Destabilization of Alfvén eigenmodes by fast particles in W7-AS [Elektronische Ressource] / vorgelegt von Stefan Zegenhagen

Sujets

• Physik

Informations

• Publié par: ernst-moritz-arndt-universitat_greifswald
• Publié le: 01 janvier 2006
• Nombre de lectures: 21
• Langue: Deutsch
• Poids de l'ouvrage: 6 Mo

Extrait

Destabilization of Alfv´en Eigenmodes by Fast
Particles in W7-AS
Inauguraldissertation
zur
Erlangung des akademischen Grades eines
doctor rerum naturalium (Dr. rer. nat.)
an der Mathematisch-Naturwissenschaftlichen Fakult¨at
der
Ernst-Moritz-Arndt-Universita¨t Greifswald
vorgelegt von
Stefan Zegenhagen
geboren am 7. 7. 1974
in Ueckermu¨nde
Greifswald, im Februar 2006Dekan: Prof. Dr. Klaus Fesser
1. Gutachter: Prof. Dr. Thomas Klinger
2. Gutachter: Prof. Dr. Kazuo Toi
Tag der Promotion: 5. 7. 2006Contents
1 Introduction 1
2 Principles of magnetic plasma confinement 5
2.1 Magnetic Field Topology . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Magnetic Field Lines . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Magnetic Field Line Curvature, Pressure and Tension . . . . . . 6
2.1.3 Flux Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.4 Magnetic Flux Coordinates . . . . . . . . . . . . . . . . . . . . 9
2.2 Particle Dynamics in Fusion Plasmas . . . . . . . . . . . . . . . . . . . 12
2.2.1 Radial Particle Drifts . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Trapped and Passing Particles . . . . . . . . . . . . . . . . . . . 16
2.3 Magnetohydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 MHD equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Stability of MHD Equilibria . . . . . . . . . . . . . . . . . . . . 22
3 Alfv´en Waves, -continua and Eigenmodes 25
3.1 Alfv´en Waves and Alfv´en Continua . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Waves in an infinite, homogeneous plasma . . . . . . . . . . . . 26
3.1.2 Inhomogeneous plasma slab . . . . . . . . . . . . . . . . . . . . 28
3.1.3 Shear Alfv´en Continuum in Cylindrical Geometry . . . . . . . . 29
3.1.4 Continuous Spectrum in Toroidal Geometry . . . . . . . . . . . 31
3.2 Alfv´en Eigenmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Global Alfv´en Eigenmodes (GAEs) . . . . . . . . . . . . . . . . 34
3.2.2 Gap Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
iiiiv CONTENTS
3.3 Beyond Ideal MHD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Wave Drive and Damping . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Wave-Induced Transport . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Kinetic Modifications of the Alfv´en Wave Spectrum . . . . . . . 45
4 Experimental and numerical tools 47
4.1 The W7-AS device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.1 Mirnov Diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2 Plasma parameter diagnostics . . . . . . . . . . . . . . . . . . . 56
4.2.3 Fast Ion Loss Detector . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Mirnov Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.1 Continuous wavelet transform . . . . . . . . . . . . . . . . . . . 62
4.3.2 Lomb periodogram analysis . . . . . . . . . . . . . . . . . . . . 64
4.4 Numerical codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.1 Equilibrium reconstruction and magnetic coordinate transforms 73
4.4.2 Alfv´en continuum calculation . . . . . . . . . . . . . . . . . . . 74
4.4.3 Calculation of the fast ion distribution function . . . . . . . . . 74
4.4.4 Growth rate calculation . . . . . . . . . . . . . . . . . . . . . . 76
5 Experimental Results 79
5.1 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.1.1 Data Availability . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1.2 Equilibrium reconstruction . . . . . . . . . . . . . . . . . . . . . 83
5.1.3 Mode Number Analysis . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.4 Eigenmode Identification . . . . . . . . . . . . . . . . . . . . . . 89
5.1.5 Ion Distribution Function . . . . . . . . . . . . . . . . . . . . . 89
5.1.6 Growth Rates and Fast Ion Losses . . . . . . . . . . . . . . . . . 92
5.2 Discharge Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2.1 Discharge Classification . . . . . . . . . . . . . . . . . . . . . . 95
5.2.2 Eigenmode Classification . . . . . . . . . . . . . . . . . . . . . . 97
6 Discussion and Conclusions 109CONTENTS v
6.1 Equilibrium Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Mirnov Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Alfv´en Eigenmodes and their Stability . . . . . . . . . . . . . . . . . . 112
