École polytechnique fédérale de Lausanne (Suisse)

Faculté des sciences de base Section de physique Russian Research Center (RRC) Курчатовский институт

Nuclear Fusion Institute (NFI) Diagnostics Group

Diploma work / дипломная работа

Radiation loss studies on T-10 tokamak using AXUV-detectors

Christian Schlatter / Кристиан Шлаттер

Marshal Biruzova street 36 / Улица Маршала Бирюзова, 36 RUS-123060 Moscow / 123060, Москва Russia / Россиа

2003, 17^{th} of March / 17. Март 2003 г.

Made with L^{A}TEX 2ε

\underline{ii}

The St Basil’s Cathedral (on the right, built 1555 - 1561) and the Moscow Kremlin (1475-1516) at night.

Diploma student:

Russian supervisor:

Swiss supervisor:

Russian tutor:

Christian Schlatter^{(1)} student in physics at the Swiss Federal Institute of Technology. Prof. Dr. Yurij Dnestrovskij Professor of plasma physics at the Moscow State University, Moscow. Prof. Dr. Minh Quang Tran professor of plasma physics and director of the Research Center of Plasma Physics in Lausanne, Switzerland. Dr. Leonid N. Khimchenko Chief of the T-10 diagnostics group. Dr. Natalia N. Timchenko Member of the T-10 diagnostics group.

The diploma work was performed at the Russian Research Center (RRC), Курчатовский институт, Nuclear Fusion Institute (NFI) in Moscow from November 2002 to March 2003.

This diploma report has been submitted on 17^{th} of March, 2003. The work was presented at the Russian Research Center on 27^{th} of March, 2003.

(1) christian@slatersoft.com Diploma work 2002-2003  Christian Schlatter

Abstract

An array of fast bolometers based on Absolute eXtreme UltraViolet (AXUV) silicon photodiodes covering the plasma cross-section of the T-10 tokamak was calibrated and successfully used for the measurement of the total radiated power as well as for the reconstruction of the radial plasma emissivity distribution by an algebraic Abel inversion method.

The present setup consists of a 16 channel pinhole camera providing a radial resolution of approximately 4 cm in the center of the vessel. The data acquisition system can resolve fast processes down to less than 20 μs.

The suitability of the semiconductor-based detector in the thermonuclear environment of T-10 was carefully checked by analyzing its behavior shown in a variety of plasma discharges but also by characterization of the detectors response after 18 months of operation on the tokamak.

Different regimes of better confinement (T-10 H-mode, density limit, biasing) investigated in recent experimental campaigns were studied and the important contribution of AXUV as valuable diagnostic facility for the further understanding of localized radiation processes was demonstrated. The outstanding fast temporal resolution allows to study short timescale processes, for example the injection of fast pellets - what cannot be performed by other diagnostics.

In view of the promising results of AXUV-diagnostics the installation of a second detector array is planned for the near future.

Keywords: Radiation processes, AXUV-detector, fast bolometry, detector calibration, T-10 confinement regime, plasma emissivity, neutral power, pellet injection, algebraic Abel inversion.

Un assemblage de bolomètres rapides basés sur des diodes photosensibles fabriquées en silicium (du type Absolute eXtreme UltraViolet, d’abréviation AXUV) qui couvrent une coupe poloïdale du plasma ont été calibrées et utilisées avec succès pour la mesure de la puissance totale rayonnée ainsi que pour le calcul de la distribution radiale de l’émissivité du plasma en utilisant une inversion d’Abel algébrique.

La configuration actuelle est composé d’une camera regroupant seize canaux d’acquisition ayant une résolution spatiale d’environ 4 cm dans le centre du vaisseau. L’électronique de mesure rend possible l’observation de processus rapides d’une durée de moins que 20 μs.

La compatibilité d’un détecteur semi-conducteur avec un environnement thermonucléaire comme le T-10 a été soigneusement etudiée en analysant le comportement des signaux mesurés dans des décharges différentes et par la caractérisation de la sensibilité des détecteurs après les avoir utilisés pendant 18 mois sur le tokamak.

Plusieurs types d’opération manifestant une inclusion améliorée du plasma (c.-à-d. le mode H T-10, la densité limitée ainsi que le biasing) réalisés récemment ont été étudiés et le rôle important en tant que diagnostique très utile pour la compréhension de processus de radiation localisés a été démontré. D’une résolution temporelle excellente, la technologie AXUV permet l’étude de phénomènes de très courte durée, par exemple l’injection de pastilles à grande vitesse - une analyse qui n’est pas possible avec un autre diagnostique.

En raison des résultats plein de promesses, l’installation d’une deuxième unité de détecteurs AXUV est envisagé dans un proche avenir.

Mots clés: Processus de radiation, détecteurs AXUV, bolometrie rapide, calibration de détecteurs, types d’opération de T-10, émissivité du plasma, puissance des neutres, injection de pastilles, inversion d’Abel algébrique.

Eine Anordnung schneller Bolometer auf der Basis von Absolute eXtreme UltraViolet (AXUV) Silizium-Photodioden, welche einen poloidalen Querschnitt des T-10 Tokamaks abdecken, wurde kalibriert und erfolgreich für die Messung der insgesamt abgestrahlten Plasmaleistung sowie zur Rekonstruktion der radialen Plasmaemissivitätsverteilung mittels einer algebraischen Abel-Inversionsmethode verwendet.

Der aktuelle Aufbau besteht aus einer Kamera obscura mit 16 Kanälen mit einer räumlichen Auflösung von ungefähr 4 cm im Zentrum des Torus. Die Elektronik der Datenerfassung kann schnelle Prozesse mit bis zu 20 μs auflösen.

Die Verwendbarkeit von Halbleiterdetektoren in der thermonuklearen Umgebung von T-10 wurde anhand von verschiedenen Plasmaentladungen sorgfältig studiert. Nach 18 Monaten im Einsatz auf dem Tokamak wurde kein nennenswerter Sensibilitätsverlust der Detektoren festgestellt.

Verschiedene Typen von Plasmaentladungen mit verbessertem Einschluss (T-10 typischer H-Modus, Dichtelimit, Biasing) aus unlängst realisierten Experimenten wurden analysiert und die wichtige Rolle der AXUV-Detektoren zum Verständnis von lokalisierten Plasmastrahlungsprozessen wurde klar aufgezeigt. Die herausragend hohe zeitliche Auflösung macht das Studium von schnellen Phänomenen (z.B. das Einschiessen von Pellets) erst möglich.

In Anbetracht der vielversprechenden Resultate wird die Installation einer weiteren AXUV-Kamera fü die nähere Zukunft ins Auge gefasst.

Schlüsselwörter: Strahlungsprozesse, AXUV-Detektoren, Schnelle Bolometrie, Kalibrierung der Detektoren, Plasmaemissivität, Leistungsverlust durch neutrale Teilchen, Pelleteinschuss, algebraische Abel-Inversion.

Contents

1 Introduction 1 1.1 Goals, content and organization of the present work . . . . . . . . . . . . . . . . 1 1.2 The T-10 tokamak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Main diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Radiation from a tokamak plasma 4 2.1 Braking radiation (Bremsstrahlung) . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Recombination radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Line radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Cyclotron radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Total power radiation from a tokamak plasma . . . . . . . . . . . . . . . . . . . 8

3 Detectors for registration of plasma radiation 10

3.1 Thermal bolometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metal foil bolometers [60] . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Pyroelectric bolometer [2] . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 AXUV detector [1], [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Scheme of the diagnostics for radiation loss measurements on T-10 17 4.1 Setup on T-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Parameters of AXUV detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.3 Pinhole camera with a 16 channels AXUV-detector . . . . . . . . . . . . . . . . 17

4.3.1 The geometry of the cones of view . . . . . . . . . . . . . . . . . . . . . . 17 4.3.2 The aperture slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.4 Multichannel data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4.1 The preamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4.2 Analog-digital converter (ADC) . . . . . . . . . . . . . . . . . . . . . . . 24

5 Estimation of the absolute values of the total radiated power 25 5.1 Absolute translation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Simulation of a radial distribution of the emissivity 30 6.1 The abelization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.2 Reconstruction of the plasma emissivity . . . . . . . . . . . . . . . . . . . . . . . 31 6.3 Extension of the parallel stripe method . . . . . . . . . . . . . . . . . . . . . . . 33 6.4 One example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Diploma work 2002-2003  i  Christian Schlatter

7 Calibration and checking of the parameters of the diagnostics system 34

7.1 Relative calibration in the laboratory . . . . . . . . . . . . . . . . . . . . . . . . 34

7.1.1 Relative calibration coefficients . . . . . . . . . . . . . . . . . . . . . . . 35 7.2 Checking of the AXUV-detectors using data from the pyroelectric detector … 36

7.2.1 Calibration of the pyroelectric bolometer . . . . . . . . . . . . . . . . . . 36 7.2.2 Checking of the flat AXUV-responsitivity range . . . . . . . . . . . . . . 38 7.2.3 Checking of the AXUV-responsitivity hole . . . . . . . . . . . . . . . . . 40 7.2.4 Measurement of low-energy responsitivity after operation . . . . . . . . . 43

7.3 Calculation of the yearly radiation dose . . . . . . . . . . . . . . . . . . . . . . . 43

8 Experimental radiation losses studies 44

8.1 Introductory notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 8.1.1 Profiles of temperature and density . . . . . . . . . . . . . . . . . . . . . 44 8.1.2 Detector discrepancy ξ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 8.1.3 Evaluation of impurities using the plasma emissivity . . . . . . . . . . . . 45 8.1.4 General sequence of a T-10 discharge . . . . . . . . . . . . . . . . . . . . 45

8.2 Spatial evolution of radiated power in regimes with improved confinement …. 46 8.2.1 Density limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 8.2.2 T-10 H-mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 8.2.3 Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

8.3 Comparison of AXUV with pyroelectric bolometer . . . . . . . . . . . . . . . . . 61 8.3.1 Disturbance of the pyroelectric bolometer by gyrotrons . . . . . . . . . . 63 8.3.2 Underestimation of radiation in the AXUV-responsitivity hole . . . . . . 64 8.3.3 Limited field of view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 8.3.4 Top-down asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 8.3.5 Power carried by neutrals . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8.4 Partial radiation evaluation: Neon puffing . . . . . . . . . . . . . . . . . . . . . 67 8.5 Localized and/or fast features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

8.5.1 Sawteeth oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.5.2 Pellet injections (revisited) . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.5.3 Diagnostic neutral beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 8.5.4 Arcing of iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 8.5.5 Pieces of the wall falling into the plasma . . . . . . . . . . . . . . . . . . 77 8.5.6 Disruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 8.5.7 AXUV as plasma displacement diagnostics . . . . . . . . . . . . . . . . . 79

9 Conclusion and outlook 81

A Compensation of the capacitance of the AXUV-photodiodes 83

B Calculation of the ohmic heating input power 85

C Calculation of Z_{eff} 87 C.1 Derivation from AXUV-signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 C.2 Derivation from plasma resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . 87 C.3 Derivation from continuum radiation . . . . . . . . . . . . . . . . . . . . . . . . 88

D Calculation of temperature profiles 89

E Realized programs 90

List of Figures

1.1 Position of diagnostics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Correspondence principle applied to the radiation distribution. . . . . . . . . . . 6 2.2 Average ion model radiation factors. . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Layering of the AXUV-detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Quantum efficiency of the AXUV-detector. . . . . . . . . . . . . . . . . . . . . . 14 3.3 AXUV-responsitivity as a function of photon energy. . . . . . . . . . . . . . . . 15 3.4 Stability of quantum efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1 Setup of bolometers on T-10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 AXUV pinhole camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Poloidal opening angle β_{P,i}. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.4 Flange for diagnostics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.5 Flange width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.6 Toroidal opening angle β_{T,i}. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.7 Aperture slit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.8 Block diagram of the AXUV data acquisition system. . . . . . . . . . . . . . . . 23 4.9 Circuit schematic of the photodiode and the preamplifier. . . . . . . . . . . . . . 24

5.1 Symmetry line location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Absolute translation factors G_{i}. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6.1 Line integration of the emissivity along the chord. . . . . . . . . . . . . . . . . . 31 6.2 Definition of the pixels for inversion. . . . . . . . . . . . . . . . . . . . . . . . . 32 6.3 Shot #31899 (high-current H-mode). Chord signals and emissivity. . . . . . . . 33

7.1 Calibration with lamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.2 Calibration profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 7.3 Relative calibration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 7.4 Checking of calibration of pyroelectric bolometer I. . . . . . . . . . . . . . . . . 37 7.5 Checking of calibration of pyroelectric bolometer II. . . . . . . . . . . . . . . . . 37 7.6 Checking of calibration of pyroelectric bolometer III. . . . . . . . . . . . . . . . 38 7.7 Checking of calibration of AXUV detectors I. . . . . . . . . . . . . . . . . . . . 39 7.8 Checking of calibration of AXUV detectors II. . . . . . . . . . . . . . . . . . . . 39 7.9 Checking of calibration of AXUV detectors III. . . . . . . . . . . . . . . . . . . 40 7.10 Carbon film on the detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 7.11 Neon spectrum on ASDEX-Upgrade. . . . . . . . . . . . . . . . . . . . . . . . . 41 7.12 Neon gas puff on T-10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.13 Relative power change due to Neon gas puff. . . . . . . . . . . . . . . . . . . . . 42 7.14 Measurement of AXUV responsitivity at 1.96 eV. . . . . . . . . . . . . . . . . . 43

Diploma work 2002-2003  iii  Christian Schlatter

8.1 Shot #35886 (pellet injected density limit). Radiation, density and temperature. 47 8.2 Shot #35886 (pellet injected density limit). Several parameters. . . . . . . . . . 48 8.3 Shot #35811 (gas puffed density limit). Radiation, density and temperature… 50 8.4 Shot #35811 (gas puffed density limit). Several parameters. . . . . . . . . . . . 51 8.5 Shot #31899 (high current T-10 H-mode). Radiation, density and temperature. 53 8.6 Shot #31899 (high current T-10 H-mode). Several parameters. . . . . . . . . . . 54 8.7 Shot #35838 (low current T-10 H-mode). Radiation, density and temperature. . 56 8.8 Shot #35838 (low current T-10 H-mode). Several parameters. . . . . . . . . . . 57 8.9 Shots #34631 (with biasing) and #34632 (without). Radiation, density and

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 8.10 Shots #34631 (with biasing) and #34632 (without). Several parameters. . . . . 60 8.11 Review of discrepancy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 8.12 Shot #35579. Increasing discrepancy with gyrotrons. . . . . . . . . . . . . . . . 63 8.13 Shot #34593. Importance of the C^{III} radiation channel. . . . . . . . . . . . . . 65 8.14 Shot #35886 (gas puffed density limit). Neutral power. . . . . . . . . . . . . . . 66 8.15 Shot #34596 (neon gas puff). Radiation, density and temperature. . . . . . . . 67 8.16 Shot #35909. Sawteeth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.17 Shot #35886. Deuterium pellet evaporation I. . . . . . . . . . . . . . . . . . . . 69 8.18 Shot #35886. Deuterium pellet evaporation II. . . . . . . . . . . . . . . . . . . . 70 8.19 Shot #35886. Deuterium pellet evaporation III. . . . . . . . . . . . . . . . . . . 70 8.20 The geometry of the snake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.21 Shot #35886. Fast signal time scale comparison. . . . . . . . . . . . . . . . . . . 72 8.22 Shot #35908. Deuterium pellet evaporation IV. . . . . . . . . . . . . . . . . . . 73 8.23 Shot #35908. Deuterium pellet evaporation V. . . . . . . . . . . . . . . . . . . . 74 8.24 Shot #31586. Low velocity lithium pellet. . . . . . . . . . . . . . . . . . . . . . 74 8.25 Shot #35771. Neutral beam I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 8.26 Shot #35771. Neutral beam II. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 8.27 Shot #35771. Neutral beam III. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 8.28 Shot #31615. Iron by arcing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 8.29 Shot #35847. Impurity film detachement. . . . . . . . . . . . . . . . . . . . . . 78 8.30 Shot #35904. Disruption at high density. . . . . . . . . . . . . . . . . . . . . . . 78 8.31 Shot #36048. Horizontal displacement (Displacement diagnostics). . . . . . . . . 79 8.32 Shot #36048. Horizontal displacement (AXUV-detectors). . . . . . . . . . . . . 79

A.1 Theoretical bode diagram of the preamplifier. . . . . . . . . . . . . . . . . . . . 83

B.1 Plasma current and loop voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . 85 B.2 Induction voltage and voltage without inductive parts. . . . . . . . . . . . . . . 86

List of Tables

5.1 Absolute translation factors G_{i}. The factors include relative calibration (f_{i}). G_{i} relates the database values to the total radiated power. . . . . . . . . . . . . 28

8.1 Z_{eff} for shot #35886 calculated from the AXUV signals and by classical Spitzer

formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.2 Z_{eff} for shot #35838 calculated from the AXUV signals and by classical Spitzer

formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 8.3 Z_{eff} for shots #34631 and #34632 calculated from the AXUV signals and by

classical Spitzer formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Diploma work 2002-2003  v  Christian Schlatter

Chapter 1

Introduction

For the development and successful operation of a future thermonuclear reactor producing energy it is of upmost importance to control the power losses of the magnetically confined plasma. In an ideal pure deuterium ^{(1)} plasma, power losses do not prevent its ignition, but only traces of heavier impurity species are enough to do so. Today, the semiconductor industry offers highspeed photodiodes (so-called AXUV devices) which are suitable for radiation measurements in thermonuclear environments and which permit to make measurements with much higher time resolution than the classically used metal foil bolometers. AXUV technology has already been installed and reported on several tokamaks for many years (Alcator C-mod [30], TCV [38], DIII [39], NSTX [37], [41], CDX-U [40], HBT-EP [35] and others). On T-10 a first AXUV-array was in operation since 2001 and experimental data for different confinement regimes is now available.

1.1 Goals, content and organization of the present work

This diploma work is composed of two parts. In a first stage the literature of radiation processes in tokamak plasmas and the existing detectors for the registration of plasma radiation was reviewed. The second and main part consisted of experimental radiation investigations using semiconductor detectors (AXUV-detectors) mounted on the Russian T-10 tokamak. After careful calibration of the measurement system, different confinement and operation regimes have been investigated. Interpretation of the reconstructed plasma power emissivity profiles was attempted using temperature and density profiles and further time-dependent measurements. In the aim to show the strong points and new possibilities of this latest generation diagnostics, various quick processes have been analyzed. Possible shortcomings of the new detector technology were analyzed carefully to discuss their importance for measurements in a thermonuclear environment.

