turbulent transport and turbulence in radiative i mode ... · turbulent transport and turbulence in...

Turbulent transport and turbulence

in radiative I mode plasmas in TEXTOR-94

J.A. Boedoa, J. Ongenab, R. Sydorac, D.S. Graya, S. Jachmichb,R.W. Conna, A. Messiaenb, TEXTOR Teamd

a Fusion Energy Research Program,Department of Applied Mechanics and Engineering Sciences,University of California, San Diego,Jacobs School of Engineering,La Jolla, California, United States of America

b Laboratoire de Physique des Plasmas–Laboratorium voor Plasmafysica,Ecole Royale Militaire–Koninklijke Militaire School,Association ‘Euratom–Belgian State’,Brussels, Belgium

c Department of Physics,University of Alberta,Edmonton, Alberta, Canada

d Max-Planck-Institut fur Plasmaphysik, Forschungszentrum Julich,Julich, Germany

Abstract. First measurements of turbulence levels and turbulence induced transport in the outer

edge of the plasma of TEXTOR-94 during radiative improved mode discharges show a reduction

by a factor of 4–7 of the radial particle turbulent transport. The quenching is most evident on the

normalized potential fluctuations and is strongest above 100 kHz. Non-linear gyrokinetic particle-in-

cell simulations of these discharges show impurity induced suppression of the electrostatic fluctuations

associated with the ion temperature gradient driven mode over most of the cross-section, including the

edge. Such a mechanism is proposed as the explanation for the improved confinement and turbulence

reduction. The reduction in the edge turbulent transport levels is consistent with increased particle

confinement time and the reduction of the SOL thickness. Particle and energy fluxes to the limiter

are reduced by an order of magnitude. A concomitant increase of the measured energy and particle

confinement times τE and τp versus radiated fraction suggests a common underlying suppression

mechanism.

1. Introduction

Tokamak plasmas can undergo transitions froma low energy confinement state (L mode) to ahigher energy confinement state [1] (H mode) sponta-neously. The transition is accompanied by a negativeradial electric field inside the LCFS and is character-ized by a steepening of the edge profiles or the for-mation of a transport barrier. Simultaneously, thereis a fast reduction of the Hα signal, correspondingto increased particle confinement. Similar behaviourto the spontaneous L–H transition was obtained inthe tokamak CCT [2] by applying an external radialelectric field to the edge plasma by biasing or ‘polar-izing’ an electrode. As such, the CCT experimentssuggested that the radial electric field and inducedpoloidal rotation play a crucial role in the L–H

transition. The stabilization of turbulence by E×Bvelocity shear is a general mechanism that has beenproposed to explain stabilization of edge turbulence[3] in tokamaks and is supported by early work atthe TEXT tokamak [4].

A new confinement regime called the radiativeimproved (RI) mode [5, 6] has been observed onTEXTOR-94. This regime is produced by injectingtrace amounts of a gas such as argon or neon intothe discharge [7, 8]. This results in a strongly radi-ating belt, located in the plasma edge, where thevarious atomic processes produce a peak in the radi-ation rate for the given impurity gas. This radiatingplasma regime allows a homogeneous dissipation ofthe discharge power over the inner wall of the toka-mak, thereby reducing the power load on plasmafacing components (PFCs).

Nuclear Fusion, Vol. 40, No. 2 c©2000, IAEA, Vienna 209

J.A. Boedo et al.

In addition to the reduced power load to thePFCS, the RI mode is characterized by high con-finement (similar in quality to either ELM-free orELMy H mode operation). The energy confinementtime increases linearly with the plasma density (upto or above the Greenwald density limit), therebyrecovering the so-called neo-Alcator scaling [9]. Inaddition, RI mode discharges exhibit high beta (upto the previously observed beta limits of TEXTOR,i.e. βn = 2 or βp = 1.5) and negligible delete-rious effect of the seeded impurity on the fusionreactivity, thereby offering the possibility of opera-tion at low edge q under quasi-stationary conditions[10]. Apart from extending the performance and theoperating range of the RI mode, the main effortof the TEXTOR-94 programme is devoted to theinvestigation of how these operational conditions arelinked to the physical mechanism(s) leading to theconfinement improvement.

