J. Plasma Fusion Res. SERIES, Vol.2 (1999) l5-18

The lnfluence of the Plasma Edge on the Performance ofTokamaks
CONNOR John W.
EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon, OXl4 3DB, UK(Received: 7 December 1998 / Accepted: 14 February 1999)

Abstract
The plasma edge region has a profound effect on the performance and operation of a tokamak. In
this paper we describe some of the experimental and theoretical evidence for this assertion, emphasising
H-mode confinement issues, such as the conditions for the L-H transition and the role of the H-mode
pedestal, edge localised modes (ELMs) and the scrape-off layer.

Keywords:
tokamak, edge region, H-mode, ELMs, scrape-off layer

1. Introduction

density and impurity levels. Thirdly, the economlc
viability of a tokamak power plant is sensitive to the

The edge of the tokamak comprises the outer partsof the plasma column and the divertor or scrape-off

normalised plasma pressure p that can be sustained, andlayer (SOL) plasmas, which are strongly coupledthis can be affected by MHD instabilities occurring in
the plasma edge region (these are also thought to berelated to the onset of ELMs). Finally, the ability of the
SOL to exhaust the steady power output of a burning
plasma without excessive heat loads on the divertor
plates depends on the width of the SOL; this problem
can be alleviated or overcome by arranging for power tobe radiated in the edge region or the plasma to be
detached from the target plates as a result of atomic
physics processes. We will review experimental

together. This region can have a profound influence on a

tokamak's performance. Firstly, the capability of thetokamak to produce a burning plasma depends on thevalue of the triple product n TicB. Two of these factors,
the density, n, and the energy confinement time, ?p, canbe strongly affected by edge phenomena. The density isoften limited to the so-called Greenwald value, probably
by atomic processes such as radiation near the plasma
periphery, while z6 is enhanced if the H-mode isaccessed. The H-mode involves an edge transport barrier
which can increase the ion temperature, 21, and thesudden transition to H-mode from the L-mode clearly

evidence and theoretical ideas concerning these topics,
emphasising the role of MHD stability.

2. The L-H Transition

depends on edge phenomena. The improvement in
confinement arises from both the 'pedestal energy',
associated with the height of the edge transport barrier,and the apparent correlation of the core energy with the

The transition from L to H-mode can usually becharacterised by a threshold heating power, P1,, andempirical scaling laws for this in terms of global
parameters have been obtained. However, the data
displays much scatter, which leads to considerable

properties ofthis pedestal energy. Secondly, the H-mode

is often associated with edge localised modes (ELMs).
These degrade confinement by periodically depositing
plasma into the SOL (the resulting transient heat loads
appearing on the divertor target plates can pose a
problem), but they are beneficial in controlling plasma

uncertainties in P1, when projecting to larger devices,@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

15Connor J.W., The Influence of the Plasma Edge on the Performance of Tokamaks

theory, where the dependence of Pn on the ion-VB drift
direction is suggestive. The theory has been revisited,taking account of the steep gradients in the plasmaand can exhibit a different behaviour at low n.
Theoretical understanding of the transition in terms of

local edge parameters might help reduce these
uncertainties. Models fall into three broad categories [l]:periphery: fluxes which are non-monotonic as functions(i) sudden suppression of turbulent transport by E x Bflow shear, where the radial electric field E, isof the edge gradients arise, permitting a bifurcation [6].

determined by the ion radial pressure balance, (ii)stabilisation of modes when some critical value of aplasma parameter is exceeded, and (iii) neoclassical

3. H-Mode Pedestal
In H-mode, an edge transport barrier forms a'pedestal' in the pressure profile and the associatedtheories.

