Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow

Hollerbach and Rudiger have reported a new type of magnetorotational instability (MRI) in magnetized Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields. The salient advantage of this "helical'' MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize than standard MRI (axial field only). We confirm their results, calculate HMRI growth rates, and show that in the resistive limit, HMRI is a weakly destabilized inertial oscillation propagating in a unique direction along the axis. But we report other features of HMRI that make it less attractive for experiments and for resistive astrophysical disks. Growth rates are small and require large axial currents. More fundamentally, instability of highly resistive flow is peculiar to infinitely long or periodic cylinders: finite cylinders with insulating endcaps are shown to be stable in this limit. Also, keplerian rotation profiles are stable in the resistive limit regardless of axial boundary conditions. Nevertheless, the addition of toroidal field lowers thresholds for instability even in finite cylinders.Comment: 16 pages, 2 figures, 1 table, submitted to PR

Studying Migrant Assimilation Through Facebook Interests

Migrants' assimilation is a major challenge for European societies, in part because of the sudden surge of refugees in recent years and in part because of long-term demographic trends. In this paper, we use Facebook's data for advertisers to study the levels of assimilation of Arabic-speaking migrants in Germany, as seen through the interests they express online. Our results indicate a gradient of assimilation along demographic lines, language spoken and country of origin. Given the difficulty to collect timely migration data, in particular for traits related to cultural assimilation, the methods that we develop and the results that we provide open new lines of research that computational social scientists are well-positioned to address.Comment: Accepted as a short paper at Social Informatics 2018 (https://socinfo2018.hse.ru/). Please cite the SocInfo versio

Magnetorotational Instability in a Rotating Liquid Metal Annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion disks, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid-metal annulus (Couette flow) is explored by local and global stability analysis and magnetohydrodynamic (MHD) simulations. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.Comment: 5 pages, 4 figures, published in MNRAS w/ modification

Numerical simulations of the Princeton magneto-rotational instability experiment with conducting axial boundaries

We investigate numerically the Princeton magneto-rotational instability (MRI) experiment and the effect of conducting axial boundaries or endcaps. MRI is identified and found to reach a much higher saturation than for insulating endcaps. This is probably due to stronger driving of the base flow by the magnetically rather than viscously coupled boundaries. Although the computations are necessarily limited to lower Reynolds numbers ($\Re$) than their experimental counterparts, it appears that the saturation level becomes independent of $\Re$ when $\Re$ is sufficiently large, whereas it has been found previously to decrease roughly as $\Re^{-1/4}$ with insulating endcaps. The much higher saturation levels will allow for the first positive detection of MRI beyond its theoretical and numerical predictions

Magnetorotational Instability in a Swirling Partially Ionized Gas

The magnetorotational instability (MRI) has been proposed as the method of angular momentum transport that enables accretion in astrophysical discs. However, for weakly-ionized discs, such as protoplanetary discs, it remains unclear whether the combined non-ideal magnetohydrodynamic (MHD) effects of Ohmic resistivity, ambipolar diffusion, and the Hall effect make these discs MRI-stable. While much effort has been made to simulate non-ideal MHD MRI, these simulations make simplifying assumptions and are not always in agreement with each other. Furthermore, it is difficult to directly observe the MRI astrophysically because it occurs on small scales. Here, we propose the concept of a swirling gas experiment of weakly-ionized argon gas between two concentric cylinders threaded with an axial magnetic field that can be used to study non-ideal MHD MRI. For our proposed experiment, we derive the hydrodynamic equilibrium flow and a dispersion relation for MRI that includes the three non-ideal effects. We solve this dispersion relation numerically for the parameters of our proposed experiment. We find it should be possible to produce non-ideal MRI in such an experiment because of the Hall effect, which increases the MRI growth rate when the vertical magnetic field is anti-aligned with the rotation axis. As a proof of concept, we also present experimental results for a hydrodynamic flow in an unmagnetized prototype. We find that our prototype has a small, but non-negligible, $\alpha$-parameter that could serve as a baseline for comparison to our proposed magnetized experiment, which could be subject to additional turbulence from the MRI.Comment: 14 pages, 13 figures, submitted to MNRA

The role of boundaries in the MagnetoRotational Instability

In this paper, we investigate numerically the flow of an electrically conducting fluid in a cylindrical Taylor-Couette flow when an axial magnetic field is applied. To minimize Ekman recirculation due to vertical no-slip boundaries, two independently rotating rings are used at the vertical endcaps. This configuration reproduces setup used in laboratory experiments aiming to observe the MagnetoRotational Instability (MRI). Our 3D global simulations show that the nature of the bifurcation, the non-linear saturation, and the structure of axisymmetric MRI modes are significantly affected by the presence of boundaries. In addition, large scale non-axisymmetric modes are obtained when the applied field is sufficiently strong. We show that these modes are related to Kelvin-Helmoltz destabilization of a free Shercliff shear layer created by the combined action of the applied field and the rotating rings at the endcaps. Finally, we compare our numerical simulations to recent experimental results obtained in the Princeton MRI experiment.Comment: 11 pages, 9 figure

Observation of a Free-Shercliff-Layer Instability in Cylindrical Geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, $Re\sim 10^3-10^6$. The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial endcap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the $r-\theta$ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number $m$ which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.Comment: 5 pages, 4 figure