~21! should lead to a similar increase in l Te ;large scatter in the temperature data prevents an accurate
determination of the power law exponent. Finally, the parallel power e-folding length is found to scale as l q @0.4 ⫺1.2
Ip , with most of the heating power dependence asPtot
cribed to temperature profile broadening. We may conclude that, to first order, the nature of SOL transport is not
modified by NBI heating, i.e., that radial transport in thelimiter SOL is governed by the same physical mechanism
in ohmic and L-mode plasmas. Although limiter H-modes
have been obtained on JET ~see Sec. II.E!, their SOL profiles have not been sufficiently studied to justify a separate discussion; H-mode SOLprofiles in divertor discharges
are discussed in Sec. II.E.
III.A.3. ICRH Discharges
In contrast to NBI heating, ICRH produces an almost
instantaneous increase in ne and Te across the SOL—on
the timescale of the rise time of the antenna, typically,200 ms—which indicates that some ICRH power iscoupled directly to the SOL plasma. This conclusion is
supported by observations, reported from a number ofmachines, of hot ions in the SOL during ICRH. These
ions lead to guard limiter ~and other wall component!
erosion by physical sputtering, thus generating local
sources of carbon and0or metal impurities, and to localized heating of plasma-facing surfaces, resulting in thermal degassing of adsorbed molecules. Such hydrogenic
and impurity influxes are well correlated with ICRH power
and are believed to be responsible for the observed increase in line average density and the broadening of the
SOL particle flux and density profiles with total input
power, Ptot ⫽ PV ⫹ PICRH . This broadening appears to behighly sensitive to the ~limiter! surface condition, i.e.,the surface concentration of hydrogen, helium, oxygen,or various metallic impurities ~mainly nickel!, due tohelium discharges, disruptions, or high-power ICRH. As
a result, density profile broadening during ICRH can be
reduced significantly by wall-conditioning discharges:
The cleaner the limiter surface, the narrower the observed SOL profile; indeed, profile broadening disappeared altogether in graphite belt limiter operation at
higher current, although the temperature profile continued to increase with ICRH power.
For nominal surface conditions, the e-folding lengthsof density and particle flux increase moderately with
0.3
ICRH power, l G @ l n @ PICRH, whereas the temperature
e-folding length exhibits a somewhat stronger depen0.5
dence, l Te @ PICRH. This behavior is also observed in
mixed ~NBI ⫹ ICRH! heated discharges for which l G @0.3
over a wide range of total heating power, Ptot ⫽ PV ⫹Ptot
PNBI ⫹ PICRH ⫽ 2 to 16 MW, and plasma current, Ip ⫽ 3
to 5 MA; comparison of the influence of PNBI and PICRH
allows the observed broadening to be ascribed largely to
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0.3
nounced broadening than the density profile, l q @ Ptot
to
0.5
Ptot . The results may be summarized as follows:

lICRH
G
lVG

0.3
⫺0.17 0.3
; L0.2PICRH
5 PICRH ; PV

and
lICRH
Te
lVTe

0.5
; PICRH,~25!

where lVG and lVTe are given by Eq. ~19!. Since the sourcesof particles ~electrons! and energy in the SOL due to
ICRH are difficult to characterize, it is equally difficult
to determine their influence on the mechanisms governing radial SOL transport. Although the effect of ICRH
can be included in the SOL transport coefficients,
vICRH
⬜n
vV
⬜n

0.3
⫺0.17 0.3
; L0.2PICRH
5 PICRH ; PV

and
ICRH
v⬜T
V
v⬜T

0.5
@ PICRH,~26!

the effect on the underlying transport mechanisms is noteasily quantified. One plausible explanation would bethat the subthermal component of SOL transport remains
unchanged, whereas ne and Te profile broadening is causedby significant hydrogenic and impurity influxes and direct heating of thermal and suprathermal electrons0ions
by electromagnetic waves in front of the antenna, e.g.,
due to sheath rectification effects.
III.B. Beryllium Limiters
In 1989, beryllium ~Be! was first evaporated on the
carbon ~C! belt limiters and walls, after which beryllium
belt limiters were installed. The findings of these experiments, which were described in Refs. 52 and 67 and arebriefly reviewed here, are of particular importance to
ITER, which is planned to start up with two beryllium
limiters.
Because of the effective pumping of the Be surface,strong fueling, either by gas puffing or pellet injection,
was necessary to control the core density. Consequently,
a larger range of densities was accessible with Be limiters than with C limiters, and the LCFS density and temperature were thereby decoupled from the line averagedensity ~Fig. 13, left!. Thus, in ohmic, gas-fueled plasmas ~Ip ⫽ 3 MA and Bf ⫽ 3.1 T!, it was found that
neLCFS @ ~ nS e ! 2 and TeLCFS @ ~ nS e !⫺1 in the fueling phase
whereas neLCFS @ ~ nS e ! and TeLCFS @ ~ nS e ! 0 in the nonfueling, i.e., wall-pumping, phase. Above some critical density, roughly nS e ' 2 ⫻ 10 19 m⫺3 for ohmic and nS e ' 3 ⫻1039

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SCRAPE-OFF LAYER TRANSPORT ON JET

Fig. 13. Be limiter results in ohmic, gas-fueled plasmas ~Ip ⫽ 3 MA and Bf ⫽ 3.1 T!. LCFS density and temperature as a functionof line average density ~left! and LCFS temperature, density, and temperature e-folding lengths, SOL Be concentration,and total Be influx from limiter as a function of LCFS density ~right!. Reproduced with permission from Ref. 67.

10 19 m⫺3 for L-mode discharges with PNBI ⫽10 MW, the
LCFS density increased, and the LCFS temperature decreased, sharply with line average density, neLCFS @ ~ nS e ! 3
and TeLCFS @ ~ nS e !⫺2 ~Fig. 14!, similar to the behavior
observed with carbon limiters. Power balance indicatesthat while the LCFS electron temperature does not exceed '40 to 60 eV, the LCFS ion temperature approaches
values of several hundred eV at low density ~Fig. 14!;
these high values are consistent with the thermal decoupling of ion and electron species at low collisionality.52
At high densities, nS e . 3 ⫻10 19 m⫺3, the ion temperature
decays sharply, consistent with effective ion-electron energy equipartition.
The variation of various SOL quantities as a functionof LCFS density in the fueled ohmic discharges is shownin Fig. 13 ~right!. It is instructive that the relation betweenedge temperature and density, which is roughly TeLCFS @~neLCFS !⫺0.5 at low density and TeLCFS @ ~neLCFS !⫺1 at highdensity, is independent of the fueling method; this criticaldensity nS e ' 2 ⫻10 19 m⫺3 corresponds to TeLCFS ; 20 eV.
Analysis of L-mode data, in which similar results although shifted to higher densities, are obtained ~compare Fig. 14!, reveals that the edge temperature, and not

the density, is indeed the controlling parameter. Below
this temperature, radiation in the edge0SOL region begins to strongly cool the edge0SOL plasma, producing
a self-enhanced thermal instability.68 Consistent withthis effect and with the analysis of Sec. II.A, the radial
e-folding lengths remain roughly constant at l n ⬇ l Te ⬇
15 mm for TeLCFS ⬎ 20 eV and increase0decrease with
@ ~ nS e ! for TeLCFS ⬍ 20 eV;
density as l Te @ l⫺1ni.e., as expected, the increased electron influx makes thedensity profile more narrow, whereas the increased radiation broadens the temperature profile. The estimatedconcentration of Be atoms in the SOL decreases steadily
with neLCFS , whereas the influx of Be from the limiters
increases gradually for TeLCFS ⬍ 20 eV, after which it
decreases sharply; this behavior has been observed overa range of heating powers up to 30 MW. For TeLCFS ⬎ 20,
the inferred particle diffusivity, calculated using Eq. ~6!,
scales roughly linearly with the sound speed, i.e., v⬜n @D4 @ ~TeLCFS ! 102 @ csLCFS , in agreement with the carbon
limiter result, Eq. ~22!. Below this critical point, it
decreases sharply with temperature, D4 @ ~TeLCFS ! 2 @LCFS⬍ 20 eV, suggesting the domincsLCFS ne,*⫺1
LCFS for Te
ating effect of collisions. A detailed derivation of the1040

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Fig. 14. Variation of neLCFS ~top left!, TeLCFS ~top right!, and TiLCFS ~bottom left! with line average density in Be limiter ohmic
and L-mode ~8 MW ICRH ⫹ 2 MW NBI! discharges ~Ip ⫽ 3 MA and Bf ⫽ 3.1 T!. Also shown is the inferred particle
diffusivity for one ohmic ~20943! and two L-mode discharges, 7 MW ICRH ⫹ 1 MW NBI ~20822! and 10 MW
ICRH ⫹ 9 MW NBI ~20684!, as a function of LCFS temperature. Reproduced with permission from Refs. 52 and 67.

particle diffusivity, and its relation to the Bohm diffusion
coefficient,
D4Bohm ⫽ 0.66TeLCFS 0B~SI0eV units! ,~27!