plasma energy, Wp"a, is a significant part of the total
plasma energy, Wnrurru. An estimate of its contribution
follows from assuming that the height of the pedestal islimited by setting the pressure gradient at the high-n (nFlow shear stabilisation is an attractive universal
paradigm: it leads to a variety of models depending onwhether E, is due to poloidal flow, V6, or ion pressure
gradient, Vpi. In the first case the L-H transition appears
as a bifurcation in the solutions to the equation for V6;
this balances drives (e.9, due to ion-orbit-loss or
Reynolds stress) against damping (e.g, due toneoclassical viscosity or charge exchange with neutral
particles). The lack of clear experimental evidence for adependence on collisionality argues against ion-orbitloss, while there is experimental evidence for a role for
Reynolds [2]. The low n behaviour of P16 could be
associated with charge exchange damping. However,while some devices see changes in Ve preceding thetransition, high resolution data from COMPASS-D and
START indicates Ve builds up afterwards [3]. Theories
based on the Vp1 contribution to E, rely on a nonmonotonic dependence of the fluxes on gradients due toflow shear. Most theories are 'local', ignoring thesecond order derivatives ofpl that contribute to VE., andallow a bifurcation in Vpi (including these undermines
this attractive picture). Such theories lead to a criticalvalue of the normalised ion Larmor radius, p*,consistent with much experimental data.
Theories involving turbulence suppression as someparameter varies include those based on drift-resistive
ballooning mode simulations and quasilinear estimatesof drift Alfv6n turbulence: these both involve criticalcollisionality and plike parameters, which show someis the toroidal mode number) ballooning limit, a = d".it,and establishing a prescription for the width of thebarrier, 4*0. More detailed analysis of coupled peelingballooning modes at the plasma edge, shows that theconventional ballooning theory must be modified
somewhat. Indeed one can expect significant 'finite-t?'stabilising corrections to ocrir (e n-2t31 t5l. This will be
particularly significant in steep edge gradients and forthe important intermediate values of n and could explain
why some experiments find a values in excess of thehigh-n limit. Calculations also show that the radialenvelope of the ballooning mode is A

* a/n2t3 f5).

To complete the prescription for Wp"a, we need an
estimate of 4peo. One could assume that Vpt reaches
such a value that the associated E x B shear is sufficient
to stabilise some instability. Thus models involving ion
temperature gradient (ITG) driven turbulence typically
predict Ap"ala n pl (l/2 a y < 213), whereas, to stabilise
MHD ballooning modes, one finds Ao.la n p-2l3. Thislatter estimate coincides with one based on the region
where there is a Reynolds stress from edge drift waves
with ttpl - 0(1), since they will have an inhomogeneousmode structure over a width A n a/nzt3 [5], as for the
MHD modes discussed above. These estimates are
consistent with deductions on JET, although recent

evidence from isotope scans has suggested thepossibilities that d * pi (similar to that on JT-60U) andA n pru"r, the fast particle Larmor radius [7].
There is also evidence (eg, from ASDEX-Upgrade

correlations with experimental data [4]. A model basedon the current driven peeling mode instability criterion[5] explains the behaviour on COMPASS-D, where P1,
increases sharply at low n. In this model, the H-mode[8]) that the core energy, V/"o.", is controlled by thepedestal values lp"a or Bp"a, consistent with predictions

occurs if the collisionality, v-, is sufficient to suppress

the edge bootstrap current and the normalised

from 'stiff' transport models (e.g, based on ITG

ballooning presssure gradient parameter, a, is sufficientturbulence), which exhibit strong transport once ato provide magnetic well stabilisation of the Ohmic

marginally stable temperature gradient is passed. Suchmodels predict fusion powers in a burning plasma which
are very sensitive to Zo"a. The representation of energy
confinement scaline as a 'two-term' form based on

current drive; experimental evidence from COMPASSD in terms of local edge parameters supports this theory.
Finallv. we mention models based on neoclassicalt6Connor J.W., The Influence of the Plasma Edqe on the Performance of Tokamaks

separate Wpea and W.o." contributions, may be moreparadigm zero-dimensional models coupling theevolution of gradients, shear flows and MHD and/or

helpful than the conventional power law scaling [7].

drift wave fluctuation levels, which on the one hand are

4. ELMs

moderated by the shear flows and, on the other,

ELMs, periodic disturbances of the plasma

determine the transport level.
We focus here on an example of the first category,
namely coupled peeling-ballooning modes [5], althoughthat due to the M-mode catastrophe involving stochastic
magnetic transport [0] exhibits a number of features

periphery in H-mode, are believed to result from MHD

activity. They can be classified into Types I and III [9].

Type I occur for heating powers P >> Prn , have afrequency, /81y, which increases with P and deposit a
signficant fraction (say - 5Vo) of plasma energy, 6W,
and particles, dN, into the SOL; they do not always
exhibit magnetic precursors and occur when o - 06.1,,
although they can 'sit' there, implying some additional
trigger is required. These features suggest pressure
driven ballooning modes are involved. On the otherobserved in experiments: fast time scales, transportavalanches and scalings for/B1y and 617. In the peelingballooning mode model, the Type I ELM cycle is seen
as a result of the following sequence: with additional

