2006, English, Book, Illustrated edition: The structure of magnetic field in the TEXTOR-DED / K. H. Finken ... [et. al].

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The structure of magnetic field in the TEXTOR-DED / K. H. Finken ... [et. al]
 
Bookmark: http://trove.nla.gov.au/version/41196174
Physical Description
  • 110 p. : ill. (some col.) ; 24 cm.
Published
  • Jülich : Forschungszentrum Jülich, c2006.
Language
  • English

Edition details

Title
  • The structure of magnetic field in the TEXTOR-DED /​ K. H. Finken ... [et. al].
Also Titled
  • TEXTOR-DED
Other Authors
  • Finken, K. H.
Published
  • Jülich : Forschungszentrum Jülich, c2006.
Physical Description
  • 110 p. : ill. (some col.) ; 24 cm.
Series
Subjects
Contents
  • Machine derived contents note: 1 Introduction 1
  • 1.1 Control of the plasma by the edge ergodization 1
  • 1.2 Description of magnetic field lines 2
  • 1.3 Onset of ergodic zone of field lines 3
  • 1.4 The DED and its operational regimes 4
  • 1.5 Goals and a short description of the report 5
  • 1.6 Bibliographic notes 5
  • 2 DED coil system and magnetic perturbations 7
  • 2.1 The DED arrangements 7
  • 2.2 Basic distribution of current over coils 9
  • 2.2.1 Current distribution for the 3:1 mode: DC operation 9
  • 2.2.2 Current distribution for the 3:1 mode: AC operation 10
  • 2.2.3 A coil configuration for the 6:2 mode: DC operation 12
  • 2.2.4 A coil configuration for the 6:2 mode: AC operation 13
  • 2.2.5 A coil configuration for the 12:4 mode: DC operation 14
  • 2.2.6 A coil configuration for the 12:4 mode: AC operation 14
  • 2.3 Density of DED current 16
  • 2.3.1 Fourier expansion of the current density 17
  • 2.3.2 Ideal coil configuration 18
  • 2.3.3 Non-ideal coil configuration 18
  • 2.4 Magnetic field perturbations 19
  • 2.4.1 Cylindrical approximation 20
  • 2.4.2 Toroidal corrections 22
  • 3 Hamiltonian field line equations 25
  • 3.1 Hamiltonian formulation of field line equations in a toroidal
  • system 25
  • 3.2 Field lines in axisymmetric tokamak equilibrium 26
  • 3.2.1 Non-axisymmetric magnetic perturbations. 28
  • 3.2.2 Perturbation field in intrinsic coordinates 29
  • 3.3 Mappings of field lines 29
  • 3.3.1 The Hamilton-Jacobi method to construct mappings 30
  • 3.3.2 Mapping with a numerical interpolation of Hamiltonian 31
  • 3.4 Models for the tokamak magnetic equilibrium 32
  • 3.4.1 Equilibrium magnetic field with the Shafranov shift 32
  • 3.4.2 The safety factor profiles 34
  • 3.5 Spectrum of Hamiltonian perturbations 36
  • 3.5.1 Asymptotics of the transformation matrix elements
  • Sm,m 38
  • 3.5.2 Asymptotic behavior of Hm,n 39
  • 3.5.3 DED magnetic perturbation 42
  • 3.5.4 Numerical determination of Hmn 42
  • 3.6 Bibliographic notes on mapping methods 45
  • 4 Properties of the ergodic and laminar zones 49
  • 4.1 Formation of the ergodic zone 49
  • 4.1.1 Qualitative estimations 49
  • 4.1.2 The m : n =​ 12 : 4 operational mode 50
  • 4.1.3 Variation of the ergodization level 51
  • 4.1.4 The m : n=​6:2 operational mode 51
  • 4.1.5 The m : n=​3:1 operational mode 53
  • 4.2 Ergodic divertor as a chaotic scattering system 55
  • 4.2.1 Basin boundary structure at the plasma edge: Laminar
  • plots 56
  • 4.2.2 Magnetic footprints 58
  • 4.3 Diffusion of field lines 60
  • 4.3.1 Global and local diffusion coefficients 61
  • 4.3.2 Quasilinear diffusion coefficients 62
  • 4.3.3 Numerical calculation of field line diffusion coefficients . 62
  • 4.4 Lyapunov exponents and Kolmogorov lengths 66
  • 4.4.1 Definition of Lyapunov exponent 66
  • 4.4.2 Finite-time Lyapunov exponent 68
  • 4.4.3 The Kolmogorov length 68
  • 4.4.4 Numerical results 69
  • 4.5 Experimental observation of the magnetic structure 72
  • 5 The Gourdon code 77
  • 5.1 Equilibrium calculation 77
  • 5.1.1 Fixed boundary value problem 79
  • 5.1.2 Semifree boundary value problem 80
  • 5.1.3 Special equilibria 80
  • 5.2 Fourier analysis of the perturbing magnetic field 81
  • 5.3 Perturbation coils for the DED 81
  • 5.3.1 Magnetic fields generated by the DED 82
  • 5.3.2 Spectra 83
  • 5.4 Poincar6 plots 84
  • 5.4.1 (m=​12, n=​4) configuration 84
  • 5.4.2 (m=​3, n=​1 - configuration 84
  • A Calculations of amplitudes and phases in Eq. (2.4) 87
  • A.1 The 3:1 operational mode 87
  • B Current density of coils 89
  • B.1 Continuous current density 89
  • B.2 Nonideal coil configuration 90
  • C Modified Bessel functions Im(z) and Km(z) 93
  • D Model of a current density profile j(r) in the DED
  • operation 95
  • E Asymptotic estimation of the integral Smm, (3.44) 97
  • F The calculation of the Jacobi matrix 101
  • References 103.
Notes
  • At head of title: Forschungszentrum Jülich GmbH, Institut für Plasmaphysik.
  • Includes bibliographical references.
Language
  • English
ISBN
  • 3893364188
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