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The excitation conditions of the magnetorotational instability are studied for axially unbounded Taylor-Couette flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wave number and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes we find the critical Lundquist number of the applied axial magnetic field the lower the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap the more spherical the cells are. The marginal rotation rate of the inner cylinder -- for fixed size of the outer cylinder -- always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{\rm in}\simeq 0.4$ while it is at $r_{\rm in}\simeq 0.5$ for insulating walls where $r_{\rm in}$ is the normalized radius of the inner cylinder. The lowest magnetic field amplitudes to excite the instability are required for Taylor-Couette flows between perfect-conducting cylinders with gaps corresponding to $r_{\rm in}\simeq 0.2$. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the nonaxisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison to those for the axisymmetric modes which is true for wide-gap containers with $r_{\rm in} \lesssim 0.3$., Comment: 12 pages, 6 figures

Laminar electrically conducting Couette flows with the hydrodynamically stable quasi-Keplerian rotation profile and non-uniform 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 \& Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does {\em 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 non-uniform conductivity distributions., Comment: 8 pages, 6 figures

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 $Pm\neq 1$. Here we demonstrate that the addition of a weak axial field component may allow 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 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 $B_\phi B_z$. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi|\gg |B_z|$, 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 {\em ideal} fluids the considered helical magnetorotational instability (HMRI) only exists for rotation laws with negative shear., Comment: 18 pages, 10 Figures

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 nonaxisymmetric perturbations which form electromotive forces defining $\alpha$ effect and eddy diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same power then the global $\alpha$ 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 $\alpha\Om$ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of ${\rm Rm}\simeq 2.000$ 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, $\eta_{\rm T}\simeq \eta$. By basically lower or larger eddy diffusivities the dynamo instability is suppressed., Comment: 12 pages, 12 figures

The stability of conducting Taylor-Couette flows under the presence of toroidal magnetic background fields is considered. For strong enough magnetic amplitudes such magnetohydrodynamic flows are unstable against nonaxisymmetric perturbations which may also transport angular momentum. In accordance with the often used diffusion approximation one expects the angular momentum transport vanishing for rigid rotation. In the sense of a nondiffusive $\Lambda$ effect, however, even for {\em rigidly} rotating $z$-pinches an axisymmetric angular momentum flux appears which is directed outward (inward) for large (small) magnetic Mach numbers. The internal rotation in a magnetized rotating tank can thus never be uniform. Those particular rotation laws are used to estimate the value of the instability-induced eddy viscosity for which the nondiffusive $\Lambda$ effect and the diffusive shear-induced transport compensate each other. The results provide the Shakura-Sunyaev viscosity ansatz leading to numerical values linearly growing with the Reynolds number of rotation., Comment: 15 pages, 9 figures

In view of new experimental data the instability against adiabatic nonaxisymmetric perturbations of a Taylor-Couette flow with an axial density stratification is considered in dependence of the Reynolds number Re of rotation and the Brunt-V\"ais\"al\"a number Rn of the stratification. The flows at and beyond the Rayleigh limit become unstable between a lower and an upper Reynolds number (for fixed Rn). The rotation can thus be too slow or too fast for the stratorotational instability. The upper Reynolds number above which the instability decays, has its maximum value for the potential flow (driven by cylinders rotating according to the Rayleigh limit) and decreases strongly for flatter rotation profiles finally leaving only isolated islands of instability in the (Rn/Re) map. The maximal possible rotation ratio $\mu_{\rm max}$ only slightly exceeds the shear value of the quasi-uniform flow with $U_\phi\simeq$const. Along and between the lines of neutral stability the wave numbers of the instability patterns for all rotation laws beyond the Rayleigh limit are mainly determined by the Froude number Fr which is defined by the ratio between Re and Rn. The cells are highly prolate for Fr>1 so that measurements for too high Reynolds numbers become difficult for axially bounded containers. The instability patterns migrate azimuthally slightly faster than the outer cylinder rotates., Comment: 17 pages, 13 figures, accepted for publishing in JPP

