The azimuthal MRI in experiment: confirmations and surprises

Transcription

1 Max-Planck-Princeton Center for Plasma Physics General Meeting, Berlin, June 28 July 1, 2014 The azimuthal MRI in experiment: confirmations and surprises Frank Stefani with thanks to V. Galindo, O. Kirillov, M. Seilmayer (HZDR) M. Gellert, G. Rüdiger, M. Schultz (AIP Potsdam), R. Hollerbach (University of Leeds) Text optional: Institutsname Prof. Dr. Hans Mustermann Mitglied der Leibniz-Gemeinschaft

2 Anyone who knows anything about astrophysics knows that magnetic fields have nothing to do with it. editor of Astrophysical Journal, rejecting Eugene Parker s first manuscript (1951) Seite 2

3 The Yin and Yang of astrophysical MHD Seite 3

4 Motivation are produced by the homogeneous dynamo effect Cosmic magnetic fields play a key role in cosmic structure formation by virtue of the magnetorotational instability Seite 4

5 Motivation Homogeneous dynamo effect: Self-excitation of magnetic fields in sufficiently strong, helical flows of conducting fluids Magnetorotational instability (MRI): Magnetic fields act like springs and trigger angular momentum transport in accretion disks around protostars and black holes Seite 5

6 History: From theory to experiment Experiments on cosmic magnetic fields since 15 years Dynamo experiments: Riga, Karlsruhe (1999), Cadarache (2006), Maryland, Madison, Perm Experiments on the MRI: Maryland, Princeton (see Gilson s talk), Rossendorf (2006) Seite 6

7 History of MRI: Magnetized Tayler-Couette flow E.P. Velikhov: Sov. Phys. JETP 9 (1959), 995 Seite 7

8 History of MRI E.P. Velikhov: Sov. Phys. JETP 9 (1959), 995 S.A. Balbus and J.F. Hawley: ApJ 376 (1991) 214 Seite 8

9 Seite 9 Theory: Viscous, resistive MHD with azimuthal wavenumber m u B B u u u 2 0 P t B u B B u B 2 t Viscous, resistive, and two Alfvén frequencies for axial and azimuthal field Induction equation: ,,, r B B k A z z A z k k Navier-Stokes equation: Dimensionless: Magnetic Prandtl, Field ratio, Reynolds, Hartmann, n m n z z A A A, Ha, Re,, Pm , z r z k k k k k with

10 Theory: Short wavelength approximation (WKB): Hydrodynamic and magnetic Rossby numbers: r Ro 2 r, Rb r 2 A A r Secular equation: p( ) det( H E) 0 with H inre1 2Re(1 Ro) iha(1 n ) Pm 2HaRb Pm 2 Re inre1 0 iha(1 n ) Pm iha(1 n ) Pm 2Ha(1 Rb) Pm 1 inre Pm 2Re Ro 2 Ha Pm iha(1 n ) Pm 0 inre 1 Pm Kirillov et al., Phys. Rev. Lett. 111 (2013), ; arxiv: Seite 10

11 Standard MRI and helical MRI Standard MRI (with purely axial field) scales with Lundquist (S) und magnetic Reynolds (Rm) Experiments on SMRI with large Rm in Maryland and Princeton (see Gilson s talk) Hollerbach and Rüdiger (PRL 2005): Helical MRI: B z replaced by B z +B j : scales with Hartmann (Ha) and Reynolds (Re) Re crit : 10 3 instead of 10 6 Ha crit: 30 instead of 1000 Potsdam ROssendorf Magnetic InStability Experiment (PROMISE) Drawback: does not work for Kepler! Seite 11

12 Relation between standard MRI (SMRI) and helical MRI (HMRI) Apparent paradox: Transition between SMRI and HMRI is continuous and monotonic, although they represent different branches of the dispersion relation Solution of the riddle: At small but finite Pm both modes coalesce at an exceptional point and exchange the unstable branches Hollerbach and Rüdiger, PRL 95 (2005), Kirillov and Stefani, Astrophys. J. 712 (2010), 52 Seite 12

13 Destabilizing Kepler flows with appropriate Rb WKB-Analysis of the viscous and resistive MRI/TI problem for arbitrary azimuthal modes m Main results: Kirillov and Stefani, Phys. Rev. Lett. 111 (2013), ; arxiv: ; arxiv: Seite 13

14 The role of Rb: Between azimuthal MRI and Tayler instability Kirillov, Stefani, Fukomoto, JFM (submitted) arxiv: Seite 14

15 Dissipation induced instability of the Chandrasekhar equipartition state Chandrasekhar theorem: An ideal fluid with equal amplitudes of Alfvén velocity and rotation velocity is stable. New result: An infinitesimal small electrical resistivity destabilizes the marginal stable solution (see also talk of O.N. Kirillov and latest results of G. Rüdiger ) Kirillov, Stefani, Fukomoto, JFM (submitted) arxiv: The threshold of instability at Ha 2 = Rm Re and Re in the (n,rb,rm) space. In the limit Rm the instability degenerates into a ray (dashed) Seite 15