The report of the diploma work is structured as follows. The rest of this chapter shortly presents the parameters of the T-10 tokamak and the used diagnostics. The next chapter reviews the radiation processes found in a typical plasma of present-day fusion reactors. The third chapter is dedicated to detector principles for the measurement of radiated power. Mainly metal foil (owing to their wide dissemination), pyroelectric bolometer (applied on T-10) and AXUV-technology (topic of the present work) are discussed. Chapter 4 describes the AXUVdetector setup on T-10, including parameters of the used photodiodes, the pinhole camera and the data acquisition system. Using the given geometry of setup and plasma discharge, the total radiated power is estimated in chapter 5. A further chapter describes the abelization of chord signals (calculation of the emissivity profile). Chapter 7 gives evidence of the careful calibration of the whole diagnostic system, necessary for the successful discussion of the regimes of improved confinement in chapter 8. This last main chapter also documents the features of AXUV-technology and tries to weigh up its deficiencies. Several appendices clarify the applied calculations of the ohmic heating power, the effective charge and temperature profiles. The last appendix lists the algorithms written in the frame of this work.

(1) later also Helium.

Diploma work 2002-2003  1  Christian Schlatter

1.2 The T-10 tokamak

T-10 is a classic tokamak, in operation since 1975, with circular cross section, major radius R = 1.5 m, a full poloidal graphite ring limiter at a minor radius of a = 0.33 m and a graphite mushroom-shaped limiter at the bottom of the vessel at a_{L} = 0.30 m. The vacuum vessel (pressure 10^{−7} Torr) of T-10 is a torus of circular cross-section (radius of 0.387 m) whose walls are made of iron tiles. Discharges have pulse duration of 1 s. The plasma is fuelled by deuterium. Electron densities lie in the range of n_{e} = 10^{9} .. 10^{14} cm^{−3}, the toroidal magnetic field can take values up to B_{T} = 2.5 T, the plasma current up to I_{P} = 330 kA. Auxiliary electron-cyclotron resonant heating (ECRH) power P_{ECRH} produced by four gyrotrons^{(2)} can provide up to 1.5 MW. ECRH power pulses have a length of 400 ms. A magnetic field of B_{T} = 2.42 T corresponds to on-axis heating.

1.2.1 Main diagnostics

The detectors for power losses measurements (pyroelectric bolometer and AXUV photodiodes, both in toroidal cross-section (C.S.) D) will be described in detail in section 3. Spectroscopic measurements are available for deuterium (D_{α}) and carbon (ionization stage C^{2+} only). Density profiles are obtained by abelization of chord measurements with microwaves, temperature is analyzed by the second harmonic of electron-cyclotron emission measurements (calibration described in appendix D). Two soft X-ray are available (one (B) looking horizontally inside the vessel, another (A) vertically, both installed in cross-section D). Further diagnostics provide continuum radiation (C.S. C), loop voltage, plasma current, a signal proportional^{(3)} to β + ℓ_{i}/2, visible light, horizontal plasma displacement and many others but not used in the frame of this work. Figure 1.1 gives an overview on position and configuration of some diagnostics.

(2)

Three of them at different cross sections (A, B, C, see figure 1.1) working at f = 140 GHz (400 kW each),

the fourth (called A5, in C.S. A) at 130 GHz (300 kW). The waves are injected horizontally to the center.

(3) ℓ_{i} is the inductance of the plasma.

Diploma work 2002-2003  Christian Schlatter

1.2 The T-10 tokamak  3

Figure 1.1: Toroidal and poloidal position of diagnostics. The left figure shows the placement of the diagnostics, gyrotrons and gas puff valve on the four cross-sections A, B, C and D. On the right approximately the poloidal positions and fields of view of diagnostics in cross-section C (red) and D (blue).

Radiation from a tokamak plasma

The spectrum of electromagnetic radiation emitted by a tokamak plasma is composed of lines and continuum over a wide range of energies. Atoms and partially stripped (i.e. not fully ionized) ions immersed in the plasma emit continuous and discrete spectra (i.e. lines). Unbound electrons emit continuous spectra, the structure of their emission is affected by interactions with the plasma particles and hence depends on the thermodynamic properties of these particles.

The next sections review quickly the radiation processes occurring in a typical tokamak plasma, namely the braking radiation, the recombination radiation, the line radiation and the synchrotron radiation.

2.1 Braking radiation (Bremsstrahlung)

Bremsstrahlung is due to the scattering of a free electron by a ion. The coulomb force between the two particles necessitate the electron to brake, hence the deceleration leads to emission of electromagnetic radiation which is described by the retarded potentials of Lienard and Wiechert [4]. The high electron temperature in tokamak plasmas principally needs a quantum mechanic treatment but semiclassical approach is standard, done by Kramers in 1923 [6]. Kramers gives the power p_{Br} radiated per unit of frequency ω and volume by a single electron of initial velocity v_{e} scattered by a random set of ions of nuclear charge Z and of density n_{i} by

\frac{dp_{Br}}{dω} = \frac{16π · Z^{2} · e^{6} · n_{i}}{3\sqrt{3} · (4πϵ_{0})^{3} · m_{e}^{2} · v_{e}} · G_{ff}  (2.1)

where G_{ff} is the free-free Gaunt factor, given for example in [6] (parameter of order of 1). To obtain the total radiated power per unit of volume caused by a distribution f of electrons of density n_{e} the calculation of

p_{Br} = n_{e} ∫ ∫_{0}^{∞} f(v) · \frac{dp_{Br}}{dω} · dv · dω  (2.2)

gives, taking a Maxwellian distribution of the electrons

p_{Br} = n_{e} · n_{i} · Z^{2} · (\frac{e^{2}}{4πϵ_{0}} )^{3} \frac{16π}{3\sqrt{3} · m_{e}^{2} · c^{3}} \sqrt{\frac{2m_{e}}{πT_{e}}} ∫_{0}^{∞} exp (−\frac{ℏω}{T_{e}} ) · G_{ff} · dω  (2.3)

Diploma work 2002-2003  4  Christian Schlatter

thus intensity is high for ℏω ⩽ T_{e}. Setting G_{ff} = 1 and considering the presence of several species of ions in the plasma, globally described by the effective charge number Z_{eff} given by

Z_{eff} = \frac{1}{n_{e}} ∑_{i} n_{i} · Z_{i}^{2}  (2.4)

the final result is

p_{Br} = 1.53 × 10^{−38} · n_{e}^{2} · Z_{eff} \sqrt{T_{e}} [W/m^{3}]  (2.5)

with the electron temperature given in eV. The last equation shows that the braking radiation increases with the square of n_{e} and with Z_{eff}. The presence of heavy impurity elements leads therefore to a higher braking radiation loss.

2.2 Recombination radiation

By ionization, the previously bound electron gets free. The inverse process, when a ion catches an electron, is called recombination.

If a collision between an electron and a ion of relative velocity v_{r} with parabolic impact parameter b is so that its kinetic energy is higher than the n^{th} state energy ℏω_{n} of the ion, the electron will be free and its deceleration leads to emission of braking radiation as described in the previous section. In the opposite case recombination takes place resulting in an bound electron. Light elements, but also heavier impurities which are not fully ionized may capture electrons. The energy of the radiation is

E_{rec} = ℏω = \frac{1}{2} · m_{e} · v^{2} + \frac{R_{y} · Z^{2}}{n^{2}}  (2.6)

with the Rydberg R_{y} = \frac{e^{4}m}{2(4πϵ_{0}h)^{2}} = 13.6 eV. To avoid a difficult quantum mechanical approach, Kramers applied Bohr’s correspondence principle by assuming that ”a certain frequency interval in the radiation emitted on the classical theory corresponds with a process by which the electron is bound in a certain stationary state” [6].

Therefore, as illustrated in figure 2.1, the radiation takes place on the n^{th} line in the frequency range

\frac{1}{2} · m_{e} · v^{2} + \frac{R_{y} · Z^{2}}{(n + \frac{1}{2})^{2}} ⩽ ℏω_{n} ⩽ \frac{1}{2} · m_{e} · v^{2} + \frac{R_{y} · Z^{2}}{(n − \frac{1}{2})^{2}}  (2.7)

The line has a frequency width of

△ω_{n} = \frac{2 · R_{y} · Z^{2}}{ℏ · n^{3}}  (2.8)

and the energy in the n^{th} line for any impact parameter b is given by

\frac{dW (b, v_{e})}{dω} · △ω_{n}  (2.9)

For the integration over all impact parameters b the result of Kramers given in the previous section can be applied again. As suggested by equation 2.9 this corresponds to multiply equation

Figure 2.1: Correspondence principle applied to the radiation distribution. The green curve represents distribution in the quantum problem, red curve shows classical radiation. Below ν_{0} = \frac{1}{2}m_{e}v^{2} (in blue) both curves coincides. The radiated energy (i.e. the surface under the curves) in a frequency interval as defined by equation 2.7 are equal for classical and quantum description.

2.1 by equation 2.8. Further the integration over velocities of a Maxwell distribution of the electrons^{(1)} yields the radiation from recombination per unit volume as

p_{rec} = n_{e} · n_{i} · Z^{2} (\frac{e^{2}}{4πϵ_{0}} )^{3} \frac{16π}{3\sqrt{3} · m_{e}^{2} · c^{3}} \sqrt{\frac{2m_{e}}{πT_{e}}}

× ∫_{0}^{∞} H (ℏω − \frac{Z^{2}R_{y}}{n^{2}} ) · exp (−\frac{ℏω}{T_{e}} ) · [\frac{Z^{2} · R_{y}}{T_{e}} \frac{2}{n^{3}} · G_{n} · exp (\frac{Z^{2} · R_{y}}{n^{2} · T_{e}} )] · dω (2.10)

where H(x) is the heaviside function. By then for low frequencies only high n give a contribution. Steps occur whenever the argument of the heaviside function attains equality (at the recombination edges). This is when the next energy level starts to contribute.

Formula 2.6 shows that each captured electron leads to the emission of a distinct line in the frequency spectrum, but since the velocities v_{e} of the electrons are distributed by a Maxwellian, the superposition of all these lines results in a continuous spectrum.

(1) for level n by using the expression v_{e} = \sqrt{2(ℏω − Z^{2}R_{y}/n^{2})/m_{e}} Diploma work 2002-2003  Christian Schlatter

2.3 Line radiation

The emission of line radiation is due to the transition of electrons between bound states of an atom or ion. Completely ionized ions have lost all their electrons. In a tokamak plasma always some partially stripped ions can be found. At the edge of the plasma the temperature is only about 10 eV and therefore even atoms with low charge number Z as deuterium may not be fully ionized here (recombination occurs). Impurities like carbon (C, Z = 6), iron (Fe, Z = 26) or wolfram (W, Z = 74) have intermediate and high Z and recombination can take place even in the hot center of the plasma, where temperatures of some keV can be found. Their intake is unavoidably related to the interactions of the plasma with the vacuum chamber, the limiter or diagnostic probes. Line radiation is the most important process for power being lost by radiation. Already very small impurity concentrations (1 % of iron or 0.1 % of tungsten [7]) can lead to the loss of the whole heating power.

Considering the elevated number of possible transitions of electrons and several species of impurities being involved, the total line radiation enclose a large range of energies and of different intensities. The line power density is given by summation over all elements and states

p_{line} = ∑_{element} ∑_{state} n_{e} · n_{Z} ∑_{i,j} ℏω_{ij} \frac{A_{ij}}{∑_{k⩽j} A_{ik}} ⟨σ_{ij} · v_{e}⟩  (2.11)

where A_{ij} are the transition probabilities and the average ⟨·⟩ is done over the distribution of electrons. The cross section σ_{ij} for electron excitation by dipole allowed transition i → j is given by [5]

σ_{ij} = 2.36 × 10^{−13} \frac{f_{ij} · G(i, j)}{ϵ · △E_{ij}}  (2.12)

with f_{ij} the oscillator strength, G(i, j) the gaunt factors, ϵ the incident electron energy and △E_{ij} = E_{i} − E_{j}.

In a plasma of weak density the rate of transitions from lower to higher energy levels due to collisions is smaller than the spontaneous rate of de-excitation, so that the density of excited states is small compared to the ground state. The population of the levels is therefore not described by a Boltzmann distribution.

2.4 Cyclotron radiation

Charged particles (mass m, charge q, density n and velocity v) are trapped by magnetic fields by following circular orbits around the magnetic field lines (cyclotron motion). The central acceleration is exerted by the Lorentz force

m · a_{r} = q · \frac{v}{c} · B  (2.13)

This leads to radiation according to the non-relativistic Larmor formula [4]

P = \frac{2}{3} \frac{q^{2}}{c^{3}} · a_{r}^{2}  (2.14)

Mainly electrons show a high level of cyclotron radiation. For a Maxwellian distribution the combination of equation 2.13 and 2.14 gives the the radiated power density

p_{cyclo} = 6.2 × 10^{−22} · n_{e} · T_{e} · B^{2} [\frac{W}{m^{3}} ]  (2.15)

with the temperature given in eV. This power is not entirely lost, since the major part of the radiation is reabsorbed by the plasma [18]. In today tokamaks the cyclotron radiation gives a neglectful small contribution to the total radiated power. But in future reactors like ITER cyclotron radiation will be an important radiation loss channel [19].

2.5 Total power radiation from a tokamak plasma

The exact calculation of the radiation emitted from tokamak plasmas requires a careful treatment of the atomic physics processes for each ionization stage and the solution of a large set of coupled rate equations for all present ionic species. A useful simplification replaces the different ionic species for each element by a single artificial average ion [8], given by the statistical average of all possible charge states. The time-dependent averaged principal shell populations \overline{P}_{n} are determined by the solution of a set of nonlinear related rate equations

\frac{d}{dt}\overline{P}_{n} = S_{n} − L_{n}  (2.16)

where S_{n} is the rate at which electrons are added to the n^{th} shell by

- dielectronic, radiative and three-body recombination,

- collisional transitions from other shells,

- radiative decay from a higher shell,

and L_{n} is the rate at which electrons are removed from the n^{th} shell by

- collisional transitions to other shells,

- radiative decay to lower shells and

- collisional ionization.

Equation 2.16 is iterated until steady state is achieved. In this so called coronal equilibrium of the average ion, the radiation due to Bremsstrahlung, recombination and line transitions is determined.

Such calculation have been presented in [9] and [10] for a wide range of elements, in [45] even for individual ionization stages. The results are available in temperature dependent radiation factors R(T_{e}, Z) permitting the calculation of the total radiation power density by

p_{line}(Z) = n_{e} · n_{Z} · R(T_{e}, Z)  (2.17)

Figure 2.2 shows the radiation factors for carbon, iron, lithium, oxygen and neon.

Light elements radiate at low energy, heavier like Fe at higher energies and there much more. Lighter elements are already fully ionized at these temperatures and don’t contribute to the radiation anymore. However, the corona model doesn’t consider ion transport. The ion may have left the plasma before the equilibrium is achieved [9]. Better models should bear the ion transport in mind.

2.5 Total power radiation from a tokamak plasma  9

Figure 2.2: Average ion model radiation factors. The radiation factors for iron, carbon, lithium, neon and oxygen are shown. The curves have been plotted using the least square fit coefficients given in [10].

Detectors for registration of plasma radiation

The knowledge of the total radiated power is essential for the control and understanding of the power balance in the tokamak. An assembly of multichannel bolometers viewing inside the vessel through a pinhole camera and whose chords are covering the whole cross section of the reactor, permit the reconstruction of the emissivity profile with sufficient spatial and temporal resolution.

The fraction P_{i} of total emitted power measured by detector i coming from the area covered by the detectors field of view which is given by its solid angle Ω_{i} is

P_{i} = ∫ dr⃗ ε(r⃗) \frac{Ω_{i}(r⃗)}{4π}  (3.1)

The total radiated power is obtained by integrating the emissivity ε(r⃗) over the cross section of the tokamak or by summing up equation 3.1 for all detectors.

Bolometers suitable for use on tokamaks have to meet several requirements. In ideal case the spectral response of such detectors is completely flat from 1 Å up to 2000 Å (corresponding to an electron temperature of 5 eV to 10 keV), as the major part of the radiation loss from the plasma can be found there (see previous chapter). During outgassing treatment of the vacuum vessel bolometers should be bakable at temperatures up to several hundreds of °K. High magnetic fields (up to 13 T) and operation in ultrahigh vacuum must be supported. The detectors have to be resistant against radiation damages due to neutrons escaping the plasma or to γ-radiation. Bolometers need a effective rejection of background signals whose origin may be found in temperature change of their mounting support, volume absorption of nuclear radiation, common-mode voltage or electromagnetic pickup. During experimental campaigns on tokamak the access to the installed bolometers is impossible and therefore a high reliability is a prerequisite. For tomographic investigation of plasmas a larger number of bolometers is necessary and their calibration must be easily reproducible. As a matter of course the calibration data should not show a temporal drift. A calibration on the spot (in situ) is desirable.

3.1 Thermal bolometers

Several types of bolometers based on the absorption of the radiation leading to a temperature rise δ of the absorber have been developed^{(1)}. All these detectors have in common a relative rough temporal resolution.

Widely used are detectors consisting of a kapton support sandwiched by a gold absorber foil on the one and a temperature measuring element on the other side. Kapton^{(2)} is a robust and reliable material that shows good mechanical strength and electrical insulation which are not degraded even after having received high radiation doses. The thickness of the gold foils is a compromise between the ability to sufficiently stop soft X-ray radiation and the achievement of high sensitivity and short rise times. The resulting thickness is of some μm.

A 4 μm thick gold foil absorbs soft X-ray down to a wavelength of 2.5 Å (corresponding to an energy of about 5 keV)^{(3)} [64]. Gold has a almost linear response to radiation up to 2000 Å, where the reflectivity increases dramatically. Neutrals are taken into account in the range of 20 eV up to 1 keV^{(4)}. Charged particles, neutrons, γ radiation and hard X-ray don’t contribute to the bolometer signal. Blackened absorber surfaces extend the measurable radiation down to infrared. A rougher surface provides better absorption for neutrals.

The balance between the incident heat radiated by the plasma and the transport of heat through the kapton is given by

ΔQ(t) = ΔQ_{in}(t) + ΔQ_{out}(t)  (3.2)

The temperature of the gold absorber increases linearly with the incident power

ΔQ_{in}(t) = C · δ(t)  (3.3)

where C is the heat capacity of gold (2 mJ/°C) and δ the temperature rise due to the incident power.

When the irradiation is switched off in t = 0, the cooling follows an exponential law characterized by cooling time τ_{C}, whose value increases with the area and the thermal insulation of the foils (typically some hundred ms):

ΔQ_{out}(t) = −C · δ(0) · exp (−\frac{t}{τ_{C}} )  (3.4)

Inserting 3.3 and 3.4 into 3.2, differentiation and evaluation in t = 0 gives then access to the immediate radiated power P(t)

P (t′) = \frac{d}{dt}ΔQ(t = 0) = C · (\frac{dδ}{dt} + \frac{δ}{τ_{C}} )  (3.5)

The frequency response of the bolometer is therefore given by

δ(ω) = \frac{P (ω)}{C} · \frac{τ_{C}}{\sqrt{1 + ω^{2}τ_{C}^{2}}}  (3.6)

(1) Metal foil bolometer [60], thermistor [59], semiconductor, thermopile, pyroelectric [2] and thermographic

(2) polyamide group

(3) 1 % transmission @ 5 keV, 20 % transmission @ 8 keV.

