Comparison of Impurity Transport in Different
Magnetic Configurations
Presented by

Kieran J. McCarthyaWith coauthors

R. Burhennb, K. Idac, H. Maassbergb, Y. Nakamurac, N. Tamuraca) Laboratorio Nacional de Fusión, Asoc. EURATOM-CIEMAT, Madrid, Spainb) Max-Planck-Institut für Plasmaphysik, EURATOM Association, Greifswald, Germanyc) National Institute for Fusion Science, Toki, Japan

International Stellarator/Heliotron Profile Database
IEA Implementing Agreement for Cooperation in theDevelopment of the Stellarator Concept
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Outline

Motivation
Introduction
Experimental Observations in Different Configurations
Similarities and Differences
Database requirements

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Motivation
Impurities: should they be of concern for stellarators?
Impurities acceptable at low concentrations
Beneficial (e.g. radiative cooling at edge, etc.)
Valuable diagnostic tools (e.g. Vr, Er, etc.)
Avoid core impurity accumulation (high-Z) during improved
energy confinement modes
Overbalance of equilibrium between radiation
losses & heating power
Degradation of plasma energy
Discharge termination

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W7-ASAn unfavourable impurity confinement dependence on density!
Fe XVI
radiationne(0) ≥
5 x 1019 m-3

Energy /kJ

Total radiation /kW

Density

SX radiation

Temperature / keV

Bremsstrahlung

At low densities

Stationary radiation levels

At high densities

Increase of intrinsic impurity radiation

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Motivation
How can core impurity accumulation be prevented?
Tokamaks

diffusion coefficient

Confinement degrading phenomena such as
ELMs and sawtooth crashes can be used to flush
out impurities.

PS
B

P
class.

collisionality

With the background plasma is in banana regime

υ can be outward
Temperature screening(from axisymetric neoclassics)
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Motivation
How can core impurity accumulation be prevented?
Tokamaks
Confinement degrading phenomena such as
ELMs and sawtooth crashes can be used to flush
out impurities. Also temperature screening.
Stellarators
Current-connected phenomena not an option
ELMs difficult to produce in a controlled manner
No principal neoclassical mechanism in standard ion root
(only in low ne +ive electric fields in roots).
3-dim magnetic topology
Additional collisionality regimes for the
background gas appear in the lmfp regions

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Motivation
How can core impurity accumulation be prevented?
Tokamaks
Confinement degrading phenomena such as
ELMs and sawtooth crashes can be used to flush
out impurities. Also temperature screening.
Stellarators

diffusion coefficientνCurrent-connected phenomena not an option
1/νPS
ELMs difficult to produce in a controlledmannerP

No principal neoclassical mechanism in standard ion root.
classfields(only in low ne +ive electricin roots).
collisionality

3-dim magnetic topology
Additional collisionality regimes for the
background gas appear in the lmfp regions
No temperature screening possible in P, ν, 1/ν, ν0.5 (υ is inward)
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Non-axisymmetricneoclassics

Motivation
How can core impurity accumulation be prevented?
Tokamaks
Confinement degrading phenomena such as
ELMs and sawtooth crashes can be used to flush
out impurities. Also temperature screening.
Stellarators
Current-connected phenomena not an option
ELMs difficult to produce in a controlled manner
No principal neoclassical mechanism in standard ion root
(only in low ne +ive electric fields in roots).
3-dim magnetic topology
Additional collisionality regimes for the
background gas appear in the lmfp regions
There is a need to investigate Stellarator specific ways
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Motivation
What can these observations tell us wrt. stellarator pathways?
W7-ASτimp scales withdensity in NC mode!
Introduction ofdivertor modules led
to HDH-mode
Significant drop in τimp
observed in HDH modeNC
R. Burhenn et al, FST 46(2004) 115
NC : „Normal“ Confinement - very elmy H-mode
HDH: High Density H-mode
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Motivation
What can these observations tell us wrt. stellarator pathways?
LHD
High-Z accumulationin specific density window
Screening of intrinsic
impurities at higher densities