may be found in Ref. 69.
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III.C. SOL Turbulence and the H-Mode in Limiter Plasmas
Edge and SOL turbulence in JET limiter ohmic plasmas was characterized in a dedicated study using a specially designed reciprocating electrical probe, composedof several probe tips and sampled in the MHz range. The
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SCRAPE-OFF LAYER TRANSPORT ON JET

assembly is known collectively as a turbulence probe.70
Consistent with observations on other tokamaks, as represented schematically in Fig. 10 in Ref. 8, one finds a
poloidal velocity shear layer in the edge region, roughly
1 cm, the width of a banana orbit, inside the LCFS. The
floating potential and the poloidal phase velocity were
found to change sign in this layer. The relative fluctuation amplitude increased with radius, whereas the turbulence flux reached a maximum at the LCFS and thendecayed radially. The measured turbulent particle flux
across the LCFS was consistent with the global energy
confinement time of these limiter plasmas; the radial diffusivity was inferred as D4 ; 1.5 m 20s.
We conclude our discussion of JET limiter plasmas
with a mention of a recent study in which the highconfinement regime ~see Sec. IV! was obtained in low
field and current ~0.8 T and 0.9 MA! limiter plasmas byapplying significant levels ~up to 7 MW! of NBI heating.71 The H-mode phases were brief ~,20 ms! but clearly
distinguishable due to a pronounced reduction in the edge
density fluctuations and Da emission and the increase of
the edge density by up to 20%. The effect of the L r H
transition on the density fluctuation spectrum was shown
to be the same as in divertor ~X-point! phases, with aquantifiable shift toward lower frequencies ~,10 kHz!.
Although the L r H transition appears to be purely electrostatic, the L r H back-transition is accompanied by aburst of magnetic fluctuations, i.e., some type of ELM~see below!.

where nS e is the line average density in m⫺3 , Bf is thetoroidal field in T, and A p is the plasma surface area
in m 2 ~Ref. 72!; i.e., the power flux crossing the LCFS

must exceed some threshold value that increases withdensity and toroidal field. The H-mode regime corresponds to the formation of an edge transport barrier~ETB! and its sporadic destruction by ELMs. Although
the divertor geometry is not a necessary condition foraccessing the H-mode, it appears to play an essential
role in preventing a rapid H r L back-transition typically observed in limiter H-modes 71 ~see Sec. III.C!;
indeed the H-mode was “discovered” soon after the installation of a divertor in the Asdex tokamak,73 and thetwo concepts ~divertor and H-mode! have been closely
tied ever since. It is thus natural to divide the discussion of divertor SOL transport on JET into two parts,
the first dealing with ohmic and L-mode discharges, thesecond with H-mode discharges. In each of these sections, we consider divertors of increasing geometricalclosure: Mk0 ~1986 to 1992! r MkI ~1994 to 1995! r
MkIIA ~1996 to 1998! r MKIIGB ~1999 to 2004!,
which also reflects the chronology of their installation.
The earliest divertor plasmas on JET formed the X
point below0above the upper0lower dump plates, which
thus played the role of horizontal divertor targets. This
Mk0 divertor configuration was almost entirely open anddevoid of any active ~cryogenic! pumping, thus resembling the simple schematic shown in Fig. 2. However, theMk0 divertor plasmas offered the opportunity of assessing the effect of divertor target materials on SOL profiles, since at one point the upper dump plate was madeof carbon and the lower one of beryllium.
The first pumped divertor installed on JET, labeled
MkI, included in-vessel coils, active cryopumping, carbon divertor targets, and toroidally tilted ~fish scale!
tile design; the ideas motivating the MkI divertor design are outlined in Ref. 75. The relatively open divertor structure provided little neutral compression, but MkI
proved to be a useful reference for comparison with themore closed MkIIA and MkIIGB divertors that soon
followed ~Fig. 5!. Since MkI was the first pumped divertor on JET, its effects on plasma behavior have beenstudied extensively. Indeed, virtually all aspects of theresulting experiments are well documented in numerous publications.7,76–106
The relatively open MkI divertor was followed by
the more closed MkIIA divertor, likewise with carbon
targets and active pumping ~Fig. 1!. The new targets
were arranged poloidally to better match the curved magnetic field lines, thus enhancing neutral particle trapping.
Not surprisingly, the increased closure of the MkIIA structure roughly doubled the divertor neutral compression~the ratio of divertor to main chamber pressures! compared to MkI ~Fig. 5! and reduced the density requiredfor detachment by ;30% ~Ref. 107!. To increase theneutral compression even further, the toroidal gaps in the
MkIIA structure were later plugged, thus reducing any
bypass leaks to the main chamber. This plugged divertor,
known as MkIIAP, further increased neutral trapping~Fig. 5! and reduced the density required for detachment.

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IV. DIVERTOR SOL
As outlined in Sec. II, there are three main featuresthat distinguish divertor from limiter SOLs:
1. the magnetic geometry, including the poloidal fieldX point and the magnetic shear
2. divertor plasma recycling due to localized ionization and neutral particle trapping
3. parallel gradients that develop as the SOL enters
the highly collisional, conduction-limited regime
and can lead to partial or total detachment of thedivertor plasma.
One startling consequence of these differences is the appearance of the H-mode regime above some thresholdheating power, Ptot ⬎ PL-H , in which the energy confinement time roughly doubles compared to that of the lowconfinement ~L-mode! regime; the L-H threshold powerhas been found to scale as
PL-H ⬇ 4.2 ⫻ 10 18 ~ nS e ! 0.64 Bf0.78 A0.94
,
p

~28!

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The overall pumping speed was increased by roughly afactor of 3 compared to MkI ~Ref. 82!.
To increase divertor closure even further, the MkIIA
divertor was eventually replaced by the more compact
MkIIGB ~gas box! design in which the inner and outer
divertor chambers were separated by a vertical septum
plate ~Fig. 1; subsequent removal of the septum and its
replacement by a horizontal metal plate revealed that it
had only a minor effect on divertor, main SOL, and coreplasma behavior!. As in MkIIA, all target tiles were madefrom carbon, and cryogenic pumping was applied via
corner slots between vertical and horizontal tiles. The
enhanced closure of the MkIIGB structure further increased divertor neutral compression and the effective
pumping speed compared to MkIIA ~Fig. 5!, thus allowing divertor plasma detachment at lower line averagedensities. The influence of puffing location on detachment in the MkIIGB configuration, as measured by plasma
flux rollover, is shown in Fig. 4. The inner divertor leg
detached most readily with gas injection in the innerchamber, whereas the detachment of the outer leg was
only mildly sensitive to puffing location, with main chamber fueling being most effective. It is noteworthy that theincreased closure of the MkIIGB divertor improved
plasma purity ~reduced Z eff ! by roughly 20% for the samevalue of line average density.108 A good review of theinfluence of divertor geometry, including the sequenceof Mk0-MkI-MkIIA-MkIIAP-MkIIGB, on plasma performance may be found in Ref. 3.
In a recent shutdown, the horizontal septum replacement plate was removed and replaced by a tilted, loadbearing tile made from carbon. This new tile allows
higher-triangularity plasmas than were possible with the
MkIIGB divertor design. Initial results were presented
in Ref. 109.
IV.A. Mk0 (1986 to 1992)
The results of the Mk0 divertor experiments are reported in Refs. 58 and 74. Unfortunately, all discharges
were performed at the same value of the plasma current,
Ip ⫽ 3.1 MA, with only a small variation in the toroidal
field, Bf ⫽ 2.2 to 3.4 T. Although both NBI and ICRH
heating was applied, detailed scaling with Ptot is not reported, aside from a generic variation between ohmic,
L-mode, and H-mode regimes,
lLn 0lVn ⬇ lLTe 0lVTe ⬇ 1.4 to 1.6 ,lVG ⬇ 3 cm,

lVTe ⬇ 6 cm .

~29!

Indeed, only the results of the density scan with the Be
target ~lower single null! are reported in detail and thus
are the focus of our discussion below.
Typical radial profiles of electron density in the SOLof Mk0 divertor discharges ~3.0 MA and 2.8 T! are shown
in Ref. 58 for three values of line average density. Under
L-mode conditions, the density e-folding length inFUSION SCIENCE AND TECHNOLOGY

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creased gradually with density, with typical values ofl n ⬇ 3 cm. In NBI-heated L-mode discharges, l n was
found to increase moderately with line average density,
neLCFS @ ~ nS e ! 2 ,TeLCFS @ ~ nS e !⫺0 to ~ nS e !⫺1 ,@ ~ nS e ! 0 to ~ nS e ! 1 ,
lLCFS
n
and
lLCFS
@ ~ nS e ! 1 ,
Te

~30!

with l n @ ~ nS e ! 0 for nS e , 2.5 ⫻ 10 19 m⫺3 and l n @ ~ nS e !1for nS e . 2.5 ⫻ 10 19 m⫺3 ; note that these exponents wereobtained by analyzing the figures presented in Ref. 58
and differ slightly from the ones reported in the article;
e.g., the decrease of TeLCFS appears to be weaker, l Te
increases linearly rather than quadratically, and the reported break in the l n dependence is not immediately
obvious. These results are independent of the gas-puffing
location ~outer midplane versus X point!, although the
X-point puff leads to larger parallel gradients along the
SOL field lines, due to the strong pumping of the Be tiles;
similar results are also found in ohmic discharges. Asidefrom the smaller TeLCFS reduction and more pronouncedl n enhancement with line average density, the above scalings are similar to the ones obtained in high-density limiter plasmas, e.g., Eqs. ~16! and ~19!. Few results arereported for Mk0 C target plasmas, the exception being
the SOL density profile broadening, l n @ ~ nS e ! 0.3 , which
is weaker than in the case of Be target plasmas, l n @~ nS e ! 0 to ~ nS e !1 , and is more reminiscent of limiter discharges ~Figs. 11, 12, and 13!.
The upstream H-mode profiles are much steeper atlower densities but approach the L-mode values at highest densities 58,74 :nS e ⬇ 1.4 ⫻ 10 19 m⫺3 ,lHpe 0lLpe ⬇ 11 mm024 mm ⬇ 0.45 ,