(4) energy reflection coefficient of a polished gold surface is about 0.2 .. 0.4 Diploma work 2002-2003  Christian Schlatter

For a given incident power the temperature rise is linear to the cooling time at low frequency but independent of τ_{C} at high frequency.

For the requirements of operation on tokamaks, the metal foil bolometer is the most commonly used type of detector (next paragraph). On T-10 a pyroelectric bolometer is used for the determination of the total radiated power. For that reason a short description is given on the next page.

3.1.1 Metal foil bolometers [60]

The temperature is measured using a gold resistor^{(5)}.

The resistance of the gold resistor, typically some kΩ at ambient temperature T_{0}, is related to the temperature rise by

R(T_{0} + δ) = (1 + α · δ) · R(T_{0})  (3.7)

where α is the resistance temperature coefficient (0.0026 °C^{−1} for gold). Hence, the electrical response U(ω) of a bolometer supplied with a highly constant current I is

ΔU(ω) = I · R(T_{0}) · α · δ(ω)  (3.8)

Using this last relation, equation 3.5 can now be written as

P (t) = \frac{C}{ατ_{C}} · [\frac{τ_{C}}{U_{0}} \frac{dΔU(t)}{dt} + \frac{ΔU(t)}{U_{0}}]  (3.9)

where U_{0} = R (T_{0}) · I. The incident power P (t) is determined by the power dependent voltage rise ΔU(t) and its time derivative \frac{dΔU}{dt}.

To mask the troublesome background signals, a so-called reference bolometer which is shielded^{(6)} against that kind of radiation the bolometer should measure. The reference bolometer is located in the immediate vicinity of the unshielded (active) bolometer and both are electrically interconnected in a Wheatstone bridge (see for example [62]). The bridge amplifier delivers ΔU and \frac{dΔU}{dt} which are added using a sum amplifier to obtain P(t) according to equation 3.9. To have a good signal-to-noise ratio for low irradiation power the output signal has to be integrated over time limiting the bolometers time resolution to typically 10 ms.

Calibration of metal foil bolometers is extremely simple by self-heating: Using square wave supply voltage a well known ohmic power is dissipated in the resistor. This can even be done remotely when mounted on the tokamak. Such calibration is easily reproducible and shows stability of about ± 10 % after longer exposure to typical tokamak plasma radiation. Metal foil bolometers may be baked up to 300 °C and are insensitive to radiation damage of more than 10^{9} rad.

Apart the disadvantage of having a temporal resolution of typically 10 ms only, metal foil bolometers have a detection limit 5 times higher (about 100μW/cm^{2}) than semiconductor bolometers.

(5) often in the form of meanders.

(6) typically a 1 mm thick aluminium plate.

Diploma work 2002-2003  Christian Schlatter

3.1.2 Pyroelectric bolometer [2]

This type of bolometer is used on the T-10 tokamak to measure the total radiated power (upper bolometer on figure 4.1).

Unlike metal foil bolometers, the temperature increase of the absorber is measured using a pyroelectric element. Materials like LiTaO_{3} exhibit a temperature-dependent spontaneous polarization ΔP_{S}.

ΔP_{S} = γδ  (3.10)

where δ is again the temperature rise of the pyroelectric crystal and γ = \frac{dP_{S}}{dT} the pyroelectric coefficient, which equals 1.8·10^{4} \frac{C}{m^{2}·K} for LiTaO_{3}. The spontaneous polarization leads to the appearance of charges on the surface of the material which can be measured as a current j by integrating the pyroelement into an electric circuit

j = −A · \frac{dΔP_{S}}{dt} = −A · γ · \frac{dδ}{dt}  (3.11)

where A is a constant. The frequency response of pyroelectric bolometers is flat and the temporal resolution is typically about 10 ms.

3.2 AXUV detector [1], [33]

AXUV stands for Absolute eXtreme UltraViolet-detector. The geometrical setup of such a detector installed on T-10 will be described in details in chapter 4.

Figure 3.1: Layering of the AXUV-detector. The thickness of the layers is not in scale. [1].

These new generation Soft X-ray detectors use silicon p-n junction photodiodes. Figure 3.1 shows the n-type layer deposited on the p+type wafers. On the upper side the active region is formed by a SiO_{2} (glass) passivating window of 3 to 7 nm of thickness. The field oxide surrounding the active surface is used to create the internal electric field.

The first ionization energy of silicon is 3.65 eV and theoretically an incident photon having this energy (or greater) permits the creation of an electron-hole pair in the depletion zone (blue photons and UV are absorbed at a path length smaller than 1 μm). Due to the internal electric field, electron and hole run in opposite direction, generating a current in an external circuit.

Figure 3.2: Quantum efficiency χ of the AXUV-detector. Experimental data delivered by the manufacturer [1], [36]. The blue line shows theoretical quantum efficiency.

In practice the probability of electron-hole carriers created per incident photon of energy E is characterized by the quantum efficiency χ (see figure 3.2, experimental data delivered by the manufacturer). Already an energy of 1.12 eV may create an electron-hole pair (but with poor probability). For photon energies greater than 3.7 eV more than one carrier pair is generated, increasing almost linearly with energy, satisfying the theoretical relation

χ = \frac{E_{[eV]}}{3.65}  (3.12)

The loss in quantum efficiency in the range of about 7 eV to 100 eV photon energy is due to absorption and reflection by the entrance SiO_{2} window. With 100 % quantum efficiency the radiation energy is integrally converted to an electric current almost attaining a responsitivity of η = 1/3.65 eV = 0.274 A/W. Figure 3.3 shows the responsitivity of the photodiodes to photons, electrons and hydrogen ions (charged particles doesn’t reach the AXUV detectors on T-10). The experimental data has been obtained using a AXUV100G array and has been measured by NIST^{(7)} [36]. Again the influence of the SiO_{2}-layer is clearly visible and for energies greater than 200 eV the response is almost flat (the flat part occupies almost the whole spectrum, the figure plots the responsitivity against logarithmic scale). This flat power response results in the application of AXUV-detectors on several tokamaks for radiated power measurements over a wide-range of energies.

An important question is the stability of the quantum efficiency [64] when irradiating the detector with high doses of UV. The interface between Si and SiO_{2} is susceptible to UV radiation. UV may neutralize the oxide charge which leads to a smaller electric field and resulting in a lower photocurrent (observed at high wavelengths). High baking temperatures

(7) American National Institute for Standards and Technology.

Diploma work 2002-2003  Christian Schlatter

Figure 3.3: Typical responsitivity η of the AXUV photodiodes to photons, electrons and hydrogen ions. The experimental data has been established by the American National Institute for Standards and Technology (NIST) and was obtained from the manufacturer. The data is representative for the AXUV-series of photodetectors. [1].

may lead to a change of the oxide layer thickness leading to higher quantum efficiencies. Another reason are dislocations near the same interface due to environmental stress which may release recombination of the electron-hole pairs. The influence of recombination centers may have little effect since with the chosen setup the concentration of minority carriers is very low near to the interface.

The manufacturer guarantees the stability of quantum efficiency for electron beams of 10 eV and 100 eV as shown in figure 3.4. Another problem may be the deposition of thin films by diffusion on the surface of the detector, which with increasing thickness, may alter the detection efficiency. See the analysis of the the low-energy responsitivity of an array which was exposed to the tokamak plasma on T-10 during several experimental campaigns (sections 7.2.3 and 7.2.4).

The incident radiation reaches the outermost detectors surface obliquely. But only the SiO_{2} layer affects the responsitivity by varying the azimuth and polarization of incident radiation. Since this window is very small, its influence was reported to be negligible [3].

Of course AXUV-detectors meet further requirements necessary for applications in nuclear fusion, i.e. they may be used in vacuum environments up to 10^{−10} Torr and are insensitive to strong magnetic fields.

The elevated sensitivity permits to make the active surface smaller. Hence small geometrical

Figure 3.4: Stability of the quantum efficiency of AXUV-photodetectors. A flux of 5 × 10^{13} photons s^{−1} · cm^{−2} at 10 eV (red) and of 3 × 10^{14} photons s^{−1} · cm^{−2} at 100 eV (blue) have been used. Data delivered from the manufacturer [1].

dimensions are a prerequisite for the construction of a imaging system with high spatial resolution, up to emissivity scale lengths of the order of the mm.

In comparison with metal foil bolometers AXUV-detectors exhibit a short nominal rise time of the order of the μs which gives access to observation of fast phenomena like MHD-activity of instabilities.

In contrast to metal foil bolometers, AXUV-detectors don’t measure neutral particles of lower energy (< 500 eV). This fact has been used on Alcator C-Mod [30] to determine the power carried by neutral particles by calculating the difference between the signals of both types of bolometer.

Scheme of the diagnostics for radiation loss measurements on T-10

4.1 Setup on T-10

On tokamak T-10 two systems permit the determination of total radiated power. First a pyroelectric bolometer whose field of view covers all poloidal positions is located at cross section D. It is based on a LiTaO_{3} pyroelement as described in section 3.1.2 and has a temporal resolution of about 10 ms. Second a 16 channel AXUV-photodiode array is located at the same cross section. This diagnostic will be described in the following sections.

Figure 4.1 shows the position of the two bolometers and the central viewing chords of the AXUV-diode based detector.

4.2 Parameters of AXUV detector

On T-10 an AXUV-photodiode array assembling 20 detectors (from which only 16 were used) and manufactured by International Radiation Detectors (IRD) [1] is in operation since May 2001. The detector model is a linear AXUV-20ELM with 3 mm^{2} sensitive area (cell size 0.75 × 4 mm) of each detector. Electrical specifications give a shunt resistance of 100 MΩ, zero-volt capacitance of typically 2 nF and a guaranteed rise-time of 0.5 μs (slope measured from 10 to 90 % of output range). This detector exhibits all the properties of the types of AXUV-photodiodes presented in section 3.2.

4.3 Pinhole camera with a 16 channels AXUV-detector

The AXUV-detector has been mounted into an aluminium box which includes also the preamplifier. The detector is placed at a distance o_{1} = 30 mm behind the aperture. The situation is shown in figure 4.2. The box itself is set up in a stainless steel cylinder which can be vacuumed and which is attached to a lower flange on T-10 (see figure 4.1).

4.3.1 The geometry of the cones of view

The aperture slit is located at a distance of o_{2} = 1120 mm from the minor axis, its horizontal position is x_{a} = 210 mm to the right of minor axis. The 16 detectors of rectangular shape (each of active area of d_{P} = 0.75 mm, d_{T} = 4 mm in poloidal and toroidal direction respectively) lie

4.3 Pinhole camera with a 16 channels AXUV-detector  18

Figure 4.1: Setup of bolometers on T-10. The upper detector is the pyroelectric bolometer looking at the whole cross section. The lower detector are the AXUV diodes. The cones of view of the 16 channels are shown.

Figure 4.2: AXUV pinhole camera. View in toroidal direction. The detectors have 0.75 × 4 mm^{2} (poloidal × toroidal) size.

side by side in poloidal direction, symmetrically in respect to the optic axis. The intersection of the central viewing line (chord) of detector i with the central arc (drawn by o_{2} around the center of the slit, see figure 4.1) as measured on the arc from the optic axis is given by

s_{i} = o_{2} · arctan (\frac{t_{i}}{o_{1}} )  (4.1)

where t_{i} is the distance of the center of the i^{th} detectors surface from the optic axis. This leads to a spacing of almost δs ≈ 40 mm on the central arc.

The poloidal opening angle β_{p} is given^{(1)} by

β_{P,i} = arctan (\frac{t_{i} + \frac{d_{p}}{2}}{o_{1}} ) − arctan (\frac{t_{i} − \frac{d_{p}}{2}}{o_{1}} )  (4.2)

Figure 4.3: Poloidal opening angle β_{P,i} of the field of view of the 16 detectors. Outer channels have a bigger distance between aperture and their active surface.

Figure 4.3 shows β_{P,i} for the chosen geometry. The fact that β_{P,i} decreases for the outer detectors is due to the fact that the distance between the detectors surface and the aperture slit increases.

The toroidal opening angle β_{T,i} of the field of view of the detectors is limited by the shape of the flange connecting the pinhole camera with the vessel. In toroidal direction the limiting edge of the flange is circular as shown in figure 4.4, concentric with the minor axis, having a constant

(1)

The fact that the slit has a finite opening increases the field of view of the detectors. Radiating points

lying in this extended region are seen by both neighboring detectors, but their location is in the half

shadow region, i.e. the illumination of the detectors surfaces is incomplete. If all these points have the

same emissivity, the overlapping of neighboring channels doesn’t lead to overestimation of the measured

power (see also calibration profile in figure 7.2).

Diploma work 2002-2003  Christian Schlatter

Figure 4.4: Flange for diagnostics. Toroidal view. The flange connecting diagnostics outside of the torus to the vessel is drawn in red (radius r_{fl} = 570 mm). In yellow the central arc of radius o_{2} = 1137 mm. The green circle has the minor vessel wall radius (a = 330 mm), the circle in purple represents the extent of the LCFS shaped by the limiter (a_{L} = 300 mm). In blue the central viewing lines (chords) of the AXUV-detectors.

curvature of r_{fl} = 570 mm. Choosing the minor axis as origin of the coordinate system, the points of intersection (x_{i}, y_{i}) of the chords

y_{i} = tan(α_{i} + α_{o}) · (x_{i} − x_{a}) + y_{a}  (4.3)

with the flange arc described by the circle

x_{i}^{2} + y_{i}^{2} = r_{fl}^{2}  (4.4)

are obtained by resolving the resulting quadratic equation, where (x_{a}, y_{a}) = (1117 , 210) mm are the coordinates of the aperture slit center and α_{i} the inclination of the chords relative to the optic axis of the pinhole camera, whose horizontal inclination equals α_{o} = 10.8°.

Figure 4.5: Flange for diagnostics. Projection of vertical view. The toroidal opening angle of chords looking to the inner part of the tokamak is narrowed by the shape of the flange.

In vertical direction the narrow flange cross section is shown in figure 4.5. For points of intersection lying on radii smaller than the major radius, the toroidal width of the flange decreases. The width w_{i} is given by equation

w_{i} = 55 − H(−x_{i}) · \frac{14 − 55}{353} · x_{i}  (4.5)

where H(x) is the heaviside unit function.

The toroidal opening angle β_{T} of the field of view is finally given by

β_{T,i} = 2 · arctan (\frac{w_{i}}{2 · (R_{fl,i} + \sqrt{o_{1}^{2} + t_{i}^{2}})})  (4.6)

where R_{fl,i} = \sqrt{(x_{a} − x_{i})^{2} + (y_{a} − y_{i})^{2}} is the distance of the point of intersection from the slit center.

Figure 4.6: Toroidal opening angle β_{T,i} of the field of view of the 16 detectors. The angles for chords # 14 - 16 are lowered due to the geometry of the flange.

Figure 4.6 shows the calculated β_{T,i}. In the chosen geometry, only channel 15 and 16 are affected by the narrowing of width of the flange towards the center of tokamak (see also figure 4.4, where the flange is drawn in red color).

4.3.2 The aperture slit

The rectangular slit of the collimator has the dimensions ℓ = 7.5 mm ×△ = 0.2 mm.

The aperture is made of a stainless steel tin of 0.8 mm thickness. A crude slit was cut using nail scissors. The precise slit width was attained by razor blades which have been welded to the aperture (see picture 4.7). The aperture itself is welded on the mounting ring of the flange.

The length ℓ of the slit is slightly greater than the projection of the flanges diameter at the outlet to the vacuum chamber so that the toroidal width of the seen cross section is maximum. This is calculated by

ℓ = d_{t} + 2 · sup_{1⩽i⩽16} tan (\frac{β_{T,i}}{2} ) · \sqrt{o_{1}^{2} + t_{i}^{2}}  (4.7)

Figure 4.7: Aperture slit. Conventional razor blades guarantee a sharp precise slit.

which is ℓ = 6.6 mm in the calculated geometry. The slit is only slightly larger to prevent the registration of radiation which has been reflected at the inner flange walls.

The width △ of the slit affects the amount of power deposited on the surface of the detector. The cross section seen by the AXUV-detectors has an extent of about ℓ_{T} = 100 mm on the minor axis in the field of view of the pinhole camera (when considering an average toroidal angle). Supposing the totality of a typical heating power P_{H} of ∽ 1.3 MW isotropically radiated, a fraction^{(2)} of P_{ℓ} = ℓ_{T} · P_{H}/2πR = 14 kW lying in the seen cross section gives a power density^{(3)} of about p_{slit} = P_{ℓ}/4πo_{2}^{2} = 760 W/m^{2} on the level of the aperture slit. Regarding the cross-section^{(4)} of the slit, a total power of roughly P_{det} = p_{slit} · A_{slit}/16 = 63 μW would be deposited on the surface of one detector.

For the given acquisition electronics^{(5)} (see the next section) and using the average responsitivity^{(6)} of the detector, this power corresponds to the maximum amplifier output signal, i.e U_{max} = η · P_{det} · R_{amp} = 4.5 V. A wider slit would lead to saturation of the amplifier (supply voltage 5 V), a smaller one to a worse signal-to-noise ratio.

(2) major radius R = 1500 mm.

(3) radius of aperture slit o_{2} = 1137 mm.

(4) A_{slit} = 0.2 × 6.6 mm^{2}

(5) R_{amp} = 300 kΩ

(6) η = 0.24 A/W Diploma work 2002-2003  Christian Schlatter

4.4 Multichannel data acquisition system

The data acquisition system for the AXUV-signals is split to a remote system in the vicinity of the reactor and a control computer in the commando room. Figure 4.8 shows the block diagram.

Figure 4.8: Block diagram of the AXUV data acquisition system. The upper part of the diagram shows units found in the control room, the lower units are installed on T-10.

The next sections give a short description of the different components.

4.4.1 The preamplifier

The 16 channel preamplifier is in the the same housing as the photodiodes. Figure 4.9 shows the equivalent circuit diagram of the AXUV-photodiode and the preamplifier. The preamplifier has to convert the photocurrent to a proportional voltage which can be digitized.

A significant problem with using photodiodes in fast applications is that the diode has a high output capacitance C_{S} (2 nF for the used AXUV-array, the diode shunt resistance is R_{S} = 100 MΩ). Together with R_{F} the capacitance C_{S} creates a low-pass filter, contributing negative phase to the feedback loop and making the circuit unstable.

A effective way to reduce instabilities is to add a high-pass filter in the same feedback path, which counteracts the undesirable low-pass filter. This is done by adding C_{F}.