The velocity shear stabilization mechanism isnow proposed to be responsible for a series ofimproved confinement regimes in tokamaks includ-ing the H mode [11] and V-H mode [12]. Recentexperiments in TFTR have related the levels of localE×B shearing rates [13] to core transport barriers inreverse magnetic shear plasmas [14]. Work at DIII-D[15] and PBX-M [16] showed that the turbulence isreduced by the triggering of the spontaneous H modeas the result of concomitant changes in the radialelectric field and the profile gradients. Polarizationexperiments in the TEXTOR tokamak [17, 18] haveconfirmed earlier CCT and TEXT results and sig-nificantly expanded the understanding of the role ofthe radial electric field and its bifurcation [19]. Morerecent experiments in TEXTOR-94 have shown theformation of a transport barrier in the plasma edge[20] as determined by the changes in the densityprofiles during polarization [21] and have correlatedthose changes to the gradients of the radial electricfield. Clear correlation between externally appliedelectric fields and a reduction in turbulence levelsin TEXTOR was first shown by our early work [22]and completed recently [23].

Interestingly, the concept of a fusion reactor witha radiating mantle has been of long standing inter-est. More recently, the experimental programme onreversed field pinches (RFPs) associated with theZT-40M experiments [24] and modelling studies per-formed in conjunction with the TITAN RFP reac-tor study [25, 26] demonstrated stable plasma oper-ation for plasmas radiating up to 85% of the inputpower [27]. However, the experiments in TEXTOR

were the first to rediscover the earlier results of ISX-B [28, 29] and demonstrate this type of operation ina tokamak. Since then, this regime has been foundin a variety of diverted and limited tokamaks suchas ASDEX-Upgrade, DIII-D and Tore Supra [30].It is important to the fusion community to improveour understanding of this new tokamak confinementregime because it opens the possibility of operatinga tokamak fusion reactor using a radiative mantle,dissipating the energy uniformly over the walls. Alimiter configured fusion reactor may even become apossibility. The homogeneous dissipation will reducethe heat flux to the divertor components — one ofthe critical issues in the design of ITER. A fusionreactor operating in this regime could simplify thedesign, and reduce the cost, of fusion reactors.

Another mechanism in consideration for explain-ing turbulence reduction and one that does notinvolve E × B velocity shearing is the direct sta-bilization of ion temperature gradient-driven (ITG)turbulence and the hybrid ITG trapped electrondrift instabilities by the radiating impurities. TheITG instability is driven by the interaction betweenthe toroidal curvature, non-uniform toroidal mag-netic field and the radial ion thermal gradient in theplasma. Vertical ion drifts due to the curvature and∇B drift are functions of energy, therefore, differentdrift rates due to the ion energy distribution leadto density and electrostatic potential perturbations.The resultant E×B convection pattern produces aninterchange of hot and cold plasma regions so thatan initial temperature perturbation will grow if hot-ter plasma is convected into the enhanced temper-ature region of the initial perturbation. The linearstabilizing effect of impurities, especially those withhighly charged states, on ITG modes has been con-sidered previously [31–35]. This effect can be mosteasily seen from the fluid limit growth rate of theITG mode including impurities and neglecting theparallel ion dynamics. For the small impurity fractionlimit, ZnZ/ne < 1, where Z is the impurity chargenumber and nZ the number density of the impurity,along with Ti = TZ , Ln = LnZ and LT = LTZ , weobtain the interchange type growth rate

γITG ≈√

[1− (Z − 1)nZ/ne]ω∗piωDi (1)

where

1/Ln =−1n

dn

dr, ω∗pi =

kθc

eBni

dpidr

210 Nuclear Fusion, Vol. 40, No. 2 (2000)

Article: Turbulent transport and turbulence in RI mode

is the ion pressure gradient drift frequency, kθ is thepoloidal wavenumber

ωDi =LnRω∗pi〈v2⊥ + v2

‖/2〉v2thi

is the energy averaged ion toroidal drift frequency,ρi = c

√miTi/eB is the ion gyroradius and vthi =√

Ti/mi. A Boltzmann response for the electrons canbe used if one assumes that the phase velocity ofthe perturbation satisfies vthe > ω/k‖ > vthi. In thesmall impurity fraction limit, the real frequency ofthe mode is ωreal ∼ ωDi > ωDZ . From Eq. (1), itcan be seen that impurities reduce the driving termof the ITG mode by:

(a) Diluting the main ion species,(b) Modifying the pressure or density gradient (and

thereby ω∗pi or the scale length Ln).

The stabilizing trend persists in a more completekinetic calculation of the growth rate which includesthe parallel ion dynamics, however the initially sta-bilizing effect of the impurities becomes destabiliz-ing when ZnZ/ne increases. Maximum stabilizationoccurs when the amounts of the two species (deu-terium, neon) are equal in terms of the charge den-sity fraction. Linear theory analysis indicates thatthe ITG and ITG trapped electron modes are unsta-ble in the core and edge regions of TEXTOR dis-charges, therefore, the presence of impurities such asneon, which contain high charge states, is stronglystabilizing for such instabilities.