We consider axially periodic Taylor-Couette geometry with insulating boundary conditions. The imposed basic states are so-called Chandrasekhar states, where the azimuthal flow $U_\phi$ and magnetic field $B_\phi$ have the same radial profiles. Mainly three particular profiles are considered: the Rayleigh limit, quasi-Keplerian, and solid-body rotation. In each case we begin by computing linear instability curves and their dependence on the magnetic Prandtl number Pm. For the azimuthal wavenumber m=1 modes, the instability curves always scale with the Reynolds number and the Hartmann number. For sufficiently small Pm these modes therefore only become unstable for magnetic Mach numbers less than unity, and are thus not relevant for most astrophysical applications. However, modes with m>10 can behave very differently. For sufficiently flat profiles, they scale with the magnetic Reynolds number and the Lundquist number, thereby allowing instability also for the large magnetic Mach numbers of astrophysical objects. We further compute fully nonlinear, three-dimensional equilibration of these instabilities, and investigate how the energy is distributed among the azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper for large m, reflecting the smoothing action of shear. On the other hand kinetic and magnetic energy spectra exhibit similar behavior: if several azimuthal modes are already linearly unstable they are relatively flat, but for the rigidly rotating case where m=1 is the only unstable mode they are so steep that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The total magnetic energy exceeds the kinetic energy only for large magnetic Reynolds numbers Rm>100., Comment: 12 pages, 14 figures, submitted to ApJ

It is known that in a hydrodynamic Taylor-Couette system uniform rotation or a rotation law with positive shear ('super-rotation') are linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindric pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with $d\Omega/dR \geq 0$. However, for magnetic Prandtl numbers Pm$\neq 1$ and for slow rotation also rigid rotation and super-rotation support the instability by lowering their critical Hartmann numbers. For super-rotation in narrow gaps and for modest rotation rates this double-diffusive instability even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile $B_\phi\propto 1/R$ included. For rigid rotation and for super-rotation the sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm$\ll 1$ and it corotates for Pm$\gg 1$ while for rotation laws with negative shear the instability pattern migrates in the direction of the basic rotation for all Pm. An axial electric-current of minimal 3.6 kAmp flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kAmp if a gallium alloy is used., Comment: 17 pages, 9 figures, submitted to PoF

With application to inner stellar radiative zones, a linear theory is used to analyze the instability of a dipole-parity toroidal background field, in the presence of density stratification, differential rotation, and realistically small Prandtl numbers. The physical parameters are the normalized latitudinal shear $a$ and the normalized field amplitude $b$. Only the solutions for the wavelengths with the maximal growth rates are considered. If these scales are combined to the radial values of velocity, one finds that the (very small) radial velocity only depends slightly on $a$ and $b$, so that it can be used as the free parameter of the eigenvalue system. The resulting instability-generated tensors of magnetic diffusivity and eddy viscosity are highly anisotropic. The eddy diffusivity in latitudinal direction exceeds the eddy diffusivity in radial direction by orders of magnitude. Its latitudinal profile shows a strong concentration toward the poles which is also true for the effective viscosity which has been calculated via the angular momentum transport of the instability pattern. The resulting effective magnetic Prandtl number reaches values of $O(10^2)$, so that the differential rotation decays much faster than the toroidal background field, which is {the} necessary condition to explain the observed slow rotation of the early red-giant and sub-giant cores by means of magnetic instabilities., Comment: 10 pages, submitted to MNRAS

The interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders is considered. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfv\'en frequency of the field are of the same order, almost independent of the magnetic Prandtl number Pm. For the very steep rotation law \Omega\propto R^{-2} (the Rayleigh limit) and for small Pm the threshold values of rotation and field for this Azimuthal MagnetoRotational Instability (AMRI) scale with the ordinary Reynolds number and the Hartmann number, resp. A laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container has been designed on the basis of this finding. For fluids with more flat rotation laws the Reynolds number and the Hartmann number are no longer typical quantities for the instability. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers \leq 1. We find that the magnetic energy grows monotonically with the magnetic Reynolds number Rm, while the kinetic energy grows with Rm/\sqrt{Pm}. The resulting turbulent Schmidt number, as the ratio of the `eddy' viscosity and the diffusion coefficient of a passive scalar (such as lithium) is of order 20 for Pm=1, but for small Pm it drops to order unity. Hence, in a stellar core with fossil fields and steep rotation law the transport of angular momentum by AMRI is always accompanied by an intense mixing of the plasma, until the rotation becomes rigid., Comment: 8 pages, 11 figures

