Integrated data analysis Lisbon 18/02/09 R. Coelho 1/29

Integrated data analysis

Outline

1 – Introduction

2 – Basics on integrated data analysis

3 – Overview on synthetic diagnostic research

R. Coelho

Associação EURATOM/IST, Instituto de Plasmas e Fusão Nuclear

Integrated data analysis Lisbon 18/02/09 R. Coelho 2/29

I – Introduction/Motivation

Data analysis in magnetic confinement plasmas involves dealing with different and frequently heterogeneous data sources (spatial/time scales, noise sources,…).

For 3D (R,Z,) quantities, a further obstacle arises due to mapping :

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

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

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

✗iterative procedure is necessary for profile consistency (e.g. constraints in equilibrium reconstruction: mag.+MSE+…)

✗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

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 : - 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”

The devise of any particular plasma diagnostic embeds fundamental questions :

Do I have a comprehensive knowledge of the physics ruling the events taking place in the plasma ?

Do I master the technology and methods to derive plasma parameters/profiles from my diagnostic implementation ?

Will it work ?

Synthetic diagnostic data 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 P.Strand (ITM-TF)

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III – Overview of synthetic diagnostic research

• 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

• 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

• Charge exchange (passive – no beam, active – with beam) provides very valuable information on : density, temperature, rotation and impurity content.

• Charge Exchange Analysis Package CHEAP). – 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)

• BES measures collisionally excited, Doppler- shifted neutral beam fluorescence at multiple spatial locations.

• Flectuations in spectral line Intensity plasma density fluctuations

• A spatial point spread transfer function (3D emission geometry) is applied to gyrokinetic simulations to simulated turbulence 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

)t(AC)t(AC)t(AC)t(AC

)t(AC)t(AC)t(AC)t(AC))t(2tan(

401446132312DC11

402446232322DC21

Principle

- Stark splitting effect from neutral beam atom /σ emission due to

electric field (pol. Angle //,perp to E).

- Polarisation angle retrieved by PEM modulations at 20 and 23kHz

Bvbeam

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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 2008

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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.

• Isotope separator code (thin carbon foil) to determine H/D/T composition (E and B dynamics)