1st IAEA Technical Meeting on
Fusion Data Processing, Validation and Analysis
1st of June - 3rd of June 2015, Nice, France.
Synthetic H-alpha diagnostics for ITER: inverse
problems and error estimations for strong nonMaxwellian effects and intense divertor stray light
A.B. Kukushkin1,2, V.S. Neverov1, A.G. Alekseev1,
S.W. Lisgo3, A.S. Kukushkin1,2
3ITER
1National
Research Centre "Kurchatov institute", Moscow, Russia
2National
Research Nuclear University "MEPhI", Moscow, Russia
Organization, Route de Vinon sur Verdon, St Paul Lez Durance, France
The views and opinions expressed herein do not necessarily reflect
those of the ITER Organization
OUTLINE
1. Introduction
1.1 Motivation
1.2 Goals
1.3 Methods used
2. Inverse problems and their solutions
2.1 Interpretation of direct observation of divertor
2.2 Predictive modeling of the divertor stray light (DSL)
spectral line shape
2.3 Interpretation of signals from main chamber with
allowance for the DSL
3. Analysis of measurement errors
4. Validation Against Data from JET-ILW
5. Plans, Conclusions
1.1 Motivation – The Role of Diagnostics on ITER
Measurement
Role
Diagnostic Function
1a1
Machine protection (MP)
1a2
Machine control (MC)
1b
Advanced scenario plasma control
2
Measurements required for evaluation and physics (PHY)
• ITER is unable to operate without a working diagnostic for every group 1a
measurement
• For advanced operation, there must be a working diagnostic for every group
1b measurement
• The machine may operate without group 2 diagnostics in operation
Diagnostic assignments:
• primary: the diagnostic is well suited to the measurement
• back-up: provides similar data to the primary, but with some limitations
• supplementary: can validate and/or calibrate the measurement, but cannot
make the measurement by itself
1.1 Motivation – The Measurement-Diagnostic Matrix
LIST OF RELATED DIAGNOSTICS
REQUIRED MEASUREMENTS
1.1 Motivation – The problem of reflections
 ITER has a metal wall and the divertor will be a strong source of
visible light  Will the main chamber Ha diagnostic be able to
make the required measurements in the presence of divertor stray
light (DSL)?
NO REFLECTIONS
50% REFLECTIVITY
(25% SPECULAR,
25% DIFFUSE)
[S. Kajita, 2013 PSI]
 Plasma from SOLPS+OSM+EIRENE  LightTools
1.1 Motivation – The problem of reflections
 ITER has a metal wall and the divertor will be a strong source of
visible light  Will the main chamber Ha diagnostic be able to
make the required measurements in the presence of divertor stray
light (DSL)?
LINE-OF-SIGHT INTEGRALS
NO REFLECTIONS
(red rectangle)
[S. Kajita, 2013 PSI]
 Plasma from SOLPS+OSM+EIRENE  LightTools
[S. Kajita, PPCF 2013]
1.1 Motivation – Non-Maxwellian atom velocity distributions
 In addition to the DSL issue, the velocity distribution function (VDF)
of neutral hydrogen atoms in the SOL is expected to have a nonMaxwellian distribution, and so advanced modelling of the Balmeralpha spectral line shapes is required
ATOM TRAJECTORIES FROM MAIN
CHAMBER RECYCLING, AS CALCULATED BY
THE EIRENE KINETIC CODE  velocity
distribution functions along specified linesof-sight are recorded during the code run
 Can line shape analysis be used to
identify the SOL and DSL
contributions to the signal for a
viewing chord in the main chamber,
including the separation of HFS and
LFS contributions to SOL emission?
(In addition to the D/T ratio.)
1.1 Motivation – Development of solution methods
 Accuracy of algorithms for processing the data and recovering the
parameters needed for ITER operation can only be estimated in
the framework of the synthetic diagnostics.
 Such diagnostics provide so-called “phantom” experimental data
by using the results of predictive numerical simulations of the
main plasma parameters.
 The synthetic diagnostics makes it possible to directly compare the
“true” values of the desired quantities with their known values in
the “phantom” data.
1.2 Goal
 Estimate the measurement errors of the parameters needed for
fusion machine operation with allowance for:
 strong DSL on the lines-of-sight in the main chamber,
 substantial deviation of the neutral atom VDF from a Maxwellian in the SOL,
 data from the direct observation of the divertor.
1.2. Goal
At this stage in the model development process, inverse problems
are being solved for recovering:
• spatial distributions of the isotope ratio and temperature for the
neutral hydrogen in the divertor;
• spectral line shape of the DSL;
• relative contributions of all three sources in the signal for a line-ofsight in the main chamber (namely, from inner and outer sections
of the SOL on the line of sight, and from the DSL);
• isotope ratios in the SOL.