This article presents a heterodyne experiment which uses a 380-520 GHz planar circuit balanced Nb-$\mathrm{Al_2O_3}$-Nb superconductor-insulator-superconductor (SIS) quasiparticle mixer with 4-8 GHz instantaneous intermediate frequency (IF) bandwidth to quantitatively determine local oscillator (LO) noise. A balanced mixer is a unique tool to separate noise at the mixer's LO port from other noise sources. This is not possible in single-ended mixers. The antisymmetric IV characteristic of a SIS mixer further helps to simplify the measurements. The double-sideband receiver sensitivity of the balanced mixer is 2-4 times the quantum noise limit $h\nu/k_B$ over the measured frequencies with a maximum LO noise rejection of 15 dB. This work presents independent measurements with three different LO sources that produce the reference frequency but also an amount of near-carrier noise power which is quantified in the experiment as a function of the LO and IF frequency in terms of an equivalent noise temperature $T_{LO}$. In a second experiment we use only one of two SIS mixers of the balanced mixer chip, in order to verify the influence of near-carrier LO noise power on a single-ended heterodyne mixer measurement. We find an IF frequency dependence of near-carrier LO noise power. The frequency-resolved IF noise temperature slope is flat or slightly negative for the single-ended mixer. This is in contrast to the IF slope of the balanced mixer itself which is positive due to the expected IF roll-off of the mixer. This indicates a higher noise level closer to the LO's carrier frequency. Our findings imply that near-carrier LO noise has the largest impact on the sensitivity of a receiver system which uses mixers with a low IF band, for example superconducting hot-electron bolometer (HEB) mixers., Comment: 13 pages, 8 figures, 2 tables, see manuscript for complete abstract

Supplementing the publications based on the first-light observations with the German Receiver for Astronomy at Terahertz frequencies (GREAT) on SOFIA, we present background information on the underlying heterodyne detector technology. We describe the superconducting hot electron bolometer (HEB) detectors that are used as frequency mixers in the L1 (1400 GHz), L2 (1900 GHz), and M (2500 GHz) channels of GREAT. Measured performance of the detectors is presented and background information on their operation in GREAT is given. Our mixer units are waveguide-based and couple to free-space radiation via a feedhorn antenna. The HEB mixers are designed, fabricated, characterized, and flight-qualified in-house. We are able to use the full intermediate frequency bandwidth of the mixers using silicon-germanium multi-octave cryogenic low-noise amplifiers with very low input return loss. Superconducting HEB mixers have proven to be practical and sensitive detectors for high-resolution THz frequency spectroscopy on SOFIA. We show that our niobium-titanium-nitride (NbTiN) material HEBs on silicon nitride (SiN) membrane substrates have an intermediate frequency (IF) noise roll-off frequency above 2.8 GHz, which does not limit the current receiver IF bandwidth. Our mixer technology development efforts culminate in the first successful operation of a waveguide-based HEB mixer at 2.5 THz and deployment for radioastronomy. A significant contribution to the success of GREAT is made by technological development, thorough characterization and performance optimization of the mixer and its IF interface for receiver operation on SOFIA. In particular, the development of an optimized mixer IF interface contributes to the low passband ripple and excellent stability, which GREAT demonstrated during its initial successful astronomical observation runs., Comment: Accepted for publication in A&A (SOFIA/GREAT special issue)

A systematic study of the temperature and magnetic field dependence of the longitudinal and transverse resistivities of epitaxial thin films of magnetite (Fe3O4) is reported. The anisotropic magnetoresistance (AMR) and the planar Hall effect (PHE) are sensitive to the in-plane orientation of current and magnetization with respect to crystal axes in a way consistent with the cubic symmetry of the system. We also show that the AMR exhibit sign reversal as a function of temperature, and that it shows significant field dependence without saturation up to 9 T. Our results provide a unified description of the anisotropic magnetoresistance effects in epitaxial magnetite films and illustrate the need for a full determination of the resistivity tensor in crystalline systems.

