Magnetic fields in planets and in many stars are generated by a dynamo process powered by convective motion. Understanding the magnetic fields of these celestial objects is important as they carry information on the structure of the body’s interior as well as controlling how a it interacts with its surrounding environment. For example magnetic fields can shield a planet from harmful radiation. While the magnetic fields of the Earth and Sun have been characterized in great detail, recent space missions and remote sensing techniques have revealed a surprising diversity in the strength, morphology and time-variability of planetary and stellar magnetic fields in general. A key challenge, which this programme will seek to address, is to develop theories and models that explain these observed spatial and temporal variations.
Direct numerical dynamo simulations solve the magnetohoydrodynamic (MHD) equations, a set of coupled non-linear partial differential equations (PDEs). The MHD equations describe the mutual interaction of magnetic fields and electrically conducting fluids, such as liquid metals or plasmas. While these equations are well established, the enormous range of spatial and temporal scales precludes direct numerical solution of the fundamental equations in the appropriate parameter regimes. Furthermore, the highly non-linear nature of the MHD equations means that they cannot be tackled analytically except in very simplified limits. Therefore, to make meaningful progress there needs to be a synergy between idealised systems, physical approximations, theoretical models and innovative numerical strategies. This presents formidable mathematical challenges that this programme aims to address. While the interplay between theory and numerical simulation is important to advancing dynamo simulations, theoretical developments also need to be guided by the rapidly growing empirical evidence on planetary and stellar magnetic fields. Over the past 20 years there have been many new observations of planetary and stellar magnetic fields, with many more expected in the near future. This growing body of empirical evidence covers not only magnetic properties but also the internal constitution of planets and stars and the large scale flow pattern, which in the case of stars is revealed by helio- and asteroseismology. This recent availability of new observations provides a unique opportunity to test theories.
This programme will emphasise the interplay between theory, numerical simulation and observations by bringing together applied mathematicians, stellar, solar and planetary scientists engaged in theory or observations, and experts from neighbouring fields. The aim of this interdisciplinary approach is to bridge gaps that exist between researchers focusing on specific dynamo processes in planets, dynamo processes in stars, or on related fundamental questions of magnetohydrodynamics. One major objective is to identify developments in applied mathematics needed to tackle challenges posed by observations and experiments. Another is to identify paths towards transforming dynamo simulations into a tool for the predictive analysis of observational data. Conversely the programme also aims to identify observations and experiments needed to put the theories to the test, and then consequently testing those theories.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Frontiers in dynamo theory: from the Earth to the stars, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
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