Magnetorotational instability (PROMISE Experiment)

Cosmic magnetic fields play a surprisingly active role in cosmic structure formation by fostering outward angular momentum transport and inward mass accretion onto central objects, like protostars or black holes, by means of the magnetorotational instability (MRI). At the PROMISE experiment, two special versions of MRI, the helical MRI and the azimuthal MRI, are investigated.

PROMISE is basically a Taylor-Couette experiment with a gap width of 4 cm and a height of 40 cm (Figure 1). The utilized fluid is the eutectic alloy GaInSn which is liquid at room temperatures. Figure 2 shows the present set-up, including a 20 kA power supply for the central rod and a pentagon-shaped return-current system for the homogenization of the azimuthal field component.

The Taylor-Couette experiment is usually carried out in the hydrodynamically stable regime, when the angular momentum is increasing outward. The helical MRI (HMRI) appears as an axisymmetric travelling wave when the azimuthal field acquires an amplitude that is comparable with that of the axial field (Figure 3). For purely or strongly dominant azimuthal field, the non-axisymmtric azimuthal MRI (AMRI) shows up (Figure 4).

Figure 1: Sketch of the PROMISE facility, comprising a Taylor-Couette cell with inner radius of 4 cm, outer radius of 8 cm, and a height of 40 cm, filled with GaInSn, an external coil and a central copper rod for the generation of the axial and the azimuthal magnetic field, respectively.	Figure 2: Present configuration of PROMISE with a 20 kA power supply (right) for the central rod and a pentagon-shaped return-current system for the homogenization of the azimuthal field component.

Figure 3: Results for HMRI. Measured velocity structure when increasing the current through the central rod, for a fixed current of 76 A in the coil (top). Approximately at 5000 A, HMRI emerges as a wave trevallinf upward. Experimentally and numerically determined dependence of the mean squared of the velocity perturbations on the applied rod current (bottom).

Figure 4: Results for AMRI. Axial velocity perturbation for Re = 1480 and Ha = 124: (a) simulation for an idealized axisymmetric field. (b) Simulation for the realistic field geometry. (c) Measured velocity. (d) Numerically predicted growth rate. (e) Simulated and measured mean squared velocity perturbation. (f) Angular drift frequency.

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Press releases

• Cosmic turbulences result in star and black hole formation
• How to feed a black hole

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Publications

• Mamatsashvili, G., Stefani, F., Guseva, A., Avila, M.
  Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow
  New J. Phys. 20 (2018), 013012
• Mamatsashvili, G., Stefani, F.
  Linking dissipation-induced instabilities with nonmodal growth: The case of helical magnetorotational instability
  Physical Review E 94 (2016), 051203
• Seilmayer, M., Gundrum, T., Stefani, F.
  Noise reduction of ultrasonic Doppler velocimetry in liquid metal experiments with high magnetic fields
  Flow Meas. Instrum. 48 (2016), 74-80.
• Stefani, F., Kirillov, O.N.
  Destabilization of rotating flows with positive shear by azimuthal magnetic fields
  Phys. Rev. E 92 (2015), 051001(R).
• Rüdiger, G., Gellert, M., Schultz, M., Hollerbach, R., Stefani, F.
  Astrophysical and experimental implications from the magnetorotational instability of toroidal fields
  Mon. Not. R. Astron. Soc. 438 (2014), 271-277.
• Kirillov, O.; Stefani, F.; Fukumoto, Y.
  Local instabilities in magnetized rotational flows: A short-wavelength approach
  Journal of Fluid Mechanics 760(2014), 591-633
• Kirillov, O.; Stefani, F.; Fukumoto, Y.
  Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
  Fluid Dynamics Research 46(2014)3, 031403
• Seilmayer, M.; Galindo, V.; Gerbeth, G.; Gundrum, T.; Stefani, F.; Gellert, M.; Rüdiger, G.; Schultz, M.; Hollerbach, R.
  Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field
  Physical Review Letters 113(2014), 024505
• Kirillov, O.; Stefani, F.
  Extending the range of the inductionless magnetorotational instability
  Phys. Rev. Lett. 111 (2013), Art. No. 061103; arXiv:1303.4642
• Kirillov, O.N., Stefani, F.
  Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
  Acta Appl. Math. 120 (2012), 177-198
• Kirillov, O.N., Stefani, F., Fukumoto, Y.
  A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
  Astrophys. J. 756 (2012), 83.
• Kirillov, O.N., Stefani, F.
  Paradoxes of magnetorotational instability and their geometrical resolution
  Phys. Rev. E 84 (2010), 036304
• Kirillov, O.N., Stefani, F.
  On the relation of helical and standard magnetorotational instability Astrophys. J. 712 (2010), 52-68.
• Stefani, F., Gerbeth, G., Gundrum, Th., Hollerbach, R., Priede, J., Rüdiger, G., Szklarski, J.
  Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping
  Phys. Rev. E 80 (2009), Art. No. 066303; arXiv:0904.1027
• Stefani, F., Gundrum, Th., Gerbeth, G., Rüdiger, G., Szklarski, J., Hollerbach, R.
  Experiments on the magnetorotational instability in helical magnetic fields
  New J. Phys. 9 (2007), Art. No. 295
• Stefani, F., Gundrum, Th., Gerbeth, G., Rüdiger, G., Schultz, M., Szklarski, J., Hollerbach, R.
  Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field
  Phys. Rev. Lett. 97 (2006), Art. No. 184502; astro-ph/0606473