Y. Nakamura et al.,
PPCF 44 (2002) 2121
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Motivation
Can core impurity accumulation be prevented?
Tokamaks
Confinement degrading phenomena such as
ELMs and sawtooth crashes can be used to flush
out impurities. Also temperature screening.
Stellarators
Current-connected phenomena not an option
ELMs difficult to produce in a controlled manner
No principal neoclassical mechanism in standard ion root
(only in low ne +ive electric fields in roots).
Different magnetic topology
additional transport regimes in lmfp regimes
Stellarator specific ways have been explored
need a clearer understanding of underlying physics
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Motivation
Is impurity behaviour in stellarators well described by thestandard theoretical models for axisymmetric devices?
If good agreement with observations
Transport is understood
Conclusions can be drawn with respect to further
improvements and extrapolations
If poor agreement with observations
Point to dominance of turbulent/anomalous transport ?
The need for Stellarator specific transport contributions ?
Further interpretation becomes difficult!!
Predictions have to be substituted by measurement.
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Motivation
Introduction
Impurity content
Impurity Transport Analysis
Experimental Observations in Different Configurations
Similarities and Differences
Database requirements

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Impurity Content
What mechanisms determine impurity content?

Impurity influx from the chamber walls, etc.
Governed by transport at open magnetic field & retention
Feng I-06 & Kobayashi I-07
Impurity transport inside closed magnetic surface
Diffusive, D, and convective, υ, terms

υ driven by T and n gradients & space potential

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Impurity Transport Analysis
Confinement time, τ imp

Global transport quantity

Highest ionization stages
PMT€ Bolometer(soft x-ray, VUV)Thin layer ofmetallic impurity

Core transport studies

PlasmaLaserhυSample chamberSoft X-ray
Detector

Visible & VUVSpectrometers

Laser blow-off
Also impurity pellet injection& gas-oscillation

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Impurity Transport Analysis
Confinement time, τ imp

Global transport quantity

Local transport quantities
Impurity fluxes, Γ, are based on neoclassical and PS
transport for axisymmetric devices€

Γ = D ⋅ ∇n + v ⋅ n

D (r) - diffusion coefficient (m2 s-1)

υ (r) - convective velocity (m s-1)
One-dimensional impurity transport models for axisymetricdevices (e.g., SITAR, MIST codes)
No stellarator specific transportfeatures implemented

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Motivation
Introduction
Impurity content
Impurity Transport Analysis
Experimental Observations in Different Configurations
W7-AS
TJ-II

Tendencies

LHD
Similarities and Differences
Database requirements

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W7-ASτAl ∝ ap2.4 ne1.2 / PECRH0.8(for ne(0) <5 x 1019 m-3)

R. Burhenn et al,
Proc 22nd EPS (1995) III 145
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W7-ASτAl ∝ ap2.4 ne1.2 / PECRH0.8#27443, 27471(for ne(0) <5 x 1019 m-3)

No Te effect!
Weak role of B!
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R. Burhenn et al,
Proc 22nd EPS (1995) III 145

TJ-II

W7-ASτAl ∝ ap2.4 ne1.2 / PECRH0.8(for ne(0) <5 x 1019 m-3)

Similar trend observed in TJ-II
for ne(0) < 1019 m-3
Hidalgo et al., Nucl. Fusion 45
R. Burhenn et al,(2005) S266
Proc 22nd EPS (1995) III 145
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W7-ASPECRH dependence in TJ-IIτAl ∝ ap2.4 ne1.2 / PECRH0.8(for ne(0) <5 x 1019 m-3)
800 kW (#37920)
400 kW (#37909)

Hidalgo et al., Nucl. Fusion 45(2005) S266

Burhenn et al., FST 46 (2004) 115

W7-ASτAl ∝ ap2.4 ne1.2 / PECRH0.8(for ne(0) <5 x 1019 m-3)

while…

τE ∝ ap2.2 ne0.5 / PECRH0.6
Dp ∝ ne-1.2 PECRH
The observed dependencies aretrends not expected for theneoclass and PS transport model
May point to additional
impact of turbulent/anomalous transport?
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R. Burhenn et al,
Proc 22nd EPS (1995) III 145

W7-AS

What lies behind density dependence?

ne profiles similar
Comparison of ECRH plasmas withdensitiesfor
no2indicationdifferent Er

Might accumulation be due to slightly more peaked Ti profile?
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υ for grad Ti from axisymmetric neoclassics!
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W7-AS

What lies behind density dependence?