~31!

and
nS e ⬇ 2.7 ⫻ 10 19 m⫺3 ,lHpe 0lLpe ⬇ 26 mm032 mm ⬇ 0.8 .
One may conclude that turbulent transport, which is effectively suppressed by the H-mode transition, increases
with edge density and0or collisionality. This effect isindependent of the puffing location ~outer midplane versus X point! and0or divertor target material ~C versus Be!
~Refs. 58 and 74!.
IV.B. MkI (1994 to 1995)
Although the vertical targets in the MkI divertor
were separated by a distance comparable to the minor
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radius of a typical JET plasma, it was possible to perform discharges with strike points placed on either thehorizontal or vertical targets. The fueling efficiency ofohmic plasmas was nearly twice larger with verticaltargets than with horizontal targets, although the density limit was not affected and corresponded to frad ;0.8, where frad ⫽ Prad 0Ptot is the radiative power fraction 76 ; in the low-clearance ~small wall gap! configuration, the density limit was reduced to frad ; 0.6. The
target profiles with vertical and horizontal targets arequite similar, with ~partial! detachment occurring firstat the magnetic strike point. Not surprisingly, the fueling efficiency was reduced as the X point was moved
farther away from the target in the horizontal divertor
configuration.76 Similarly, the density corresponding tothe onset of detachment, as indicated by the particle
flux rollover, was reduced. Tomographic reconstructions of bolometric measurements showed that for small
X-point-to-target distances, the radiative cloud moved
toward and beyond the X point at frad ; 0.6, whereas
for larger distances it remained predominantly in thedivertor SOL up to the density limit at frad ; 0.8. This
movement of the radiative zone, which coincides withthe region of high impurity density, has been broadly
reproduced by 2-D fluid modeling of detachment, including the EDGE2D0NIMBUS code,7 although the results are sensitive to the assumptions of radial transportand plasma-surface interaction. The key mechanism driving impurities toward the X-point region has been identified as the temperature gradient force ~in contrast, thefriction force tends to drive them toward the targets!.
During detachment, as the ionization0recombination front
moves toward the X point, the net force on the impurities changes sign, leading to impurity accumulation andstrong radiation in the X-point region.
Plasma detachment in the MkI divertor, which typically was observed when frad exceeded 0.7, is comprehensively reviewed in Refs. 16 and 77. The onset ofdetachment in typical ohmic0L-mode discharges, as measured by the “rollover” of the ion flux to the MkI divertor
targets, is shown in Fig. 4. Note that the inner divertor leg
not only detaches earlier than the outer leg but also exhibits a qualitatively different profile evolution. This may
be inferred by considering the width of the particle flux
profile at the target, which is proportional to the ratio of
the integrated and peak fluxes, l G ⬇ *Gt dr0Gtmax. Thisratio is roughly constant at the inner target but decreases
by more than a factor of 2 at the outer target,
att
Inner: ldet
G 0l G ⬇ 1 ,att
Outer: ldet
G 0l G ⬇ 0.4 ,~32!

where the superscripts att and det refer to the high recycling ~attached! and detached regimes. Although
EDGE2D0NIBMUS modeling is able to capture the rollover behavior of the integrated flux, it does not repro1044

duce the outer target broadening. To capture this effect,
the radial particle diffusivity D4 , which was kept constant during the simulation, would have to increase in theouter divertor during the course of detachment, i.e., withlocal density, as is indeed indicated by the increased levels of fluctuations with the onset of detachment.
Temporal evolution of upstream and outer target radial profiles of ne , Te , and pe in the course of a MkI L-mode
density scan is shown in Fig. 7. All three profiles gradually broaden with the approach of detachment, such thatattldet
pe 0l pe ⬇ 22 mm013 mm ⬇ 1.7 ,att
ldet
Te 0l Te ⬇ 72 mm033 mm ⬇ 2.2 ,

and
att
ldet
ne 0l ne ⬇ 42 mm022 mm ⬇ 1.9 ,~33!

where att and det refer to attached and detached condidet
att
0peu⬇ ~ nS eu ! det0~ nS eu ! att ⬇ 1.6 in thistions. Since peu
discharge, one finds that l pe increases roughly linearlywith the upstream pressure and0or the line average density, l pe @ peu @ nS eu ; here, the subscript u refers to the
upstream value on the LCFS. In Fig. 7, the upstream
and target pe profiles in the above L-mode discharge
are compared with an H-mode density scan at similarfield and current. In the H-mode case, one finds thatattldet
pe 0l pe ' 15 mm07 mm ' 2.1, which is consistent
with the L-mode result, l pe @ peu , considering the error
in the upstream pressure estimate in this discharge ~seeFig. 7!.
The reduced trapping of hydrogenic neutrals, that is,
the reduced closure of the MkI versus the Mk0 divertor
structure, was clearly observed in ohmic plasma detachment.79 Examination of MkI divertor target profiles revealed the growth of an additional peak as the density
was increased in the high-recycling regime; the disappearance of the peak was found to be concurrent with theonset of detachment.80 A substantial part of the volumetric power, ;1 MW in ohmic discharges, was found to be
removed by charge-exchange neutrals with energies in
the range 1.5 to 3 eV ~Ref. 81!. The charge-exchange
region, as well as the region of strong line radiation,
moved toward the X point during detachment.
In reversed field discharges, i.e., with B ⫻ ¹B awayfrom the X point, the L-mode SOL density profiles became significantly steeper when the strike point was
moved from the horizontal target, lhorn ⬇ 3.1 cm, to the
⬇
1.6
cm
~Ref.
84!;
this change wasvertical target, lvern
not observed, or was much smaller, in normal-field discharges, i.e., with B ⫻ ¹B toward the X point. The effect
was also more pronounced at higher density, for whichhorlvern ⬍ l n ~Ref. 86!. The following scalings are reported
for the horizontal target under L-mode conditions:
0.5 0.25
lhor
Ptot ,
n @ ~ nS e !

0.75~ nS e ! 0.4 Ptot

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and
lhor
pe @ ~ nS e ! ,~ nS e ! 0.75 Ptot ,~35!

with the first expressions for Ptot ⬍ 4 MW and the secondfor Ptot ' 4 to 8 MW; for the vertical target under L-mode
conditions, the e-folding length was independent of den0sity, lvern @ ~ nS e ! ~Refs. 87 and 88!. Note that the increaseof l n with nS e is indicative of ~the approach to! plasma
detachment, as predicted by 2-D fluid0neutral codes ~see
below! and observed experimentally in the MkI divertor~Fig. 7!.
These results emphasize the importance of neutral
recycling on upstream density profiles as highlighted inRef. 15 and illustrated schematically in Fig. 3. They arealso consistent with the complex SOL expression, Eq. ~10!,
and with the picture of the influence of sources on radial
profiles discussed in Sec. II.A. This picture may be summarized as follows: Since, on average, the recombining
neutrals leave the divertor target in a direction normal toits surface, they tend to travel away0toward the separatrix in horizontal0vertical divertor configurations andthus ionize in the far0near SOL in these two cases, thefar-SOL plasma being relatively cold and dilute compared to that in the near SOL. In the vertical divertor
case, the near-SOL flux tubes can thus become overionized; i.e., the particle source can exceed the local sink to
the target, producing a backflow toward the upstream
region. Such flow reversal, as the effect is generally
known, tends to increase the radial density gradient andhor
thus decrease lvern compared to l n , in agreement withexperiment. Unfortunately, since the role of neutral sources
is comparable to that of radial transport, a detailed, quantitative analysis requires 2-D coupled plasma-neutral
codes; it is thus reassuring that numerical modeling performed using the EDGE2D0NIBMUS code confirmed
this picture and reproduced the experimental data reasonably well.88,89
The scalings of l n and l Te with various plasma andfield parameters in JET MkI divertor ohmic and L-mode
discharges are discussed in Ref. 90, together with datafrom other large tokamaks. In the high-recycling~conduction-limited! regime, the following scalings arereported for JET MkI discharges:
0.37 0.29
lLCFS@ ~ nS e 0nGW ! 0.42 q95
Ptot
n

~36!

0.39 0.46@ ~TeLCFS !⫺1.34 q95
Ptot ,
lLCFS
Te

~37!

and

where nGW is the Greenwald density,110
nGW ⫽ 10 14

Ip
pa 2

~SI units! .

~38!