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large-scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large-scale magnetic tension is always reduced by the turbulence with the possibility of a `catastrophic quenching' for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence with short correlation time (`white noise') but it is reduced by turbulence with long correlation time. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St> 1. The turbulence-induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large-eddy simulations the magnetic quenching is only mild but then also the turbulence-induced Maxwell tensor components for weak fields remain rather small., Comment: 7 pages, 5 figures, submitted to Astron. Nachr

The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems under the presence of an homogeneous axial magnetic field is considered with focus to the excitation of nonaxisymmetric modes and the resulting angular momentum transport. The excitation of nonaxisymmetric modes requires higher rotation rates than the excitation of the axisymmetric mode and this the more the higher the azimuthal mode number m. We find that the weak-field branch in the instability map of the nonaxisymmetric modes has always a positive slope (in opposition to the axisymmetric modes) so that for given magnetic field the modes with m>0 always have an upper limit of the supercritical Reynolds number. In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum field strength of about 1 Gauss is necessary. For weaker magnetic field the nonaxisymmetric modes decay. The angular momentum transport of the nonaxisymmetric modes is always positive and depends linearly on the Lundquist number of the background field. The molecular viscosity and the basic rotation rate do not influence the related {\alpha}-parameter. We did not find any indication that the MRI decays for small magnetic Prandtl number as found by use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of about 1 Gauss the {\alpha} proves to be (only) of order 0.005.

We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation); this reflects the miniband structure and the associated van Hove singularities of the antidot lattice. The polarization functions depend on the azimuthal angle of the {\bf q}-vector. We develop approximations to ease the numerical work, and critically evaluate the performance of the various schemes. We also compute the plasmon dispersion law, and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic, and the developed approximation schemes agree well with the full calculation.

We present a 380-520 GHz balanced superconductor-insulator-superconductor (SIS) mixer on a single silicon substrate. All radio-frequency (RF) circuit components are fabricated on a $9 \mu$m thick membrane. The intermediate frequency (IF) is separately amplified and combined. The balanced mixer chip, using Nb/Al/Al$_{2}$O$_{3}$/Nb SIS junctions, is mounted in a tellurium copper waveguide block at 4.2 K using Au beam lead contacts. We find uncorrected minimum receiver double-sideband noise temperatures of 70 K and a noise suppression of up to 18 dB, measured within a 440-495 GHz RF and a 4-8 GHz IF bandwidth, representing state-of-the-art device performance., Comment: 10 pages, 4 figures, Accepted by Superconductor Science & Technology

The nonaxisymmetric Tayler instability of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two coaxial cylinders without endplates. The inner cylinder is considered as so thin that even the limit of R_in \to 0 can be computed. The magnetic Prandtl number is varied over many orders of magnitudes but the azimuthal mode number of the perturbations is fixed to m=1. In the linear approximation the critical magnetic field amplitudes and the growth rates of the instability are determined for both resting and rotating cylinders. Without rotation the critical Hartmann numbers do {\em not} depend on the magnetic Prandtl number but this is not true for the growth rates. For given product of viscosity and magnetic diffusivity the growth rates for small and large magnetic Prandtl number are much smaller than those for Pm=1. For gallium under the influence of a magnetic field at the outer cylinder of 1 kG the resulting growth time is 5 s. The minimum electric current through a container of 10 cm diameter to excite the kink-type instability is 3.20 kA. For a rotating container both the critical magnetic field and the related growth times are larger than for the resting column., Comment: 7 pages, 9 figures, submitted to Astron. Nachr

To find out whether toroidal field can stably exist in galaxies the current-driven instability of toroidal magnetic fields is considered under the influence of an axial magnetic field component and under the influence of both rigid and differential rotation. The MHD equations are solved in a simplified model with cylindric geometry. We assume the axial field as uniform and the fluid as incompressible. The stability of a toroidal magnetic field is strongly influenced by uniform axial magnetic fields. If both field components are of the same order of magnitude then the instability is slightly supported and modes with m>1 dominate. If the axial field even dominates the most unstable modes have again m>1 but the field is strongly stabilized. All modes are suppressed by a fast rigid rotation where the m=1 mode maximally resists. Just this mode becomes best re-animated for \Omega > \Omega^A (\Omega^A the Alfven frequency) if the rotation has a negative shear. -- Strong indication has been found for a stabilization of the nonaxisymmetric modes for fluids with small magnetic Prandtl number if they are unstable for Pm=1. For rotating fluids the higher modes with m>1 do not play an important role in the linear theory. In the light of our results galactic fields should be marginally unstable against perturbations with m<= 1. The corresponding growth rates are of the order of the rotation period of the inner part of the galaxy., Comment: 7 pages, 9 figures, submitted to Astron. Astrophys