Algorithms for targeting the final goals of the ITER Main Chamber Ha
diagnostic are in development
1.3. Methods and Data used
a. SOLPS4.3 (B2-EIRENE) predictive modeling of background plasma on
the flat-top stage of Q=10 inductive operation of ITER;
b. EIRENE stand-alone calculations of neutral deuterium VDF on the
SOLPS4.3 background (similarly to [1] but with allowance for
poloidally resolved recycling from the first wall [2]);
c. model [3] for spectral line shape asymmetry in the SOL, caused by
the net inward flux of relatively fast atoms;
d. model [4] for recovering main parameters (effective temperatures
and their relative content) of non-Maxwellian VDF of neutral
hydrogen atoms in the SOL;
e. model [5] for the spectral line shape of the DSL.
[1] V.S. Lisitsa, M.B. Kadomtsev, V. Kotov, V. S. Neverov, V. A. Shurygin. Atoms 2, 195 (2014)
[2] S.W. Lisgo, et al., J. Nucl. Mater. 415, 965 (2011)
[3] A.B. Kukushkin, V.S. Neverov, et al., J. Phys.: Conf. Series 548 (2014) 012012
[4] V. S. Neverov, et al., Plasma Phys. Rep., 41, 103 (2015)
[5] A.B. Kukushkin, et al. Proc. 24th IAEA FEC, San Diego, USA, 2012, ITR/P5-44
OUTLINE
1. Introduction
1.1 Motivation
1.2 Goals
1.3 Methods used
2. Inverse problems and their solutions
2.1 Interpretation of direct observation of divertor
2.2 Predictive modeling of the divertor stray light (DSL)
spectral line shape
2.3 Interpretation of signals from main chamber with
allowance for the DSL
3. Analysis of measurement errors
4. Validation Against Data from JET-ILW
5. Plans, Conclusions
2.1. Interpretation of direct observation of divertor
total number of
spectral channels (pixels)
normalized line shape
of measured spectrum
total number of
observation tracks
partial contribution of the
i–th fraction of atoms
partial contribution of a
certain hydrogen isotope
temperature of the i-th
fraction of atoms
Unknowns are
labeled in red
wavelength of the
Balmer-alpha line center
partial contribution of the Zeeman
pi-component to the total spectrum
Zeeman splitting
Gaussian function
isotope mass in eV
Calculating the phantom
speed of light
experimental
spectrum:
local emissivity (i.e. the
power density of the
emitted radiation)
Possible
layout of
the 16
observation
tracks
distribution of the number
of the atoms in the
projection of the velocity
in the distance x along the
viewing chord
Parameters marked with a tilde “~”, are
averaged over the solid angle of of the
observation cone associated with x.
2D distribution of the Balmer-alpha
emissivity* in the SOL and divertor in
ITER, in logarithmic scale.
* SOLPS 4.3 (B2-EIRENE) simulation
Three-temperature fitting of the phantom experimental signals
measured on the 16 lines-of-sight that directly observe the divertor
2.2. Predictive modeling of the DSL spectral line shape for a main
chamber view
partial contribution
major radius of the point of the maximum
of the Zeeman
emissivity on the track tr
-component to the
total DSL line shape (free parameter)
Parameters marked with the cap,
“^”, are the input parameters found
by solving the inverse problem for
divertor.
Comparison of the DSL spectra
calculated by a semi-analytic
model1 (black) and equation
defined above (blue)
1A.B.
Kukushkin, et al. Proc. 24th IAEA Fusion
Energy Conf., San Diego, USA, 2012, ITR/P5-44.
2.3. Interpretation of signals from main chamber
partial contribution
of the i-th
non-Maxwellian
fraction of atoms
fraction of the DSL
in the total signal
normalized line shape, which describes
the signal from the non-Maxwellian
fractions of atoms
partial contribution of the Zeeman
-component to the
total DSL line shape
subscript p indicates that the
parameter can have different values
for the inner and outer sections of
the SOL
characteristic wavelength shift, which
describes the attenuation of the
inward flux
Only new parameters are labeled
Heaviside function
Fitting the phantom experimental signals for the Da line for one main
chamber emission region (inner and outer SOL) at a time (no DSL)
Inner section of the SOL
Outer section of the SOL
Spectral resolution
is 0.005 nm
low density in the far
SOL in the L-mode
high density in the far
SOL in the H-mode
Observation track
along major radius
from equatorial port
plug, Z = 0.623 m
“Non-Maxw”
indicates the
non-Maxwellian
fraction of the VDF
OUTLINE
1. Introduction
1.1 Motivation
1.2 Goals
1.3 Methods used
2. Inverse problems and their solutions
2.1 Interpretation of direct observation of divertor
2.2 Predictive modeling of the divertor stray light (DSL)
spectral line shape
2.3 Interpretation of signals from main chamber with
allowance for the DSL
3. Analysis of measurement errors
4. Validation Against Data from JET-ILW
5. Plans, Conclusions
3. Analysis of measurement errors
Signal contains the light from the both sections of the SOL but not the DSL
Different input
(i.e. phantom
experimental)
values of the
fraction of
inner SOL light
in the signal.