The l n expression is broadly consistent with Eq. ~34!. In
the l Te scaling, the reduction with TeLCFS is partly offset
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by the increase with the heating power. Since the twoparameters are generally related, this scaling appears tocontain a degree of redundancy, which we discuss in thefollowing section. In the low-recycling ~sheath-limited!
regime, JET MkI data are discussed only as part of themultimachine scaling, which indicates that, roughly
speaking,lLCFS, lLCFS@ ~A p 0Ip ! 0.7
n
Te

~39!

across many machines.
The radial heat diffusivity in the SOL, inferred from
Eq. ~8!, ranged between 0.1 and 0.6 m 20s in the MkI
divertor experiments and increased roughly linearly withtotal heating power.86 These values were confirmed basedon modeling using both the onion skin method 92 ~OSM!
and the EDGE2D0NIMBUS code,7 which suggested D4 ⬇
0.1 m 20s and x4 ⬇ 0.5 m 20s in L-mode discharges ~Hmode values were a factor of 2 lower!; note that thisvalue of D4 is at least an order of magnitude smaller thanthe Bohm diffusivity, Eq. ~27!. The OSM-extracted radial profiles of x4 suggest a reduction of the diffusivity⫺1, and a gradual increase
with the heating power, x4 @ Ptotof x4 away from the LCFS, consistent with a flatteningof the SOL power profiles,91 i.e., the increase of l q awayfrom the LCFS, as can be seen directly in Fig. 7. EDGE2D0NIMBUS simulations 7 indicate that the flattening of thetemperature profile can largely be explained by the reduction of parallel electron conduction at lower temperatures ~Sec. II.C!. The effect of the L r H transition on
MkI divertor detachment in investigated in Ref. 16, wheredetachment in three types of ELMy H-mode plasmas are
considered: ~a! unfueled, natural density, ~b! deuterium
fueled with Type-I ELMs, and ~c! nitrogen seeded with
Type-III ELMs. In the D2 fueled case, the divertor plasma
only detaches in the inter-ELM phase and promptly reattaches during the ELMs; i.e., the ELMs carry sufficientenergy to burn through the cloud of neutrals0impurities
at the detachment front and reestablish fully ionizedplasma contact with the target plate, Fig. 16, MkI ELMy
H-mode detachment. In contrast, nitrogen seeded
H-modes, in which the ELMs are substantially smaller,
allow the plasma to remain detached at all times. The
seeded nitrogen tends to accumulate in the divertor during detachment, yielding enrichment factors of 30 ormore.7–9
As mentioned previously and illustrated in Fig. 7, theupstream pressure profile during H-mode conditions gradually broadens with the approach of detachment. Although the degree of broadening is consistent with thatobserved under L-mode conditions, which is roughly linear with the upstream pressure, l pe @ peu , Eq. ~33!, theinter-ELM H-mode profiles are narrower than the corresponding L-mode profiles and tend to converge with increasing density,
Attached: lHpe 0lLpe ' 7 mm013 mm ' 0.55
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andDetached: lHpe 0lLpe ' 15 mm022 mm ' 0.7 ,~40!

in line with the Mk0 result, Eq. ~31!.
IV.C. MkIIA (1996 to 1998)
Although changing the strike point location fromhorizontal to vertical targets in MkIIA did not affect thedivertor neutral pressure, it increased the density limit by;10%, suggesting that the fueling efficiency was slightly
reduced. Whereas in the MkI divertor, detachment of
the inner and outer divertor legs occurred at similar densities, in MkIIA the inner divertor leg detached muchearlier when the strike points were located on the horizontal targets and at roughly the same density as the outerleg when they were placed on the vertical targets.107 The
approach to detachment was also much more gradual in
the vertical divertor configuration. All of these changes
can be ascribed to differences in the ionization and recycling patterns, as shown in Fig. 3 and discussed inSecs. II.A and IV.B. MkIIA divertor studies also established a clear link between the onset of detachment andvolumetric recombination, which was detected based on
spectroscopic line ratios and was found to be concentrated near the strike points at both divertor targets. Thisobservation implied that plasma temperature dropped
below 1 eV at the targets following detachment. As with
the MkI divertor, the radiation cloud was seen to move to
the X-point region, where in ohmic and L-mode discharges, recombination was also detected. Despite thelower upstream neutral pressure with MkIIA and MkIIAP
divertors, the level of impurities in the core plasma was
not affected; i.e., Z eff remained unchanged from the MkI
scaling.
Similar to the MkI study, the divertor target ne and Te
profiles were measured across the MkIIA divertor target
with an array of Langmuir probes in a large number ofohmic, L-mode, and H-mode discharges of varying Ip ,Bf , q95 , Ptot , and nS e ~Ref. 111; see Fig. 15!; in all cases
the SOL plasmas were attached and ranged over bothsheath-limited and conduction-limited regimes. A twopoint onion skin method was then used to map these
profiles to the upstream SOL and to calculate the resulting radial e-folding lengths and heat diffusivity profiles~Fig. 17!. The OSM method was validated based on alimited number of ~MkI! discharges for which the upstream profiles were measured directly with the reciprocating probe and Li beam diagnostic, and which were
found to be in fair agreement with the OSM predictions.91 The complete MkI ⫹ MkIIA database included
more than 40 discharges, two dozen of which are compiled in Table I of Ref. 111. Under ohmic and L-mode
conditions, the resulting e-folding lengths fall in the rangelLCFS' 5 to 40 mm and lLCFS' 7 to 60 mm, generallynTeincreasing away from the separatrix ~Fig. 17!. Such pro1046

file broadening in the far SOL, which is more pronounced for l Te than for l n , is consistent with earlier
observations in MkI discharges ~Fig. 7!. Comparison ofdischarges with vertical versus horizontal targets and withlow versus high flux expansion revealed no clear differences in upstream SOL profiles, suggesting that main
SOL transport is largely independent of the degree ofdivertor closure.
In Ref. 111 it is concluded that the near-SOL e-folding
lengths lLCFS
and lLCFS
are not correlated with any sinnTe
gle main plasma parameter. Nonetheless, a multivariable
regression analysis of these lengths with Bf , q95 , PSOL,
and nS e ~note that PSOL ⫽ Ptot ⫺ Prad and Ip @ Bf 0q95 aredecoupled in L-mode discharges due to the presence ofauxiliary heating! yields close agreement between theexperimental values and the following relations:
1.3
⫺0.4
lLCFS
@ Bf⫺0.8 q95~ nS e ! 0.1 PSOL
n

~41!

1.3
⫺0.5
lLCFS
@ Bf⫺0.8 q95~ nS e ! 0.7 PSOL
,
Te

~42!

and

or repeating the regression with nS e and PSOL replaced by
neLCFS and TeLCFS ,1.3@ Bf⫺0.8 q95~neLCFS ! 0.5 ~TeLCFS !⫺1.2
lLCFSn; L 5 ~ne*LCFS ! 102

~43!

and
1.3
@ Bf⫺0.8 q95~neLCFS ! 0.8 ~TeLCFS !⫺1.4
lLCFS
Te

; L 5 ~ne*LCFS ! 102 ,~44!

with correlation factors .0.8. The inverse scaling with
1.3
@ Ip⫺1.3, in
Ip —note that for constant magnetic field, q95
agreement with Eq. ~19!—and the positive scaling withnS e are similar to the limiter results of Eq. ~19!, but theinverse scaling with PSOL is contrary to the results reported earlier with the MkI divertor @see Eq. ~34!#. It is
not clear whether this is due to actual differences between MkI and MkIIA discharges or to the approximate
nature of OSM modeling, the absence of current and fieldscaling in Eq. ~34!, or some other, unknown factors, e.g.,
the uncertainty in the separatrix location. It is worth
noting that lLCFS
scales inversely with TeLCFS across allTeplasma regimes, including inter-ELM H-mode. This dependence, which can be approximated as l Te Te ; constant, is consistent with the broadening of the SOL
temperature profile with radial distance away from the
LCFS ~Fig. 17!.
Combining Eqs. ~43! and ~8!, one obtains the effective radial velocity
LCFS
LCFS 0.5v⬜n@ L0.3! ~TeLCFS !⫺0.8
5 ~nee; ~ne*LCFS ! 102 ,FUSION SCIENCE AND TECHNOLOGY~45!
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Fig. 15. Radial profiles of electron density and temperature at the MkIIA divertor outer target in ohmic, L-mode, and H-mode
discharges. Note the increase in the fluctuation levels of both ne and Te with the heating power. Reproduced withpermission from Ref. 111.

which is found to increase roughly with the square rootof the collisionality. This divertor ~conduction-limited!
result differs substantially from the limiter ~sheathLCFS
limited! result, Eq. ~22!, where v⬜ne
was found to be*LCFS
independent of neand directly proportional to
csLCFS. Similarly, the heat diffusivity derived using OSM
modeling increases linearly with collisionality, x4LCFS @~TeLCFS!⫺2 @ ne*LCFS, with typical near-SOL values in therange of 0.03 to 0.3 m20s ~Fig. 17!. Once again, these
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values are somewhat larger than the earlier results, whichindicate x4LCFS ; 0.2 to 1 m 20s in ohmic and L-mode
discharges.
derived using Eq. ~8!,
The absolute values of vLCFS⬜nwhich are found to vary between 10 and 30 m0s, are ingood agreement with typical radial effective velocities
measured by the turbulence probe in ohmic MkIIA plasmas 112 ; these values are consistent with diffusion coefficients of ;0.15 to 0.3 m 20s. This direct measurement
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Fig. 16. Inner divertor Da and jsat ⫽ Gt 0e for an ELMy H-mode
density scan in the MkI divertor with Be targets; notethat ELM frequency generally increases, and hence
ELM size decreases with gas puffing and line averagedensity. At the lowest densities ~left!, the divertor
plasma is attached at all times, such that both Da andjsat increase during ELMs. In contrast, at the highest
densities ~right!, it detaches in the inter-ELM period,
reattaching briefly during the ELM, such that jsat increases but Da decreases during the ELM. This effectis sometimes referred to as a negative ELM. Note that
Be emission remains negligible at all times, implying
a low ~,10 eV! electron temperature even during the
ELM. Reproduced with permission from Ref. 16.

indicates that v⬜n is substantially smaller in the divertor~X-point! phase compared to the limiter phase of thesame discharge and is insensitive to the divertor configuration ~horizontal versus vertical!. The difference between limiter and divertor SOL is mainly due to higher
density fluctuation levels in the limiter SOL, and to alesser extent to increased correlation between densityand potential fluctuations.112 One also observes that v⬜ndecays gradually with radius in the limiter far SOL but
remains roughly constant across the divertor far SOL; it
is not possible to comment on the near-SOL region since
the exact position of the separatrix is not known in the
X-point phase. The constancy of v⬜n with radius suggeststhat Eq. ~45! remains applicable across the SOL, since neoften decreases faster than Te , thus keeping the collisionality roughly constant ~see Sec. IV.D!.
The variation of both pedestal and separatrix densities, normalized by the line average density with ELM

Fig. 17. Radial profiles of density and temperature e-folding
lengths and radial heat diffusivities in MkI ~,36 000!
and MkIIA ~.36 000! divertor ohmic, L-mode, andH-mode discharges extracted from target profiles ofdensity and electron temperature using the onion skinmethod. Reproduced with permission from Ref. 111.