16 A lesson from dissipation induced instabilities Much as in the mid-nineteenth century, the point was missed that for fluid equations of the Navier-Stokes type the ideal limit with zero dissipation coefficients has essentially nothing to do with the case of small but finite dissipation coefficients D. Montgomery: Hartmann, Lundquist, and Reynolds: The role of dimensionless numbers in non-linear magnetofluid behavior. Plasma Phys. Control. Fusion 35 (1993) B105-B113 Seite 16

17 PROMISE: Previous experimental results for helical MRI Stefani, F. et al., Phys. Rev. Lett. 97 (2006), , New J. Phys. 9 (2007), 295, Phys. Rev. E 80 (2009), Seite 17

18 PROMISE: Constructed in 2005 Seite 18

19 PROMISE: Selected results for HMRI Example 1: Increase of the ratio o / i of the rotation rates of the outer and inner cylinder Observed MRI is indeed an absolute (global) instability, and not only a convective one Stefani et al., Phys. Rev. E 80 (2009), Seite 19

20 PROMISE: Selected results for HMRI Example 2: Increase of axial current (i.e. of the ratio of azimuthal to axial magnetic field) Stefani et al., Phys. Rev. E 80 (2009), Seite 20

21 PROMISE: Comparison Experiment/Simulation Seite 21

22 Azimuthal MRI (AMRI): m=1 mode under influence of (pure) B j New power supply provides currents up to 20 ka Very important: Simulation of the real geometry including the slight symmetry breaking of the applied magnetic field Seite 22

23 Azimuthal MRI (AMRI): Slight symmetry breaking of magnetic field Seite 23

24 Azimuthal MRI (AMRI): Slight symmetry breaking of magnetic field Finite Volume Simulation OpenFOAM+induced current (partly + Biot-Savart s law [1]) Ideal and real field configuration In the ideal case,the waves are separated. In the real case, they interpenetrate each other. ideal real Seite 24 [1] Weber et al., New J. Phys. 15 (2013),

25 Evidence for AMRI: m=1 mode under influence of a purely (?) B j Very important: Simulation of real geometry (V. Galindo) Seilmayer et al., Phys. Rev. Lett., in press; arxiv: Seite 25

26 Can the slightly asymmetric magnetic field destabilize Keplerian flows? Seite 26 A positive answer would completely change the scaling behaviour of MRI in low Pm parts of accretion disks from (Rm,S) to (Re,Ha)!!!

27 Kink-type Tayler instability (TI) Astrophysical motivation: Alternative mechanism of solar dynamo (Tayler-Spruit) Braking of neutron stars Instabilities in cosmic jets Seite 27 First experiment at HZDR: Good correspondence of measured critical currents and growth rates of theti with numerical simulations. Seilmayer et al., Phys. Rev. Lett. 108 (2012),

28 Tayler instability in large-scale liquid metal batteries Problem: Tayler instability Simple solution: Guide the current back through the center Seite 28 Stefani et al., Energy Conv. Managem. 52 (2011), 2982 Weber et al., J. Power Sources 265 (2014), 166

29 Simulation of TI and AMRI with integro-differential equation code The critical current increases with decreasing aspect ratio. Plateaus appear at full and half wavelength. Realistic simulation of the TI experiment with correct geometry and material parameters. Weber et al., New J. Phys. 15 (2013), Seite 29

30 Seite 30 DRESDYN

31 Prospects: DRESDYN The DREsden Sodium facility for DYNamo and thermohydraulic studies is a platform for geo- and astrophysics experiments as well as for liquid metal applications in energy related technologies. Precession driven dynamo experiment Magnetorotational instability (MRI) and Tayler instability (TI) Liquid metal batteries (storage of intermittent renewables) Measuring techniques (Magnetic flow tomography etc... ) Thermohydraulics of liquid metal fast reactors Stefani et al., Magnetohydrodynamics 48 (2012), 103 Seite 31

32 DRESDYN: General features New building ~500 m 2 Total sodium inventory: 12 tons Large experimental hall for MRI/TI experiment, sodium loop, X-ray lab, liquid metal batteries Precession driven dynamo experiment with separate strong basement and containment for Argon flooding Seite 32

33 DRESDYN: General features New building ~500 m 2 Total sodium inventory: 12 tons Large experimental hall for MRI/TI experiment, sodium loop, X-ray lab, liquid metal batteries Precession driven dynamo experiment with separate strong basement and containment for Argon flooding Seite 33 Construction site as of May 2014

34 DRESDYN: General scheme Seite 34

35 Planned combined MRI/TI experiment...will (hopefully) allow to study helical MRI, azimuthal MRI, standard MRI, and their combinations with Tayler instability R in =0.2 m R out =0.4 m H=2 m f in =20 Hz f out =6 Hz B z =120 mt (will need some 500 kw) Rm=40 Lundquist=8 Seite 35

36 An unrealizable (??) dream: MRI dynamo Seite 36

37 Seite 37 Thank you