Local transport coefficients – experiment and prediction(SITAR, for axisymmetric devices only)
ECRH

Medium Density
High Density

experimental D, v
match different
time behaviour

Model predictions fordifferent backgroundimpurity concentrations

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W7-AS

What lies behind density dependence?

Local transport coefficients – experiment and prediction(SITAR, for axisymmetric devices only)
ECRH

Medium Density
High Density

experimental D, v
match different
time behaviour

For Medium Density, thefast onset of a stationary
radiation level is welldescribed by high D.

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W7-AS

What lies behind density dependence?

Local transport coefficients – experiment and prediction(SITAR, for axisymmetric devices only)
ECRH

Medium Density

1.7sHigh Density

experimental D, v
match different
time behaviour

Increasing radiation for
High-Density is compatible
with lower D, in particular atedge, where low D`s governtime constant for transport.
Reduced impurity influxes
cause long timescale.
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W7-AS

What lies behind density dependence?

Local transport coefficients – experiment and prediction(SITAR, for axisymmetric devices only)
ECRH

Medium density
High density

experimental D, v
match different
time behaviour

Stationary radiation level
depends on impurity sources!
Small sources >> acceptable
Wall conditioning!
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W7-AS

ECRH / NBI plasmas comparison with theory
LBO Al injection into
ECRH and NBI plasmas+ Predictions foraxisymmetric device.
Qualitative agreement

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R. Burhenn et al,
FST (2004) 115

W7-AS

ECRH / NBI plasmas comparison with theory
LBO Al injection into
ECRH and NBI plasmas+ Predictions foraxisymmetric device.
Discrepancy in D:
Experimentally derived D‘…
x3–8 times lower (!) thanthose predicted by model
Is this discrepancy due toneglect of stellarator
features?

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R. Burhenn et al,
FST (2004) 115

W7-AS

ECRH / NBI plasmas comparison with theory
Model modified with
non-axisymmetric terms„non-axisymmetric“
neoclassical D seems tomatch experiment better …
… but not υ …
Stronger accumulation
expected
but not observed!

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R. Burhenn et al,
FST (2004) 115

W7-AS

HDH mode

Island Divertor modules
Transition from NC to HDH at a power
dependent threshold densityτimp decreases
τE increases
Density profile flattens
Temperature profile is similar

R. Burhenn et al, 30th EPS (2003) 27A

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R. Burhenn et al, 30th EPS (2003) 27A

W7-AS

HDH mode
HDH mode
For plasma core:Island Divertor modules
1. Diffusion
coefficients
Transition
fromsimilar
NC to HDH at a power
2. Inward dependent
convectivethresholdvelocity isdensity
reducedAt first glance,
it might appear obvious to explain degradedconfinement in terms of the neoclassical/PS
model-> flattening of ne profile >> reduction of υin

R. Burhenn et al, 30th EPS (2003) 27A

Not the whole story ...

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R. Burhenn et al, 30th EPS (2003) 27A

W7-AS

HDH mode
Need to consider plasma edge also!!
Strong increase of υin ! (K. Ida)
Long confinement timerather thandegraded confinement!
Need to compensate with high D atedge to achieve the short confinement
times observed in HDH.
This means:* Changes of core transport important, but* edge impurity transport essentiallydetermines global confinement!

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R. Burhenn et al, 30th EPS (2003) 27A

Motivation
Introduction
Impurity content
Impurity Transport Analysis
Experimental Observations in Different Configurations
W7-AS
TJ-II
LHD

Tendencies

Similarities and Differences
Database requirements

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LHD
Density Ramp-up
Low density

Y. Nakamura et al. ISW 2002, No. OIV:5

Y. Nakamura et al.,
PPCF 44 (2002) 2121
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LHD
Density Ramp-up
Accumulation windowat medium density

Y. Nakamura et al. ISW 2002, No. OIV:5

See accumulation
with long time
constant!