New observations on the behaviour of the turbu-lence levels and the radial turbulent particle flux inthe outer plasma edge, as measured with a fast scan-ning probe, are presented in this article. A reductionin the RMS levels of density and poloidal electric fieldresult in diminished radial particle flux. Non-linearsimulation results are presented and it is proposedthat the turbulence reduction is a direct consequenceof the neon seeding causing a reduction in the growthrate and saturation levels of low frequency microtur-bulence arising from ITG instabilities. The reducedradial particle flux is correlated with the measuredincrease in particle and energy confinement. The sig-nature of velocity shear stabilization is not presenton the turbulence data during RI mode, in either thespace or frequency domain. It is important to men-tion that the RI mode confinement seems to be afairly continuous function of radiated fraction and itis triggered at γ ∼ 0.6.

2. Experiment

TEXTOR-94 is a long pulse medium size, circularcross-section tokamak (major radius R = 1.75 m,minor radius a = 0.46 m, pulse lengths of about10 s) equipped with the pumped toroidal belt limiterALT-II [36]. The experiments described below areconducted in quasi-stationary RI mode dischargeson TEXTOR-94. The discharges have a radiatedpower fraction γ = Prad/Ptot (where Ptot is the totalinput power and Prad is the radiated power) between0.3 and 0.95. The other discharge parameters are:plasma current Ip = 400 kA, toroidal magnetic fieldBt = 2.25 T and line averaged central density, ne,between 4 and 6 × 1013 cm−3. Additional heatingof up to 2–3 MW consists of co-injection (D+ →D0 injection at about 48 keV) combined with ICRFheating (at ω = 2ωCD , i.e. at a frequency of 32 MHz,with π phasing of the two antenna pairs, one withand one without a Faraday screen). The energy con-tent of the plasma during the stationary phase hasbeen feedback controlled by acting on the level ofICRF heating. The radiation level is kept constantby feedback control of the neon gas inlet valve usingthe intensity of a Ne VIII line [37]. The sink for neonparticles is provided by the pump limiter ALT-II [38].

Profiles of electron temperature Te(r), densityne(r), saturation current Isat (r), poloidal electricfield Eτ (r), floating potential Vf (r) and fluctuations,were obtained using a fast reciprocating probe array[39] located in the low field edge of the plasma. Theprobe penetrates 2 cm inside the LCFS of TEXTOR-94 (45.6 cm < r < 50 cm, r is the minor radius)under these high power conditions. The data for theturbulent measurements are digitized at 1 MHz witha 10 bit resolution digitizer and filtered by low pass,500 kHz, anti-aliasing filters. We find that the powerspectra of all the signals decays very quickly withfrequency and is significant only up to 200 kHz. Theturbulent particle flux Γr is calculated in terms ofthe RMS values of the density 〈n2

e〉1/2, poloidal elec-tric field 〈E2

θ 〉1/2 fluctuations and the local toroidalfield Bφ, which are measured by the probe array, as[40]

Γr =〈Eθne〉Bφ

=〈n2e〉1/2〈E2

θ 〉1/2Bφ

〈Eθne〉〈n2e〉1/2〈E2

θ 〉1/2

=〈n2e〉1/2〈E2

θ 〉1/2Bφ

γEn cosα (2)

where the brackets denote ensemble averaging andthe product of the coherence, γEn, and the cosine

Nuclear Fusion, Vol. 40, No. 2 (2000) 211

J.A. Boedo et al.

0.0 100

5.0 101 6

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1.5 101 7

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Γ r (cm

-2 s

-1)

Radius (cm)

ALT-II Limiter

L-mode

RI-Mode

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2.0 101 2

2.5 101 2

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3.5 101 2

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-3)

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30

40

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ms (

V)

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0.1

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0.3

0.4

0.5

0.6

cosα

a)

b)c)

d)

γ=0.85

γ=0.34 γ=0.40 γ=0.70

Figure 1. Radial profiles of (a) radial turbulent particle flux Γr, (b) density RMS level, (c) phase

angle between density and poloidal field RMS levels, α, and (d) poloidal electric field RMS level for

L mode (open symbols) and RI mode (solid symbols). The limiter position is shown as a shaded

rectangle.

of the phase angle between the density and poloidalelectric field fluctuations, cosα, is defined as