heating the plasma enters a regime in which thestabilising magnetic well, proportional to o, overcomesthe instability drive due to Ohmic edge currents (forhigh v- this is possible since the bootstrap current drivethen disappears, as discussed in the L-H model for
COMPASS-D in Section 2); it then heats up to theballooning stability boundary where it sits, relatively
benignly; with further heating the Ohmic and bootstrap
currents increase until the peeling mode is triggered; thehand, Type III occur when P 2 P*, have fg1y decreasing

with P and remove much smaller values of dW (say l%o) ftom the plasma edge; they occur when d 1 d",i1and generally do exhibit magnetic precursors (typicallywith 5 < n < l5). These features are suggestive of a
resistive MHD explanation for Type III ELMs: they
disappear as the resistivity drops with increasing
heating. However, we shall discuss an alternativedescription of both types in terms of peeling-ballooning

resulting loss of pressure gradient is further
destabilising, leading to a catastrophic loss of pressure,and then the cycle repeats. The Type III cycle, relevant
to cooler plasmas, can be understood as an earlier exitfrom the stable regime as diffusive processes build up
the destabilising edge current density gradient fasterthan the stabilising edge pressure gradient. Stability
calculations show that one can access a second stability
regime in the presence of the peeling mode, provided
there is a sufficiently deep magnetic well [5]. Suchaccess could allow the pressure gradient to build up tomodes later.

The presence of ELMs has a number of impacts on
tokamak performance, some beneficial, others less so.
On the one hand, the removal of particles from the edge

helps control of plasma density and impurities.
However, one consequence of this, certainly for Type I
ELMs, is the appearance of damaging transient heatloads on the divertor target plates. Furthermore, r.
degrades as /prrnr increases, a consequence of the factthat the pedestal pressure gradient fails to heat up to its
limiting value during an ELM period; this feature isevident on JT-60U and JET. One therefore has tobalance the large value of 614/ from Type I with the highvalues of/61y associated with Type III ELMs: Type III
are to be prefened.

such a level that when it eventually triggers someinstability, a very damaging ELM-like event results;
plasma shaping may help to prevent this.

5. Scrape-off Layer and Exhaust
Phenomena in the plasma periphery, and the SOL
in particular, control the exhaust of plasma particles andenergy. In the presence of ELMs and with sufficientpumping capacity, particle and impurity content appears
controllable; the transient heat loads from ELMs point
to the need to operate with Type III ones, as discussed
in Section 4. That leaves the issue of the steady state
power loadings on divertor target plates. The heat loadintensity depends on the total incident power, Pn",, andA number of models have been advanced to explain
ELM behaviour [9]. Some, based on stability criteria forvarious modes, are of a 'conceptual' nature, while others
provide actual dynamical models. In the former category

are models based on ideal or resistive peeling or
ballooning modes appearing in the plasma periphery, oreven the SOL; alternatively tearing and, indeed, microtearing modes have been advanced. In the second

category are models which are based on either
simulations of the primitive MHD equations (e.9,resistive interchanses in the SOL) or solutions of

the width on the target plates, 45s1, the heat is spreadover. Pn", can be reduced by either introducing seed
impurities in a radiating edge layer of the core plasma,l7

Connor J.W., The Influence of the Plasma Edge on the Performance of Tokamaks

or arranging for a cold radiating region in the divertor
chamber to allow detachment of the divertor plasma
from the target plates.

explain these phenomena, MHD stability considerations
appear to play a significant role.

We do not discuss this further here, but concentrate

Acknowledgements
This work is jointly funded by UK DTI andon what controls /561. Balancing transport processes

parallel and perpendicular to thc magnetic field,
characterised by diffusion coefficients 711 and 76y
respectively, one estimates /sor- - (yl7lrt2L11 for a

EURATOM.

collisional SOL plasma (here Zx is the distance along thefield line to the divertor plates); thus it depends cruciallyon 1, which is often chosen simplistically in, otheru'ise,complex edge modelling codes. However, a substantial
number of models for 11have been proposed in theliterature. A comparison of the resulting predictions for/56twith data from collisionless SOLs in COMPASS-D
and collisional SOLs in Alcator C-MOD and JET has.
remarkably, shown that the same subset of models
consistently provides the 'best-fits' u1l. These 'best'models invoke electromagnetic processes connectedwith the collisionless and collisional skin-depths or

tll G.M. Staebler, Plasma Phys. Control. Fusion 40,

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6. Gonclusions
The plasma periphery influences tokamak
performance: it controls or affects H-mode access, Hmode confinement, properties of ELMs and plasma

694EXP2/O6.

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