Appendix A shows how C_{F} can be optimized to effectively reduce oscillations on the output but not to lower the slew rate too much. The preamplifier was assembled using a FET input amplifier AD823 from Analog Devices which has a unity gain frequency of at least 12 MHz, the detectors a capacitance of C_{S} = 2 nF and R_{F} was chosen 300 kΩ, resulting in a C_{F} (calculated accordingly equation A.4) of 10 pF. That’s all theory and therefore in the final setup C_{F} has further been optimized by adjusting its value until the best compromise between suppression of oscillations and high slew rate was achieved. Finally a value of 27 pF was selected.

Figure 4.9: Circuit schematic of the photodiode and the preamplifier. Only one single channel is shown. The circuit is supplied asymmetrically by 5 V (not shown). Dimensioning is R_{F} = 300 kΩ and C_{F} = 27 pF for the used detector with C_{S} = 2 nF and R_{S} = 100 MΩ.

4.4.2 Analog-digital converter (ADC)

The remote computer (figure 4.8) is equipped with a one channel A/D conversion PCI card (model L783 from Л-Кард [27]) with a resolution of 11 bits for an input voltage in the range of 0 .. 5 V. The 16 AXUV-channel are polled by a multiplexer with a period of 16 μs. The timer which controls the digitization of the data is started by the chief experimental physicist about 100 ms before the plasma current starts to grow. The raw bits are stored to the remote PC and to the main diagnostic database server. The control PC in the command room serves to check the measured data for plausibility.

Estimation of the absolute values of radiated power taking into account the geometry of a plasma discharge

As the whole cross-section is covered by the field of view of the detectors, the total radiated power is obtained by summing up the channel powers. How are the channel powers derived from the measured signals?

The temporal evolution of the preamplifier output voltage u_{i,raw}(t) is digitized as described in section 4.4 and stored to the diagnostics database in binary format. To get the raw preamplifier voltages u_{i,raw} the database value u_{db} has to be multiplied by Υ = U_{b}/2^{b}, i.e.

u_{i,raw} = u_{db} \frac{U_{b}}{2^{b}}  (5.1)

where U_{b} = 5 V is the analog-digital converter (ADC) voltage range and b = 11 the number of bits of the ADC. These raw signals are read and any negative offset due to electronics offset voltage is removed. The offset is calculated

u_{i,m} = min_{t_{start}⩽t⩽t_{end}} u_{i,raw}(t)  (5.2)

with t_{start} and t_{end} start and end time of the shot. Further the signals are multiplied by the relative calibration factors f (these will be calculated in section 7.1.1), i.e. by calculating

u_{i}(t) = f_{i} · (u_{i,raw}(t) − u_{i,m}) [V] ∀t ∈ (t_{start}, t_{end})  (5.3)

The relative calibration factors f_{i} achieve equal sensitivity among the individual detectors. f_{i} are of order of 1 and do not strongly modify the absolute values.

The measured characteristic (DC-input voltage) of the current-to-voltage converter gives an effective feedback resistor R_{eff}= 300 kΩ. The preamplifier output voltage therefore corresponds to a photocurrent of

i_{ph}(t) = \frac{u_{i}(t)}{R_{eff}} [A]  (5.4)

Using the average responsitivity of η = 0.24 A/W the current corresponds to a amount of power deposited on the detector of

P_{det,i}(t) = \frac{i_{ph}(t)}{η} [W]  (5.5)

\underline{26}

The deposited power is related to the power emissivity ϵ(V) (in [W/m^{3}]) of the plasma by the geometry of the detectors. The emissivity is defined as the flux of radiation power δP through the limiting surfaces of the volume dV it is originating from, i.e. by

δP = ϵ(V) · dV  (5.6)

The fact that on T-10 the cross-section of the plasma is circular and that a discharge has in general a radial symmetry implies that the emissivity for a given place in the cross-section depends only on its distance r from the minor axis. Because of that, points with constant emissivity lie on concentric rings. For a ring of radius r, emissivity ε(r) and width equal to dr, a point on the surface of the detector sees this ring twice, an inner pixel at a distance R_{1} from the aperture slit of volume approximately dV_{1} = dR · dΩ_{det} · R_{1}^{2} (dR is the width of the pixel along the line of sight of the detector) and an outer pixel at a distance R_{2} of volume dV_{2} = dR · dΩ_{det} · R_{2}^{2}, where dΩ_{det} = β_{P} · β_{T} is the solid angle of the detector, with β_{P} and β_{T} calculated by equations 4.2 and 4.6. According to equation 5.6, a pixel at distance R from the slit emits the flux of power

δP (R) = ϵ(r) · dR · dΩ_{det} · R^{2}  (5.7)

On the other hand the amount of the isotropically radiated power by a point of the cross-section crossing the aperture slit is given by the solid angle describing how the aperture slit is seen by that point, i.e by

dΩ(R) = \frac{dA_{apt}}{R^{2}}  (5.8)

with dA_{apt} the cross-section of the aperture slit as seen by the point source and R the distance of the point from the aperture slit. Therefore the power crossing the slit is given by

dP_{apt} = δP (R) · \frac{dΩ(R)}{4π} = ϵ(r) · dR\frac{dA_{apt}}{4π} · dΩ_{det}  (5.9)

which which does not depend on R anymore. That means, that the amount of power coming from the farer pixel equals the amount coming from the closer one. This result permits to move the pixels elsewhere (with their size perpendicularly to the line of sight shaped by dΩ_{det}, longwise unchanged equal to dR) without the registered power being influenced.

In the following all pixel will be placed on the symmetry^{(1)} surface (this is advantageous for the inversion, see chapter 6), crossways to the line of sight, given by the set of points lying in the center between two pixels of same emissivity (see figure 5.1). The distance R_{i,sym} of this symmetry surface for detector i measured from the aperture is given by

R_{i,sym} = o_{2} · cos(α_{i})  (5.10)

where o_{2} is the distance of the aperture from the minor axis and α_{i} the inclination of the central viewing line from the optic axis (see section 4.3.1). The emissivity of the pixels may further be replaced by a single radiation source located at the point of intersection of the central viewing line and the symmetry surface since the cones of view are small.

This center point of the symmetry surface sees the detector under a solid angle corresponding to the projection of the width of the aperture slit on the detector surface. The chord i sees the aperture slit width effectively as △_{i} = △ · cos(α_{i}) wide, where α_{i} is the angle of the chord with the optic axis. In toroidal direction, the whole length d_{T} = 4 mm of the detector is illuminated.

(1) symmetry in respect to the rings of constant emissivity.

Diploma work 2002-2003  Christian Schlatter

Figure 5.1: Location of the symmetry surface for the outermost right channel.Taking a radial symmetry for granted, the whole emissivity in the field of view could be moved to the symmetry surface without changing the registered power.

As R_{i,sym,tot} = R_{i,sym} + \sqrt{t_{i}^{2} + o_{1}^{2}} (see again 4.3.1 for their definitions) is the distance of the i^{th} symmetry center point from the surface of detector i, in poloidal direction the width of the projection is △_{i} · \frac{R_{i,sym}}{R_{i,sym,tot}}, so that the solid angle dΩ of the symmetry center point is given by

\frac{dΩ_{sym}}{4π} = \frac{d_{T} · △_{i} · \frac{R_{i,sym,tot}}{R_{i,sym}}}{4π · R_{i,sym,tot}^{2}}  (5.11)

The amount of deposited power corresponds then to a isotropically radiating power source on the symmetry center point of

P_{sym,i} = \frac{4π}{dΩ_{sym}} · P_{det,i} [W]  (5.12)

with P_{det,i} given in 5.5. The transverse surface at the symmetry point limited by the field of view of the detector has an extent of

d_{T,sym,i} = w_{i} + 2 · tan (\frac{β_{T,i}}{2} ) · (R_{i,sym} − r_{fl,i})  (5.13)

in toroidal direction. This permits to define a power density on the symmetry surface per unit of toroidal length (in [W/m])

p_{sym,i}^{ℓ} = \frac{P_{sym,i}}{d_{T,sym,i}}  (5.14)

That is a very useful quantity, since the total radiated power in the whole vessel (when ignoring the possible radiation increase at the limiter, which cannot be determined by the diagnostics system) then simply writes

P_{tot} = 2π · R_{T} · ∑_{i} p_{sym,i}^{ℓ} [W]  (5.15)

where R_{T} = 1.5 m is the tokamak major radius.

chord # G_{i} [W/V]  chord # G_{i} [W/V]
1 3,7955 ·10^{4}  9 2,8091 ·10^{4}
2 3,4545 ·10^{4}  10 2,8785 ·10^{4}
3 3,3638 ·10^{4}  11 3,0288 ·10^{4}
4 3,2772 ·10^{4}  12 3,1938 ·10^{4}
5 3,4932 ·10^{4}  13 3,0951 ·10^{4}
6 3,2019 ·10^{4}  14 3,1466 ·10^{4}
7 2,8785 ·10^{4}  15 3,5766 ·10^{4}
8 2,8091 ·10^{4}  16 3,5272 ·10^{4}

Table 5.1: Absolute translation factors G_{i}. The factors include relative calibration (f_{i}). G_{i} relates the database values to the total radiated power.

5.1 Absolute translation factors

The above calculation only depends on geometry and electronics and therefore is always the same for each shot and time. It is handy to calculate direct translation coefficients between the signals in the database and the total radiated power. Combining equations 5.3 to 5.15 yields

G_{i} = \frac{2π · R_{T} · p_{sym,i}^{ℓ}}{u_{i}} = \frac{8π^{2} · R_{T} · f_{i} · R_{i,sym,tot} · R_{i,sym}}{R_{eff} · η · d_{T} · △_{i} · d_{T,sym,i}}  (5.16)

Using the last equation together with 5.1 and 5.2, the total radiated power will then be obtained by summing up, i.e. by

P_{tot}(t) = ∑_{i} G_{i} · ((Υ · u_{db}) − u_{i,m})  (5.17)

where u_{db} is the database value, Υ the ADC coefficient and u_{i,m} the offset correction (see the beginning of this section).

Table 5.1 lists and figure 5.2 shows G_{i}.

5.1 Absolute translation factors  29

Figure 5.2: Absolute translation factors G_{i}. The factors include relative calibration (f_{i}). G_{i} relates the database values to the total radiated power.

Simulation of a radial distribution of the emissivity

The calculation of the space distribution (the so-called emissivity) of the radiation loss from the AXUV chord signals is presented in this chapter.

The knowledge of the plasma emissivity is the starting point for the understanding of the behavior of impurities in the plasma. Together with temperature and density profiles, the nature of the radiation processes leading to the power loss can be estimated.

6.1 The abelization

The reconstruction of emissivity from power chord measurements is achieved using an Abel inversion method. The assumption of radial and toroidal symmetry of the radiation processes (i.e. of the emissivity ε) simplifies this task considerably.

The measured chord brightness g_{i} of detector i corresponds to the integration of the emissivity along its chord, i.e.

g_{i} = ∫_{−x_{1}}^{x_{1}} ε(x, y) · dx  (6.1)

where x and y are the cartesian coordinates of the poloidal cross-section, x_{1} the outermost chord position on the cross-section (see figure 6.1). The x-axis has been chosen in direction of the chord of the detector. After change of variables and using the fact of radial symmetry, equation 6.1 yields the Abel equation

g_{i} = 2 ∫_{y}^{r_{1}} \frac{r · ε(r)}{\sqrt{r^{2} − y^{2}}} dr  (6.2)

The exact decision of the Abel equation is given by [12]

ε(r) = −\frac{1}{π} ∫_{r}^{r_{1}} \frac{g′(y)}{\sqrt{y^{2} − r^{2}}} dy  (6.3)

where g′(y) = \frac{dg(y)}{dy}. The exact decision is difficult to realize in practice since equation 6.3 essentially depends on g′(y).

Several approaches to decide the Abel equation exist:

Figure 6.1: Line integration of the emissivity along the chord. The detectors central line of sight is shown at height y parallel to the x-axis.

• The solution is searched by expansion on orthogonal functions. The decision is realized by iterating the solution until the expansion coefficients reproduce the chord measurements calculated by 6.2

• The integral in the Abel equation 6.2 is replaced by a sum over areas of constant emissivity, permitting to calculate the emissivities algebraically.

On T-10 the first approach is used for the calculation of the profile of density and for abelization of the soft X-ray measurements. For the reconstruction of the emissivity from the AXUV-signals a method of the second type is applied (see the following section).

6.2 Reconstruction of the plasma emissivity

The sum which replaces the integral in the Abel equation is taken over areas a_{ij} defined by the intersection of parallel stripes i = 1,..,m (representing the field of view of detectors^{(1)}, with width of 4 cm in y and 1 cm in toroidal direction) with concentric rings j = 1,..,m of constant emissivity (see figure 6.2). This method has been first used in [12]. The chord brightness 6.2 for detector i can therefore be written as

g_{i} = ∑_{j} a_{ij} · ε_{j}  (6.4)

where ε_{j} is the emissivity in the j^{th} ring.

The areas a_{ij} are calculated (see figure 6.2 for the definition of the angles γ) by integration

a_{ij} = 2 ∫_{y_{j+1}}^{y_{j}} [\sqrt{r_{j}^{2} − y^{2}} − \sqrt{r_{j+1}^{2} − y^{2}}] dy =

2 [∫_{γ_{i+1,j}}^{γ_{i,j}} r_{j}^{2} · cos^{2}(γ) dγ − ∫_{γ_{i+1,j+1}}^{γ_{i,j+1}} r_{j+1}^{2} · cos^{2}(γ) dγ]  (6.5)

(1)

The emissivity is constant transverse to the line of sight, except near the interface between adjacent rings.

When the field of view of the detectors is sufficiently narrow, the error introduced by this approximation

is small.

Diploma work 2002-2003  Christian Schlatter

Figure 6.2: Definition of the pixels by rings of constant emissivity and the detector stripes. The area of the pixels are calculated analytically (see formula 6.5).

In this model the emissivity of the rings can be calculated analytically starting with the outermost ring by

g_{1} = a_{11} · ε_{1} ⇒ ε_{1} = a_{11}^{−1} · g_{1}
g_{2} = a_{21} · ε_{1} + a_{22} · ε_{2} ⇒ ε_{2} = a_{22}^{−1} · (g_{2} − a_{21} · a_{11}^{−1} · g_{1})  (6.6)
...  ...

The set of equations 6.4 can be written in matrix form as

g⃗ = 𝔸 · ε⃗  (6.7)

where 𝔸 = {a_{ij}}.

Multiplying with the inverse matrix 𝔸^{−1} yields the emissivities

ε⃗ = 𝔸^{−1} · g⃗  (6.8)

This method has the benefit that the matrix 𝔸^{−1} has only to be calculated once as it only depends on geometry. The emissivity can be reconstructed for the two halves of the cross-section (separated by the optic axis of the pinhole camera) separately (see discussion in chapter 8).

6.3 Extension of the parallel stripe method

According to the calculation of the radiating pixel positions at the symmetry center surfaces in the previous chapter a more precise calculation of the emissivity is achieved by shaping the parallel stripes by the size of the field of view at the position of that surface. The transverse surface at the symmetry point limited by the field of view of the detector has an extent of

d_{P,sym,i} = β_{P,i} · R_{i,sym}  (6.9)

in poloidal direction which defines the width of the parallel stripes. β_{P,i} was given in formula 4.2 and R_{i,sym} in 5.10.

6.4 One example

The decision of the Abel equation essentially depends on the derivative of the chord brightness g(r). This property is clearly seen in H-modes (see discussion in chapter 8.2.2), where the chord signals show a steep gradient at the outer radii. Actually the reconstruction makes allowances by showing a strong emissivity peak at these positions. Figure 6.3 shows chord signals and their reconstruction for the high-current T-10 H-mode discharge #31899.

Figure 6.3: Reconstruction of the chord signals. Plasma discharge #31899 of the high-current T-10 Hmode regime. The left figure shows the chord signals. On the right the emissivity profile after reconstruction.

Various further examples of reconstructed emissivity profiles can be found in chapter 8.

Calibration and checking of the parameters of the diagnostics system

7.1 Relative calibration in the laboratory

To control fabrication-related spread of responsitivity, differences in amplification and offset values of the preamplifier, a relative calibration to weigh the detectors response among each other has been realized. For this purpose the assembly of the diagnostics on the tokamak has been reproduced on a scale of 1:1 in the laboratory. For lack of possibility to calibrate using radiation other than visible and infrared light, the calibration has only been done using a standard halogenoid lamp (blackbody radiation) which has been moved along a straight line perpendicular to the detectors axis. Such a calibration could be a bad generalization to other wavelengths of radiation if during operation on the tokamak some thin films affecting the absorption of visible would have been deposited on the detector in a discontinuous way. The results of calibration have been compared to a brand-new array of the same type measured using the same setup and identical responsitivity values were found. Further measurements for this purpose using a weakened laser beam are described in section 7.2.4.

Figure 7.1: Determination of relative calibration coefficients. Reproduction on scale 1:2 of the tokamak geometry in the laboratory. Halogen lamp as (blackbody) radiation source.

7.1.1 Relative calibration coefficients

As the calibration has been done by moving the lamp (considered as point source) along a straight line (at a distance σ_{2} from the aperture, see figure 7.1), the obtained intensity levels have to be corrected to account the increasing distance for the outer channels between lamp and detector surface (r_{i} = (σ_{1} + σ_{2}) / cos(α_{i}), where (σ_{1} is the distance between the array of detectors to the aperture slit) and the spot size as seen by the lamp (A_{spot} = △·cos(α_{i})·\frac{σ_{1}+σ_{2}}{σ_{2}} ·d_{T}, where △ is the slit width of the aperture, d_{T} the toroidal extent of the detector surface) of the image of the lamp on the detector. Taking into account the power density dependence in 1/r_{i}^{2}, the amplifier output voltage u_{i} have been modified as follows

ũ_{i} = u_{i} \frac{4π · r_{i}^{2}}{A_{spot}} = u_{i} · \frac{4π (σ_{1} + σ_{2}) σ_{2}}{△ · cos^{3} (α_{i}) d_{T}} , i = 1, .., 16  (7.1)

The voltage ũ_{i} would then be the same for all channels (representing the lamp light intensity), if all detectors and amplifiers would be identical. This is not the case, as it can be seen on figure 7.2. The slopes of the trapeze-shaped sensor response are a result of partial illumination of the sensors surface. The fact that the experimental profiles show smaller width of top level intensity is due to reflections of light on the glass bulb of the lamp.

Figure 7.2: Calibration profile. In red the position and width of the field of view calculated for perfect detectors and equal preamplifiers. In blue the profile measured in the laboratory. The intensity levels have been corrected to eliminate all geometry related influences and normalized to the center channels.

Since absolute calibration can’t be done in the laboratory, only relative calibration coefficients f_{i} have been calculated by normalizing the corrected voltages of equation 7.1 by its value of detector 8, i.e. by

f_{i} = \frac{ũ_{8}}{ũ_{i}} , i = 1, .., 16  (7.2)

Figure 7.3 shows the obtained calibration coefficients using this procedure.

