Main Points
 The OEDGE code (Onion-Skin Modeling
+EIRENE + DIVIMP for edge analysis) is being
developed for the interpretation of edge data
with the objective of identifying the controlling
physics processes in tokamak edge plasmas.
 First results are reported on the application of
OEDGE to a set of DIII-D Simple-as-Possible –
Shots (SAPP): L-mode, low density, attached at
both targets. These SAPP shots were
particularly well diagnosed as to edge
quantities.
 Only a small fraction of the SAPP data has
been confronted in this initial report and
conclusions are therefore necessarily tentative.
 Principal Conclusion: The level of agreement
between code and experiment is quite good for
the most part, apparently indicating that many
of the controlling processes have been included
in the model – at least for this lowest density,
simplest of all possible conditions.
1
Ultimate Objective: to Predict
but
Do We Understand the Edge?
 To test our understanding of the edge we
must confront the detailed measurements.
 i.e., can our modeling match all the data
to within experimental error?
 i.e., have we identified all the zerothorder, controlling physics?
 When we have, then we can claim to
understand the edge –
 – which is the first and essential step to being
able to predict
2
Interpretive code simulations: even more essential
for divertor/edge than for core
 The edge is intrinsically more complicated than the core:
more states of matter involved; shape of region more
problematical: long, narrow, twisted, inaccessible; core
plasma transport can be accurately modeled as 1D, the
edge at best, as 2D. Diagnostic coverage is often
inadequate as a consequence of the 2D nature and
inaccessibility of the edge. Meaningful interpretive
exercises therefore require that a data set of edge
measurements, which is as large as possible, be
confronted simultaneously – which requires a code.
 The significance of many edge data is not directly
evident and they can only contribute to a picture of the
edge using an interpretive code.
 Edge data sets are invariably incomplete but
extrapolation is not usually adequate because variations
along B are often non-linear.
All this tends to place interpretive codes at the center of
edge studies with the various lines of diagnostic
information feeding into the hub as well as our ideas about
what the controlling physics effects might be. The
objective is understanding and, ultimately, the ability to
predict.
3
DIII-D Edge is
Particularly Well Diagnosed
1. Divertor Thomson System (DTS), unique
to DIII-D, measures the 2D distributions of
ne and Te throughout the divertor.
2. The Tangential-View camera system,
spatially comprehensive and uniquely
including the VUV, provides intensitycalibrated 2D pictures of the divertor plasma
in hydrogenic and impurity light.
3. The spatially-comprehensive IRTV (Infra
Red TV) system regularly measures heat
fluxes to edge structures.
4. Bolometry measures complete poloidal
distribution of volumetric power loss.
4
5. The Filterscope + Multi-chord Divertor
Spectrometry (MDS) systems, calibrated and
spatially-extensive, provide line-of-sight
measures of the intensities of hydrogenic and
impurity line emissions.
6. The DiMES (Divertor Material
Evaluation Studies) material sample
manipulator, and flexible DIII-D shaping
control, allow for precise Plasma-Surface
Interaction studies with a specific plasma
condition. The diagnostic coverage is
comprehensive: five different spectroscopy
systems view the DiMES sample.
7. Comprehensive target Langmuir probe
coverage measures plasma conditions across
the targets.
8. Edge reflectometry provides radial
profiles of ne in the SOL.
5
9. The SOL+edge Thomson provides
detailed radial profiles of ne and Te across
the edge and into the core.
10. The SOL+edge CER provides similar
spatial profiles of the ion density, ion
temperature, ion toroidal velocity and ion
poloidal velocity – both for the deuterons as
well as for the different charge states of each
impurity species present .
11. Reciprocating fast Langmuir probes
measure ne and Te across the SOL at 2
poloidal locations; also Mach number and
fluctuations.
12. Beam Emission Spectroscopy, BES,
measures edge density fluctuations.
13. Pressure gauges at various poloidal
locations measure hydrogen neutrals.
6
7
SAPP
 Where to start? Best not with complicated edges, e.g.
with ELMs, detachment, etc. Start with Simple-asPossible-Plasmas (13 February 2001):
 L-mode (no ELMs), lower single null, 2.7 MW, <ne>
= 2.5, 3.5, 4.5 x 1019 m-3
 all edge diagnostics operated
 X-point sweeping to map divertor ne,Te in 2-D (DTS)
 6 repeat shots at each <ne> for additional data and
for different wavelengths (MDS, tangential cameras)
 these shots were also set up for exposing Li sample
(DiMES)  further diagnostic opportunities:
spectroscopic lines for every line-emitting charge
state of Li were measured
 for <ne> = 2.5 x 1019 m-3, plasma attached at both
inner and outer targets, making for the simplest edge
 the case presented here.
8
UEDGE and OEDGE
 UEDGE is a ‘standard’ 2-D multi-fluid
edge code developed by LLNL over the
past decade, primarily for DIII-D.
