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We present an optimized design of our recently realized disc dynamo. Like the original set-up, the optimized dynamo consists of a flatmulti-arm spiral coil and a co-axially placed disc which is connected to the former by sliding liquid metal contacts. In contrast to the original set-up, the disc and the coil in the optimized design have different sizes. This allows the disc to capture more of the high-density magnetic flux generated in the inner part of the coil and to avoid the reverse flux in the outer part of the coil. By optimizing the coil and dics radii, the critical magnetic Reynolds number can be reduced from -34.6 when the disc and the coil have equal inner and outer radii with the ratio ri/ro -0.36 to Rm-11.6. This lowest possible disc dynamo threshold is attained when the disc and the coil have relatively narrow widths. Using a slightly suboptimal but more practical set-up with the inner and outer radii of the disc and coil equal to (0.3,0.9) and (0.74,1), respectively, self-excitationis expected at Rm-14.6. [ABSTRACT FROM AUTHOR]

The magnetic fields take place in different astrophysical objects, such as stars, planets, galaxies, accretion discs etc. Their evolution is usually described by the dynamo model. The equations of the dynamo are quite difficult to be solved, so different approximations are often used. One of the most successful ones are connected with the no- model which has been developed for thin discs that can be a good model for galaxies and accretion discs. In this paper we study the magnetic field evolution in the case of Keplerian rotation law. The results have been obtained for the simplest case and for the model with helicity fluxes. This approach can be useful while researching the role of convective flows in the discs. It is shown that the magnetic field can have oscillations in this case. Also we show the evolution of the energy which can significantly change because of the convective flows. [ABSTRACT FROM AUTHOR]