Measurement data obtained on T-10 is then weighted by multiplying by the correction factor

u_{i} = f_{i} · u_{i,measured}  (7.3)

7.2 Checking of the AXUV-detectors using data from the pyroelectric detector 36

Figure 7.3: Relative calibration factors f_{i}.

7.2 Checking of the calibration of AXUV-detectors in a plasma discharge using data from the pyroelectric detector

The absolute total radiated power measured with AXUV-detectors was compared to that measured with the pyroelectric bolometer. For the beginning, the absolute calibration of the latter will quickly be discussed.

7.2.1 Calibration of the pyroelectric bolometer

The pyroelectric bolometer is calibrated using shots where almost 100 % of the heating power is radiated is assumed. Such discharges are found by calculating the ratio

ς = \frac{u_{pyroelectric}}{P_{OH} + P_{ECRH}}  (7.4)

in stable regimes before disruptions for a large number of shots. u_{pyroelectric} is the uncalibrated amplifier output voltage of the pyroelectric bolometer, P_{OH} the ohmic input power and P_{ECRH} the gyrotron heating power (if present). The maximum value of ratio 7.4 is supposed to represent the situation where P_{radiation} = P_{heating}, leading to calibrate pyroelectric signal = input power. The calibration is used to store absolute values in the database. Figure 7.4 shows the power balance for discharge #33180. The ohmic heating input power has been calculated by estimating the inductive part of the loop voltage, as described in appendix B. This shot took place at the beginning of a campaign when a lot of impurities were present in the tokamak (the vessel was at air before) and therefore a high level of impurity line radiation comes across. During the time interval from t = 100 to t = 370 ms the plasma current I_{p} is built up to 130 kA (see figures in appendix B). After t = 400 ms the radiated energy follows the level of the ohmic heating input energy. Physically this situation is instable and would lead immediately to the collapse of the plasma. Assuming a precision of 10 % of the signals the

Figure 7.4: Checking of the calibration of the pyroelectric bolometer.

Shot #33180. Ohmic heating power and power loss measured by the pyroelectric device.

conclusion is that almost 100 % is radiated (from TEXTOR it was reported [53] that ratios up to 95 % showed still a stable behavior). The plasma is almost not supplied with energy up to 780 ms, where the boundary plasma touches the limiter and and a lot of carbon is sputtered (seen on the increase of the carbon line which is not shown here). The change in resistivity increases the heating power until the current and toroidal magnetic field are switched off in t = 930 ms.

Figure 7.5: Checking of the calibration of the pyroelectric bolometer.

Shot #32441. Radiation from the center.

The pyroelectric bolometer is checked from time to time with shots showing a high level of radiation. At the day the shot shown in figure 7.5 was taken, a diagnostic probe was introduced closer and closer to the plasma - too close for shot #32441. The head of the probe was made essentially from tungsten and was immediately evaporated when it got in contact with the plasma. The heavy tungsten impurity atoms (Z = 74) are not fully stripped even in the core plasma and are the most important channel for radiation loss, also at elevated temperatures (see for example [10]). Around t = 700 ms the radiation level meets the amount of input power, leading to the radiative collapse of the plasma starting at t = 720 ms.

Figure 7.6: Checking of the calibration of pyroelectric bolometer.

Shot #35579. The left figure shows power, the right figure the energy balance.

For the most recent campaign (winter 2002/2003) figure 7.6 shows the interval of ohmic heating of the density limit discharge #35759 (n_{e} = 4 × 10^{14}cm^{−3} in the center). The plasma current reached constant level of I_{p} = 96 kA in t = 210 ms. It seems that the calibration coefficient of the pyroelectric bolometer is slightly too high since it obviously overestimates the radiated power around t = 350 ms (but still less than 10 %).

The pyroelectric detector shows a highly stable power response and calibration needn’t correction in the past.

7.2.2 Checking of the flat AXUV-responsitivity range

To calibrate AXUV detectors using the pyroelectric device only shots showing no or very few power carried by low-energy neutrals may be used, since AXUV don’t measure them. For the first, the calibration is done for radiation at higher photon energy (where the responsitivity is flat, as shown in figure 3.3). Shots emitting an important amount of power in the low energy range (where the responsitivity of AXUV is lowered) has been avoided for this task.

A good candidate for this procedure is again ”wolfram” shot #32441. Figure 7.7a compares the signal from the calibrated pyroelectric bolometer with the sum of all 16 AXUV channels. The signals of the individual AXUV detectors have previously been multiplied by the estimation factors calculated in chapter 5 which include geometry and relative calibration presented in section 7.1.1. Figure 7.7b shows the ratio of both signals, i.e. \frac{∑_{i}(P_{i,AXUV} )}{P_{pyroelectric}} in function of time. In the following, this ratio will be called discrepancy (see also later in section 8.1.2).

In shots where the density was by increased by injection of pellets a rather low amount of power is lost by low-energy neutral particles since a higher agreement between the pyroelectric bolometer and the sum of AXUV signals is achieved. The confinement regime itself will be discussed later in section 8.2.1. Figure 7.8 shows the power signals and the discrepancy for shot #32470. Just before the injection of the second pellet (t = 630 ms) both power signals

Figure 7.7: Checking of calibration of AXUV detectors. Shot #32441 with a high level of tungsten line radiation. The left figure shows the signal from the pyroelectric bolometer and the sum of all 16 AXUV channels. On the right figure the ratio between the pyroelectric bolometer and the sum of the calculated AXUV signals is plotted.

overlap. The reason for the drop of the bolometer signal around t = 800 ms is not understood since no change is obtained in other signals for this time.

Figure 7.8: Checking of calibration of AXUV detectors. Shot #32470 with high density. Figure a.) shows again total radiated power and figure b.) the discrepancy ratio.

A last example for radiation dominating the power losses is discharge #31615, where in t = 585 ms arcing [22] released some iron atoms from the diagnostic flanges (figures 7.9). The flanges are made of stainless steel and exhibit rather sharp edges, where the electric field may become important and lead to a corona discharge. The arcing flash was observed by a video camera looking inside the vessel. Iron is ionized and shows a high level of line radiation. Discrepancy is above 90 % up to t = 970 ms, where the current was switched off.

The previous figures lead to the conclusion that the calculation using an averaged responsitivity gives very good results for radiation of higher photon energies. The total radiated power mea-

Figure 7.9: Checking of calibration of AXUV detectors. Shot #31615 with a high level of iron line radiation. Figure a.) shows again total radiated power and figure b.) the discrepancy ratio.

sured by the entirety of AXUV detectors corresponds to the value measured by the pyroelectric device in situation where both detectors should measure the same. When using the estimated translation factors (table 5.1) a further absolute calibration is therefore not necessary.

7.2.3 Checking of the AXUV-responsitivity hole

The AXUV detectors used in the frame of this work have been installed on T-10 in May 2001 and were operational up to the beginning of the year 2003. After the removal of the detector from the pinhole camera, the entrance window seemed to be covered by a very thin film of (probably) carbon. The color of the film (see figure 7.10) is something between green and grey in the center and gets dark blue for the outermost used channel (around 500 nm). The visible color corresponds to the constructive thin-film interference of light reflected on the top and on the bottom of the film. The minimum thickness d of the film is related to the wavelength λ by

d = \frac{λ}{4 · n_{film}}  (7.5)

where n_{film} is the index of refraction of the film. With n_{film} = 1.9 [15] the thickness of the film may be guessed to be at least 70 nm.

To know if this film absorbs incoming radiation or not is an important question, and, when constantly growing during experimental campaign, would probably affect the responsitivity of the diodes in the visible spectrum.

To answer this question, plasma discharges using neon as puff gas have been analyzed. Figure 7.11 shows the spectrum for a shot taken on ASDEX-Upgrade tokamak [48] when neon was puffed in H-mode regime, illustrating the position and relative intensity of Neon lines. The lines are located in the photon energy range of 10 to 50 eV and dominate emissions of other atoms. The most intense peak is at 27 eV (46.6 nm).

Figure 7.12 shows the comparison of two similar discharges on T-10, one without (#34593) and the other with (#34596) puffing of neon gas (puff at more or less t = 725 ms). All

Figure 7.10: Carbon thin-film deposited on the detectors surface. Situation after three experimental campaigns (2001-2002).

Figure 7.11: Neon spectrum on ASDEX-Upgrade. Spectrum measured with SPRED spectrometer (Survey Poor Resolution Extended Domain) in a H-mode discharge. The red line shows the spectrum prior and after addition of neon.

Figure 7.12: Influence of neon gas puff on radiation. Shot #34593 without and shot #34596 with gas puff.

parameters (not shown) except the intensity of the C^{III}-line are identical for these two shots. To qualify how much the presence of neon is seen by the AXUV-detectors, shot #34596 has been scaled to take care of the differences in C^{III} by removing the offset between both shots at t = 650 ms. Figure 7.12 shows the evolution of the pyroelectric bolometer and the sum of the AXUV signals when the additional radiation due to the puffing is calculated with a responsitivity equal to 0.18 A/W, corresponding to the highest peak of neon radiation (at 27 eV, see figure 3.3 for the corresponding responsitivity). Indeed the resulting increase on both diagnostics is the same (ΔP_{pyroelectric} = ΔP_{AXUV}) in t = 900 ms. where C^{III} intensities again reach the level shown in t = 650 ms (for intermediate times the signals should not be compared).

Figure 7.13: Relative radiation modification due to neon gas puffing. The difference between shots #34593 and #34596 is shown for pyroelectric bolometer and AXUV-photodiodes.

This is clearly seen on figure 7.13, where only the difference between the two shots is shown. This result leads to the conclusion that the film does not alter the responsitivity down to 30 eV, and it is seen that the responsitivity provided by the manufacturer perfectly describes the measurements.

7.2.4 Measurement of low-energy responsitivity after operation

A further experiment using a Helium-Neon laser (wavelength λ = 632.8 nm corresponding to photons of energy equal 1.96 eV) was performed to investigate the influence of the observed carbon thin-film on the lower end of the responsitivity curve. The wavelength of the laser is located on the right slope (1.96 eV) of the lowermost responsitivity peak in figure 3.3 The power of the laser (2.8 mW) was reduced by 4 ‰using absorbing glasses. When centralized on a detector surface, 82 % (9.2 μW) of the remaining beam power were deposited on the active surface ^{(1)}. The known input power^{(2)} was compared with the response of the used array and a brand-new array (of different production lots). The result is shown in figure 7.14. The new array has a higher responsitivity (0.46 A/W) than specified by the manufacturer, but its value is quite stable. The used array shows still higher responsitivity (0.62 A/W), the film seem to increase the responsitivity at these low energies, as reported in [64] for increased oxide layer thickness. Also in [64] it is shown that this increase in responsitivity is only found in a very narrow energy range and it will not have an influence on measurements of plasma radiation.

Figure 7.14: Measurement of AXUV responsitivity at 1.96 eV. The manufacturer tells a value of η = 0.33 A/W. The new array shows 0.46 A/W, the used even 0.62 A/W in mean.

7.3 Calculation of the yearly radiation dose

The total deposited power on the AXUV-detectors installed on T-10 during all discharges of the two experimental campaigns in 2002 was calculated^{(3)} to be 6 mJ per detector in mean. When naively assuming the totality of this energy carried by photons with energy of 100 eV, the corresponding and largely overestimated total photon fluence would be less than 4×10^{14} a year. Even after several years of operation, the limit specified by the manufacturer (10^{16} photons of 100 eV, see figure 3.4) would not be reached. This estimation assumes that the pinhole camera is removed from the diagnostics port during the vessel conditioning (glow discharges) at the beginning of each experimental campaign.

(1) determined by scanning the profile of the spot of the laser with an AXUV-detector

(2) the remaining power in the beam was not measured absolutely, but the laser power is known by 0.1 mW.

(3) By integrating the total power measured by the detectors for all shots over time.

Diploma work 2002-2003  Christian Schlatter

Experimental radiation losses studies

During the autumn/winter campaign in November and December 2002, several regimes have been investigated by the AXUV detectors. Some of them illustrate the capabilities of the semiconductor photodiodes, other show problems when using AXUV technology for the monitoring of total radiation for power control purposes.

8.1 Introductory notes

8.1.1 Profiles of temperature and density

The following sections will show plots of what is seen on the AXUV-detectors (time dependence of chord signals and radial emissivity) throughout these different regimes. For qualitative interpretations of the power behavior the density and temperature profiles have been calculated, but both are not very accurate. Density reconstruction was achieved using the expansion function reconstruction algorithm of the DAS Tools package^{(1)} using sometimes less than 8 chord measurements. Temperature profiles were calculated according to the procedure depicted in appendix D. The absolute values in the center and the shape of the profiles are in general satisfactorily reconstructed, but values for minor radii greater than r = 20 cm should be taken with a pinch of salt.

8.1.2 Detector discrepancy ξ

Due to their different measurement principles, pyroelectric bolometer and AXUV-photodiodes do not measure the same. Low energy neutrals are only accounted by the former device, as discussed in section 3.2. The calculation of the ratio between the total power measured by both detectors, i.e.

ξ = \frac{∑_{i=1}^{16} P_{i}^{AXUV}}{P^{pyro}}  (8.1)

(as already done in the previous chapter) gives an estimation of the importance of neutrals in the power loss of the plasma. ξ ≃ 1 means that power is lost by radiation only, ξ = 0.8 means that 80 % of the loss is radiated and the rest is carried away by neutrals. In the following ξ will be called the discrepancy between both detectors. In section 8.2 the discrepancy will be calculated for the presented discharges but its main discussion and significance is postponed to section 8.3.

(1)

DAS Tools is the software front-end of the T-10 SQL database, gathering all measurement diagnostics

and providing various data plotting and data processing features.

Diploma work 2002-2003  44  Christian Schlatter

8.1.3 Evaluation of impurities using the plasma emissivity

As shown in section 2.3, the line radiation of heavy impurities is the most important power loss in tokamak plasmas. The presence of heavy impurities in the plasma can be estimated by the calculation of the effective charge Z_{eff} defined in equation 2.4. Appendix C.1 shows three different ways how Z_{eff} can be found (from continuum radiation, Spitzer resistivity formula and from the power measured by AXUV detectors). The latter method assumes coronal equilibrium of the ionization stages, absence of neutrals and carbon as the unique present impurity. Of course this can lead to important errors in the estimation of the radiated power since in T-10 coronal equilibrium is not always achieved and also heavier impurities were observed. The following list quickly resumes the possible reasons for underestimation of the power loss.

impurities out of coronal equilibrium: carbon radiates up to more than three orders of magnitude for temperatures higher than 10 eV, iron up to more than two orders of magnitude for temperatures higher than 100 eV but may also be mistaken up to 20 times at low temperatures of some eV [28].

heavier impurities: one iron atom radiates two to three orders of magnitude more than a carbon atom (see figure 2.2), tungsten even four orders of magnitude more at T_{e} = 1 keV [10].

presence of neutrals: in coronal equilibrium, the presence of 1 % (10 %) of neutral deuterium increases the radiation up to more than two (three) orders of magnitude for temperatures greater than 10 eV [29]. The increase is due to charge-exchange recombination of higher carbon ionization states resulting in a shift of the ionization balance towards less ionized (and thus more radiative) charge state distributions.

In the worst case Z_{eff} derived from the AXUV signals (equation C.1) will be also too big by the same orders. Nevertheless, if very low Z_{eff} are found, the real Z_{eff} will be equal or lower, the calculated Z_{eff} can be considered as upper limit. On the other hand, a Z_{eff} (determined from AXUV) very close to that calculated from the Spitzer formula indicates that coronal equilibrium is achieved, no heavier impurities than carbon are present and that no important charge-exchange takes place. All this should be kept in mind when interpreting the sometimes elevated Z_{eff} given in the following.

Better estimation of the radiation and its origin needs the explicit simulation of the time dependent population of the ionization stages taking into account charge-exchange and more spectroscopic measurements showing the presence of heavier impurities.

8.1.4 General sequence of a T-10 discharge

Plasma discharges on T-10 begin with the timing signal provided by the operator, which starts all diagnostics equipment. 100 ms later begins the preparation of the plasma by gas puffing, in the same time the ohmic heating current is induced, whose programmed value is ramped up during 200 .. 300 ms (see for example figure B.1). In some regimes additional heating is provided by one or more gyrotrons, which are in general applied later than t = 500 ms. The plasma current can be maintained up to t = 1 s, if no disruption has occurred until then.

8.2 Spatial evolution of radiated power in regimes with improved confinement 46

8.2 Spatial evolution of radiated power in regimes with improved confinement

The cones of view of the AXUV detectors cover several regions of the plasma cross section permitting to study localized radiation processes or compare the evolution of the radiation coming from the plasma core to the radiation issued at the edge. On T-10 three regimes exhibit improved confinement:

- Density limit

- T-10 H-mode

- Biasing

The next paragraphs present these three regimes by correlating the radiated power to the common plasma parameters.

8.2.1 Density limit

On T-10 the density limit regime is investigated by pellet injection or deuterium gas puffing. The first method is presented in the following, the latter thereafter.

Density limit by pellet injection

In discharge #35886, the density was increased by two deuterium pellets. The measured signals and parameters are presented on the following figures. Compilation figure 8.1 shows the radiation as measured by the AXUV detectors, the electron density and the electron temperature. On the left part of the page these quantities are shown in function of time (line-integrated chord signals for the density and the radiation power) for some different radial positions, whereas on the right plots of profiles for some selected times can be found. Figure 8.2 gathers some parameters of interest for this discharge.

The toroidal magnetic field was B_{T} = 24 kG. Between t = 100 and 400 ms the vessel was supplied with deuterium (see the gas puff signal) and the plasma current (not shown) was built up to I_{p} = 305 kA in t = 400 ms. In t = 556 ms a first deuterium pellet was injected, followed by a second in t = 657 ms. The injections are clearly visible on all signals. Before the injection temperature and electron density are almost constant, the addition of deuterium causes the density to increase, hence a possibility to achieve high densities (n_{e} > 1.2×10^{14} cm^{−3} in the center before the disruption). The cold frozen pellet is evaporated and getting completely ionized on the way entering the plasma, both processes lead to an immediate lowering of the electron temperature. Despite the breakdown of the temperature the overall confinement gets better with the pellets injected, as shown on the plot showing the signal proportional to the pressure β.

The radiation measured by AXUV-detectors is increased after each injection, particularly after the second pellet the radiation loss is strongly increased in the center, evidently due to the violent drop in temperature leading to the population of lower but more radiative ionization stages of the ions. Although the behavior of n_{e} and T_{e} are similar after both injections, the picture seen on AXUV is different: The outer chords measure a decrease in radiation after the second pellet (see behavior from t = 670 to 700 ms), but the radiation from the center increases all the more, i.e. the emissivity profile gets more peaked on the minor axis. For

Figure 8.1: Shot #35886: Pellet injected density limit regime. The left column shows temporal evolution of signals, on the right the profiles (radial dependence) of the corresponding quantity. From the top to the bottom the radiated power P (measured by AXUV-detectors), the electron density n_{e} and the electron temperature T_{e}.

