Optimized boundary driven flows for dynamos in a sphere

Journal Article · Thu Nov 15 04:00:00 EST 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4764048· OSTI ID:22072595

Khalzov, I V; Brown, B P; Cooper, C M; Weisberg, D B; Forest, C B ^[1]

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1. Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706 (United States)

We perform numerical optimization of the axisymmetric flows in a sphere to minimize the critical magnetic Reynolds number Rm{sub cr} required for dynamo onset. The optimization is done for the class of laminar incompressible flows of von Karman type satisfying the steady-state Navier-Stokes equation. Such flows are determined by equatorially antisymmetric profiles of driving azimuthal (toroidal) velocity specified at the spherical boundary. The model is relevant to the Madison plasma dynamo experiment, whose spherical boundary is capable of differential driving of plasma in the azimuthal direction. We show that the dynamo onset in this system depends strongly on details of the driving velocity profile and the fluid Reynolds number Re. It is found that the overall lowest Rm{sub cr} Almost-Equal-To 200 is achieved at Re Almost-Equal-To 240 for the flow, which is hydrodynamically marginally stable. We also show that the optimized flows can sustain dynamos only in the range Rm{sub cr}

• OSTI ID: 22072595
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 11 Vol. 19; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
AXIAL SYMMETRY
BOUNDARY LAYERS
INCOMPRESSIBLE FLOW
LAMINAR FLOW
MAGNETIC REYNOLDS NUMBER
NAVIER-STOKES EQUATIONS
NUMERICAL ANALYSIS
OPTIMIZATION
PLASMA
SPHERES
SPHERICAL CONFIGURATION
STEADY-STATE CONDITIONS
VELOCITY