γEn cosα =〈Eθne〉

〈n2e〉1/2〈E2

θ 〉1/2. (3)

The particle flux can be calculated alternatively infrequency space in terms of the density and potentialfluctuation cross-power spectra Pnφ(ω), the poloidalwavenumber kθ(ω), and the phase between thedensity and potential fluctuations, αnφ(ω), as [41]

Γ =2Bφ

∫|Pnφ(ω)|kθ(ω) sinαnφ(ω)dω. (4)

The reciprocating probe is located at the outer mid-plane of the tokamak (TEXTOR’s edge plasma istoroidally symmetric due to the ALT-II toroidal beltlimiter). However, the measurements are similar tothose taken with a second probe located at the topof TEXTOR and separated 90 poloidally from theprimary probe.

3. Results and discussion

3.1. Turbulence and turbulent radial flux

The results (at the LCFS) obtained for otherwiseidentical L mode and RI mode discharges are

(a) Absolute density nrms and poloidal field Eθrms ,fluctuation levels are reduced by factors of ∼2–3 as seen in Figs 1(b) and 1(d). Note thatthe Boltzmann relation, which is usually notfulfilled in the SOL/edge, is recovered duringRI mode conditions (Figs 2(a,b)).

(b) Radial turbulent particle transport Γr(Fig. 1(a)) is reduced by a factor of about4–7; mostly due to the lower nrms and Eθrms

levels with a small increase due to cross-phaseeffects (Fig. 1(c)).

(c) Normalized potential fluctuation levels eφ/kTedecreased by a factor of 2 (Fig. 2(b)).

(d) Normalized density fluctuation levels remainunchanged (Fig. 2(a)).



0.00

0.20

0.40

0.60

0.80

1.00

n rms/n

ALT-II Limiter

0.00

0.20

0.40

0.60

0.80

45 46 47 48 49 50

φ rms/k

Te

Radius (cm)

RI-Mode

L-mode

a)

b)

Figure 2. Radial profiles of (a) normalized density and

(b) potential fluctuation levels as a function of radius for

L mode and RI mode discharges. The normalized levels

are more similar for RI mode conditions.

(e) The quenching of turbulent fluxes occurs at allfrequencies (Fig. 3) but most strongly above∼100 kHz so the resulting particle transport issignificant only at low frequencies.

(f) The edge radial electric field remains almostunchanged (the floating potential increasesslightly inside the LCFS but the temperaturedecreases, so the plasma potential, Vp = Vf +3.5 kTe, is roughly constant, see Figs 5(a) and(b)), thus the turbulence reduction is not con-nected to an increase in the local Er×Bφ shearstabilization.

The turbulent quantities can also be examinedin frequency space as per Eq. (3). The data sam-ples between 45.5 and 46.0 cm (in the edge, not inthe SOL) are used to assure good statistics, result-ing in a spatial average over ∼0.5 cm. Further aver-aging over frequency is performed in Figs 3(a–d).

The main characteristic features remain constant forvarious radial positions. During the RI mode, thecross-power (Fig. 3(a)) and radial particle transport(Fig. 3(c)) are quenched at frequencies greater than70–100 kHz. The cross-phase αnφ (Fig. 3(b)) doesnot vary significantly (except over a narrow rangeat very low frequencies) and kθ (Fig. 3(d)) becomesmore negative at lower frequencies. The coherence isabout 0.6 across the spectrum, except at high fre-quencies, where the power drops. The data duringRI mode lose significance above 250–300 kHz due tothe strong signal reduction.

To interpret the behaviour of turbulent fluctu-ations before and after neon injection, we con-sider a model in which ITG modes play a domi-nant role. There are several reasons to consider thissource mechanism. First, linear theory calculationsusing TEXTOR experimental profiles show that ITGmodes are unstable over most of the plasma vol-ume and when radiating impurities are introducedthe growth rate of these modes is reduced. Sec-ond, the reduction of the higher frequency portionof the turbulent fluxes, shown in Fig. 3, suggeststhat short wavelength ITG modes are suppressedsince the frequency of the fluctuations is found tobe proportional to the poloidal wavenumber. Finally,the modifications of the density and thermal profilesoccurring after the RI mode transition are consis-tent with reduced levels of ITG turbulence. It shouldbe emphasized that the model of ITG turbulenceconsidered in this article should be considered as afirst step in a more comprehensive turbulence modelof the core–edge interaction. Further improvementsto the model would include non-adiabatic electroneffects arising from trapped electrons and electron–ion collisions, which have been found to increasethe growth of ITG modes [42] as well as ion–ioncollisions.