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Fig. 18. The variation of pedestal and separatrix densities, normalized by the line average density, with ELM frequency ~left! andof the separatrix density with the rate of particle loss due to ELMs ~right! in MkIIA ELMy H-mode plasmas. The plots
compare data from low-triangularity ~LT! plasmas with data from high triangularity ~HT! plasmas with horizontal andvertical target divertor configurations. Reproduced with permission from Refs. 82 and 113.

frequency, fELM, is shown in Fig. 18. Whereas neped 0nS e
was clearly independent of fELM, neLCFS 0nS e was found toincrease linearly with fELM , from 0.1 to 0.2 at 5 Hz to 0.4
to 0.6 at 15 Hz; this scaling is consistent with the ohmic
and L-mode dependence ~Fig. 20! in that fELM generally
increased with nS e . The constant of proportionality, C ⫽neLCFS 0nS e fELM, was larger with horizontal targets thanwith vertical targets and with high plasma triangularity
than with low plasma triangularity.113 The latter dependence could be eliminated by replotting neLCFS versus therate of particle loss due to ELMs, fELM Dneped ~Fig. 18!,
suggesting a correlation between triangularity and theELM frequency. The remaining difference between vertical and horizontal targets can be ascribed to the difference in neutral compression and recycling patterns inthese two configurations. Energy confinement degradation was likewise related to the ELM frequency, or moreaccurately to the product fELM tped ⫽ tped 0tinter-ELM [jELM , where tped is representative of the time taken toreheat the edge plasma following an ELM, i.e., to rebuild
the H-mode pedestal. The H97 confinement factor ~corrected for fast ions! was well reproduced by the following expression:
H97 ⫽ 1.23 ⫺ 0.57jELM @1 ⫺ exp~⫺10jELM !# , ~46!
where tped ⬇ 34 ms was inferred from the experimental
data. MkIIA results also showed that confinement degradation is better correlated with the ELM frequency, andhence with the upstream LCFS density, than with the
upstream neutral pressure, as was postulated based on
MkI data. In other words, H97 decreased monotonically
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with neLCFS 0nS e , with H97 ' ~1.0, 0.9, 0.8, and 0.7! forneLCFS 0nS e ⫽ ~0.1, 0.5, 0.7, and 0.8!.
IV.D. MkIIGB (1999 to 2004)
The MkI ⫹ MKIIA database discussed in Sec. IV.C
was extended by a further two dozen ne and Te target
profiles in the MkIIGB divertor, all but one of these inohmic and L-mode plasmas under attached conditions.
As before, a two-point OSM method was used to map thetarget profiles to the upstream SOL. For selected cases,
this technique was also compared against an advanced
OSM method in which the parallel transport equations
were solved by computational fluid dynamic techniques
between the target and upstream regions.114–116 Although
the absolute values differed by up to a factor of 2 between
the two techniques, the upstream e-folding lengths agreed
reasonably well. The advanced OSM method was further
validated against the upstream ne and Te profiles measured using the reciprocating probe in selected MkIIGB
L-mode discharges ~Fig. 19!. Note that the inferred heatdiffusivity profiles tend to increase away from the separatrix, with x4 ' 0.1 to 0.2 m 20s in the near SOL to x4 '0.4 to 0.6 m 20s in the far-SOL regions, consistent withearlier results ~Fig. 17!, and with the broadening of the
Te ~r! profile.
The complete MkIIGB database is summarized inTable 2 of Ref. 117, with the most notable results presented in Fig. 20. It is interesting to note that the upstream separatrix density and temperature across many
LCFS
discharges appear to be related as neu@ ~TeuLCFS ! 2 ,1049

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Fig. 19. Comparison of radial profiles of upstream electron and ion temperatures, electron density, total pressure, and parallel
Mach number computed using an advanced OSM solver based on target profiles and measured directly by a reciprocatingprobe in an MkIIGB L-mode discharge. Also shown are the radial heat diffusivity profiles inferred by the OSM method,which are seen to increase radially away from the separatrix. Reproduced with permission from Ref. 114.

albeit with a large scatter. Moreover, the same dependence appears to hold approximately across the SOL for
upstream profiles in any given discharge, i.e., neu @ Teu2
~Fig. 20!. Since L 5 ⬇ pRq95 has only a small variation
across discharges and varies by less than a factor of 2
across the SOL, these relations imply that the upstream*
collisionality remains bounded roughly by 20 ⬍ neu⬍ 80
across the entire MkIIGB database ~Fig. 20!. The approximate constancy of ne* across many discharges can be
attributed to the fact that only high-recycling-regime plasmas were selected, which from the discussion in Sec. II.C,
implies that 10 ⬍ ne* ⬍ 100. The constancy of ne* radiallyacross the SOL is more difficult to explain; we return tothis observation later. Finally, the ratio of the upstream

and line average densities increases from ;0.2 for lowest
densities to ;0.8 for highest densities ~Fig. 20!.
The magnitudes of upstream e-folding lengths are
somewhat smaller in MkIIGB than in the MkI ⫹ MkIIA
database: lLCFS' 5 to 30 mm and lLCFS' 8 to 40 mm.
nTeThis might be ascribed to the fact that virtually all the
MkI ⫹ MkIIA data were obtained in the horizontal divertor configuration, whereas the MkIIGB results wereobtained in the vertical configuration, in which the divertor recycling pattern becomes more important andtends to produce somewhat narrower SOL widths. More
important, the MkIIGB lengths are only weakly correlated with the MkI ⫹ MkIIA scalings, Eqs. ~41! through~44!. Indeed, the MkIIGB data exhibit a significantly

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Fig. 20. Relation between OSM-derived upstream density and temperature in MkIIA ohmic, L-mode, and H-mode plasmas ~upper
left!. Similar relation for MkIIGB, including several reciprocating probe measurements ~upper right!. Collisionality
diagram for MkIIA and MkIIGB points ~bottom left!; all data fall in the conduction-limited regime, i.e., are bounded bystraight lines indicating ne* ⫽ 10 sheath-limited and ne* ⫽ 80 detached regimes. Ratio of upstream to line average density~bottom right!. Reproduced with permission from Refs. 117 and 118.

larger scatter than the MkI ⫹ MkII data, such that evenand lLCFS
yields correlation factors
the best fit for lLCFSn
Te
of less than 0.4. The origin of this scatter is not clear andstrongly suggests some hidden variable. One possible
cause is the approach to divertor detachment, which occurs for lower upstream densities with vertical, rather
than with horizontal, targets. Since the two-point OSM
method is not applicable for detached plasmas, it might
produce significant errors in the presence of vertical targets. This should be kept in mind when reviewing the
MkIIGB results discussed here.
Roughly speaking, both e-folding lengths were foundto be inversely proportional to upstream quantities,
lLCFS@ ~TeLCFS !⫺0.85 @ ~neLCFS !⫺0.38
n

~47!

lLCFS
0L 5 @ PSOL ~neLCFS !⫺1.2
q
and
x4LCFS @ ~PSOL L 5 ! 2 ~neLCFS !⫺2.7 ,@ ~TeLCFS !⫺0.65 @ ~neLCFS !⫺0.45 .
lLCFS
Te

~48!

Consequently, the power e-folding length and the inferred heat diffusivity tend to decrease with both the
upstream density, x4LCFS @ ~neLCFS !⫺1.25 , and the power⫺1.07
into the SOL, x4LCFS @ PSOL
. The following scalings,
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give a reasonable fit to the MkIIGB ohmic and L-mode
results, provided these are plotted on a logarithmic scale,such that the inherent scatter in the data is reduced; note2
the appearance of the anticipated x4 @ L25 @ q95
scaling in
Eq. ~50!. The above relations, with the factor 1.2 re13
placed by _74 ⫽ 1.75 and 2.7 replaced by _4 ⫽ 3.25, can bederived for the conduction-limited regime from Eq. ~7!
by estimating the power into the SOL as PSOL L 5 @ q5 l q .
This leads to the estimate of the upstream temperature,
Teu @ ~PSOL L 5 ! 409 ~neLCFS x4LCFS !⫺209 ,

and

~49!

~51!

and the following relations between x4LCFS and lLCFS
;
Te
lLCFS
:
q
lLCFS
0L 5 @ ~PSOL L 5 !⫺509 ~neLCFS x4LCFS ! 709
q@ ~TeLCFS !⫺504 ~neLCFS x4LCFS ! 102 .

