The central scientific question "Global behavior in (partial) chaotic transport" is on one hand deduced from experimental
achievements and sightings and on the other hand from theory itself. Among other projects subproject A1 especially shows
(with close collaboration to subproject A2) why structured stochastic magnetic fields are of great experimental relevance in
laboratory plasmas. Astrophysical observations point beyond that into the same direction: Magnetic fields possess predominantly
a nontrivial structure and contain in many cases an additional stochastic component (see A3 and A6).
For both ranges, "laboratory plasmas and astrophysical systems" this means that increasingly models with chaotic magnetic lines of flux (of
incompletely chaotic up to turbulent) lie in the center of the interest.
The subproject A1 dedicates itself to the special aspects, that occur when the incomplete chaos prevails and strikes thereby a bridge also to
The analysis of magnetic field systems lives crucially on the fact that it concerns (continuous) Hamiltonian systems.
As the first goal we pursue the "simplification" of such complex nonlinear systems.
We want to reach this goal by an improvement of the illustration technology and a comparison of illustrations with the complete (continuous) system.
The characterisation of the incomplete chaos is the center of attention thereby.
In the form of discrete illustrations, which show the structure of the accurate system well, the tool for statistic evaluations (average
values, variances) is to be supplied. This "simplification" should be able to deal quite generally with Hamiltonian systems , thus for
magnetic field systems, in addition, for gyration centers on the basis of "guiding center equations" into partial chaotic systems.
Open in this relationship are still the questions about corrections of higher order, the convergence and stability (the numeric algorithms
which are based on it).