Madison Plasma Couette Experiment (MPCX): (a) sketch; (b) partial vertical cross section. Rings of permanent magnets of alternating polarity line the inside of the cylinder with their poles oriented normally to the walls. Ring anodes and cathodes are placed between the magnets. The resulting drift is in the azimuthal direction. By varying the potential between the anodes and cathodes, the velocity forcing at the outer boundary can be customized.
Structure of axisymmetric equilibrium von Kármán flow driven by electromagnetic system at the boundary for Mach number , fluid Reynolds number , and magnetic Reynolds number : (a) number density; (b) velocity; (c) magnetic field. Cross-sections in plane are given. Left panels of (b) and (c) show stream lines of poloidal parts (- and -components) of flux and magnetic field , respectively, superimposed on absolute values of these parts depicted in colors. Right panels of (b) and (c) show azimuthal components of corresponding fields.
Structure of axisymmetric equilibrium von Kármán flow driven by differentially rotating walls for Mach number and fluid Reynolds number : (a) number density; (b) velocity. The same elements as in Fig. 2 are shown.
Time dynamics of kinetic energy of different azimuthal harmonics in purely hydrodynamical von Kármán flow for Mach number and fluid Reynolds number . Corresponding azimuthal mode numbers are shown.
Kinetic energy of different azimuthal harmonics in hydrodynamically stable von Kármán flow as a function of (a) fluid Reynolds number for Mach number ; (b) Mach number for fluid Reynolds number . Corresponding azimuthal mode numbers are shown.
Critical magnetic Reynolds number as a function of (a) fluid Reynolds number for Mach number ; (b) Mach number for fluid Reynolds number . Vertical line in (a) separates the regions of axisymmetric and nonaxisymmetric equilibrium von Kármán flows.
Time dynamics of kinetic and magnetic energies of different azimuthal modes in von Kármán flow for Mach number , fluid Reynolds , and magnetic Reynolds , with azimuthal mode numbers labeled. [(a),(b)] Single-fluid MHD case . Flows are of even modes while fields are odd in . [(c),(d)] Hall MHD case . Initial behavior is similar to the single-fluid MHD case, but as the fields become strong , the Hall effect becomes important. The final equilibrium includes both odd and even .
Magnetic field lines of saturated dynamos: (a) single-fluid MHD case ; (b) Hall MHD case . Thickness of the line is proportional to the magnitude of the field, while lighter (darker) color corresponds to upward (downward) direction of the field.
Magnetic energy of different azimuthal harmonics in saturated Hall MHD dynamo as a function of the Hall number . Azimuthal mode numbers are shown. Dashed line corresponds to scaling .
Parameters of MPCX.
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