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

Presented by: 
AA Schekochihin [Camrbridge]
Wednesday 15th September 2004 - 10:10 to 10:35
INI Seminar Room 1

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.

Related Links

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons