Optimized boundary driven flows for dynamos in a sphere

Khalzov, I. V.
(
Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
);
Brown, B. P.
(
Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
);
Cooper, C. M.
(
Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
);
Weisberg, D. B.
(
Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
);
Forest, C. B.
(
Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
)
show affiliations
Physics of Plasmas, Volume 19, Issue 11, article id. 112106 11 pp. (2012).

Published in Nov 2012

We perform numerical optimization of the axisymmetric flows in a sphere to minimize the critical magnetic Reynolds number Rm_{cr} required for dynamo onset. The optimization is done for the class of laminar incompressible flows of von Kármán 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_{cr}≈200 is achieved at Re ≈240 for the flow, which is hydrodynamically marginally stable. We also show that the optimized flows can sustain dynamos only in the range Rm_{cr}〈Rm 〈Rm_{cr2}, where Rm_{cr2} is the second critical magnetic Reynolds number, above which the dynamo is quenched. Samples of the optimized flows and the corresponding dynamo fields are presented.
Keywords:
arXiv:
Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics

PACS Codes:
02.30.Jr; 02.60.Pn; 52.30.Cv; 52.40.Hf

PACS:
Magnetohydrodynamics; Numerical optimization; Partial differential equations; Plasma-material interactions; boundary layer effects

Free Keywords:
Navier-Stokes equations; laminar flow; numerical analysis; optimisation; plasma boundary layers; plasma magnetohydrodynamics

2012: American Institute of Physics