Phantom inner
and outer SOL
light spectra
are show in
dashed lines,
while the
recovered
spectra are
shown in solid
lines.
The accuracy of the recovery of the fraction of inner SOL light in the
total signal (without DSL included)
Comparison with the “true“,
phantom experimental values
Six potential ITER operation
scenarios examined:
density in the far SOL
d
e
f
g
h
i
low
moderate
high
mode
L
H
L
H
L
H
The recovered value, averaged
over six scenarios, is shown in
gray curve.
Without the DSL, the absolute value of the error in estimating the
fraction of the inner SOL light in the total signal does not exceed 0.2.
The accuracy of the tritium fraction recovery in the
deuterium-tritium mixture (without DSL).
The error increases with the increasing
fraction of the inner SOL light. However, the
error can reach 100% even without any light
from the inner SOL.
One cannot recover the isotope ratio in
D+T mixture by solving the inverse
problem in its current formulation.
But for D+H mixture everything is OK.
The accuracy of recovering the inner SOL light fraction of the total SOL
light with the DSL included in the total signal
DSL fraction: 20%
DSL fraction: 40%
DSL fraction: 60%
DSL fraction: 80%
Fitting the phantom experimental signals for the 80% fraction of the DSL
and 2% fraction of inner SOL light in the total signal
Legends and
titles show
the fraction
of the inner
SOL light in
the total
SOL light
(not in the
total signal).
The solver of the inverse problem becomes confused
when distinguishing the contributions of the DSL and
the inner SOL.
This is caused by the difference between the
phantom DSL spectrum recovered from
direct observation of the divertor and the
shape from the semi-analytic formula for the
DSL (used here)
What if we would be able to simulate the DSL with a higher accuracy?
Substitution of the semi-analytic spectrum1 at all stages of the
(𝐷𝑆𝐿)
analysis, including for the phantom data (and keeping the 𝐶𝜋
a
free parameter), provides much better accuracy.
DSL fraction: 60%
DSL fraction: 80%
With increasing accuracy of the DSL, it is possible to recover the
inner and outer SOL contributions with high accuracy, even for an
(𝐷𝑆𝐿)
unknown fraction of the Zeeman pi-component, 𝐶𝜋
, and even
for the DSL fraction as high as 80%.
OUTLINE
1. Introduction
1.1 Motivation
1.2 Goals
1.3 Methods used
2. Inverse problems and their solutions
2.1 Interpretation of direct observation of divertor
2.2 Predictive modeling of the divertor stray light (DSL)
spectral line shape
2.3 Interpretation of signals from main chamber with
allowance for the DSL
3. Analysis of measurement errors
4. Validation Against Data from JET-ILW
5. Plans, Conclusions
4. Validation Against Data from JET-ILW
Theoretical model [1], suggested for the ITER H-alpha (and Visible
Light) Diagnostics, was extended and applied [2, 3] for the
interpretation of the data from the JET ITER-like wall (ILW)
experiments.
The results [2, 3] confirmed the importance of non-Maxwellian effects
for interpreting the Balmer-alpha emission from the far SOL and
suggested the necessity, for the presence of a strong DSL signal, to
incorporate data from direct observation of the divertor (the latter is
done in Sections 2-3 of the present report).
[1] A.B. Kukushkin, et al. Proc. 24th IAEA Fusion Energy Conf., San Diego, USA, 2012,
ITR/P5-44.
[2] A. B. Kukushkin, et al. AIP Conference Proceedings 1612, 97 (2014).
[3] A. B. Kukushkin, et.al. Proc. 25th IAEA Fusion Energy Conf., St. Petersburg, 2014,
EX/P5-20.
Theoretical Model of ITER High Resolution H-alpha
Spectroscopy for a Strong Divertor Stray Light and
Validation Against JET-ILW Experiments
A multi-parametric inverse problem with allowance for (i) a strong divertor stray light (DSL) on the main-chamber
lines-of-sight (LoS), (ii) substantial deviation of neutral atom velocity distribution function from a Maxwellian in the SOL
(a model for line shape asymmetry), (iii) data for direct observation of divertor.