Linear theory is not sufficient to explain reduc-tions in turbulent transport since the saturationand non-linear regime of ITG modes involves effectssuch as the E ×B convective non-linearity and self-generated poloidal flows; thus it must be demon-strated that there is also a reduction of turbu-lence in the non-linear regime. Furthermore, it mustbe proven that such a reduction is measurableby our diagnostics at the plasma edge. A non-linear gyrokinetic particle-in-cell simulation modelin toroidal geometry, which has been extended toinclude multiple ion species [42], is used to inves-tigate the behaviour of turbulent ITG fluctuationsand transport before and after impurity species are


J.A. Boedo et al.

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Γ r (cm

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c)

Figure 3. Frequency space plots of (a) cross-power spectrum, (b) cross-phase angle, (c) turbulent

particle flux and (d) poloidal wavenumber kθ. Signals are strongly suppressed at frequencies higher

than 100 kHz.

introduced into an L mode (and ITG unstable) TEX-TOR plasma. The maximum number of toroidalmode numbers used was n = 40 and the total num-ber of particles was 10 × 106. The particle simu-lation algorithm was made highly efficient by par-allelization using a domain decomposition methodin the toroidal direction. The simulations were car-ried out using TEXTOR plasma parameters; aspectratio R/a = 3.8, minor radius a ≈ 200 ρi andpoloidal wavenumber range 0.01 < kθρi ≤ 1. Den-sity, temperature, safety factor q, and impurity con-centration profiles taken before and after neon injec-tion from TEXTOR discharges are used as initialconditions.

Results from these simulations are shown in Fig. 4indicating a strong suppression of the electrostaticfluctuations over the entire plasma volume and areduction of the growth rate of the instabilities.Figure 4(a) shows the time evolution of the vol-ume averaged electrostatic potential fluctuations in

discharges with and without impurities. The electro-static potential fluctuations are reduced by a fac-tor of ∼10 for a total neon concentration of 1% ofthe background density. The ion thermal flux dropsby a factor of 4–5. This result should be comparedwith that shown in Fig. 2, where a reduction in therelative fluctuation level of the potential by a fac-tor of 2 is observed experimentally and with that ofFig. 1(d), where the RMS level of the poloidal electricfield decreases by a factor of 2. The turbulence sup-pression is observed across a large part of the plasmacross-section, mostly from a/r = 0.4–1.0, as seen inFig. 4(b), where the radial profile of the electrostaticpotential is shown during the saturation phase ofthe turbulence. The extended effect over the cross-section is due to the fact that the higher charge statessuch as Ne8+, Ne9+ and Ne10+ have wide radial dis-tributions, as shown in Fig. 5. The potential fluctu-ations in Fig. 4(b) are poloidally and time averagedover a correlation length/time (tωci = (3–4)× 104).



10-6

10-5

10-4

10-3

10-2

10-1

100

0 1 2 3 4 5

Ωit (x104)

|Φ|2~

With Neon Injection

Without Neon Injection

10-13

10-11

10-9

10-7

10-5

0 0.2 0.4 0.6 0.8 1

before neon injection

r/a

after neon injection

|Φ|2~

(b)

(a)

Figure 4. Evolution of potential fluctuations versus

(a) time (time in multiples of ωci) and (b) radius as calcu-

lated by the non-linear particle-in-cell gyrokinetic simula-

tion. The system contains TEXTOR RI mode type plas-

mas as input with 1% neon content and without impurity

seeding. The evolution of the system has been followed

until saturation is reached.

It is important to note that the stabilization effectsextend radially to the edge of the plasma, where theprobe is located and our measurements taken. It isfound that the fluctuation suppression is due to

(a) The combined effects of ion temperature profilemodification due to the presence of the radiatingimpurity,

(b) Density peaking from reduced particletransport,

(c) Direct stabilization of the ITG modes viadilution.

Recent data [43] refute original claims of E ×Bshear [44] playing a dominant role in the core ofTEXTOR during RI mode, however, since the ITGmode growth rate is reduced by impurity seedingeffects (Eq. (1)), the existing E×B shear rate might

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Ne10+

n Ne(x

1011

cm-3

)

r/a

Ne9+Ne8+

Figure 5. Radial profiles for the higher states of neon.