 UEDGE is a proven success – one of
the most consistently-maintained and
experimentally-focused edge codes.
 OEDGE, a less developed approach,
tackles the problem of edge interpretation
from a different but complimentary
direction. It’s utility still remains to be
demonstrated, largely, but the approach
should be able to benefit from a number
of potential advantages.
9
OEDGE
an Interpretive Edge Code
OEDGE:
Onion-Skin Modeling
+ EIRENE
+ DIVIMP
for edge analysis
is used for interpretation of edge data.
 EIRENE: a neutral hydrogen Monte
Carlo code (Detlev Reiter, KFA Juelich).
 DIVIMP: an impurity neutral and ion
Monte Carlo code (Toronto, JET).
 Monte Carlo codes require a ‘plasma
background’ as input.
 Onion-Skin Modeling, OSM: can provide
such a plasma background.
10
Onion-Skin Modelling
 Solve the 1D, along-B, plasma
conservation equations using across-B
boundary conditions from experiment, e.g.

and Te across targets from Langmuir
I sat
probes to produce a 2D solution.
 Iterate the OSM plasma solver with
EIRENE and DIVIMP, to provide the
particle, momentum and power terms
associated with hydrogen recycle and
impurities, respectively.
SOL
 DSOL
: not required as input.
and



Cross-field information is implicitly
contained in the cross-field boundary
conditions. In fact, they can be extracted
from OSM analysis ( ‘Edge TRANSP’).
11
CHOOSING THE LOCATION OF
THE BOUNDARY CONDITIONS
 In standard 2-D fluid code modeling, the
 plane
BCs are assigned upstream, e.g. nmid
e , separatrix
SOL
and PeSOL
,
P
, in
i , in , i.e. essentially at one point
(one also needs to assign values of
SOL
).
DSOL
 , 

In OSM one has a choice: upstream,
downstream (target), mid-way, a mix, etc.
The BCs are applied across the SOL, thus
one is introducing much more
information from experiment than in
standard 2-D modeling.
To see the potential benefits of using target
BCs, consider the simple ‘0-D’ model of the
SOL, the 2-POINT MODEL.
12
THE BASIC 2-POINT MODEL OF
THE SOL
For the Conduction-Limited Regime,
High-Recycling Regime.
conservation of momentum and energy gives:
2n t Tt  nu Tu
Tu
7/2
 Tt
7/2

7 qL
2  oe
q  n t kTt cst
Choice of BCs:
1. Take upstream quantities as the BCs, nu
and Tu, (or nu and q||), then calculate target
quantities: nt and Tt.
2.
Or take the target quantities as the BCs, nt
and Tt, then calculate upstream quantities,
nu and Tu.
13
THE BASIC 2-POINT MODEL OF
THE SOL
1.
With nu and Tu as BCs:
Tt  Tu5/nu2
2.
and
nt  nu3/Tu4
With nt and Tt as BCs:
Tu  nt2/7Tt3/7
and
nu  nt5/7Tt4/7
Target quantities are highly sensitive to
upstream BCs,
‘VOLATILE’ solutions,
while upstream quantities are rather
insensitive to target BCs,
‘ROBUST’ solutions
14
Target Langmuir Probe Profiles
Across outer target.
Inner target profile is quite similar but is mapped less
completely.
15
Computational grid with ‘onion-skin’ rings
(PFZ) Ring No. 32
(n=0.9878)
(SOL) Ring No. 10
(n=1.0015)
to (PFZ) Ring No. 35
(n=0.9986)
to (SOL) Ring No. 19
(n=1.0434)
Rings No. 32-35 are in PFZ.
Rings No. 10-19 are in SOL.
16
Comparison of Code and Divertor Thomson ne
Red: DTS. Green: target probe. Line: code.
First 4 rings, Nos. 32-35: outer Private Flux Zone, PFZ.
Remaining rings, Nos. 10-19: outer SOL.
Large DTS scatter is partly due to plasma fluctuations. Average
DTS Te is near code in both PFZ and SOL but tends to be
somewhat higher. The ne-jump in front of the target, s|| =0, is due
to the acceleration of the plasma to sound speed.
separatrix
Experimental error in the Thomson ne varies from 5% to 60% with an average of 15%.
17
Comparison of Code and Divertor Thomson Te
Red: DTS. Green: target probe. Line: code.
First 4 rings, Nos. 32-35: outer Private Flux Zone, PFZ.
Remaining rings, Nos. 10-19: outer SOL.
Large DTS scatter is partly due to plasma fluctuations. Average
DTS Te is below code in/near PFZ, but near code away from
PFZ. The reason for the discrepancy is not known.
separatrix
Experimental error in the Thomson Te varies from 10% to 60% with an average of 30%.