Figure 8.2: Shot #35886: Pellet injected density limit regime. From the left top to the right bottom are shown: ohmic input power and power loss measured by AXUV and the pyroelectric bolometer; the discrepancy; the deuterium gas puff intensity; the signal proportional to the pressure β; line radiation intensity for the D_{α} and C^{III} lines; and finally the signal proportional to Z_{eff}. The toroidal magnetic field was B_{T} = 24 kG and the plasma current I_{p} = 305 kA (constant from t = 400 ms on).

time [ms] Z_{eff} (AXUV) Z_{eff} (Spitzer)
400  5,37  8,72
500  6,65  2,17
600  5,25  1,43
700  11,80  (2)

Table 8.1: Z_{eff} for shot #35886 calculated from the AXUV signals (2^{nd} column) and by classical Spitzer formula (last column).

the center, both, increasing electron temperature and decreasing electron density after the injection would lead to less line radiation, so the growing central radiation could be explained by an accumulation of impurities in the center.

The interpretation of calculated Z_{eff} from AXUV-signals leads to the same conclusion, table 8.1 shows that Z_{eff} is doubled after the injection of the second pellet. The bad agreement between Z_{eff}^{AXUV} and Z_{eff}^{Spitzer} may be due to the presence of heavier impurities, which radiate much more even with smaller ion densities, hence Z_{eff} would be decreased when taking them into consideration. Further the coronal equilibrium may not have been realized, what again leads to an overestimation of Z_{eff}. Due to the lack of sawteeth on the soft X-ray signals after the second pellet, the q=1 surface could not be determined for these times, and therefore no value can be calculated using Spitzer’s formula. The increased Z_{eff}^{AXUV} after the second pellet is somehow confirmed by the time dependence of the relative global Z_{eff} measured from the continuum (last figure in compilation 8.2, in arbitrary units), calling again for impurity accumulation in the core plasma.

After injection of the pellet a decrease of Z_{eff} is somehow expected, since the impurities are diluted by the added deuterium. The rise of Z_{eff} after the second pellet is therefore surprising. The increased intensity of the C^{III}-line points to a higher influx of carbon to the plasma [7], hence more impurities.

Gas-puffed density limit

A completely different approach to reach the density limit is obtained when the density is increased by deuterium gas puffing. Figures 8.3 and 8.4 show compilations of the signals and main plasma parameters for shot #35811. The toroidal magnetic field was 23.2 kG. The plasma is heated ohmically by a current of 205 kA which is switched on as usual in t = 100 ms, reaches its constant value in t = 300 ms and is maintained up to t = 900 ms. Further heating is achieved using gyrotrons working at the electron cyclotron frequency, which are successively powered-on to provide further heating. The two gyrotrons (B+C) are switched on in t = 550 ms (550 kW), followed by two (A+A) in t = 600 (700 kW), the last (A5) in t = 625 ms (550 kW) supplying a total heating power of 1800 W. The low magnetic field results in off-axis heating, as seen on the temperature profile.

The electron-cyclotron signals used for the determination of the temperature are heavily disturbed by the power-on of the gyrotrons, as if temperature would fall back to zero for a short time. As the gyrotrons they work on the second harmonic of the ECE frequency.

(2) the q-profile could not be determined for this time.

Diploma work 2002-2003  Christian Schlatter

Figure 8.3: Shot #35811: Density limit regime with gas puffing. The left column shows temporal evolution of signals, on the right the profiles (radial dependence) of the corresponding quantity. From the top to the bottom the radiated power P (measured by AXUV-detectors), the electron density n_{e} and the electron temperature T_{e}.

Figure 8.4: Shot #35811: Density limit regime with gas puffing. From the left top to the right bottom are shown: ohmic and gyrotron input power and power loss measured by AXUV and the pyroelectric bolometer; the discrepancy; the deuterium gas puff intensity; the signal proportional to the pressure β; line radiation intensity for the D_{α} and C^{III} lines; and finally the signal proportional to Z_{eff}. The toroidal magnetic field was B_{T} = 23.2 kG and the plasma current I_{p} = 200 kA (constant from t = 300 ms on).

To increase the density of the plasma, an intense gas puff is unleashed together with the first gyrotron. The puff lasts about 100 ms. Indeed the electron density starts to increase strongly to reach a value of 1.6×10^{14} cm^{−3} in the center. During puffing the emissivity shows highest level at the boundary (see profile for t = 600 ms) and shows, after shutting of the intake valve, highest emissivity in r = - 20 cm before the power-down of the gyrotrons (900 ms, see profile in t = 850 ms). After reconstruction, the innermost emissivity was slightly negative, its value have been set to zero.

The D_{α}-line goes up as long the deuterium-puff valve was open but decrease after its shutting. This looks like D_{2} gets rarefied (worse recycling) at the boundary (only here temperatures are sufficiently low to enable it to radiate). As often observed, also C^{III} intensity grows with the operation of the gyrotrons, although temperature at the boundary almost stays constant (not reliable for |r| > 20 cm). Since emissivity is extremely low in the center, possible impurities with higher Z must be at the boundary. Indeed, overall Z_{eff} derived from the continuum measurement seems to be very low. Spitzer’s formula gives Z_{eff} = 2.79 and 2.3 for t = 500 and 850 ms respectively. Impurities are getting diluted by the strong deuterium puffing. During operation of ECR-heating the confinement is improved, as indicated by the signal proportional to β.

This regime systematically shows very bad agreement between pyroelectric bolometer and radiated power determined by AXUV technology. The strong increase of power loss seen by the pyroelectric detector is not found on the photodiodes, which shows four times less power. After putting into operation of the gyrotrons, discrepancy decreases to poor 20 % (see further discussion in section 8.3).

8.2.2 T-10 H-mode

High-current T-10 H-Mode

This type of H-mode is only obtained with high plasma currents. In the winter campaign 2002/2003 current was not enough high for this regime being achieved. Compilation figures 8.5 and 8.6 present such a high-current T-10 H-mode, which exhibits some particular T-10 features. This shot has already been realized in 2001. The plasma is supplied by deuterium puffing up to t = 350 ms (see gas puff signal and evolution of density). The plasma is ohmically heated by a plasma current of I_{p} = 280 kA which is attained from t = 425 ms on). At t = 550 ms the gyrotrons start to deposit a constant heating power of P_{ECRH} = 1.1 MW at the inner side of the vessel (the magnetic field is B_{T} = 21.5 kG), increasing both temperature and density throughout the plasma. In the region of heating the ECE-signals did not provide physical information, therefore temperature (assumed symmetrical) is only shown for positive minor radii. The profile of density, well-rounded when only ohmic heating was active, gets now bumped. Using external magnetic field coils, the plasma has been moved towards the center of the tokamak, as it can also be seen on the shifted density profile.

The onset of H-mode takes place in t = 740 ms. Temperature and density get increased, leading to better confinement (see the signal proportional to β). The mode is stable up to t = 950 ms, when the gyrotrons has been switched off.

AXUV-signals provide further insight on how the plasma behaves in this shot. After the heating current becomes stable, all channels show almost constant radiation level, decreasing

Figure 8.5: Shot #31899: High current T-10 H-mode regime. The left column shows temporal evolution of signals, on the right the profiles (radial dependence) of the corresponding quantity. From the top to the bottom the radiated power P (measured by AXUV-detectors), the electron density n_{e} and the electron temperature T_{e}.

Figure 8.6: Shot #31899: High current T-10 H-mode regime. From the left top to the right bottom are shown: power loss measured by AXUV and the pyroelectric bolometer; the discrepancy between them; the deuterium gas puff intensity; the signal proportional to the pressure β; line radiation intensity for the D_{α} and C^{III} lines but also visible light due to glowing of the limiter; and finally the signal proportional to Z_{eff}. The toroidal magnetic field was B_{T} = 21.5 kG and the plasma current I_{p} = 280 kA (constant from t = 425 ms on).

density in the center after the stop of gas puffing and the increase of temperature due to heating seem to balance out the radiation processes. ECRH-heating leads to an immediate increase in all channels, which are then again constant up to the bifurcation to H-mode. Whereas the total radiated power seems almost unchanged after the transition (the pyroelectric bolometer and the sum of all AXUV chords do not alter remarkably), individual chords show very different behavior. In the center the radiation level decreases, but at r = 20 cm the power loss increases strongly. The emissivity profile has been reconstructed separately for inner and outer chords and the apparition of the high and narrow emissivity peak at r = 20 cm indicates a possible transport barrier at this position. Since neither temperature nor density show a behavior which could explain this emissivity peak, it may again be due to a neoclassical accumulation of impurities at this position. As a result of the inward shift of the plasma this picture can not be seen for the inner part of the vessel, the plasma touches the limiter (see the high density at r = - 34 cm) and bring it to glow. Glowing is indicated by the visible light signal (on the same figure as the carbon and deuterium lines) which is measured on a chord pointing to the limiter; its signal strongly increases with the onset of H-mode. Indeed the innermost AXUV-channel shows highest radiation loss, what can also clearly be seen on the inner emissivity profile. The outermost (r = 26.6 cm) AXUV channel lies still inside the last closed flux surface (LCFS), where density and temperature are very low (however, remember that the signals may not be very accurate for this position). With the onset of H-mode radiation from there decreases also (see the time evolution of this AXUV signal), possibly due to the reduced transport of radiating ions from inside the plasma.

The onset of H-mode shows a decrease of intensity of the C_{III} and D_{α} lines, a feature commonly observed in H-mode regimes. The level of C^{III} radiation is much higher than for example in shot #35886 (figure 8.2, the scales are in arbitrary units, but may be compared among each other) which may be explained by the flatter temperature profile at the outer boundary, where this ionization stage can be found.

Calculation of the effective charge in the center using AXUV gives Z_{eff}^{AXUV} = 43, 58 and 23 for the times t = 600, 700 and 940 ms respectively. The relative evolution is qualitatively confirmed by the global Z_{eff} derived from the continuum radiation (see the accompanying figure). For the peak in emissivity on r = 20 cm in t = 940 ms results Z_{eff} may also be calculated, resulting in senseless Z_{eff}^{AXUV} = 195, definitely showing the limits of the simple model used for its derivation. Too, due to the fact that the neighboring AXUV channels overlap a little (the slit is not infinitesimally narrow), the real emissivity peak may still be higher and narrower. Of course, with a modelling taking into account the real composition of the plasma (also heavier impurities) and including corrections for non-coronal equilibrium more reasonable values would be obtained. In principle, with such an improved model, Z_{eff} could be calculated for each ring of emissivity.

Low-current T-10 H-Mode

In winter campaign 2002/2003 only this type of H-mode regime (with plasma current below the limit for which the previous type of H-mode can be obtained) was produced. Figures 8.7 and 8.8 describe shot #35838 of this regime. Indeed the plasma current was smaller by 30 kA than for shot #31899 (the previously discussed high-current T-10 H-mode), i.e. I_{p} = 250 kA (reaching this value in t = 340 ms). For discharge #35838 the toroidal magnetic field was B_{T} = 25 kG. The onset of the H-mode seems not to take place immediately in t = 600 when the full

Figure 8.7: Shot #35838: Low current T-10 H-mode regime. The left column shows temporal evolution of signals, on the right the profiles (radial dependence) of the corresponding quantity. From the top to the bottom the radiated power P (measured by AXUV-detectors), the electron density n_{e} and the electron temperature T_{e}.

Figure 8.8: Shot #35838: Low current T-10 H-mode regime. From the left top to the right bottom are shown: total heating power and power loss measured by AXUV and the pyroelectric bolometer; the discrepancy; the deuterium gas puff intensity; the signal proportional to the pressure β; line radiation intensity for the D_{α} and C^{III} lines; and finally the signal proportional to Z_{eff}. The toroidal magnetic field was B_{T} = 25 kG and the plasma current I_{p} = 250 kA (constant from t = 340 ms on).

time [ms] Z_{eff} (AXUV) Z_{eff} (Spitzer)
500  1,45  2,50
610  2,57  7,21
750  2,89  (3)

Table 8.2: Z_{eff} for shot #35838 calculated from the AXUV signals (2^{nd} column) and by classical Spitzer formula (last column).

power of the gyrotrons is unleashed (spontaneous H-mode). Density and especially central temperature are strongly increased, continue increasing everywhere in the plasma during constant ECR-power deposition, leading to a better confinement, as it can be again seen on the signal proportional to the pressure β. After inversion of the density chords, a slightly hollow density profile is found. The mode ends with the disabling of the gyrotrons. In contrast to the high-current T-10 H-mode the D_{α} line intensity doesn’t decrease when bifurcation takes place, since lines show an increased level during the activity of the mode. The AXUV-chord signals show similar behavior in both types, in the center radiation decreases again, whereas at the edge an increase is seen, indicating possible accumulation of impurities at r = 20 .. 25 cm, a bit further from the center than in high-current T-10 H-mode shot #31899. In the center, less radiation is issued, emissivity is almost zero. The increased carbon line may be produced again by the heavy load of the limiter (sputtering), as shown on the emissivity profile. This time, discrepancy between pyroelectric bolometer and AXUV total power is not violently modified by the operation of gyrotrons and stays almost unchanged during the H-mode.

Table 8.2 shows Z_{eff}. Although Z_{eff} increases slightly in the center its value is very low, confirming the absence of heavy impurities in the center. Overall Z_{eff} from continuum intensity is also very low (the ordinate is in arbitrary units, but its range is the same for all plots in this chapter and may be compared among each other).

8.2.3 Biasing

On T-10 a third regime with improved confinement is achieved by biasing the plasma by an electrode [17]. Different experiments have shown that biasing modifies the profiles at the edge and in the SOL, influences the recycling of particles and can lead to better confinement (review paper [16]).

The head of the biasing electrode is introduced into the plasma at a radius of approximately r = 28 cm. At a given time, a grid of capacitors (capacity C = 0.15 mF), loaded to a voltage of 400 V against the wall, are discharged through the electrode (anode (+)). This increases the potential at the edge, hence the radial electric field E_{r} is modified (E_{r} points outwards). Changing E_{r} concerns the cross-field transport of ions, i.e. confinement. Positive biasing voltage decreases the width of the SOL due to steeper gradients of density, what in turn improves the particle screening efficiency. Compilation figures 8.9 and 8.10 show the comparison of a discharge with (#34631) and without biasing (#34632). Dark colors show signals with biasing, light colors without. For the time dependent signals, blue represents signals measured at the edge, red color shows the behavior in the center. For profiles, blue signals show the situation just before, red after biasing was enabled for shot #34631.

(2) the q-profile could not be determined for this time.

Diploma work 2002-2003  Christian Schlatter

Figure 8.9: Shots #34631 (with biasing) and #34632 (without). The left column shows temporal evolution of signals, on the right the profiles (radial dependence) of the corresponding quantity. From the top to the bottom the radiated power P (measured by AXUV-detectors), the electron density n_{e} and the electron temperature T_{e}.

Figure 8.10: Shots #34631 (with biasing) and #34632 (without). From the left top to the right bottom are shown: total heating power and power loss measured by AXUV and the pyroelectric bolometer; the discrepancy; the deuterium gas puff intensity; the signal proportional to β; line radiation intensity for the D_{α} and C^{III} lines and finally the signal proportional to Z_{eff}. The toroidal magnetic fields were B_{T} = 25 kG and the plasma currents I_{p} = 215 kA (constant from t = 300 ms on).

time [ms] Z_{eff} (AXUV)  Z_{eff} (Spitzer)
#34631 #34632  #34631 #34632
400  76,5  77.6  2.17  2.84
800  175  128  2.24  1.95

Table 8.3: Z_{eff} for shots #34631 and #34632 calculated from the AXUV signals (2^{nd} column) and by classical Spitzer formula (last column).

The plasma current was constant from t = 300 ms on (I_{p} = 215 kA) and one single gyrotron (active from t = 520 to 875 ms) deposited a total power of 350 kW on-axis (the magnetic field was B_{T} = 25 kG). In t = 600 ms the biasing current was switched on for shot #34631 only. Profiles and temporal evolution shown in figure 8.9 may infer that biasing doesn’t have an important influence on electron temperature and electron density at the boundary, but it should be recalled that both profiles are not dependable for these radii (greater than r = 20 cm). Nevertheless, no important relative change between the regime with and without biasing is observed leading to the conclusion that if there is modification of temperature, it must be small. But in the center, both, n_{e} and T_{e}, show an important increase and confinement is therefore ameliorated (see β).

The total power measured by the pyroelectric bolometer and AXUV-detectors show increasing radiation during biasing, whilst radiation showed constant level in its absence. In contrast to what is seen on density and temperature, the AXUV chords do not only see an important change in radiation in the center, but also at the boundary. As the discrepancy is almost identical between the two shots, biasing seems not to have an influence on charge exchange. Also the intensity of the lines (D_{α} and C^{III}) are practically the same. On discrepancy the limited time resolution of the pyroelectric bolometer is clearly seen, when the gyrotron is switch on (off), an upward (downward) ripple is encountered due to the immediate radiation level increase (decrease) which can not be resolved by the pyroelectric device.

Table 8.3 compares Z_{eff} for both shots before biasing and ECRH-heating (t = 400 ms) and during biasing of shot #34632 (t = 800 ms). Before biasing Z_{eff} is similar, for the later time Z_{eff} is increased. This is also confirmed by the relative evolution of the global Z_{eff} calculated from the continuum radiation. The overall increase of emissivity and Z_{eff} without notable modification of density and temperature at the edge really indicates the well-known property that biasing modifies the transport of impurities.

8.3 Comparison of AXUV with pyroelectric bolometer

In the previous sections the discrepancy (as defined in equation 8.1) for different regimes was shown. Figure 8.11 reviews different behaviors of discrepancy found within different regimes. The presence of heavy impurities like iron (#31615) or tungsten (#32441) lead to a discrepancy close or equal to 1, as shown in section 7.2.2. These regimes report the correct calibration of the AXUV detectors, since in absence of low-energy neutrals, both detectors must show the same response.

As a rule, the power measured by AXUV is much less than that obtained with the pyroelectric detector, often a discrepancy ξ of about typically 50 % is observed. depending an the regime

Figure 8.11: Review of discrepancy for different confinement regimes. From top left to right down are shown: discharges #31615 (arcing of iron); density limit regimes: #35886 (deuterium pellet injection) and #35811 (deuterium gas puffing); T-10 H-modes: #31899 (high-current) and #35838 (low-current); finally biasing (#34631).

and heating method. With the opening of the low-temperature neutral gas puffing in t = 100 ms the discharge starts with a discrepancy of almost zero (these neutrals are not seen on AXUV). With increasing current, temperature increases and the atoms are ionized, hence radiation gets the longer the more important and hence discrepancy grows. See for example shot #35886, where ξ grows almost linearly as long the plasma current increases. Once the latter is stable, also ξ stays constant.