The higher ionized states of neon, Ne8+, Ne9+ and Ne10+,

have a wide radial distribution.

contribute to further stabilize the ITG modes. Thesignatures of E ×B shear stabilization:

(i) Strong reduction (factors of 5) in the Eθrms

levels,(ii) Reduction in density fluctuation levels,(iii) Finally, and most importantly, change in

the phase angle between Eθrms and nrms

that causes a strong reduction of the radialparticle flux,

are not observed in our data during RI mode dis-charges. Therefore, stabilization of turbulence by ashear layer in the edge or an internal shear layer thataffects the edge by non-local effects [45, 23] due tolong radial correlation lengths are not supported byknown behaviour.

Another mechanism for the observed edge tur-bulence reduction could be the quenching of non-ITG related turbulence related to the decrease inpressure, density and temperature gradients at theedge/SOL. Although we cannot completely disre-gard such a possibility, the non-linear simulationspredict an ITG related reduction in the turbulenceat the edge (and core) by factors of ∼5 that arein agreement with observations. Furthermore, recentRI mode experiments in DIII-D [46] feature coreand edge turbulence reductions that vary concomi-tantly with impurity type and amount, reinforcingthe assumption that the mechanism at play is global.

3.2. Edge and SOL profiles

The reduction in radial particle transport andincreased radiative losses result in a lower particle


J.A. Boedo et al.

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oten

tial (

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.)

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Den

sity

(cm

-3)

Radius (cm)

RI-Mode

L-Mode

ICRHAntennae

a) b)

c) d)

LCFS

Figure 6. Edge radial profiles of (a) floating potential, (b) temperature, (c) electron pressure

and (d) density are shown for two discharges with L mode (γ = 0.34) and RI mode (γ = 0.85)

confinement. The LCFS and the radial regions for fitting the profiles are indicated.

and energy inventory available for the edge and SOL,which determine the capabilities of the RI mode toameliorate heat and particle loads to the plasmafacing components and properly supply particles tothe pumping apparatus. The edge and SOL Te andne profiles (Figs 6(a),(d)) were measured with highradial resolution (1.5 mm) with the scanning probein order to address the above issues.

The density profiles in the SOL (Fig. 6(d)) exhibittwo distinct exponential decay lengths; the firstbetween the LCFS and r ∼ 48 cm and the sec-ond (which is associated with other objects in theSOL such as the RF antennas and/or ponderomo-tive effects) between r ∼ 48 cm and the liner wall.Fits to the first decay length, herein dubbed localfits, and to the overall SOL profile, yield values oftemperature Teb, and density neb, at the LCFS and

profile decay lengths, λn and λlocaln , which show sim-

ilar behaviour with plasma parameters but can differin absolute value. Typical decay lengths in the SOLare 0.6–1.5 cm; thus the position of the LCFS, andof the profile resolution, must be known precisely toobtain accurate fits. The drop in the floating poten-tial Vf (Fig. 6(a)) allows an accurate determinationof the position of the LCFS within 2 mm, and itis found that the discharge to discharge variation ofthis position is as high as 10 mm, or nearly 100% ofthe density decay length.

Both edge density and temperature (Fig. 7(a,b))are reduced by factors of 2–3 as the energy avail-able at the edge diminishes due to radiation. Thetemperature profile (Fig. 6(b)) during the RI modeis very flat with a superimposed decay length λT ∼0.5 cm in the SOL which is fairly insensitive to the



0.0

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0.1

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rp (

m2s-1

)

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local (m2s

-1)

1-γ

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n e(a)

x 10

12 (

cm-3

)

0

10

20

30

40

50

60

Te(a

) (

eV)

a) b)

c) d)

Figure 7. Scalings with radiated fraction of (a) electron density neb and (b) electron temperature

Teb measured at r = a, (c) local and global decay lengths and (d) perpendicular diffusion coefficients.

radiated fraction within the significant data scatter.The flatness of the profile indicates either that thereis a significant power source, or sink, in the SOL orthat the ratio of perpendicular to parallel thermalconductivity is higher than that in L mode.

Accurate edge parameters allow us to calculatethe power flux at the LCFS, which can be written interms of the sheath transmission factor δ (which is∼8), the boundary density nb and temperature Teb,and the sound speed cs(a), as

q‖ = δnbcs(a)Teb.

The reduction in edge density and temperature resultin diminished power flux to the limiter (Fig. 8) byup to a factor of 7; the power flux features a lineardecrease with radiation fraction.

The density decay lengths, extracted from thelocal and global exponential fits, are reduced by a fac-tor of 1.5–2 as shown in Fig. 7(c), reflecting reducedradial particle fluxes. Although both decay lengthsbehave similarly with radiative fraction, there is afactor of 2–3 difference between them. We emphasizethat the decay length dubbed ‘local’ is considered tobe more accurate than the global one. The changes


J.A. Boedo et al.

