19 July - 13 August 2010
Organisers: Professor W Dorland (Maryland), Professor S Nazarenko (Warwick) and Dr A Schekochihin (Oxford)
Perhaps the greatest challenge in plasma science is to understand the multiscale interaction between small-scale fluctuations and large-scale plasma dynamics. This is crucial both in fundamental astrophysical and space physics research (e.g., turbulence in the solar wind) and in more practical terrestrial contexts (e.g., the performance of the international fusion reactor, ITER, will be limited by the transport caused by small-scale fluctuations). Multiscale plasma dynamics also represent a formidable and fascinating mathematical challenge, as new analytical and numerical methods have to be developed in order for major breakthroughs to become possible.
In the last 25 years, a new mathematical approach, gyrokinetics, has been developed to treat low-frequency fluctuations in plasmas. In this approach, the fast orbital "gyromotion" is averaged to produce kinetic equations for rings of charge. This is a mathematically rigorous description that is far more tractable than the full kinetic theory. Despite some practical successes in code-building and simulations, the mathematical properties and physical implications of gyrokinetics are insufficiently well understood. In space and astrophysics, the wide applicability and power of the gyrokinetic theory has yet to be fully recognised and exploited. To realise the benefits of this approach, it is essential that gyrokinetics be put on a firm mathematical and physical footing.
Gyrokinetics is a nonlinear theory in a 5D phase space. When the collisionality is low, the ring distribution develops a broad range of scales in this phase space. This gives rise to a kinetic turbulent system that is richer and more complex than fluid turbulence. Some of the fundamental questions are:
In the process of addressing these questions, many nontrivial methodological challenges arise:
The programme, while addressing these questions, will aim to step beyond the traditional focus on gyrokinetics for fusion plasmas: to confront a broader group of applied mathematicians and numericists with the practical challenges posed by gyrokinetics; to explore applications to space and astrophysical plasmas; and thus to help forge a cross-disciplinary and versatile community of physicists, astrophysicists and mathematicians, diverse in expertise and background, aware of the spectrum of problems, methods and applications in each other's areas, and dedicated to tackling the grand challenge of understanding kinetic plasma turbulence and transport via a broad collaborative effort.
Unofficial webpage for the event is here.