Dynamo theory and its experimental validation
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1 Dynamo theory and its experimental validation Karl-Heinz Rädler Astrophysical Institute Potsdam Stockholm February 2009
2 Outline The idea of the self-exciting dynamo and elements of dynamo theory The Riga experiment The Karlsruhe experiment The Cadarache experiment Experiments under preparation What did we learn from dynamo experiments and what can we learn in future?
3 Effects of the geomagnetic field known for long... - Evidence for a simple compass in Mexico about 3000 years ago - Compass in China in the first century BC - Petrus Peregrinus 1269: ''Epistola de magnete'' - William Gilbert 1600: ''De magnete -- The Earth is a big loadstone! - Gellibrand 1635: Westward drift of the declination - Carl Friedrich Gauss 1836: ''Allgemeine Theorie des Erdmagnetismus'' - David and Brunhes 1904/05: Reversals of the geomagnetic field -...
4 In 1908 G. E. Hale discovered strong magnetic fields (~ 0.1 T) in sunspots - There is also a (weaker) general solar magnetic field. - The 2 x 11 years sunspot cycle coincides with the cycle of the general oscillatory solar magnetic field.
5 The cosmic dynamo Sir Joseph Larmor 1919 How could a rotating body such as the Sun become a magnet? Magnetic field due to electric currents generated and maintained after the pattern of a self-exciting dynamo!
6 The self-exciting dynamo Werner von Siemens 1867 Charles Wheatstone 1867 Anianus Jedlick 1851/53 Sören Hjorth 1854 Samuel Alfred Varley 1866
7 Disc dynamo
8 Disc dynamo
9 Kinematic dynamo theory The magnetic field B has to satisfy the induction equation inside the fluid body and proper initial and boundary conditions. magnetic Reynolds number Dynamo Necessary for dynamo
10 (Anti-)Dynamo theorems Concerning the geometry of the magnetic field There is no dynamo with an axisymmetric magnetic field. Cowling 1934,... Concerning the geometry of the fluid motion There is no (spherical) dynamo with a completely toroidal fluid motion (if the conductivity is constant or depends on radius only). Elsasser 1946, Bullard and Gellman 1954,... Various related theorems...
11 Examples of working dynamos Herzenberg 1958 Ponomarenko 1973 Roberts 1972
12 Mean-field dynamo theory Situations with complex behaviors of the fluid motion und magnetic field with respect to space and/or time. Split velocity and magnetic fields into mean and fluctuating parts, with means fields defined by some averaging procedure that satisfies the Reynolds averaging rules. Mean-field induction equation contains the mean electromotive force
13 Mean-field dynamo theory In the case of helical fluctuating motions has a part parallel or antiparallel to the mean magnetic field -- the The α-effect, α-effect allows mean-field dynamo models which reflect essential features of real dynamos. The dynamo is one of the basic phenomenae in the universe.
14 Mean-field dynamo theory In the case of helical fluctuating motions has a part parallel or antiparallel to the mean magnetic field -- the α-effect, Homogeneous isotropic non-mirrorsymmetric (helical) turbulence
15 In the last six decades... - magnetic fields at A and other stars (~ 0.1 T) - magnetic fields at most of the solar planets - strong magnetic fields at some white dwarfs (~ 10^2 T) - magnetic cycles at sun-like stars - large-scale galactic and intergalactic magnetic fields (~ 10^-9 T) - extremely strong magnetic fields at neutron stars (~ 10^11 T)
16 The full dynamo problem Dimensionless parameters E.g., geodynamo
17 The full dynamo problem Earth's core E.g., geodynamo Note that Re = Rm/Pm
18 Direct numerical simulations Parameters far away from realistic ones for the Earth's core Glatzmaier and Roberts 1995
19 Disc dynamo considering the back-reaction of the magnetic field on the rotation rate ( eddy current braking )
20 Disc dynamo Back-reaction of the magnetic field on the rotation rate Steady case
21 Disc dynamo considering the back-reaction of the magnetic field on the rotation rate and an imposed magnetic field
22 Disc dynamo Back-reaction of the magnetic field plus imposed magnetic field Steady case
23 Dynamos under laboratory or similar conditions Dynamo requires No Bonsai version of a cosmic dynamo!
24 Self-excitation of magnetic fields in fast-breeder reactors? The danger of self-excitation of magnetic fields in large liquid-metal circuits of reactors has been pointed out in a memorandum of Max Steenbeck 1971 to the Soviet Academy of Sciences Meeting in Obninsk near Moscow 1974 This possibility has been independently considered by Bevir 1973 and Pierson 1975 Measurements at the Belojarsk BN-600 reactor by Kirko Investigations related to the French Super Phoenix by Plunian et al / 99
25 Self-excitation of magnetic fields in fast-breeder reactors? The danger of self-excitation of magnetic fields in large liquid metal circuits of reactors has been pointed out in a memorandum of Max Steenbeck 1971 Meeting in Obninsk near Moscow 1974 Steenbeck 1974 in a letter to the president of the Academy of Sciences of the GDR and several Soviet scientists: Dynamo experiment with about 10 m Na and volumetric flow rates of more than 10 m³/s
26 The need for experimental investigations In magnetohydrodynamics one should not believe the product of a long and complicated piece of mathematics if unsupported by observation. Fermi (reported by Roberts 1993) Laboratory experiments with dynamos are more than demonstrating or checking an important principle. Natural dynamos with complex interactions of motion and magnetic field are hardly accessible to direct numerical simulations, e.g., because of the smallness of realistic values of Pm and the complex turbulence phenomenae. Experiments should improve our knowledge in this field. The interaction of theory and experiment pushes the understanding of dynamo processes forward.