~52!
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SCRAPE-OFF LAYER TRANSPORT ON JETGood accounts of the derivation may be found in Ref. 117
and Chap. 65 of Ref. 13.
One of the main conclusions emerging from the above
studies is the close relationship between the density andtemperature e-folding lengths, with l n 0l Te ; 1. To see
this more clearly, consider the density and temperature
profiles for MkIIGB ohmic plasma at three different densities, obtained simultaneously from a variety of diagnostics ~see Figs. 3 and 9 in Ref. 20!. Here, the density
was measured by two reciprocating Langmuir probes separated toroidally by 180 deg, as well as a lithium beamand edge LIDAR diagnostics.20 The temperature wasinferred from the floating potential–temperature relation
for a Langmuir probe.20 One observes a gradual broadening of the Te ~r! profile, with l Te increasing graduallywith distance away from the separatrix, from ;10 to
20 mm in the near SOL to .50 mm in the far SOL. In
contrast, the n~r! profile is characterized by a single
e-folding length, l n ' 15 to 25 mm, roughly constantacross the SOL. One thus finds l n 0l Te ⬎ 1 in the nearSOL and l n 0l Te ⬍ 1 in the far-SOL regions.
It is not immediately obvious why the two lengths
should be comparable in a complex SOL, where thesources of particles and energy are clearly decoupled. A
simple explanation may be obtained from taking the ratioof Eqs. ~6! and ~7!. Assuming radially advective transport with v⬜n ⬇ v⬜T ⬇ v4 representing the effective radial
velocity of turbulent filaments or blobs, the ratio l n 0l Te
reduces to the ratio of parallel loss times of particles andelectron energy,

constant across the SOL, with v⬜n ⬇ 100 m0s and D4 ⬇
0.7 m 20s. Although these values are a factor of 3 larger
than those measured in MkIIA ohmic plasmas, one should
keep in mind that they correspond to lower field, current,and density. However, the observation that v ⬜n ;constant is consistent with the v⬜n @ ne*102 scaling,
Eq. ~45!, and the approximate constancy of ne* across the
SOL. The L-mode results indicate that v⬜n is insensitive
to the NBI heating power, at least between 1 and 5 MW,
and tends to decrease radially from '50 m0s in the near
SOL to '25 m0s in the far SOL; i.e., the turbulent structures appear to decelerate as they move away from the
LCFS.
One novel element introduced during the MkIIGB
period was the statistical description of SOL transport. In
JET, as in other devices, the probability distribution function ~PDF! of radial turbulent fluxes showed significant
non-Gaussian features, bearing evidence to high levels ofintermittency in SOL turbulence 122 ~Fig. 21!. It was foundthat the PDF of radial turbulent fluxes could be rescaled
using a finite-size scaling law 126 :PDF~G4ES ! ⫽ L⫺1 g~G4ES 0L! ,~54!

where we neglected factors of order unity and evaluatedthe final expression for a deuterium plasma with equal
ion and electron temperatures. Although Eq. ~53! neglects several important effects, e.g., ion-electron energy
collisional exchange, which tends to couple l Te and l Ti ,it clearly illustrates why l n 0l Te ; 1 in the conductionlimited regime for MkIIGB SOL, for which typically
ne* ; 40 to 80 ~Fig. 20!. Note that Eq. ~53! predicts a
linear decrease of l n 0l Te with ne* , such that l n 0l Te ⬎⬎ 1
for ne* ⬍⬍ 60 and l n 0l Te ⬍⬍ 1 for ne* ⬎⬎ 60. Similar arguments, but based on the diffusive rather than the advective assumption, may be found in Ref. 118 and Chap. 5 ofRef. 13.
SOL turbulence studies were actively pursued in
MkIIGB divertor plasmas and are described in several
articles.122–138 As with the MkIIA divertor, a turbulenceprobe was used to measure the radial E ⫻ B particle flux
profiles in MkIIGB ohmic, L-mode, and H-mode discharges.120 In the ohmic plasma investigated, the effective radial velocity and particle diffusivity remained

where G4ES is the radial turbulent flux, g is an arbitrary
function, and L is a scaling factor, which was directly
related with the root-mean-square value of jsat fluctuations, i.e., L @ RMS~ jD sat !. The empirical similarity inturbulent fluxes suggests that edge plasma turbulent transport evolves into a state in which transport PDFs exhibit
the same behavior over the entire amplitude range.121
The effective radial velocities of turbulent structures~blobs, filaments! have also been characterized by statistical methods. In particular, different multiprobe systems
have been developed to investigate the links between
transport, gradients, and poloidal and parallel flows.124,125
The effective radial velocity was of the order of 30 m0s,
consistent with earlier measurements ~e.g., Ref. 119! andwith transport modeling, e.g., using B2-EIRENE and
EGDE2D0NIMBUS. The size and velocity of turbulent
structures were found to be correlated, such that bothincreased when the plasma deviated from the average~most probable! gradient. Since most of the time thisdeviation was small, the ejection of large, fast blobs occurred only sporadically. The effective radial velocity
increased up to 500 m0s during these rare but intense
plasma bursts. It is worth noting that the magnitude of
the turbulent fluxes measured by the probe was generally
too high to be consistent with global particle balance. At
present, this disagreement still has not been satisfactorily
resolved, although the arguments presented earlier concerning poloidal asymmetries ~ballooning character! of
the turbulence appear to offer the most promising explanation for this discrepancy.
Investigations of the naturally occurring poloidal velocity shear layer ~see Fig. 10 in Ref. 8! in the edge
region of JET MkIIGB plasmas revealed a link between

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ln
l Te

⬇

t5 n
t5 T

⬇

x5 e
cs L 5⬇

vte l eivti L 5⬇

冉 冊

Te m i 102 1
Ti m e

ne*

⬇

60
ne*

,

~53!

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Fig. 21. PDFs of radial effective velocity ~left! and radial correlation length of the floating potential ~right! as measured by the
turbulence probe in the upstream edge0SOL MkIIGB L-mode plasmas. Three radial positions of the probe are shown,corresponding to the far-SOL ~top!, near-SOL ~middle!, and edge ~bottom! regions, for which r ⫺ rLCFS ⫽ 2 to 3 cm,
1 to 2 cm, and ⫺1 to 0 cm, respectively. Note the increasing skewness of both PDF profiles with distance away from the
LCFS, indicating strongly intermittent transport dominated by sporadic, large bursts. Reproduced with permission from
Ref. 123.

fluctuations, parallel flows, and marginal stability.122
The E ⫻ B shear ~zonal! flow in the neighborhood of the
LCFS appeared to self-organize so as to maintain theradial gradients in the thermodynamic variables at marginal stability. The influence of sheared flows on thestatistical properties of fluctuations has also been studied, showing that PDFs become more Gaussian in thepresence of radial gradients in the poloidal E ⫻ B velocity.123 It was also established that turbulence can act bothas a sink and as a source of energy for the mean ~zonal!
flow in the shear layer, while measurements of the turbulence production indicated the importance of threedimensional effects in the energy transfer between flows
and turbulence.127 Finally, a dynamical coupling between turbulent transport and parallel SOL flows wasdemonstrated and quantified.128,130
Recently, first attempts at edge0SOL turbulence modeling of JET ohmic and L-mode plasmas were undertaken. The simulations, as described in Ref. 24, made useof an edge-SOL electrostatic ~ESEL! code,139–141 coupled to first-principles expressions for parallel losses andcollisional damping rates.24 Although the radial temperature profiles were well reproduced, the simulated density profiles were somewhat broader than in the experiment.
As usual, the effect of the L r H transition onradial SOL fluxes and effective SOL diffusivities in
MkIIGB plasmas was investigated using the turbulenceprobe.120 Typical results indicate that radial transport in
the near-SOL region was clearly reduced during the
H-mode compared to the ohmic phase and that this reFUSION SCIENCE AND TECHNOLOGY

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duction disappeared in the far-SOL region. These results suggest that the H-mode affects SOL ~turbulent!
transport primarily via the extension of the ETB into
the near-SOL region.
The techniques used for the statistical characterization of edge0SOL turbulence in ohmic and L-mode discharges were also applied to ELMy H-mode plasmas tocharacterize the radial propagation of turbulent blobs and
ELM filaments.131 A similar gradient-velocity relation
was detected for both types of structures ~Fig. 22!. Moreover, ELM filament radial velocities corresponded to those
expected of largest turbulent blobs, v4 ; 1 km0s. Thisfinding was further reinforced by the observed link between the radial velocity and the amplitude ~size! of ELM
filaments—with less frequent, larger ELMs traveling⫺1faster, approximately as v4 @ fELM
@ DW0W ~Ref. 129;m
see Fig. 22!. In particular, it was concluded that competition between parallel and radial transport was responsible for the observed particle and energy losses to thedivertor plates associated with ELMs ~Refs. 142 and 144!.
In spite of the large particle fluxes measured in the far
SOL during type-I ELMs, the energy carried by electrons
to the main chamber plasma-facing components by the
ELM filaments was found to be quite small ~,5% of
the ELM energy losses! in the discharges considered.129
Indirect measurements of energy loss to the wall associated with ELMs confirmed the hypothesis that larger
m This suggests that similar mechanisms are involved in the

dynamical evolution of both structures.
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Fig. 22. Expected value of the radial effective velocity for a given saturation current gradient at different radial positions in the
SOL of an ELMy H-mode MkIIGB plasma ~left! and the average ELM filament velocity as a function of ELM frequency~right!. Note that ELM size typically scales inversely with ELM frequency, which means that larger ELMs generally travel⫺1@ DW0W. Reproduced with permission from Refs. 129 and 131.
faster, approximately as v4 @ fELM

filaments moved faster and indicated fractional loss up to
40% for the largest ELMs ~Ref. 143!.
The above results were confirmed by time-of-flightmeasurements of ELM filament velocities using limiter
Langmuir probes.142 The time of arrival of the ELM filament increased linearly with the radial distance of theprobe from the separatrix, whereas its width @full-widthat half-maximum ~FWHM!# increased as the square rootof this distance ~Fig. 23!. Averaged over the SOL, theELM filament velocities were estimated to be ;600 m0s
and their radial diffusivities, i.e., the degree of radialbroadening, to be ;500 m 20s. The corresponding elec-tron temperature in the ELM filament at the limiter radius was measured as ;25 eV, compared to the pedestal
temperature of ;1 keV. On the other hand, the ion temperature in the ELM filaments reaching the wall, as measured by a retarding field analyzer probe head mounted
on the reciprocating probe head assembly, was found tobe substantially larger than the electron temperature, typically Ti 0Te ; 2 to 3 ~Ref. 145!. All the above data were
well reproduced by a parallel loss model, in which theradial propagation velocity of the filament was takenfrom the experiment and parallel losses of particles andenergy were calculated in the filament frame of Ref. 144.

max
Fig. 23. Average peak time delay, Dta⫺n⫽ tnmax ⫺ tamax , for each probe versus average probe radius ^r& ~left!. Average peak current
FWHM for each probe versus the square root of the average probe radius ~right!. Reproduced with permission from
Ref. 142.

