An Isaac Newton Institute Workshop

MAGNETOHYDRODYNAMICS OF STELLAR INTERIORS <br> Supported by the European Commission, Sixth Framework Programme - <br> Marie Curie Conferences and Training Courses - MSCF-CT-2003-503674

Magnetic-field generation in low-magnetic-Prandtl-number plasmas

Authors: A.A.Schekochihin (DAMTP/Cambridge), S.C.Cowley (UCLA & Imperial), J.L.Maron (Iowa & Rochester), J.C.McWilliams (UCLA & NCAR)

Abstract

Magnetic Prandtl number Pm is a key parameter for astrophysical MHD fluids. The Pm>>1 regime is realised in high-temperature low-density plasmas of galaxies and clusters. It has been firmly established both theoretically and numerically that large-Pm turbulent plasmas can generate equipartition-level magnetic fluctuation energy via the small-scale dynamo. In numerical simulations, this regime qualitatively persists down to values of Pm~1 [astro-ph/0312046]. The plasmas in stellar (solar) convective zones and protostellar discsare denser and have low Pm. There is ample observational evidence that the solar photosphere contains large amounts of small-scale magnetic field. This field may be generated by small-scale dynamo or induced via shredding by turbulence of the large-scale ("mean") solar field --- or both. We have recently shown numerically that small-scale dynamo in the low-Pm is problematic: it either does not exist at all (i.e., there is a critical Pm_c) or requires extremely large magnetic Reynolds numbers (i.e., there is a critical Rm_c) numerically inaccessible at current resolutions [PRL 92, 054502 (2004)]. I will discuss these numerical results as well as report some new ones that improve on them. I will also discuss theoretical arguments in favour of and against the dynamo. I emphasise that there is no numerical or laboratory evidence available at present that would show that low-Pm turbulence is a dynamo, nor is there a physical scenario that would explain how such a dynamo is possible. In this context, small-scale magnetic fluctuations induced by a mean field acquire renewed relevance. While it is not possible to perform adequately resolved simulations that incorporate both the self-consistent generation of the large-scale fields and the small-scale turbulence, it is certainly possible to study the effect of an imposed mean field on the latter. I will report an extensive numerical study of the properties of induced small-scale fields (in nonhelical turbulence). Their possible role in explaining the photospeheric fields and in quenching the mean-field dynamo mechanisms will be discussed. Furthermore, these results are subject to direct comparison with experimental liquid-metal results of laboratory dynamo experiments in unconstrained geometries (e.g., Lyon, Maryland, and Wisconsin). Finally, I will present some analytical considerations on the interaction between large- and small-scale dynamo-generated magnetic fields in the case of large scale seprations between the system size, the turbulence scale, and the magnetic dissipation scale.

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