A tokamak plasma can loose an important amount of power through low-energy neutrals by charge-exchange processes. Reference [30] reports the domination of power loss by neutrals on radiation at the edge. Fast neutrals can be found throughout the vessel but due to the high plasma density, low energy neutrals (≦ 500 eV) can only be found on the very edge of the plasma.

Following the procedure presented in [30], the measurement of total power loss of the AXUV detectors can be subtracted from the pyroelectric detector to obtain the total power lost through slow neutrals. But the very low discrepancy often encountered in the gas puffed density limit regime (see shot #35811) raise some questions if such a procedure can be applied in the environment of T-10. Studying this regime, [32] reported an intense flux of neutrals carrying energy away from the plasma, somehow expected due to the strong puffing of the SOL by deuterium. Anyhow it is hard to believe that 80 % of the power is taken away by neutrals. The following list shows possible problems which must carefully be analyzed because they may be reasons for an underestimation of the radiated power and therefore falsify the neutral power determined by above procedure.

- The pyroelectric bolometer is disturbed by the operation of the gyrotrons.

- The contribution of radiation in the range of reduced AXUV responsitivity (2 - 20 eV) is underestimated.

- The total field of view of the AXUV detectors doesn’t cover the whole field of view of the pyroelectric device.

- The plasma discharge exhibits a strong top-down asymmetry.

The following sections try to give answers.

8.3.1 Disturbance of the pyroelectric bolometer by gyrotrons

Both, the gas puffed density limit (high density) and the high-current T-10 H-mode (also rather high density) show a drop of discrepancy during the operation of gyrotrons.

The pyroelectric bolometer is protected from the deposition of gyrotron heating power by means of a fence reflecting the microwaves. In biasing (low density) and low-current H-mode (high temperature, mean density) the operation of the gyrotrons does not alter discrepancy remarkably.

Figure 8.12: Discrepancy increase with the operation of the gyrotrons. The gas puffed density limit plasma discharge #35579 is shown .

On the other hand, the gas puffed density limit discharge #35579 (already presented in figure 7.6, in the ohmic stage of the discharge, almost 100 % of the heating power is radiated) shows an increase in discrepancy (figure 8.12) with the operation of the gyrotrons, leading to the conclusion that the fence supplies an effective screening of the pyroelectric bolometer against the gyrotron microwaves.

8.3.2 Underestimation of radiation in the AXUV-responsitivity hole

When using the AXUV-photodiodes with an average responsitivity of η = 0,24 A/W to measure absolute values of the total radiated power, it is necessary to verify that no important amount of the radiation is found in the region where η is reduced. Considering a typical (T-10) deuterium plasma with essentially carbon and traces of heavier impurities, the lines of D_{α} (121.5 nm ˆ= 10.2 eV) and two of the most intense of C^{III} (97.7 nm ˆ= 12.7; 117.6 nm ˆ= 10.6 eV) lie in the responsitivity hole and must be evaluated.

On T-10 both, the D_{α} and the lower C^{III} line are measured, but no absolute calibration is available.

D_{α}-line

The deuterium line is only observed at very low temperatures, the maximum is found in T_{e} = 2 eV [31]. Such low temperatures are only found at the LCFS or in the SOL, where the density is very low. On Alcator C-mod the emissivity of D_{α} was found too low by three orders of magnitude to explain an influence on the total measured power due to the reduced responsitivity (η = 0.11 A/W).

Irrespective of the results on Alcator C-mod, the same conclusion is found on T-10. A good candidate for the analysis of the importance of the D_{α}-line is the density limit discharge with a lot of deuterium puffing, #35811. During gas puffing (see again figures 8.4) the measured D_{α}-line increases indeed extremely strong (in comparison with other shots). The discrepancy follows first the behavior of the line (t = 550 to 650 ms). After the end of puffing, the line decreases to almost the initial level, but discrepancy stays low.

Another example is the low-current T-10 H-mode (#35838, figures 8.8). The D_{α}-line intensity goes up by 6 times but discrepancy stays remarkably stable.

Both discharges show that due to its minor contribution to the total radiated power, the lowered responsitivity of the D_{α}-line detection can be neglected.

C^{III}-line

Carbon is the main impurity on T-10 and therefore the most important channel for power loss through line radiation. The two intense C^{III}-lines in the responsitivity hole are dominated by lines of higher ionization states, since C^{III} is only populated at the boundary or by important charge exchange shifting the equilibrium to lower ionization stages.

In the aim to judge the importance of the C^{III} line, again a comparison of the behavior of the line with its impact on the pyroelectric bolometer may be carried out. For the gas puffed density limit discharge #35811 (figures 8.4), at first sight the strong fall of discrepancy could be explained by the increase of the C^{III}-line, but what about its increase after t = 900 ms when the pyroelectric power falls? Here AXUV shows an increase instead.

Further insights give figure 8.13, which shows the evolution of the pyroelectric bolometer together with the measured intensity of the C^{III}-line for shot #34593 (T_{e} = 1.8 keV and \overline{n}_{e} = 4×10^{13} cm^{−3}). In comparison with other shots, the line looks quite intense, so this shot represents the situation where power loss through the C^{III} line could become important. The figure

Figure 8.13: Importance of the C^{III} radiation channel (Shot #34593). The behavior of the power measured by the pyroelectric bolometer together with the intensity of the C^{III} line is shown.

speaks volumes about the importance of the line: At t = 700 ms the intensity drops by more than 90 %, but this causes a decrease in power of 10 % only on the bolometer (temperature and density are constant in this time). The length of the reduction of the carbon signal is long enough (60 ms) to exclude a delayed response of the bolometer due to integration by electronics. This example shows that the contribution of C^{III} to the total radiated power is not very big and therefore the power measured by AXUV-detectors is not strongly altered by the lower detection efficiency of that line.

8.3.3 Limited field of view

The currently used setup of the AXUV-detectors covers almost the whole cross-section of the plasma. The outermost point whose radiation intercepts the whole surface of the detector has a position of d = 28.6 cm on the central arc. Therefore the inner and outer part of the scrape-off layer are not covered by the AXUV-detectors (but by the pyroelectric bolometer, whose extended field of view also covers the SOL, see figure 4.1).

In general, no important radiation is expected from the scrape-off layer, due to the low density. Earlier studies of plasma radiation on T-10 have reported important plasma radiation in the SOL during gas-puffed density limit discharges [32]. One reason for the discrepancy ξ = 20 % seen in this regime (#35811) may be due to the fact that AXUV not sees all radiation sources in the SOL.

With a new preamplifier and extended multiplexer with four additional channels the unused outermost detectors of the AXUV-array could also be used and the whole vessel would then be grabbed, making the problem of limited field of view obsolete.

8.3.4 Top-down asymmetries

As explained in chapter 5, the calculation of the total radiated power is based on the assumption of radial symmetry of the radiation processes. In the gas puffed density limit regime optic measurements (visible light) using scanning by a mirror showed strong asymmetric radiation from the top of the vessel. Being closer (farer) to the pyroelectric bolometer (AXUV-detectors), the radiation from this region is overestimated (underestimated), what may be again an explanation of the low ξ = 20 % for shot #35811 of this regime.

8.3.5 Power carried by neutrals

The determination of the power lost by neutrals by the discrepancy of pyroelectric bolometer and AXUV detector is nonsense in case of top-down asymmetry or if both devices don’t cover the same domain of radiation sources. However, these two arguments were only found in the gas puffed density regime and therefore the procedure reported in [30] for the calculation of the neutral power can be envisaged in the other regimes. Figure 8.14 shows the result for the density limit shot #35886.

Figure 8.14: Power carried by low-energy neutrals. Density limit discharge #35886 with deuterium gas puffing. The total power measured by the pyroelectric bolometer, the sum of the calibrated AXUV-signals and the difference between both representing the power lost by low-energy neutrals.

It would also be desirable to carefully simulate the neutral power, in the aim to confirm the discussed approach.

8.4 Partial radiation evaluation: Neon puffing

The lack of spectroscopic measurements makes it in general impossible to distinguish the different radiation processes involved. However, the existence of shots of a same regime, where only a single parameter was changed, permits to visualize weak processes (due to the change of this parameter), that are normally swallowed up by the dominating background radiation.

An illustration of such a procedure was already presented in figures 7.12 and 7.13 (shots #34593 and #34596) where the effect of neon gas puffing on the total radiation was shown.

Figure 8.15: Shots #34596 with neon gas puffing. Top left the AXUV chord neon power (the background radiation of all other than neon was removed) and top right the corresponding neon emissivity profiles. Down left the electron density profile n_{e} and down right the electron temperature profile T_{e}.

In shot #34593 without neon puff it was seen that the emissivity profile in the time interval from t = 650 to 900 ms wasn’t modified (figure 7.12 shows constant total AXUV power). In shot #34596 (with neon puff) the ”background” radiation level in t = 650 ms has been subtracted from the chord signals past the neon puff (around 700 ms) what gives the net power radiated by the added neon. The fact that the decision of the Abel equation 6.8 is linear in the chord brightness permits to reconstruct the partial power radiated by neon. Compilation figure 8.15 shows the reconstruction of the neon emissivity. The puffing of neon was in t = 700 ms.

Interestingly two emissivity peaks appear quite far from the edge, at r = - 13 and + 20 cm (the asymmetry is due to the fact that the plasma was moved outwards for this shot, visible also on temperature and density). The electron temperature is about 400 eV there (for these radii temperature may still considered as reliable) and the maximum of radiation is rather expected to be in r = - 20 and + 25 cm or at least further outside, where temperatures are about 40 eV and neon line radiation is much more important (see figure 2.2). Maybe there is no neon at the boundary...

8.5 Localized and/or fast features

This last section presents fast and/or localized processes, which can be investigated thanks to the high time response and the spatial resolution of the array of AXUV-detectors. Apart from the sawteeth oscillations presented in the following section, the shown pictures can not be found using a diagnostic facility other than the AXUV system.

8.5.1 Sawteeth oscillations

Relaxation instabilities in the core of the plasma when the safety factor q falls below one and magnetic reconnection brings magnetic islands to grow are regularly seen on T-10, the slow increase of the instability and its rapid collapse producing the famous sawteeth signals on density and temperature. Sawteeth are nicely seen on the soft X-ray signals, whose chords have a spatial resolution of about 1 cm in the center of the vessel. Sawteeth can also be seen with AXUV photodiodes, but the existing setup with rough resolution of about 4 cm makes them not very attractive. Figure compares sawteeth on soft X-ray and AXUV for discharge #35909. The slope change (the instability grows inside but decreases outside the magnetic surface with q = 1) was used in the previous sections to determine the position where q = 1 [55], necessary for the calculation of Z_{eff} in the center, as described in appendix C.1.

Figure 8.16: Evaluation of sawteeth (discharge #35909). The left figure shows the signals of the soft X-ray chords, on the right those measured with the AXUV-photodiodes.

8.5.2 Pellet injections (revisited)

As shown in section 8.2.1, the density of the core plasma is comfortably increased when little pellets of frozen deuterium are injected with high velocity (1 km/s) into the vessel. The fast time resolution combined with the spatial determination of local features (even if spatial resolution is not that fine) gives the possibility to examine the radiation properties of the evaporating pellet.

Figure 8.17: Deuterium pellet evaporation. Chord measurements for discharge #35886. Peak positions in t_{1} = 556.46, t_{2} = 556.66 and t_{3} = 556.76 ms are shown.

Deuterium pellet

Pellet injections have been recently [66] been investigated using a video camera. The videotape was filtered on a computer to show the most intense deuterium line only (wavelength 1215 Å[26]) and it was found, that evaporation is observed in the middle third of minor radius only.

Figures 8.17 and 8.18 show the chord brightness and the reconstructed radial emissivity in the vicinity of the injected pellet for shot #35886. In principle the inversion can not be applied in such situations, since the emissivity is distributed very asymmetrically, often even anisotropically inside a (half)ring of assumed constant emissivity and towards the center the error of the reconstruction increases. But the figure shows nevertheless true information from the outside/inside up to the outermost/innermost peak, where it is shown how localized the radiation sources are. The maximum of radiation evolves like a snake, probably due to toroidal rotation of the plasma, since similar behavior was found on the Joint European Torus (JET) when hydrogen pellets were injected [24].

8.5 Localized and/or fast features  70

Figure 8.18: Deuterium pellet evaporation. False radial emissivity profile for discharge due to asymmetric power distribution. #35886.

Figure 8.19: Deuterium pellet evaporation. Attempt of calculating profiles showing the evolution of the peak of radiation for discharge #35886.

The evolution of the chord measurements of the AXUV-detectors show the peak appear, migrate and attenuate on a very short time interval. On figure 8.17 the maximum of the radiation intensity for three times is highlighted. The first and highest peak appears at t_{1} = 556.46 ms on r = - 10 cm (opposite to the side of injection^{(4)}). Then the peak migrates to r = + 10 cm where it can be found at t_{2} = 556.66 ms. Supposing this behavior due to toroidal rotation of the plasma (of course the one-dimensional AXUV-chord measurements don’t permit to verify this conjecture surely), the plasma would have turned half around the vessel in 200 μs. That would correspond to a rotation speed of 23 km/s (measured on the minor axis).

During evaporation of the pellet, the material spreads along the magnetic surface where evaporation takes place. However, on surfaces with rational q the investigations on JET showed that this spreading reduces to a single line and density is locally strongly increased, leading to enhanced radiation seen by soft X-ray detectors (see also [25]).

Figure 8.20: Geometry of the snake. On the q = 1 surface with m = 1 and n = 1, spreading of the material takes place along the red line. By rotating this geometry along the torus, the response of the AXUV chords looks like a snake.

Investigations of the soft X-ray signals show that the q = 1 surface is located in r = 10.8 cm, so just the position of most distance from the center of the snake. The geometry of the magnetic surface with m = 1, n = 1 is a tilted circle (see figure 8.20) and when this structure rotates along the torus, a snakelike emission profile results. This fast first evolution of radiation is observed for almost all deuterium pellet injection shots, the behavior for later times (on t_{3} = 556.76 ms the peak is back on r = 2 cm) show different migrations between left and right channels, mostly very fast attenuated.

Between t_{1} and t_{2} the peak travels across the cones of view of 6 channels - in only 200 μs. The time resolution of the AXUV-detectors is therefore better than 200 μs/6 = 33 μs (this is double the time of channel multiplexing during digitalization, see section 4.4).

The origin of the high time resolution of AXUV is the very fast response time of these detectors, as it can be seen on figure 8.21. Time synchronization of the T-10 diagnostics is

(4)

The pellets are injected from the outer side of the tokamak, with an inclination of 30° to the vertical

direction in cross-section C.

Diploma work 2002-2003  Christian Schlatter

Figure 8.21: Signal response after pellet injection. Plasma discharge #35886. The first plot shows AXUV signals for r = -10 cm (black), 2 cm (red) and 10 cm (green). Below the electron temperature signals for the same positions and lowermost the averaged central chord electron density.

believed to by very precise, and strangely a time delay of the changes in temperature and density is observed. On the soft X-ray chords the perturbation starts in the same time as on AXUV. The temperature changes for all chords (both on ECE and soft X-ray) at the same time (only three are shown) and for density measurements only the average central chord signal has an enough fast time response for comparison.

The snakelike radiation attenuation of the pellet is not always observed. Figure 8.22 shows the situation after the pellet injection for shot #35908. To better see the perturbation after the injection of the pellet, the same shot at the same time interval is shown in figure 8.23 - but with the underlying radiation level (determined at t = 770 ms when the perturbation was completely attenuated) removed. Chord #7 (at radius r = 6 cm) measures a stable radiation level from t = 758 on during 4 ms, clearly increased in respect to the neighboring channels, as if rotation of the plasma has stopped.

Figure 8.22: Perturbation stability. Shot #35908. Chord measurements.

Lithium pellet

In earlier campaigns Lithium pellets have been used to increase the density in the plasma center. The speed of injection is 100 m/s only (ten times less than deuterium shooting) and the migration of the pellet towards the center can be followed on the signals from AXUV detectors. Figure 8.24 shows the perturbation of radiation for the first 2 ms after the pellet has been shot (discharge #31586). Unlike for deuterium pellet the evolution towards the center is almost symmetrical - the peak appear simultaneously on the inner side of the vessel on the same radius, converging together in the center after about 2 ms. Due to the lower injection speed the vaporized lithium has enough time to spread over the magnetic surface and therefore

Figure 8.23: Perturbation stability. Shot #35908. Only the propagation of the perturbation is shown. The underlying radiation level was removed.

Figure 8.24: Lithium pellet. Shot #31586. Again only the propagation of the perturbation is shown. The underlying radiation level was removed.

Figure 8.25: Neutral beam. Shot #35771. Chord signals.

the inner channels see the additional radiation also.

8.5.3 Diagnostic neutral beam

During discharge #35771 a diagnostic neutral beam has been injected into the plasma. Figure 8.25 shows chord signals and figure 8.26 the emissivity for the time when the beam was present (704.3 to 705.1 ms). The beam is seen by the three innermost right channels (r = 2, 6 and 10 cm), which grow linearly in intensity and decay within two time samples (32 μs).

Figure 8.27 shows the evolution of the channel looking at r = 6 cm and the discrepancy. The duration of the beam is too short for the pyroelectric bolometer to react. After stabilization of the bolometer, the discrepancy shows a higher amount of neutral particles carrying energy away. The sharp peak on discrepancy represents the fast measuring AXUV-detectors.

The introduction of neutral particles pushes the ionization balance towards lower ionization stages, which radiate more power at the same temperature. At least, this example illustrates again the high temporal resolution of the AXUV photodiodes.

8.5.4 Arcing of iron

Discharge #31615 has already been presented in section 7.2.2, where the good agreement between AXUV and the bolometer was shown (see figure 7.9). The arcing introduces only a very small quantity of iron atoms since the line integrated average density (not shown) indicates no step when the arc was observed^{(5)} (t = 585 ms). Figure 8.28 illustrates how all chord signals show a violent increase in radiation followed by a strong, large and stable radiation zone in the

(5) by a video camera looking inside the vessel.

Diploma work 2002-2003  Christian Schlatter

8.5 Localized and/or fast features  76

Figure 8.26: Neutral beam. Shot #35771. Reconstructed emissivity.

Figure 8.27: Temporal shape and discrepancy. Shot #35771. The left figure gives the temporal picture

seen by the channel looking at r = 6 cm. The right figure shows discrepancy.

Diploma work 2002-2003  Christian Schlatter

center. The reconstructed emissivity profile shows pointed emissivity during sparking, which is symmetrically observed in the channels next to the limiter. Iron atoms apparently go on a walk to the center where they radiate up to r = ± 15 cm. Radiation decays only slowly - at the switch-off of the current (t = 970 ms) still 70 % of the initial level was seen.

Figure 8.28: Arcing introduces iron into the plasma. Shot #31615. Arcing took place in t = 585 ms. The left figure gives the chords, on the right the reconstructed emissivity evolution.