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SOL target profiles of particle flux, electron temperature and hence electron power flux, and the OSMreconstructed upstream profiles in ELMy H-mode
MkIIGB plasmas were found to be similar to those obtained in MkIIA plasmas.117,118 The determination of
the total power deposited on the divertor required theknowledge of the ion temperature, which cannot bemeasured with Langmuir probes. Measurement of total,
ELM-averaged power using infrared thermography wascomplicated by the presence of surface layers and spatial resolution of the optical system. In this regard,
an important innovation introduced in the MkIIGB period was the development of an additional diagnostic
technique capable of measuring the total, ELM-averaged
power deposited on the divertor plates.146,147 This technique was based on slowly lifting the plasma in rigid
body motion over the course of the discharge, such thatthe strike points traveled over the locations of embedded thermocouples. By reconstructing the thermocouple traces using finite element modeling of the divertor
tiles, the average power deposition profile could be extracted. ELM-averaged outer target profiles measured
by the three diagnostic techniques ~Langmuir probes,
infrared thermography, and thermocouples! for a highpower, unfueled ~natural density! type-I ELMy H-mode
plasma are shown in Fig. 24. Also shown are inner andouter profiles obtained by lifting the plasma ~strike point!

SCRAPE-OFF LAYER TRANSPORT ON JET

on a shot-by-shot basis and examining the partitionof deposited energy, as measured by thermocouples,
between two vertical tiles. All techniques indicate anarrow power deposition profile of less than 5 mm,
mapped to the outer midplane, i.e., less than the poloidal ion gyroradius evaluated at the pedestal temperature. The peak total power load on the outer divertor
tile increased stronger than linearly with deposited power
in unfueled ELMy H-mode plasmas, whereas the electron power ~measured by the Langmuir probes! increased weaker than linearly. The excess power, which
has been attributed to ELMs and0or energetic ions in
the inter-ELM phases of the discharge, increased withheating power or decreased with collisionality. It is noteworthy that the excess power was quite small in the
more collisional strongly fueled ELMy H-mode plasmas and0or in helium plasmas, for which the ELMs
were also much smaller ~type III versus type I! than indeuterium plasmas.
The above techniques formed the basis of a dedicated power exhaust study, including variation in field,
current, heating power, density, field ~B ⫻ ¹B! direction,and ion species ~D versus He!. For a review of theseexperiments the reader is referred to Refs. 8 and 150. In
JET H-mode discharges, the integral width of the total
power deposited on the outer divertor target has beenfound to scale as

Fig. 24. Comparison of steady-state power deposition profiles measured with thermocouples, infrared thermography, and Langmuir probes at the outer target for an MkIIGB ELMy H-mode plasma ~2.5-MA, 2.4-T, 16-MW NBI! ~left!. The infraredprofiles have been averaged over the ELMs. The scale of the electron heat flux ~Langmuir probes! is four times smallerin the high-power case. Also shown are the profiles obtained for a 12-MW type-I H-mode ~same field and current!, using
the shot-by-shot thermocouple method. For comparison, the poloidal gyroradius at the outer midplane is shown for threevalues of the ion energy. The right frame shows the steady-state total ~thermocouple! and electron ~Langmuir probe! peakheat loads for D and He plasmas as a function of power entering the SOL. The thermocouple values increase faster thanlinearly with Pt . The excess power becomes more pronounced in D for high-power H-modes. Reproduced with permission
from Ref. 8.
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Fig. 25. Ratio of theoretical ~neoclassical! and experimental l q values for neoclassical and classical ion conduction, A2 and A1,
two collisionally modified ion orbit loss estimates, X ⫺ n * and X ⫺ A1, and the poloidal gyroradius, rui ~left!. Comparisonof outer target total peak heat loads: best fit to all normal field data versus the experiment, for both field directions andboth targets ~right!. Reproduced with permission from Ref. 8.

a b ⫺1.03 0.6 ⫺0.41 0.25
lall
q95 Ptneu ,q @ A Z Bfa ⫹ b ⫽ 1.04 ,~55!

if all discharges are included and as
0.41 ⫺0.48 0.15
Pt
neu
lHq @ A a Z b Bf⫺0.93 q95

0.88 0.39 ⫺0.08 0.8
Ti, ped ne, ped R.
lXq @ A 0.35 Z ⫺0.8 Bf⫺0.89 q95,

a ⫹ b ⫽ 1.11 ,~56!

if only H-mode plasmas are considered.8,148,149 To establish the underlying mechanism of ~ELM-averaged! SOL
energy transport, the measured profile scalings werecompared with two dozen theoretical models of radial
heat diffusivity in the SOL. The best overall agreement
between theory and experiment was obtained with ~neo!classical ion conduction.8,148 The appearance of neoclassical diffusion is consistent with the extension of theedge transport barrier into the near-SOL region andthe associated reduction in near-SOL turbulence. The
comparison between various neoclassical predictions andthe measured power widths, shown in Fig. 25, indicate acollisional ion orbit loss as the most likely neoclassicalprocess to explain the observed profile. Collisionless,or direct, ion orbit loss, which was postulated to explain the observations of narrow power profiles in earlier
studies ~e.g., Ref. 105!, was discounted based on the
results of a reversed field experiment together with Monte
Carlo simulations of ion orbit loss using the ASCOT
code.149,151–153 Although the code predicted the ion orbit
loss profiles to be strongly affected by field reversal, nosuch effect was observed in the experiment ~Fig. 25!. The
1056

footprint of direct ion orbit loss on the outer divertor
target was calculated based on ASCOT simulations overa wide range of R, Bf , q95 , A, and Z ~Refs. 8 and 151!:~57!

This result was used to define two alternative formulations of the collisional ion orbit loss width 8 :lX⫺n⫽ lXq ni*102
q
*

and
X
⫽ 2.4zlA1
lA1⫺Xqq ⫹ ~1 ⫺ z!l q ,~58!

where z ⫽ ni* 0~1 ⫹ ni* !. Both expressions offer excellent
fits, within the experimental error of 20%, to the measured power widths ~Fig. 25!.
IV.E. Effect of Divertor SOL on Plasma Purity, Radiation,
and Confinement: MkI to MkIIGBThe effective charge of the core plasma in attached,
MkI diverted discharges was found to scale, to a fairapproximation, according with 78
Z eff ⬇ 1 ⫹7Prad
A p ~ nS e ! 2

.

~59!

That is, Z eff ⫺ 1 increased linearly with the radiative
power per unit area Prad 0A p and decreased quadraticallywith the line average electron density nS e . During density
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SCRAPE-OFF LAYER TRANSPORT ON JET

Fig. 26. Variation of the radiative power fraction with the gas puffing rate ~left!, of the Lawson product ntE normalized by the
ITER-93 energy confinement time scaling and the Greenwald density versus the line average density normalized by theGreenwald density ~right! in MkI, MkIIA, and MkIIAP ELMy H-modes. Reproduced from Ref. 82.

Fig. 27. Variation of Z eff with average density in Mk0, MkI, MkIIA, and MkIIAP ELMy H-modes ~left!. Comparison of theexperimental and best fit expression, which closely resembles Eq. ~59!, in ELMy H-mode plasmas ~right!. The best fit
expression is shown in the right frame, where PR represents the radiative power and S the plasma area. Reproduced from
Refs. 82 and 83.

scans performed in MkI diverted plasmas ~see Sec. IV.B!,
Z eff followed this attached scaling well into the detachedregime, with similar behavior observed in both L-mode
and ELMy H-mode plasmas.
The impact of divertor closure ~MkIIA versus MkI! n
on plasma purity, radiation, and confinement ~normalizedn The results obtained with the MkIIGB divertor were consis-

tent with the MkIIA versus MkI trends.
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Lawson product! of the core plasma in ELMy H-mode discharges is shown in Figs. 26 and 27. For a given gas ~deuterium! puffing rate, the radiative power fraction
was reduced by increasing the divertor closure ~MkI r
MkIIA r MkIIAP!, without affecting the plasma confinement, which followed the H 93 scaling up to a
Greenwald fraction of 60% ~Fig. 26!. Similarly, divertor closure had little effect on the confinement propertiesof nitrogen-seeded plasmas, which generally resulted in
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type-III ELMy H-mode, with confinement reduced by;25% with respect to deuterium-fueled, type-I ELMy
H-mode ~Fig. 26!.
Despite the lower upstream neutral pressure withMkIIA~P! compared to MkI, and consequently smaller
charge exchange fluxes onto the main chamber wall, thelevel of impurities in the core plasma ~both intrinsic andextrinsic! was not reduced; i.e., Z eff roughly followed the
MkI scaling, Eq. ~59!, irrespective of divertor closure.
This is evident from Fig. 27, which shows Z eff from MkI
to MkIIAP together with a best fit scaling.83 The lack ofdependence of Z eff on upstream neutral pressure suggeststhat plasma impact, rather than sputtering by chargeexchange neutrals, was the main cause of impurity influxes from the wall. In particular, similar Z eff values
were observed with MkI, MkIIA, and MkIIAP divertors
with carbon targets ~Z eff in MkI with Be targets was only
moderately reduced!.
SOL transport of intrinsic impurities, mainly carbon,
in MkIIGB plasmas was studied by injecting known
amounts of methane ~CD4 ! gas at various poloidal andtoroidal locations into the torus and calculating the change
in the core impurity levels ~Z eff ! compared to injectionof similar amounts of D2 gas.158–160 Partial resultsfor L-mode, inter-ELM H-mode, and ELM-averaged
H-mode conditions are shown in Fig. 28, from which it isevident that Z eff was larger in H-mode plasmas, in boththe inter-ELM and ELM-averaged sense, consistent withthe larger energy input per particle and the L-mode carbon screening dependence @see Eq. ~61!#.
The L-mode impurity content decreased with density and increased with power as

0.2
Z eff @ Ptot
~ nS e !⫺0.4 .

~60!