6.3.1 GAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3.2 TAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3.3 EAEs and High-Frequency Eigenmodes . . . . . . . . . . . . . . 115
6.3.4 Unidentified Eigenmodes . . . . . . . . . . . . . . . . . . . . . . 116
6.4 Alfv´en Eigenmodes and Fast-Ion Losses . . . . . . . . . . . . . . . . . . 117
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 Summary 121
A Differential Geometry 125
A.1 Reciprocal sets of vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.2 Curvilinear Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.3 Co- and Contravariant Components . . . . . . . . . . . . . . . . . . . . . 127
A.4 Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.5 Important Vector Identities . . . . . . . . . . . . . . . . . . . . . . . . 131
B Boozers magnetic coordinates 135
B.1 Covariant B Components . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.2 Boozer Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
C List of Discharges and AEs 141
C.1 Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
C.2 Observed Alfv´en Instabilities . . . . . . . . . . . . . . . . . . . . . . . . 145
C.2.1 GAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
C.2.2 TAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
C.2.3 EAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C.2.4 NAE, HAE and MAE Modes . . . . . . . . . . . . . . . . . . . 148
C.2.5 Unidentified Alfv´en Eigenmodes . . . . . . . . . . . . . . . . . . 148vi CONTENTSChapter 1
Introduction
Controlled nuclear fusion of hydrogen isotopes in a plasma promises to provide a nearly
inexhaustible source of energy and high environmental safety as compared to nuclear
fission. The most favourable fusion reaction is the one between deuterium and tritium
4D + T−→ He + n + 17.6 MeV,
which provides the highest yield of energy. In order to reach ignition conditions, where
the fusion born α-particles heat the plasma sufficiently strong to compensate for the
heat losses, the plasma must be heated up to temperatures of T ≥ 10 keV and must
be confined long enough to satisfy the Lawson criterium [1]
20 3nτ > 1.5× 10 s/m ,E
where τ is the energy confinement time (the ratio of heating power to energy lossE
rate) and n the plasma density.
The most advanced approach towards the achievement of relevant fusion reactor pa-
rameters is the confinement of the plasma in a closed, toroidal magnetic field with
twisted, helical field lines. Two different concepts are currently pursued that differ
in the way the magnetic field is created. The Tokamak is an axisymmetric device
that creates a strong toroidal field with large external coils. The necessary poloidal
field component is generated by toroidal currents induced by a transformer, with the
plasma forming the secondary winding. This does not allow steady-state operation
because of the alternating current requirement in the transformer. Intense research is
performed on alternative schemes to drive current in Tokamak plasmas. The second
class of magnetic confinement devices is the Stellarator, where the helical magnetic
field is generated completely by external coils. Stellarators are therefore independent
of permanently flowing plasma currents, but, in contrast to tokamaks, they are not
axisymmetric.
The performance of todays fusion experiments is not only limited by technical con-
straints. The sources of free energy available in bounded plasmas with strong gradi-
ents are commonly tapped by instabilities that degrade the confinement of particles
12 CHAPTER 1. INTRODUCTION
Figure 1.1: Prediction of the fraction of redistributed energetic α particles caused by
Alfv´en eigenmodes in optimized stellarators. Taken from Ref [11].
and energy. One of the most important type of instabilities are Alfv´en eigenmodes,
which are still subject to extensive studies.
Alfv´en waves were discovered by Hannes Alfv´en in the 1940’s, a pioneer in the physics of
charged fluids [2, 3]. Besides being observed in astronomical and laboratory plasmas,
they dominate much of the low-frequency dynamics in fusion plasmas. The Alfv´en
wave describes a basic oscillation between plasma kinetic energy and magnetic field
energy. The most familiar example is the shear Alfv´en wave, characterized by ”field line
bending”, that is analogous to a wave travelling along a massive string. It propagates
along the magnetic field lines at the Alfv