18
Comparison of Code
and Upstream Thomson ne and Te
Data from 5 identical shots combined. Red band shows
fluctuation variation. Green: average Thomson value.
Blue: code. Z = distance along axis of Thomson laser.
Experimental error in the Thomson ne varies from 5% to 50% with an average of 20%.
Experimental error in the Thomson Te varies from 10% to 80% with an average of 35%.
19
Comparisons Code and Filterscopes, Outer Target
D across outer target.
D across outer target.
CIII (4650A) across outer.
Filterscope data produced by sweeping of the X-point.
20
Comparisons with Code and Tangential Filterscopes
at the Outside Midplane
21
Comparisons with Code and Upper-Looking
Filterscopes
22
Comparison of Code and Bolometry Signals
outer
strike
point
inner
strike
point
Poloidal variation of bolometry signal (power
received on each bolometer detector) across the
divertor region. Code: sum of total deuterium (from
EIRENE) and total carbon (from ADAS and
DIVIMP) radiation.
23
Comparison for Complete Ploidal Bolometry
Evidently there is stronger plasma-surface
interaction occurring at inside wall, also at the walls
near the 2 strike points, than is given by the code.
This is also supported by the results from the
fs12 filterscope (D, CIII) which views across the
midplane from outer wall to inner: the code signals
are only about 1/3 of the experimental value. Since
code matches (or over-matches) the filterscopes
viewing only the outer wall, the implication is that the
inner wall interaction is stronger than in the code.
24
Comments and Conclusions
Major Caveat: Only a small fraction of the SAPP
data has been confronted in this initial report
and all conclusions are therefore necessarily
tentative.
Principal Conclusion: The level of agreement
between code and experiment is good for the
most part, apparently indicating that most of the
controlling processes have been included in the
model – at least for this lowest density, simplest
of all possible conditions.
Outstanding Issues:
 Problem of comparing highly fluctuating edge
experimental data and code values. It is evident
that the fluctuation level in the edge is very large.
The 2 Thomson systems have ~10 ns integration
times and thus capture different phases of the
fluctuations of ne and Te. As can be seen from the
plots here, the fluctuation levels are of about the
same magnitude as the average levels, The codes
used here know nothing of fluctuations and
25
presumably have to be taken as giving average
quantities. This raises the question of whether the
comparisons should be to simple (un-weighted)
averages of the data - which is the sole method
used here – or to some weighted average. It is
easy to make the case for the latter: for example,
spectroscopic intensities are likely to be nonlinearly dependent on Te, and perhaps on ne also.
Yet the matches to the filterscope signals of D,
D and CIII are rather good – particularly for the
outer target. This matter requires further
investigation.
 The Private Flux Zone involves unknown physics
processes. As known earlier, there is some major
deficiency in our understanding of the PFZ. Here
it is clear that, while the values of Te obtained by
the target Langmuir probes and the (average)
DTS agree quite well the further one goes out into
the SOL away from the PFZ, this agreement
degrade substantially as one approaches and
enters the PFZ. When DTS and probe results
disagree, often the probe interpretation has been
questioned; however, the agreement between
code (thus probe) and filterscopes at the outside
target, including in the PFZ, seems to confirm the
26
probe profiles. This matter requires further
investigation.
 The code value of upstream density is high
compared with experiment. The matches to the
upstream Thomson are largely good, however,
the code is clearly too high for ne near the
separatrix. Does this indicate, again, some
missing physics in/near the PFZ? Or is this
related to uncertainties in the separatrix
location? (In this report the separatrix location,
and generally the location of all flux surfaces,
have been taken as being correctly given by
EFIT).
 There may be plasma contact with the inner wall.
The intensity of Plasma-Surface Interaction, PSI,
including impurity production, near the strike
points would appear to be ~correctly handled by
the code. Further, the intensity of PSI at the
outside walls and at the top of the main chamber
also appears to be ~correctly handled. On the
other hand, it appears - from the bolometer
signals near, but not right at the strike points, as
well as at the inner wall - that there is stronger
PSI in those regions than the code is accounting
for. This requires further investigation.
27
Interpretive Modeling
of DIII-D Edge Measurements
using the OEDGE Code
P.C. Stangeby1,5, J.D. Elder1,
M. Fenstermacher2, G.D. Porter2, D. Reiter3,
J.G. Watkins4,W.P. West5, and D.G. Whyte6
1. University of Toronto Institute for Aerospace
Studies, 4925 Dufferin St., Toronto, M3H 5T6,
Canada
2. Lawrence Livermore National Laboratory,
Livermore, California
3. University of Duesseldorf, Duesseldorf, Germany
and KFA, Jülich, Germany
4. Sandia National Laboratories, Albuquerque, New
Mexico
5. General Atomics, San Diego, California
6. University of California, San Diego, California
28