Untersuchungen zu magnetohydrodynamischen Instabilitäten in Flüssigmetallen

Von Martin Seilmayer

Reihe Maxwell ; 2


TUDpress 2016. Kartoniert, ca. 24 x 17 cm, XV, 261 S., mit 32 Farbseiten und weiteren s/w Abb.


This dissertation, “Studies on magnetohydrodynamic instabilities in liquid metal flows”, focuses on two different experiments in a cylindrical Taylor-Couette (TC) geometry. This fundamental set-up consists of an inner and an outer cylinder, which are mounted concentrically. The different radii are defined by the parameters ri and ra. The rotation of both cylinders can be set independently by their angular frequencies Oi = 2pi fi and Oa = 2pi fa. The gap between them is filled with the fluid whose flow is to be investigated. For an ideal non-viscous fluid, Rayleigh’s criterion states that the flow between two concentric cylinders with infinite length is stable against small perturbations as long as the angular momentum increases outward, d/dr (r²O(r)) > 0 [1]. Rayleigh’s criterion can be interpreted in a way that an ideal TC-flow remains laminar if the pressure and centrifugal forces are in a stable equilibrium state. A more general setting is now introduced with an azimuthal magnetic field Bphi(r) being applied to the electrical conducting fluid. For this different situation Michael [2] and Chandrasekhar [3] derived an extended stability criterion only for axisymmetric perturbations which is valid for an ideally conducting and non-viscous fluid. The first experiment described in the present dissertation consists of a TC-setup using the eutectic alloy Ga67In20,5Sn12,5 as working fluid. In addition to the common installation an insulated current on the rotation axis with up to 20 kA generates the necessary magnetic field Bphi ~ 1/r. Michael’s criterion indicates in that case that the flow is stable with respect to axisymmetric perturbations. However, this does not apply for non-axisymmetric perturbations. It was shown theoretically by Rüdiger et al. [4, 5] that the interaction of an azimuthal magnetic field with a laminar rotational flow may become unstable against non-axisymmetric disturbances. This phenomenon is called Azimuthal Magnetorotational Instability (AMRI). The present work gives the first experimental evidence for AMRI in a liquid metal TC-experiment. It is shown that a hydrodynamically stable flow can be disturbed by an applied current free azimuthal magnetic field . The instability itself is then identified as a travelling wave co-rotating with the cylinders. The second configuration investigated in this work is characterized by a magnetic field profile proportional to the radius Bphi ~ r. The basis for such an experiment is the remarkable stability criterion from Tayler [6, 7]. It tells that even an ideal fluid at rest can become unstable against non-axisymmetric disturbances. The Tayler instability (TI) in liquid metals can be considered as the incompressible version of the kink instability that is widely known in plasma physics. The TI-experiment confirms the numerical results given by Rüdiger et al. [8, 9] who calculated the onset for the instability in an incompressible liquid metal column with finite conductivity at round about 3 kA. Both observed phenomena are strongly related to astrophysical processes in which angular momentum transport plays an essential role. What was missing so far was a clear experimental evidence for the described interaction mechanisms between a rotational flow and a magnetic field. The submitted dissertation reports the analysis and results of the first experiments on the two fundamental instabilities AMRI and TI. References [1] Rayleigh, Proc. R. Soc. London, Ser. A, 93(648), 148-154, 1917. [2] D. H. Michael, Mathematika, 1, 45-50, 1954. [3] S. Chandrasekhar, Proc.Roy.Soc.-A, 216(1126), 293-309, 1953. [4] G. Rüdiger et al. MNRAS, 377(4), 1481-1487, 2007. [5] G. Rüdiger et al. Astron. Nachr., 328, 1158-1161, 2007. [6] R. J. Tayler, Proc. R. Soc. London, Ser. B, 70(1), 31-48, 1957. [7] R. J. Tayler, MNRAS, 161(4), 365-380, 1973. [8] G. Rüdiger et al., Astron. Nachr., 332(1), 17-23, 2011. [9] G. Rüdiger et al., Astrophys. J., 755(2), 181, 2012. 


ISBN: 978-3-95908-032-3 

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