@article{RuedigerSchultz2022,
  author    = {R{\"u}diger, G{\"u}nther and Schultz, Manfred},
  title     = {On the toroidal-velocity antidynamo theorem under the presence of nonuniform electric conductivity},
  series = {Astronomische Nachrichten = Astronomical notes},
  volume    = {343},
  journal   = {Astronomische Nachrichten = Astronomical notes},
  number    = {5},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0004-6337},
  doi       = {10.1002/asna.20224011},
  pages     = {10},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}
@article{RuedigerSchultz2020,
  author    = {R{\"u}diger, G{\"u}nther and Schultz, Manfred},
  title     = {Large-scale dynamo action of magnetized Taylor-Couette flows},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {493},
  journal   = {Monthly notices of the Royal Astronomical Society},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/staa293},
  pages     = {1249 -- 1260},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{RuedigerSchultzHollerbach2021,
  author    = {R{\"u}diger, G{\"u}nther and Schultz, Manfred and Hollerbach, Rainer},
  title     = {Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields},
  series = {Journal of plasma physics},
  volume    = {87},
  journal   = {Journal of plasma physics},
  number    = {2},
  publisher = {Cambridge University Press},
  address   = {London},
  issn      = {1469-7807},
  doi       = {10.1017/S0022377821000295},
  pages     = {19},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}