We present observations of the rotational ortho-water ground transition, the two lowest para-water transitions, and the ground transition of ionised ortho-water in the archetypal starburst galaxy M82, performed with the HIFI instrument on the Herschel Space Observatory. These observations are the first detections of the para-H2O(111-000) (1113\,GHz) and ortho-H2O+(111-000) (1115\,GHz) lines in an extragalactic source. All three water lines show different spectral line profiles, underlining the need for high spectral resolution in interpreting line formation processes. Using the line shape of the para-H2O(111-000) and ortho-H2O+(111-000) absorption profile in conjunction with high spatial resolution CO observations, we show that the (ionised) water absorption arises from a ~2000 pc^2 region within the HIFI beam located about ~50 pc east of the dynamical centre of the galaxy. This region does not coincide with any of the known line emission peaks that have been identified in other molecular tracers, with the exception of HCO. Our data suggest that water and ionised water within this region have high (up to 75%) area-covering factors of the underlying continuum. This indicates that water is not associated with small, dense cores within the ISM of M82 but arises from a more widespread diffuse gas component., Comment: 5 pages, 4 figures. Accepted for publication in A&A

The linear stability of MHD Taylor-Couette flows in axially unbounded cylinders is considered, for magnetic Prandtl number unity. Magnetic fields varying from purely axial to purely azimuthal are imposed, with a general helical field parameterized by \beta=B_\phi/B_z. We map out the transition from the standard MRI for \beta=0 to the nonaxisymmetric Azimuthal MagnetoRotational Instability (AMRI) for \beta\to \infty. For finite \beta, positive and negative wave numbers m, corresponding to right and left spirals, are no longer identical. The transition from \beta=0 to \beta\to\infty includes all the possible forms of MRI with axisymmetric and nonaxisymmetric modes. For the nonaxisymmetric modes, the most unstable mode spirals in the opposite direction to the background field. The standard (\beta=0) MRI is axisymmetric for weak fields (including the instability with the lowest Reynolds number) but is nonaxisymmetric for stronger fields. If the azimuthal field is due in part to an axial current flowing through the fluid itself (and not just along the central axis), then it is also unstable to the nonaxisymmetric Tayler instability, which is most effective without rotation. For large \beta this instability has wavenumber m=1, whereas for \beta\simeq 1 m=2 is most unstable. The most unstable mode spirals in the same direction as the background field., Comment: 9 pages, 11 figures

The potential of the nonaxisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory the neutral-stability maps for m=1 are computed. Rigid rotation must be subAlfvenic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvenic rotation exists. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm=1 and becomes much weaker for Pm unequal 1. The effective angular momentum transport by the instability is directed outwards(inwards) for subrotation(superrotation). The resulting magnetic-induced eddy viscosities exceed the microscopic values by factors of 10-100. This is only true for superAlfvenic flows; in the strong-field limit the values remain much smaller. The same instability also quenches concentration gradients of chemicals by its nonmagnetic fluctuations. The corresponding diffusion coefficient remains always smaller than the magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the ratio of the effective viscosity and the diffusion coefficient. The magnetic instability transports much more angular momentum than that it mixes chemicals., Comment: 9 pages, 12 figures, submitted

The nonaxisymmetric 'kink-type' Tayler instability (TI) of toroidal magnetic fields is studied for conducting incompressible fluids of uniform density between two infinitely long cylinders rotating around the same axis. It is shown that for resting cylinders the critical Hartmann number for the unstable modes does not depend on Pm. By rigid rotation the instability is suppressed where the critical ratio of the rotation velocity and the Alfven velocity of the field (only) slightly depends on the magnetic Prandtl number Pm. For Pm=1 the rotational quenching of TI takes its maximum. Rotation laws with negative shear (i.e. d\Omega/dR<0) strongly destabilize the toroidal field if the rotation is not too fast. For sufficiently high Reynolds numbers of rotation the suppression of the nonaxisymmetric magnetic instability always dominates. The angular momentum transport of the instability is anticorrelated with the shear so that an eddy viscosity can be defined which proves to be positive. For negative shear the Maxwell stress of the perturbations remarkably contributes to the angular momentum transport. We have also shown the possibility of laboratory TI experiments with a wide-gap container filled with fluid metals like sodium or gallium. Even the effect of the rotational stabilization can be reproduced in the laboratory with electric currents of only a few kAmp., Comment: 9 pages, 11 figures, subm