synthetic h-alpha diagnostics for iter: inverse problems and error estimations for strong non-...

Synthetic H-alpha diagnostics for ITER: inverse problems and error estimations for strong non-

Maxwellian effects and intense divertor stray light

A.B. Kukushkin1,2, V.S. Neverov1, A.G. Alekseev1, S.W. Lisgo3, A.S. Kukushkin1,2

1National Research Centre "Kurchatov institute", Moscow, Russia2National Research Nuclear University "MEPhI", Moscow, Russia

3ITER Organization, Route de Vinon sur Verdon, St Paul Lez Durance, France

1st IAEA Technical Meeting onFusion Data Processing, Validation and Analysis

1st of June - 3rd of June 2015, Nice, France.

The views and opinions expressed herein do not necessarily reflect those of the ITER Organization

OUTLINE1. 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

• 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

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)

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

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)?

1.1 Motivation – The problem of reflections ITER has a metal wall and the divertor will be a strong source of

visible light

Plasma from SOLPS+OSM+EIRENE LightTools

50% REFLECTIVITY(25% SPECULAR, 25% DIFFUSE)

NO REFLECTIONS

[S. Kajita, 2013 PSI]

1.1 Motivation – The problem of reflections

Plasma from SOLPS+OSM+EIRENE LightTools

LINE-OF-SIGHT INTEGRALS(red rectangle)

[S. Kajita, PPCF 2013]

NO REFLECTIONS

[S. Kajita, 2013 PSI]

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)?

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 non-Maxwellian distribution, and so advanced modelling of the Balmer-alpha spectral line shapes is required

ATOM TRAJECTORIES FROM MAIN CHAMBER RECYCLING, AS CALCULATED BY THE EIRENE KINETIC CODE velocity distribution functions along specified lines-of-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.

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

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-of-

sight 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

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.

1.3. Methods and Data used

[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


1.1 Motivation

1.2 Goals

1.3 Methods used








2.1. Interpretation of direct observation of divertortotal number of spectral channels (pixels)

total number of observation tracks

normalized line shape of measured spectrum

wavelength of the Balmer-alpha line center

Zeeman splitting

partial contribution of the Zeeman pi-component to the total spectrum

Gaussian function isotope mass in eV

temperature of the i-th fraction of atoms

partial contribution of the i–th fraction of atoms

partial contribution of a certain hydrogen isotope

Unknowns are labeled in red

Calculating the phantomexperimental spectrum:

speed of light

local emissivity (i.e. the power density of the emitted radiation)

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.

Possible layout of the 16 observation tracks

* 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

Parameters marked with the cap, “^”, are the input parameters found by solving the inverse problem for divertor.

major radius of the point of the maximum emissivity on the track tr

partial contribution of the Zeeman -component to the total DSL line shape (free parameter)

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

subscript p indicates that the parameter can have different values for the inner and outer sections of the SOL

fraction of the DSL in the total signal

partial contribution of the Zeeman -component to the total DSL line shape

partial contribution of the i-th non-Maxwellian fraction of atoms

Heaviside function

normalized line shape, which describes the signal from the non-Maxwellian fractions of atoms

characteristic wavelength shift, which describes the attenuation of the

inward flux

Only new parameters are labeled

Observation track along major radius from equatorial port plug, Z = 0.623 m

Outer section of the SOL

“Non-Maxw” indicates the non-Maxwellian fraction of the VDF

Fitting the phantom experimental signals for the Da line for one main chamber emission region (inner and outer SOL) at a time (no DSL)

high density in the far SOL in the H-mode

Inner section of the SOL

Spectral resolution is 0.005 nm

low density in the far SOL in the L-mode


1.1 Motivation

1.2 Goals

1.3 Methods used








3. Analysis of measurement errorsSignal contains the light from the both sections of the SOL but not the DSL

Phantom inner and outer SOL light spectra are show in dashed lines, while the recovered spectra are shown in solid lines.

Different input (i.e. phantom experimental) values of the fraction of inner SOL light in the signal.

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 mode

dlow

L

e H

fmoderate

L

g H

hhigh

L

i 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 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 the tritium fraction recovery in the deuterium-tritium mixture (without DSL).

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%


Fitting the phantom experimental signals for the 80% fraction of the DSL and 2% fraction of inner SOL light in the total signal

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)

The solver of the inverse problem becomes confused when distinguishing the contributions of the DSL and the inner SOL.

Legends and titles show the fraction of the inner SOL light in the total SOL light (not in the total signal).

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 analysis, including for the phantom data (and keeping the a free parameter), provides much better accuracy.

With increasing accuracy of the DSL, it is possible to recover the inner and outer SOL contributions with high accuracy, even for an unknown fraction of the Zeeman pi-component, , and even for the DSL fraction as high as 80%.



1.1 Motivation

1.2 Goals

1.3 Methods used








[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 [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).

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.

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

• Direct observation of the divertor from top

• Observation of main-chamber inner wall along tangential and radial LoS (KSRB Track 11) from equatorial ports

• Analysis of HRS data on resolving the power at D+H Balmer- spectral lines

The results support the expectation of a strong impact of the DSL upon H-alpha (and Visible Light) Spectroscopy Diagnostic in ITER.

Fitting of measured spectrum, time 10.05 s. Asymmetry of Balmer- spectral line shapes for

inner- and outer-wall SOL is due to non-Maxwellians (and small admixture of H).

Fractions of inner-wall SOL, outer-wall SOL, and DSL, in total signal vs. time.

Normalized total power of H+D Balmer- emission in divertor.

Theoretical Model of ITER High Resolution H-alpha Spectroscopy for a Strong Divertor Stray Light and

Validation Against JET-ILW Experiments

A.B. Kukushkin 1 (1) 25th IAEA-FEC 2014, St. Petersburg, Russia, EX/P5-20 16/10/2014

Time, s 5 10 15 20

aa1.0

0.8

0.6

0.4

0.2

0

DSL

inner SOL

outer SOL

totaldivertor

, nm 655.9 656.1 656.3 656.5

DSL

inner SOL

outer SOL

Exp.

Fit

Counts/(s pixel),10(5)

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

2.0

1.5

1.0

0.5

0

1.0 eV (20%)6.4 eV (6%) non-Maxw: 6%276.6 eV (9%)

Temperatures of atomic fractions (their fractionin total intensity)

0.1 eV (3%)1.5 eV (30%) non-Maxw: 6%24.9 eV (7%) non-Maxw: 7%

Non-Maxw.fractions within warm and hot Maxwellians

DSL/Total=0.25OuterSOL/Total=0.40H/(H+D)=0.038


1.1 Motivation

1.2 Goals

1.3 Methods used









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.

synthetic h-alpha diagnostics for iter: inverse problems and error estimations for strong non-...

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