Y. Nakamura et al.,
PPCF 44 (2002) 2121

Y. Nakamura et al.,
NF 43 (2003) 219

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LHD
Density Ramp-up
Accumulation windowat medium density

ne density trend similar to W7-AS
Inward fluxes cannot
reproduced
axisymmetric
Y. be
Nakamura
et al. ISWby
2002,
No. OIV:5
neoclassics
See accumulation
with long time
constant!
but possibly by …

(Y. Nakamura et al., PPCF 44 (2002) 2121))(H. Maassber et al., PFCF 41 (1999) 1135 )non-axisymmetric neoclassics (no Ti screening) ???
Y. Nakamura et al.,
PPCF 44 (2002) 2121

Y. Nakamura et al.,
NF 43 (2003) 219

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LHD
Density Ramp-up„Flush-out“

Y. Nakamura et al. ISW 2002, No. OIV:5

Y. Nakamura et al.,
PPCF 44 (2002) 2121

Y. Nakamura et al.,
NF 43 (2003) 219

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LHD
Density Ramp-up„Flush-out“

Such a beneficial effect observed only in HDH (W7-AS)
Y. Nakamura et al. ISW 2002, No. OIV:5

Outward fluxes are expected from traditional
neoclassics (Ti screening)(Y. Nakamura et al., PPCF 44 (2002) 2121-2134)

but not from …
non-axisymmetric neoclassics (no Ti screening) !?
(H. Maassberg et al., PFCF 41 (1999) 1135 )Y. Nakamura et al.,
PPCF 44 (2002) 2121

Y. Nakamura et al.,
NF 43 (2003) 219

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LHD
What are the reason(s) for
the accumulation window?
Ambipolar field Er Positive Er

Low
High
collisionality collisionalityin „e-root“
outward flux
in core„i-root“Ne+10

Y. Nakamura et al., ISW 2002, No. OIV:5
Y. Nakamura et al., NF 43 (2003) 219
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impurity flux
highChanging Er seems tocause „accumulation“
May be causedby dominant
effect of T gradin PS (ne flat)“Temperature
Screening”
effectLHD
Why purification beyond
the accumulation window?
… long impurity
confinement times

Ambipolar field Er

Assumption:
If τI and Er would
continue to rise (?) …
… then „purifucation“
window means:τI and Er at high ne interesting… a decrease of influx
but still long impurity
confinement ?

If „Yes“ >>> similar ne-dependence in LHD as W7-AS, TJ-II
at least for core confinement

Y. Nakamura et al., ISW 2002, No. OIV:5

Dexp >> Dneo, cannot be related just to turbulent transport(mayneed „still
Y. Nakamura
et toal.,beNFunderstood“
43 (2003) 219non-axisymetric features)
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Motivation
Introduction
Impurity content
Impurity Transport Analysis
Experimental Observations in Different Configurations
W7-AS
TJ-II
LHD
Similarities and Differences
Database requirements

17th International Toki Conference on Physics of Flows and Turbulence in Plasmas
and 16th International Stellaretor/Heliotron Workshop

Similarities and differences
Indications for anomalous/turbulent transport at low and medium densities(TJ-II, W7-AS, LHD)
Tendency to approach neoclassics at high density (LHD, W7-AS)
Improvement of impurity core confinement with density(TJ-II, W7-AS, LHD (high ne))Impurity screening mechanisms at high density similar/different in
W7-AS and LHD?
Many features are qualitatively… consistent with traditional neoclassics - but not quantitatively… not consistent with traditional neoclassics
Need for non-axisymmetric neoclassics ?

17th International Toki Conference on Physics of Flows and Turbulence in Plasmas
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Motivation
Introduction
Impurity content
Impurity Transport Analysis
Experimental Observations in Different Configurations
W7-AS
TJ-II
LHD
Similarities and Differences
Database requirements

17th International Toki Conference on Physics of Flows and Turbulence in Plasmas
and 16th International Stellaretor/Heliotron Workshop

Database requirements
In DB, data needed for scaling:τimp (B,n,T,P,i, maximum Er, heating system…)D,υ or D(r) ,υ(r) at e.g. 2 radial positions, maximum Er …
To achieve a better understanding of physics of transport:
For comparison need dedicated discharges with well documented(τimp, local D,υ or with profiles of ne,Te,Ti,Er, Pheat, ….)
Basis for understanding:1) Consideration of stellarator specific features in neoclassical model(3-D magnetic topology, gradB-drift, D(E,Z, ν*) >> no analyticalsolution for ambipolarity,..)>> strong impact: e.g. no Ti-screening
2) When can plasma be described with a neoclassical modeland when is it anomalous/turbulent >> key: D(r)3) Er diagnostic very important for comparison of experimental υ withneoclassical model.
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