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3.5 107

0.0 0.2 0.4 0.6 0.8 1.0

Q|| (

W/m

2)

1-γ

Figure 8. Heat flux convected to the limiter (W/m2) is

reduced by a factor of 7 during RI mode conditions.

in radial transport can be quantified by calculating aperpendicular diffusion coefficient D⊥ as a functionof the density decay length λn, the sound speed csand the parallel connection length L‖,

D⊥ =λ2ncs

2L‖.

We obtain values of D⊥ and Dlocal⊥ corresponding to

the use of either λn or λlocaln and shown in Fig. 7(d)

for a connection length of ∼20 m. The diffusion coef-ficient in the SOL is of the order of 0.4 m2 s−1, orabout half the Bohm value, and decreases markedlywith radiated power; this indicates a reductionin radial particle transport by factors of 2–3, allof which is consistent with the decreased radialturbulent particle transport.

It is important to note that the reduction in heatflux is concomitant with a reduction in density anddensity decay length, which results in a lower par-ticle flux to the pumping apparatus. The integratedflux (integrated over the SOL width) to the ALT-IIlimiter during the RI mode is 15% of the L modeflux. The reduction in density decay length fromλn ≈ (1/2–1)∆L to λn ≈ (1/4–1/2)∆L (where ∆L

is the radial thickness of the limiter head) starves ofparticles the collection apparatus of the pump lim-iter [36], which is located behind the limiter surface.A divertor can handle this issue by positioning of thestrike point at the pump.

3.3. Particle and energy confinement

The reduction in radial particle transport occursacross the LCFS, decreasing the particle losses fromthe main plasma and contributing to the increasedparticle confinement time that can be calculated [47]

0

10

20

30

40

50

60

70

80

0

10

20

30

40

50

60

70

80

0.0 0.2 0.4 0.6 0.8 1.0

τp

τE

τ p (m

s)

τE (m

s)

1-γ

Figure 9. Particle τp and energy τE confinement times

as a function of the radiated fraction. The confinement

times increase by a factor of ∼3–5 for γ ≥ 0.5 as the

discharges enter RI mode.

by relating the edge temperature Teb , input powerPtot , radiated power Prad , total number of particlesNtot and sheath transmission factor δ as

τp =NtotTebδ

(Ptot − Prad). (5)

The assumptions behind this calculation are: the par-allel heat transport is convective, Teb is poloidallyhomogeneous, no significant sources of particles orheat exist in the SOL and the particle and heat wet-ted areas are roughly similar. The experimentallydetermined values of Ptot , Prad and Ntot from theTEXTOR diagnostic systems, and Teb from the fastscanning probe, are used. The total radiated poweris obtained from integration of the thermographicreconstruction with 2% accuracy. Photoionization byUV neon radiation is calculated to be negligible (lessthan 2%) in the SOL. The ratio of Te and Ti in theedge is about 1.3, and thus the sheath transmissionfactor is taken to be ∼8. The calculated τp is shownin Fig. 9 and compared with the energy confinementtime τE . Two main features emerge from this figure:

(a) Discharges at values of γ below 0.5–0.6 featurea nearly constant τp,

(b) for γ above 0.5–0.6 the increase in τp is steepwith γ, by up to a factor of 4.

These observations are consistent with Hα mea-surements and with RI mode discharges recoveringNeo-Alcator scaling. The turbulent particle flux con-vected power is 20% that of the radiated power inL mode conditions (37% radiated power) and drops



Table 1. Key edge and core parameters that define the

ratio of the particle and energy confinement times

γ Te(a) Te0 αt αn τE/τp

L mode 0.34 40 1400 2.5 0.75 4.1

RI mode 0.85 25 1350 2.26 1.16 1.7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0

E/

p

1-γ

ττ

Figure 10. Ratio of energy and particle confinement

times τE/τp as a function of radiated fraction. The

relationship found is linear. The calculated ratios from

Eq. (8) are marked with boxes.

to 1% of the radiated power in RI mode conditions(95% radiated power); thus the particle confinementdoes not play a critical direct role in the energyexhaust.