Unfortunately temperature has not been measured for this shot, by consequence the calculation of Z_{eff} is not possible.

8.5.5 Pieces of the wall falling into the plasma

Sporadically some pieces of impurities (deposited films) detach from the wall and fall inside the plasma. The burning of these small quantities of material is very fast, giving rise to a high and localized peak on the AXUV-chord looking at its position. This process is only seen on AXUV, the pieces are not big enough to increase the electron density or to lower the electron temperature. There is not enough time for spreading the particles over the magnetic surface and the peak is asymmetrically seen only in one half of the vessel. Figure 8.29 shows this situation for shot #35847 where detachment was observed in t = 540 ms. Also the signal of the channels seeing the maximum of power (r = 18 and 22 cm) is shown, the green peak has a width of only 20 μs, thus the limit of the acquisition system (working at a multiplexing period of 16 μs).

8.5.6 Disruptions

At high density, the amount of radiated power may become very important. Figure 7.7 already presented a disruption, where the radiated power exceeds the heating and leads to a power exhaust of the plasma. Disruptions are very fast processes, and when they develop, often an immediate increase of radiated power throughout all AXUV channel is seen, as presented in figure 8.30 (early disruption after multi-pellet injection). The plasma current does not immediately decay and often fast succession of short single disruptions is seen (until the plasma current has completely decayed). Further shots show disruptions with radiated power (probably) much more higher than the applied heating power, but the AXUV channels are saturated in these cases. To investigate

Figure 8.29: Impurity film detachement. Shot #35847. Detachment observed in t = 540 ms. The left figure gives the evolution of the chord signals, on the right the frequently seen peaking on the channels looking to the place where the material is fired is shown.

Figure 8.30: Disruption at high density. Shot #35904. Early disruption after injection of multiple deuterium pellets. The left figure shows the strong radiation increase in all channels, on the right the series of disruptions for the same shot is shown.

such regimes^{(6)}, the acquisition electronics would necessitate higher feedback resistors.

8.5.7 AXUV as plasma displacement diagnostics

Special magnetic coils permit to create magnetic fields which shift the plasma horizontally. During plasma discharge #36048 the field has been modified in a way, that the plasma was moving outwards. Initially located symmetrically in the center (up to t = 550 ms) the shift was 30 mm off-axis at the time when the plasma current was switched off (see figure 8.31).

Figure 8.31: Horizontal plasma displacement. Shot #36048. The displacement signal is measured using coils. In t = 550 ms the outward shift begins, after current switch-off, shift still increases.

After the stop of the plasma current the horizontal movement still increases and reaches a plasma position of 100 mm before the plasma definitely collapses.

Figure 8.32: Horizontal plasma displacement. Shot #36048. The left figure shows the radial chord distribution, on the right the reconstructed emissivity for the small displacements.

(6) For example to study the probable contraction of the radiating layer towards the center.

Diploma work 2002-2003  Christian Schlatter

The migration of the plasma towards the outer side of the tokamak can easily be followed on the chord signals of AXUV. Figure 8.32 shows their state for different times (on the left). The plasma emissivity was reconstructed (on the right) in the hope that the covering of the rings with constant emissivity is not violated to much and results are quite promising.

Conclusion and outlook

Radiation processes are various in tokamak plasmas, presenting a wide range of possible power loss channels. The newest generation of detectors for the measurement of radiated power is based on semiconductor technology and has already gain currency on numerous fusion devices.

In the frame of this work an array of 16 AXUV-photodiodes has been used to investigate the radiation losses on the T-10 tokamak. The setup, i.e. the geometry of the pinhole camera and the flanges as well as the dimensioning of the electronic acquisition system was calculated and calibrated in laboratory for the already installed and operational detectors.

The total radiated power has been estimated by taking into account the geometry of the plasma discharge and agreement with the pyroelectric bolometer was found. The power detection efficiency was checked after operation on tokamak and important sensitivity loss due to deposited surface film or elevated radiation dosage was not found, confirming the adaptability of AXUV-technology in thermonuclear environments.

The plasma emissivity has been reconstructed from the calibrated AXUV-chord signals using an Abel inversion method reflecting the geometry of the fields of view of the single detectors.

Different plasma discharges of recent experimental campaigns have been analyzed, in particular the density limit regime, the T-10 H-mode regime and biasing experiments, all together showing improved confinement. The found emissivity profiles give additional information on local plasma properties indicating transport barriers (H-mode regime) and accumulation of impurities (density limit regime with pellet injections). Attempts at explanation of the picture seen on the spatial distribution of emissivity were carried out taking into account approximately calculated temperature and density profiles.

An effort was pursued to prove the usability of AXUV-detectors as bolometers. The contribution of carbon and deuterium lines located in a region of reduced responsitivity of the diode to the total radiated power was found to be of minor importance, permitting to calculate the power lost through low-energy neutral particles, since unlike the pyroelectric device AXUV-detectors don’t measure them. Mind you that AXUV-photodiodes will not replace classic bolometers like metal foil or pyroelectric devices in future, because for power balance control the neutral power must also be considered.

The most promising feature of AXUV-detectors is their very fast time resolution. For the current setup the time resolution is limited by the acquisition system having a sampling time of roughly 20 μs. The investigation of fast, short and localized processes like pellet migration and evaporation, arcing and seeding of impurities are made possible by AXUV and cannot be followed by any other diagnostic system.

Different programs have been written for data analysis, detector calibration )making modifications on the setup of the detectors easy to handle), profile calculation and automated analysis of an elevated number of discharges.

In future it would be very worthwhile to realize an algorithm simulating radiation processes including ion transport, non-coronal ionization stage population and neutral emissivity to substantiate the results obtained by AXUV and to attain further understanding of the underlaying physical processes in the plasma.

A second AXUV-array is already available and will be installed at a different poloidal angle in the same cross-section as the present detector, permitting to investigate top-down asymmetries found in the gas puffed density limit regime. With an appropriate algorithm the plasma emissivity could be better reconstructed using a tomographic inversion.

Appendix A

Compensation of the capacitance of the AXUV-photodiodes

Figure A.1: Theoretical bode diagram of the photodiode and preamplifier. f_{p} is the pole frequency due to the photodiode capacitance C_{S}. To stabilize the circuit, a zero at f_{X} using a feedback capacitance must be introduced.

As shown in the Bode plot on figure A.1, the net input capacitance C_{S} forms a pole at a frequency f_{p} in the noise gain transfer function which is given by

f_{p} = \frac{1}{2πR_{F} · C_{S}}  (A.1)

If left uncompensated, at the frequency f_{X} where the noise gain intersects the open loop gain, the phase shift causes instability. Introducing a zero at f_{X} by adding capacitor C_{F} stabilizes the circuit and yields a phase margin of about 45 degrees. f_{X} is given by

f_{X} = \frac{1}{2πR_{F} · C_{F}}  (A.2)

The pole frequency is only slightly decreased if C_{F} << C_{S} and the frequency f_{X} is the geometric mean of f_{P} and the unity gain bandwidth frequency f_{U} of the operational amplifier,

f_{X} = \sqrt{f_{P} · f_{U}}  (A.3)

The combination of equations A.2 and A.3 can be solved for C_{F}

C_{F} = \sqrt{\frac{C_{S}}{2πR_{F} · f_{U}}}  (A.4)

Appendix B

Calculation of the ohmic heating input power

The ohmic heating input power is calculated from the plasma current I_{p} and the loop voltage U_{loop}. Figure B.1 shows a typical picture for current and voltage (shot #33180).

Figure B.1: Plasma current (left) and loop voltage (right). Shot #33180. The current is switched on in t = 100 ms and reaches the programmed level of I_{p} = 130 kA in t = 370 ms. The loop voltage contains an inductive part.

When the plasma current is not constant (during its build-up), the loop voltage contains an inductive part U_{ind}

U_{ind} = −L · \frac{dI_{p}}{dt}  (B.1)

where the inductivity is given by

L = L_{ext} + L_{int} = ln (\frac{8 · R}{a · κ}) − 2 + ℓ_{i}/2  (B.2)

where R = 1.5 m is the major radius, a = 0.3 m the minor radius, κ = 1 the elongation, and ℓ_{i} = 0.8 .. 1.4 the inductance of the plasma.

Figure B.2 shows the induction voltage U_{ind} and the voltage

Ũ = U_{loop} + U_{ind}  (B.3)

Figure B.2: Induction voltage (left) and voltage without inductive parts (right).

Shot #33180. ℓ_{i} = 1.3.

for shot #33180. The ohmic heating input power is now calculated

P_{OH} = Ũ · I_{p}  (B.4)

shown in figure 7.4. If the inductance of the plasma is not known, Ũ can be calculated for different ℓ_{i} until Ũ shows no step at the moment when the current gets stable.

Appendix C

Calculation of Z_{eff}

C.1 Derivation from AXUV-signals

As shown in section 2.3, the encountered radiation is essentially due to line radiation of impurity ions. A handy quantity to measure the impurity content of the plasma is its effective charge Z_{eff}, as defined by equation 2.4. Assuming coronal equilibrium, Z_{eff} may be deduced from the measured radiation using the radiation coefficients R(T_{e}, Z) published by Jensen & Post [10], i.e. by combining 2.4 and 2.17 to get

Z_{eff}^{AXUV} (r = 0) = \frac{ε (r = 0) · ⟨Z⟩^{2}}{n_{e}^{2} · R(T_{e}, Z)}  (C.1)

where ε(r = 0) is the average emissivity between the central emissivity determined by inverting outer and inner channels. Further only the presence of carbon has been assumed (the average carbon charge < Z > is also given in [10]).

C.2 Derivation from plasma resistivity

Another way to calculate Z_{eff} (which is not restricted to the assumption of a single impurity species) consists in its derivation from the resistivity of the plasma. From the definition of the safety factor q=1 surface, i.e.

q = 1 = \frac{r(q = 1) · B_{T}}{R · B_{P}}  (C.2)

where B_{T} is the toroidal and B_{P} the poloidal magnetic field (given in teslas), R the major radius and r(q=1) the minor radius where the q=1 surface can be found. This position can be determined by investigating the soft X-ray signals, which show a change in the orientation of their sawteeth (see figure 8.16).

Ampères law

μ_{0}I = ∮ \overrightarrow{B}\overrightarrow{dℓ}  (C.3)

and equation C.2 permit to calculate the plasma current flowing inside the q=1 surface,

I_{0} = \frac{2π · r^{2}(q = 1) · B_{T}}{μ_{0} · R}  (C.4)

Diploma work 2002-2003  87  Christian Schlatter

The average conductivity inside the q=1 surface is therefore

σ_{0} = \frac{j}{E} = \frac{2π · r^{2}(q = 1) · B_{T} · 2π · R}{πr^{2}(q = 1) · μ_{0} · R · U} = 10^{7} \frac{B_{T}}{U}  (C.5)

where U is the measured loop voltage in volts.

This conductivity is compared to the classical Spitzer conductivity [14]

σ^{Spitzer} = \frac{4π · ε_{0}}{100} 8.7 × 10^{13} \frac{T_{e}^{3/2}}{ln Λ} \frac{1}{Z_{eff} (0.29 + (\frac{0.46}{Z_{eff} +1.08}))}  (C.6)

where the first fraction transforms Spitzer’s formula to SI units. To compare equation C.5 with C.6 the density and temperature profile is calculated and interpolated inside the q=1 surface and a mean value of the expression \frac{T_{e}^{3/2}}{ln Λ} in above equation is calculated by integrating numerically

< \frac{T_{e}^{3/2}}{ln Λ} >= ∫_{−r(q=1)}^{+r(q=1)} \frac{T_{e}^{3/2}(r)}{ln Λ(T_{e}(r), n_{e}(r))}  (C.7)

where the coulomb logarithm ln Λ is approximated by [13]

ln Λ = 24 − ln \frac{\sqrt{n_{e}}}{T_{e}};  (C.8)

Z_{eff} is then found by seeking for roots of the combination of C.7, C.6, C.8 and C.5 to the equation

< σ^{Spitzer} > −σ_{0}^{AXUV} = 0  (C.9)

C.3 Derivation from continuum radiation

A third possibility (useful for getting the relative evolution of Z_{eff}) to get (an overall averaged) Z_{eff} is obtained by calculating

Z_{eff} ∝ \frac{P_{cont}}{< n_{e} >^{2} ·\sqrt{T_{e}}}  (C.10)

where P_{cont} is the continuum power of the radiation (measured in a domain of the spectrum where no lines exist), < n_{e} >^{2} is the center line (chord integrated) electron density and T_{e} the temperature in the center.

Appendix D

Calculation of temperature profiles

During the ohmic heating of the discharge, the profile of temperature was found to depend only on the plasma current I_{P} and the central chord line integrated density \overline{n}_{e} [23]. For given values of these parameters, the shape of the temperature profile before ECRH-heating is switched on is given by formulae D.1 to D.6.

T_{e}(\overline{n}_{e}, I_{P} , r) = T_{e}^{0}(\overline{n}_{e}, I_{P}) · (1 − (\frac{r}{a_{L}} )^{α(I_{P})})^{β(I_{P})}  (D.1)

where the peak fit parameter are

α(I_{P}) = \frac{I_{p}^{0.435}}{5}  (D.2)

β(I_{P}) = 2.5 − \frac{(I_{P} − 112.5)^{2}}{50000}  (D.3)

and the central temperature amplitude

T_{e}^{0}(\overline{n}_{e}, I_{P}) = A (I_{P}) · (\overline{n}_{e} + 0.5)^{B(I_{P})}  (D.4)

where

A(I_{P}) = 1400 · (1 − exp (−\frac{I_{P} − 48}{25}))  (D.5)

B(I_{P}) = 0.3 · (1 − exp (−\frac{I_{P} − 75}{25}))  (D.6)

Numeric values for density are in 10^{19} m^{−3} per 40 cm of chord length, plasma current in kA and temperatures in eV.

The profile is calculated for a selected time past the stabilization of the plasma current and prior ECRH-heating. Temperature profile during and after ECRH-heating are obtained by scaling the measured and offset-corrected electron-cyclotron emission signals using the calculated ohmic profile. Various examples of this procedure are shown in chapter 8.

Appendix E

Realized programs

For the realization of this work many programs were written for the purpose of data analysis, calculation and preparation. Programming was accomplished in Matlab 6.5. The following list gives a non-exhaustive overview.

Calibrator.m Calculation of the relative calibration factors f_{i} (equation 7.2) and the absolute translation factors G_{i} (equation 5.16) from a given pinhole camera setup. The factors are stored to disk and loaded by any program accessing the raw data in the experimental database.

dbc.m Generates a local DAS database of selected diagnostics data for given shots.

dbcheck.m Determines the diagnostics calibration coefficients stored in the database.

dens.m Calculates electron density profiles using the DAS-Tools inversion routine. Data can be exported to formatted text files for plotting with Origin.

diffplot.m Plots differences between data signals of two given shots.

dosereader.m Calculates the total deposited power on the AXUV-detector for a given shot interval. Useful for the determination of the photon flux.

fZeffpeak.m Subroutine needed by fZeffpeak.m for the calculation of Z_{eff} from classical Spitzer conductivity.

imp.m Calculates the impurity radiation curves from the coefficients of Jensen & Post [10].

impx.m Calculates the impurity radiation factor for a given temperature from the coefficients of Jensen & Post [10].

invt10.m Calculates the reconstruction matrix for the Abel inversion taking into account the geometry of the fields of view of the detectors.

lasercheck.m Calculates the responsitivity from a laser with known power by considering the power distribution of the beam. Useful for the checking of the low-energy responsitivity of the AXUV-detectors.

loader.m Universal data diagnostics database data loading routine. paran.m Calculation of different parameters of the discharge from a wide variety of diagnostic

signals (total ohmic heating power etc.) Plots results and/or stores them to formatted ASCII files for easy data import within Origin. Does also calculate calibrated AXUVchord signals, total radiated power and discrepancy.

pellet.m Creates three-dimensional plots of the AXUV chord signals with configurable temporal resolution. Automated exporting to Encapsulated Postscript files and Computer Modern font for inclusion within LaTeX. Permits to produce perturbation plots, where the signal background is masked.

pyrocheck.m Calibration checker for the pyroelectric bolometer.

recon.m Abel inversion program (chapter 6). Uses the inversion matrix calculated by invt10.m. Single profile calculation or whole shot reconstruction is possible. Various data formatting and saving scenarios.

Temp.m Calibration of temperature signals and temperature profiles using the approach in appendix C.1. Automatic deletion of bad channels.

Zeffpeak.m Calculation of Z_{eff} using the three methods described in appendix C.1. Makes use of temp.m, dens.m, impx.m and recon.m.

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[66] Khimchenko, Leonid N.; private communication.

Acknowledgements

I am deeply indebted to the head of the T-10 diagnostics group, Dr. Leonid Khimchenko and one of its members, Dr. Natalia Timchenko. Both of them played a key role in the successful organization and realization of my stay at Kurchatov institute. They decided to start a daring adventure when they took responsibility for the experiment to receive a foreign diploma student in their group. Their assistance and support for the solution of physical, social and Russian day-to-day life problems did never stop and took a lot of their energy and time. It is mostly due to them, that I spent a wonderful winter in Moscow.

Further thankyou’s goes to the whole rest of the T-10 diagnostics group, especially Dmitry Sarychev, assisting in practical work and pointing out a lot of errors in my written report, Gennady Kirnev for helping to solve computer problems and discussion about biasing and other plasma physics topics, Eugeny Gerasimov who showed my the Russian black market and supplied me with Russian music, Natalia Kirneva for the explanation of the calculation of plasma current profiles and Viacheslav Budaev for the talks about Japan.

An important time I could spend in the beautiful apartment of Natalia and Ilya Simanova, which they left for the time of my stay to move to their Datscha on countryside but weekly shuttling back to the capital for the flawless housekeeping.

The professors Dr. Yurij Dnestrovskij (Moscow State University) and Dr. Minh Quang Tran (Swiss Federal Institute of Technology in Lausanne) had the gratitude to supervise, analyze and judge my work in plasma physics. I owe them many thanks for going along with it.

Many, many thanks to the whole staff and scientists of the Nuclear Fusion Institute, who contributed to the experiments of T-10 and to whose results I had unlimited access in the experimental database. I would also like to thank the administration of the Kurchatov Research Center to clear all hurdles concerning my work on their grounds.

I’m much obliged to Regina Rentsch, Roggwil, Switzerland for financially paving my long visit abroad.

Many thanks indeed to Dr. Walter Roder, Jakar, Bhutan for donating the flight tickets between Geneva and Moscow.

... and all I’ve forgotten to mention.

Students on T-10 (from the left: Eugeny Gerasimov, Dmitri Igontov and Christian Schlatter). December 2002.

T-10 diagnostics group schaschlik session in Svinigorad. Christian Schlatter and Gennady Kirnev (from the left). February 2003.