3 Mar 2004; Mat-Nat Faculty (UITO), room U7. Wednesday 12:15-14:00

Einar Mjølhus "Solitons in Space".

Recently, a research group (Staciewicz et al. febr. 2003) published observations by means of the Cluster formation of satellites, which they interpreted as “solitons”. Cluster is a formation of four satellites which go in orbit around the earth, at a distance of a few earth radii. This formation makes it possible to obtain a rough spatial resolution of measurements; for example, one can then distinguish between time variation at a point (which is what an instrument on one single satellite measures) and propagation of spatial structures.

The observed structures which were interpreted as “solitons” are assumed to be the same as has for more than a decade been detected by single satellites and termed “magnetic holes”.

The theory of Magneto-Hydro-Dynamical (or MHD) solitons (or solitary waves) which Staciewicz et al. applied, was developed by McKenzie and Doyle (2001, 2002), but many similar contributions existed before that, dating back to early 1960s. I shall describe the measurements in slightly more detail. Then I shall describe and interpret the theory of McKenzie and Doyle; in particular, I shall classify the solitary wave families in terms of amplitude-velocity relationships, and discuss an important observable: the polarization through the solitary structures. The small amplitude limit governed by the Korteweg-deVries’ equation is not sufficient in this context.

Finally, I wish to discuss the problems associated with extending the theory to warm plasma. This is necessary in the present context, and is also done in the theory of McKenzie and Doyle, but the question is whether the model is adequate. I hope to end the discussion by posing a problem of existence of a spatially confined solutionwhen the governing differential equations are equivalent to a two degrees of freedom Hamiltonian system with a saddle point.

Pr-requisite: only a basic knowledge of differential equations. Physics: an advantage, but not absolutely necessary.