Not only τp but also τE shows a sharp increasewith radiated fraction [48], showing a good correla-tion between the increase in energy and particle con-finement and indicating that the mechanism respon-sible for the enhancement affects both the particleand the energy confinement. The τE/τp ratio exhibitsa tendency to increase with density in RI mode dis-charges, as shown in Fig. 10, meaning that τp risesfaster with radiated power than τE . It is of interestto understand, and to investigate, the possibility ofcontrolling τE/τp, because the particle confinementaffects the SOL critically (and particle and powerexhaust) and a related quantity, ρ∗ = τ∗p /τE , has rel-evance for helium exhaust. The energy and particleconfinement times are related by an expression [49]including the total energy content E, the total num-ber of particles Ntot , the input power Ptot , radiated

power Prad , the boundary temperature in electron-volts, Teb and the sheath transmission factor δ,

τEτp

=E(Pin − Prad )δTbNPin

=E(1− γ)δTbN

. (6)

The energy content and total number of particles areobtained by integration of the density and temper-ature profiles, which are assumed parabolic with ashaping factor α, and written in terms of the peakdensity ne0 and temperature Te0 for a plasma ofmajor radius R0 and minor radius a. The suffixese and i denote ions and electrons, respectively. Wewrite for the electrons,

ne(r) = ne0[1− (r −R0)2/a2]αn

Te(r) = Te0[1− (r −R0)2/a2]αT .(7)

Fits to the measured density and temperature pro-files equation (7) show increased peaking during thewell developed RI mode, as shown in Table 1. Wecan include the profile shapes (Eq. (7)) in Eq. (6)to obtain Eq. (8), which can be simplified further(Eq. (8)) by setting Ti0 = Te0 and αi = αe, asexpected from the core conditions,

τEτp

=32

(1− γδ

)(1 + αnTb

)×(

Ti01 + αn + αi

+Te0

1 + αn + αe

)(8)

τEτp

= 3(

1δ

)(1− γ)

(Ti0Teb

)(1 + αn

1 + αn + αe

)= 3(

(1− γ)Teb

)(Ti0δ

)(1 + αn

1 + αn + αe

). (9)

When data from profiles (Table 1) are entered intoEq. (9), it is found that the confinement time ratiochanges by a factor of 2.2 between L mode (γ = 37%)and RI mode (γ = 95%), in agreement (Fig. 10)with the ratio of measured confinement times. Theobserved change in the ratio τE/τp is mildly depen-dent (10%) on the profile shaping (Table 1) andstrongly dependent on the ratio (1− γ)/Teb, i.e. theratio of the radiated fraction to the boundary tem-perature, mainly due to the fact that there is a largerreduction in 1 − γ (factor of 3–5) than in Teb (fac-tor of 2) with increased radiated power. However,the decrease of τE/τp with γ can be counteractedby further reducing Teb by either increasing the den-sity [50] or by using higher-Z impurities or a mixof impurities that determine a lower Teb. The τE/τpratio can be changed by a factor of 30 by tuning theedge temperature from 12 to 400 eV.


J.A. Boedo et al.

4. Conclusions

This article presents the first measurements ofturbulence and turbulent transport in the edge ofimpurity seeded discharges exhibiting RI mode con-finement. The turbulent radial transport is reduceddue to quenching of the levels of density and poten-tial fluctuations, particularly at high frequencies. Noevidence for velocity shear stabilization is found inthe outer edge of the plasma. The measurementshave been compared with results from a fully non-linear gyrokinetic simulation of ITG modes in thesame discharges. The simulation predicts a reductionof turbulence across the full cross-section, includ-ing the edge; therefore we propose stabilization ofITG modes as a mechanism to explain the reductionin turbulence in RI mode discharges. These resultshave wide application in toroidal confinement devicesand ongoing work will strive to separate the differ-ent mechanisms at play, with the aim to improve theperformance of fusion devices.

The reduction of turbulence causes an increase inboth energy and particle confinement which producea marked reduction in temperature and density inthe plasma edge during the RI mode and result in afactor of nearly 10 reduction in the power and parti-cle load to the plasma facing components. The sta-bilization is triggered at γ ≈ 0.6. We find a linearrelation for the τE/τp ratio versus γ, which indicatesa faster rise for particle than energy confinement. A1-D calculation which reproduces the experimentalratio of τE/τp, and its scaling as a function of theradiated power fraction, indicates that the changesin the ratio τE/τp are strongly dependent on the rela-tion between the edge temperature and the radiatedpower.

Acknowledgements

This work has been supported by USDOE GrantNo. DE-FG03-85 ER 51069. The authors want toexpress their gratitude to K. Burrell, T. Evans,G. Tynan and M. Schaffer for many useful interac-tions and to L. Russo for unwavering support.

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(Manuscript received 30 August 1998Final manuscript accepted 8 October 1999)

E-mail address of J. Boedo: [email protected]

Subject classification: D2, Te; F2, Te; I1, Te


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