JPN 85844: Ip=2 MA, Bt=2.8 T, Ne0=5.8 10(19) m(-3), Te0=2.6 keV, Paux(NBI)=7.5 MW, Paux(ICRH)=2 MW
• Direct observation of
1.0
aa
Counts/(s pixel),
DSL/Total=0.25
inner
Exp.
the divertor from top
total
2.0 10(5)
SOL
OuterSOL/Total=0.40
• Observation of maindivertor
0.8
Fit H/(H+D)=0.038
chamber inner wall
Non-Maxw.
along tangential and
1.5 Temperatures of
fractions
within
atomic fractions
radial LoS (KSRB
0.6 outer
warm and hot
(their fraction
Track 11) from
SOL
Maxwellians
in total intensity)
equatorial ports
1.0 1.0 eV (20%)
0.1 eV (3%)
0.4
• Analysis of HRS data
1.5 eV (30%)
6.4 eV (6%)
on resolving the power
non-Maxw: 6%
non-Maxw: 6%
24.9 eV (7%)
at D+H Balmer-a
0.5 276.6 eV (9%)
0.2
non-Maxw: 7%
spectral lines
inner
DSL
outer SOL
SOL
DSL
The results support the
0
0
expectation of a strong
Time, s 5
10
15
20
, nm
655.9
656.1
656.3
656.5
impact of the DSL upon
Fitting of measured spectrum, time 10.05 s.
Fractions of inner-wall SOL, outer-wall
H-alpha (and Visible
Asymmetry of Balmer-a spectral line shapes for
SOL, and DSL, in total signal vs. time.
Light) Spectroscopy
inner- and outer-wall SOL is due to
Normalized total power of
Diagnostic in ITER.
H+D Balmer-a emission in divertor.
non-Maxwellians (and small admixture of H).
A.B.Kukushkin, V.S.Neverov, M.F.Stamp, A.G.Alekseev, S.Brezinsek, A.V.Gorshkov,
M.vonHellermann, M.B.Kadomtsev, V.Kotov, A.S.Kukushkin, M.G.Levashova, S.W.Lisgo,
V.S.Lisitsa, V.A.Shurygin, E.Veshchev, D.K.Vukolov, K.Yu.Vukolov, and JET Contributors
A.B. Kukushkin 1 (1)
25th IAEA-FEC 2014, St. Petersburg, Russia, EX/P5-20
16/10/2014
OUTLINE
1. Introduction
1.1 Motivation
1.2 Goals
1.3 Methods used
2. Inverse problems and their solutions
2.1 Interpretation of direct observation of divertor
2.2 Predictive modeling of the divertor stray light (DSL)
spectral line shape
2.3 Interpretation of signals from main chamber with
allowance for the DSL
3. Analysis of measurement errors
4. Validation Against Data from JET-ILW
5. Plans, Conclusions
5. Plans, Conclusions
 The inverse problems are formulated for recovering the
parameters of neutral hydrogen in fusion reactors with allowance
for
 high background radiation (“divertor stray light”, DSL) and
 strong non-Maxwellian effects in the velocity distribution
function (VDF) of neutral atoms.
 Error assessment for the line-of-sight along the major radius from
the equatorial port-plug in ITER shows that further extension of
the developed approach is needed.
The recovery of these parameters requires the solution of additional
inverse problems, which should:
• incorporate the results of solving the inverse problems
formulated in the present paper,
• use the data on the background plasma (density, temperature) in
the SOL from other diagnostics in ITER,
• use available semi-analytic models for kinetics of
atomic/molecular flux from the wall (e.g., Ballistic Model [1]),
• use the bifurcated-line-of-sight measurements scheme [2],
namely, targeting at an optical dump and very close to it.
[1] M. B. Kadomtsev, V. Kotov, V. S. Lisitsa, and V. A. Shurygin, in Proc. 39th EPS
Conf. Plasma Phys., Stokholm, 2012, ECA 36F, P4.093 (2012)
[2] A.B. Kukushkin, et al. Proc. 24th IAEA Fusion Energy Conf., San Diego, USA,
2012, ITR/P5-44
Acknowledgements
The authors are grateful to
•
V.S. Lisitsa, K.Yu. Vukolov, A.V. Gorshkov, M.B. Kadomtsev, M.G.
Levashova, V.A. Shurygin, D.K. Vukolov (NRC “Kurchatov
Institute”),
•
V. Kotov (FZ Juelich),
•
E. Veshchev (ITER Organization),
•
M.F. Stamp, S. Brezinsek, M. von Hellermann (JET-Eurofusion),
for their collaboration in studies on the ITER H-alpha (and Visible
Light) Spectroscopy.