Transcript Slide 1

Integrated data analysis
R. Coelho
Associação EURATOM/IST, Instituto de Plasmas e Fusão Nuclear
Outline
1 – Introduction
2 – Basics on integrated data analysis
3 – Overview on synthetic diagnostic research
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I – Introduction/Motivation
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Data analysis in magnetic confinement plasmas involves dealing
with different and frequently heterogeneous data sources
(spatial/time scales, noise sources,…).
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For 3D (R,Z,f) quantities, a further obstacle arises due to
mapping :
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Plasma equilibria given by magnetic surfaces.
These in turn depend on the plasma pressure and, therefore,
modelling of the plasma equilibrium is required.
Consistency checks
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Different diagnostic sources measuring the same quantity.
Straightforward combination based on the individual error
assignments a demanding task.
Redundancy assists validation of measurements.
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II - Basics on Integrated data analysis
Traditional approach
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Different diagnostics based on different physical process are
separately analysed and the resulting profiles are combined
by fitting a joint profile (e.g. minimising a cost function).
✓ may recover the underlying trend/profiles
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iterative procedure is necessary for profile
consistency (e.g. constraints in equilibrium reconstruction:
mag.+MSE+…)
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personalization of the software/hardware processing
burdens the process and renders it non-generic
✗ may fail in cases of systematic errors, e.g. due to
misalignments or outliers.
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Alternative approach – Integrated data analysis
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Combine all available experimental data (including
complementary), physical constraints, physical model
describing measurements and noise statistics :
 Statistical modelling of the diagnostics and the
underlying measurement process
✓ easily accommodates heterogeneous data
✓ underlying trend/profiles derived as pdf
✓ only forward modelling is necessary (no
iterations)
✓ all statistical and systematic uncertainties are
incorporated on equal grounds.
✓ washes out inconsistencies and evidences lack of
knowledge
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Iterative data analysis vs Integrated data analysis
The concept of Integrated Data Analysis of complementary experiments R. Fischer and A.
Dinklage
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Bayesian probability theory
Bayes Theorem
 Conditional probability framework
 P(A\B) is a posterior probability
 P(A) is a prior probability (ignores B exists)
With further constraints :
Source : wikipedia
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Bayesian probability theory
Bayes Theorem
Drug test :
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identify a drug user as testing positive 99% of the time
identify a non-user as testing negative 99% of the time
Prior : 0.5% of the workers take the drug
Question : given a positive test, is it a true one ?
Source : wikipedia
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Bayesian approach...concept
Fischer PPCF 44,
1501
Generalization
 P(Te,ne\d,σ,I) – pdf to find the parameters given data, noise
(σ) and other information (I)
 P(d\Te,ne,σ,I) – likelihood pdf to find the data given the
parameters, noise (σ) and other information (I)
 P(Te,ne\I) is a prior probability (boundary conditions, slope,…)
 Marginalization wrt to nuisance yields P(Te,ne\d) pdf.
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Bayesian approach...more detail
Fischer PPCF
44, 1501
Likelihood
 dk is the actual measurement.
 Dk is the ideal measurement…..but how to get it ?!
 P(Te,ne\I) is a prior probability (boundary conditions, sign,…)
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How to derive “Ideal data”
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The devise of any particular plasma diagnostic embeds
fundamental questions :
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Do I have a comprehensive knowledge of the physics ruling the
events taking place in the plasma ?
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Do I master the technology and methods to derive plasma
parameters/profiles from my diagnostic implementation ?
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Will it work ?
 Synthetic diagnostic data
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Self-consistent module, analytical/numerical model,
encapsulating all details of diagnostic implementation. The
plasma is the input.
Assists the integrated data analysis effort and to assist numerical
modelling validation.
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Integrated Device modelling approach
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III – Overview of synthetic diagnostic research
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Microwave Reflectometry
Charge exchange
Beam Emission Spectroscopy
Motional Stark Effect
Neutral particle analyser
Fast electron bremsstralung
Phase Imaging
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III – Overview of synthetic diagnostic research
Microwave Reflectometry
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Prime diagnostics for the measurement of the edge density profile
and density turbulence in ITER.
Successful measurement depends on careful optimization of the
antenna placement and geometry, combined with knowledge of
the diagnostic response function.
2D full-wave codes which model the EM-wave propagation in the
plasma in ordinary or extraordinary mode polarization may not suffice
for ITER.
European Reflectometer Code Consortium (ERCC), formed in 2007
coordinates the resources and expertise (IPP, CFN, CIEMAT, IPF,
FZJ, LPMI, LPTP and CEA). The group currently operates under the
auspices of the EFDA Integrated Tokamak Modelling task force.
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Charge exchange
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Charge exchange (passive – no beam, active – with beam)
provides very valuable information on : density, temperature,
rotation and impurity content.
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Charge Exchange Analysis Package CHEAP).
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Uses the atomic ADAS data source
CX_ simulation for the modelling of active and passive spectra plus
continuum background)
Error analysis based on instrumentation, plasma condition and beam
characteristicsc)
MSE_simulation for the modelling of Motional Stark Features (
Magnetic Field Measurements) plus the associated
Bulk-ion CXRS features (deduction of local fuel ratio
deuterium/tritium
Fast Ion CXRS simulation including anisotropic fast beam ion
velocity distribution functions and isotropic fusion alphas distribution
functions
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Beam Emission Spectroscopy (BES)
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BES measures collisionally excited, Doppler- shifted neutral
beam fluorescence at multiple spatial locations.
Flectuations in spectral line Intensity
plasma density
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fluctuations
A spatial point spread transfer function (3D emission geometry)
is applied to gyrokinetic simulations to simulated turbulence
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fluctuation spectra (k-space)
C.Holland, Comparison of Gyrokinetic Simulation Against Core Turbulence
Fluctuation Measurements via Synthetic Diagnostics
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Motional Stark Effect
Principle
- Stark splitting effect from neutral beam atom /σ emission due to
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vb eam  B electric field (pol. Angle //,perp to E).
- Polarisation angle retrieved by PEM modulations at 20 and 23kHz
tan(2(t)) 
C21ADC(t)  C22A23(t)  C23A46 (t)  C24A40 (t)
C11ADC(t)  C12A23(t)  C13A46 (t)  C14A40 (t)
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Motional Stark Effect
Modelling
- Simplified model
• “cone” line of sight and NB ray  single point emission
• δ-delta beam velocity and interference filter
- Comprehensive model
• “cone” line of sight and NB beamlet grid  emission volume
• f(v) NB velocity distribution with CX ion Fokker Planck
transport.
• Consistent interference filter finite response.
e.g. De Bock et al, REV. OF SCI. INSTRUM. 79, 10F524
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Neutral particle analyser
• A NPA attempts simultaneous measurements of energy
distribution of efflux of atoms of different hydrogen isotopes (H,
D and T) from the plasma.
• The atomic flux is produced by CX reactions between plasma
ions and thermal hydrogen isotope atoms, radiative
recombination.
• Two codes, low energy (<150keV, thermal edge recycled
dominated), and high energy (>300keV, impurity dominated) to
calculate the emissivity profile and thus the neutrals densities in
plasma.
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Isotope separator code (thin carbon foil) to determine H/D/T
composition (E and B dynamics)
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