These results were expressed and explained in terms of
the screening parameter SC , defined as the rate of changeof core carbon content divided by the rate of carbon
injection; e.g., for outer midplane injection, it was foundthat SC increased roughly with the energy per particle~;PSOL 0nS e ! and with the square root of the SOL connection length, or more accurately,
0.85
0.5
SC @ PSOL~ nS e !⫺1 q95.

~61!

Under L-mode conditions, SC was 3 to 20 times smaller
in diverted plasmas than in limited plasmas, showing thebeneficial effect of distancing the source of impurities
away from the LCFS. Similarly, SC was much smaller, by
roughly a factor of 5 or more, for CD4 injection from thedivertor than from the outer midplane. It was also 1.5 to
2 times larger in H-mode, compared to L-mode, plasmas.
This variation of the screening parameter was then used
to explain the intrinsic carbon levels; e.g., the reductionof Z eff with density was partly due to improvement ofcarbon screening ~lower SC ! and partly due to decreased
carbon influxes. In MkIIGB diverted L-mode plasmas,
intrinsic carbon concentration could be explained in termsof low main chamber influxes that were poorly screened
and much higher divertor influxes that were well screened,with the net contribution of the two being comparable.
Although the same mechanism applied to H-mode plasmas, there the core carbon appeared to originate primarily due to carbon influxes from the divertor, especially
due to ELMs.

Fig. 28. Core plasma Z eff ~left! and intrinsic carbon main chamber and divertor influxes ~right! versus line average density in
L-mode, inter-ELM H-mode ~shaded regions!, and ELM-averaged H-mode MkIIGB plasmas at two levels of NBI
heating. Reproduced from Ref. 159.
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Fig. 29. Ratio of Z eff normalized by the L-mode scaling, Eq. ~60!, as a function of the energy confinement enhancement factor H89~left!, and the rate of change of core carbon content, N^ c [ dNC 0dt, and influx of carbon from the divertor GD and the mainchamber wall GD as a function of power entering the SOL ~right!. Reproduced from Ref. 159.

Differences between L-mode and H-mode impurity
content are highlighted in Fig. 29. As the confinement
increases beyond the L-mode value, so does the core
impurity content. Although one detects a positive correlation between these two quantities, the substantial scatter in the data suggests some hidden variable not contained
within either scaling. On average, type-I ELMs lead tohigher impurity influxes than type-III ELMs, which islikely a consequence of the ELM size ~energy per ELM,
DWped ! and0or the pedestal height ~primarily the temperature of the ions, Ti, ped , expelled by the ELM!, both ofwhich are larger for type-I ELMs, thus producing morecarbon via physical sputtering ~primarily of the divertor
targets!. However, it is important to note that one could
not differentiate between the two types of ELMs on thebasis of their Z eff 0Z L versus H89 scaling. The shaded
region in Fig. 29 reflects the levels of carbon accumulation during the ELM-free period, 0.2 s before the first
ELM. During this period, the carbon content increasedroughly 4 to 8 times faster than either the deuterium or
the energy content; the increase was well correlated withthe carbon influx from the divertor, as shown in the rightframe of Fig. 29.
The major trends of carbon transport in the SOL
were consistent with numerical modeling using both multifluid ~EDGE2D0NIMBUS! and Monte Carlo ~DIVIMP!
transport codes, indicating that the experimental results
could be explained based on the physical processes contained in these models. In short, modeling indicated thatcarbon ions were swept toward the divertor whenever the“downstream”-pointing convective forces exceeded the“upstream”-pointing temperature gradient forces. In particular, carbon removal by parallel loss to the divertor
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occurred primarily in the far SOL and benefited fromcool plasma conditions, allowing more effective collisional coupling between impurity ions and strong hydrogenic parallel flows. For comprehensive reviews ofmaterial migration in MkIIGB plasmas, including theeffect of ELMs, the reader is referred to Refs. 156 and157.
Another important result, first obtained with the
MkIIGB divertor, is the connection between methane
puffing into the main SOL and the rise in the far-SOL
density profile.154 In a dedicated study CD4 was injected
near the outer midplane and its effect on the density
profile was compared with D2 injection near the top of
the vessel. The results, shown in Fig. 30, show a clear
increase of the peripheral density profile, which is directly proportional to the total fluence of injected CD4molecules.o Since the ionization mean-free-path for CD4
is shorter than that for D2 , it was initially postulated thatthe excess density is due to local overionization of the
SOL flux tubes in the vicinity of the CD4 with r ⫺ rLCFS ⬇
2 cm, which corresponds to the most probable ionization
location. However, EDGE2D0NIMBUS modeling indicated that such overionization had only a small effecton the density profile since parallel losses were alsoenhanced. To match the observed profiles, it was necessary to increase the radial particle transport in the regiono

Not surprisingly, the increased far-SOL density had a beneficial effect on lower hybrid power coupling with both D2 andCD4 puffing in ELMy H-mode plasmas. This effect was observed provided the gas was injected onto field lines that weremagnetically connected with the rectangular area in front of
the antenna grill.155
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Fig. 30. Upstream density profiles in an MkIIGB L-mode discharge during a D2 puff from the top of the torus and CD4 puff fromthe outer midplane for the same line average density ~left!. Peripheral density rise ~shaded area in the left plot! versus CD4
injection fluence ~right!. Reproduced from Ref. 154.

r ⫺ rLCFS ⬇ 1 ⫺ 3 cm. Indeed, such enhancement of theradial E ⫻ B fluxes was measured by the turbulenceprobe. When the inferred diffusivity profile was inserted
into EDGE2D0NIMBUS, good agreement was obtainedwith the measured density profiles. It is significant thatthe absolute value of the diffusivity had to be reduced bya factor of 5 compared to the peak value of D4 ⬇ 4 m 20s
measured with the turbulence probe. Similarly, poloidally uniform diffusivities, D4 ' 0.5 to 1.5 m 20s, combined with EDGE2D0NIMBUS were found to offer agood match to the experimentally measured ne and Te
profiles shown in Figs. 3 and 9 in Ref. 20. The excess ofouter midplane, compared to poloidally averaged, diffusivities is consistent with the known ballooning characterof turbulent transport, in which significant radial outflux
occurs only in a small poloidal region around the outer
midplane. The estimated poloidal extent of this active
region ~Du ; 2p05 ; 70 deg! is in fair agreement withthat measured on Tore Supra 59 and inferred from JET
limiter discharges, Sec. III.A.1.

V. CONCLUSIONS~C versus Be!, and confinement regimes ~ohmic, L-mode,and H-mode!. Broadly speaking, the dominant parameter
determining the width of the SOL is the plasma current,
which is inversely related to the SOL e-folding length. In
addition, a weak density scaling of l n is sometimes reported. The limiter and divertor SOLs exhibit similar
behavior. Both are dominated by the competition between radial advection of turbulent structures ~blobs! andparallel losses. Similar profiles are found in ohmic and
L-mode conditions. H-mode profiles are narrower byroughly a factor of 2. There is some, but only moderate,
effect of divertor recycling on upstream profiles, e.g., asreflected in the comparison of vertical versus horizontal
targets. Similarly, there is a small effect of target material~Be versus C! due to radiation and dilution of the plasma.
During H-mode, the ETB is found to extend into the
SOL, such that the ELM-averaged profiles appear to be
dominated by ~neo!classical rather than by turbulent transport. Although the ELM transport in the SOL was notdiscussed here, it was noted that ELM buffering ~radiation of ELM energy! by impurity seeding is not possible.
ACKNOWLEDGMENTS

In this chapter, the progress made in the understanding of boundary plasma, or SOL, physics on JET has
been reviewed, focusing mainly on the hydrogenic plasma.
The main findings of these investigations are summarized in Table I, which lists selected empirical scalings of
LCFS quantities and radial e-folding lengths under various SOL types ~limiter versus divertor!, target materials

The author thanks S. K. Erents, G. F. Matthews, R. A.
Pitts, A. Loarte, V. Philipps, P. C. Stangeby, and V. Naulin for
helpful discussions. The work was funded jointly by the U.K.
Engineering and Physical Sciences Research Council and by
the European Communities under the contract of association
between EURATOM and UKAEA. The view and opinions expressed herein do not necessarily reflect those of the European
Commission.

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37. J. W. CONNOR, Plasma Phys. Control. Fusion, 40, 191 ~1998!.

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