TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred A1 - Hollerbach, Rainer T1 - Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields JF - Journal of plasma physics N2 - In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor-Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is Pm not equal 1. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for Pm of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative z direction along the rotation axis depending on the sign of B phi Bz. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if vertical bar B phi vertical bar >> vertical bar B-z vertical bar, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear. KW - plasma instabilities KW - astrophysical plasmas Y1 - 2021 U6 - https://doi.org/10.1017/S0022377821000295 SN - 1469-7807 VL - 87 IS - 2 PB - Cambridge University Press CY - London ER - TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred T1 - Large-scale dynamo action of magnetized Taylor-Couette flows JF - Monthly notices of the Royal Astronomical Society N2 - A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining a effect and eddy diffusivity. If both degenerated modes with m = +/- 1 are excited with the same power then the global a effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite alpha effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an alpha(2) dynamo. Moreover, an alpha Omega dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm similar or equal to 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, eta(T) similar or equal to eta. By basically lower or larger eddy diffusivities the dynamo instability is suppressed. KW - dynamo KW - instabilities KW - MHD KW - magnetic fields Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa293 SN - 0035-8711 SN - 1365-2966 VL - 493 IS - 1 SP - 1249 EP - 1260 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred T1 - On the toroidal-velocity antidynamo theorem under the presence of nonuniform electric conductivity JF - Astronomische Nachrichten = Astronomical notes N2 - Laminar electrically conducting Couette flows with the hydrodynamically stable quasi-Keplerian rotation profile and nonuniform conductivity are probed for dynamo instability. In spherical geometry, the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or - much more complex- that it only depends on the azimuthal or the axial coordinate. The transformation of the plane-flow dynamo model of Busse and Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does not support the dynamo mechanism. The Elsasser toroidal-velocity antidynamo theorem, according to which dynamos without any radial velocity component cannot work, is thus not softened by nonuniform conductivity distributions. KW - antidynamo theorem KW - MHD KW - Taylor-Couette flow Y1 - 2022 U6 - https://doi.org/10.1002/asna.20224011 SN - 0004-6337 SN - 1521-3994 VL - 343 IS - 5 PB - Wiley-VCH CY - Weinheim ER -