27 Past dynamo-related MHD experiments Lehnert 1958 Cylindrical vessel with 58 l sodium Differential rotation due to a rotating plate Poloidal toroidal magnetic field
28 Past dynamo-related MHD experiments Lowes and Wilkinson 1963/68 Herzenberg 1958
29 Past dynamo-related MHD experiments Lowes and Wilkinson 1963/68
30 Past dynamo-related MHD experiments Riga α-box Steenbeck, Kirko, Gailitis, Klawinia, Krause, Laumanis, Lielausis 1967
31 Past dynamo-related MHD experiments Riga α-box
32 The Riga dynamo experiment The motivation: low excitation threshold Ponomarenko dynamo Ponomarenko 1973
33 Riga dynamo experiment
34 Riga dynamo experiment The 1987 experiment Gailitis, Lielausis,...
35 Riga dynamo experiment
36 Riga dynamo experiment
37 Riga dynamo experiment November 10/11, 1999
38 The Karlsruhe dynamo experiment The motivation Earth's core Busse 1970,... Müller, Stieglitz, Experiment
39 Karlsruhe dynamo experiment An experiment as later carried out in Karlsruhe has been prosed by Busse 1975 Gailitis' idea 1967
40 Karlsruhe dynamo experiment H = 0.70 m R= 0.85 m a = 0.21 m
41 Karlsruhe dynamo experiment
42 Karlsruhe dynamo experiment
43 Karlsruhe dynamo experiment Roberts dynamo G. O. Roberts 1972 Fluid velocity, e.g., Non-decaying magnetic fields if
44 Karlsruhe dynamo experiment Roberts dynamo Non-decaying magnetic fields if Most easily excitable B modes contain parts independent of x and y. (limit of small k)
45 Karlsruhe dynamo experiment Roberts dynamo allows mean-field description: with mean fields defined by averaging over x and y. anisotropic alpha-effect (limit of small k)
46 Karlsruhe experiment Two branches in the theory of the experiment Direct numerical simulations Busse, Tilgner Mean-field theory Apstein, Brandenburg, Fuchs, Schüler, Rädler, Rheinhardt
47 Karlsruhe dynamo experiment m=0 m=1 m=1 m=1
48 Karlsruhe dynamo experiment m=1
49 Karlsruhe dynamo experiment Self-excitation if exceeds a critical value. VC volumetric flow rate through central channel VH... through helical channel of a spin generator Isolines of Cα
50 Karlsruhe dynamo experiment Spingenerator flow Isolines of Cα
51 Karlsruhe dynamo experiment
52 Karlsruhe dynamo experiment
53 Karlsruhe dynamo experiment
54 Disc dynamo Back-reaction of the magnetic field plus imposed magnetic field
55 Karlsruhe dynamo experiment The saturation of the dynamo is accompanied by developing a piston-like flow profile. The temperature dependence of the excitation condition is mainly due to the temperature dependence of the electric conductivity. The onset of dynamo action is shifted to lower mean axial flow rates if this flow varies periodically in time with periods of the order of the magnetic diffusion time.
56 The Cadarache (VKS) dynamo experiment Pinton et al.
57
58 Experiments under preparation Grenoble Paris Madison Maryland New-Mexico Perm
59 Experiments under preparation Magnetostrophic motions Grenoble --- in a differentially rotating spherical shell under the influence of an imposed magnetic field Paris Madison Maryland New-Mexico Perm Nataf, Schaeffer,...
60
61 Experiments under preparation Grenoble Paris Madison Maryland New-Mexico Perm Leorat et al.
62 Experiments under preparation Grenoble Paris Madison Maryland New-Mexico Perm Forest,...
63
64 Experiments under preparation Grenoble Paris Madison Maryland --- New-Mexico Perm Lathrop,...
65 First Maryland experiment Lathrop and coworkers 2000
66 Lathrop and coworkers 2000
67 Maryland
68 Maryland 3 m diameter sphere
69 Experiments under preparation Grenoble Madison Maryland New-Mexico Perm αω dynamo similar to such in astrophysical objects Colgate,...
70 Experiments under preparation Grenoble Madison Maryland New-Mexico non-stationary dynamo Perm Frick et al. Newark July 2008
71 The Perm dynamo experiment (under preparation) Proposed by Denisov, Noskov, Sokoloff, Frick, Khripchenko 1999 Background: Ponomarenko 1973 divertor non-stationary dynamo
72 The Perm dynamo experiment Large radius 0.40 m small radius 0.12 m 115 kg Na 50 rps 140 m/s braking time 0.1 s Dynamo action if
73 Water experiments Large radii m and m Helical features in large and small scales
74 The gallium experiment Large radius of the torus 88 mm small radius 23 mm Noskov, Denisov, Frick, Khripchenko, Sokoloff and Stepanov Magnetic field rotation in the screw gallium flow EPJ 2004
75 What did we learn from the experiments? The dynamo is a robust phenomenon The kinematic dynamo theory describes the onset of dynamos well Mean-field theory of the Karlsruhe dynamo experiment works well In both the Riga and the Karlsruhe cases the dynamos saturate due to deformation of the flow profiles by the magnetic field. Turbulence plays a subordinate role. In other cases (in particular Cadarache und Madison) fluid motions on small scales seem to be important.
76 Which problems could be addressed by future experiments? The role of smaller scales of motion in less constrained flows Saturation mechanisms Dynamos due to magneto-rotational instability Reversals of magnetic fields
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