A mapping approach to synchronization in the "Zajfman trap". II: the observed bunch

We extend a recently introduced mapping model, which explains the bunching phenomenon in an ion beam resonator for two ions [Geyer, Tannor, J. Phys. B 37 (2004) 73], to describe the dynamics of the whole ion bunch. We calculate the time delay of the ions from a model of the bunch geometry and find that the bunch takes on a spherical form at the turning points in the electrostatic mirrors. From this condition we derive how the observed bunch length depends on the experimental parameters. We give an interpretation of the criteria for the existence of the bunch, which were derived from the experimental observations by Pedersen et al [Pedersen etal, Phys. Rev. A 65 042704].Comment: 25 pages, 6 figures; added new section 5 and clarified text; submitted to J. Phys.

The basic cohomology of the twisted N=16, D=2 super Maxwell theory

We consider a recently proposed two-dimensional Abelian model for a Hodge theory, which is neither a Witten type nor a Schwarz type topological theory. It is argued that this model is not a good candidate for a Hodge theory since, on-shell, the BRST Laplacian vanishes. We show, that this model allows for a natural extension such that the resulting topological theory is of Witten type and can be identified with the twisted N=16, D=2 super Maxwell theory. Furthermore, the underlying basic cohomology preserves the Hodge-type structure and, on-shell, the BRST Laplacian does not vanish.Comment: 9 pages, Latex; new Section 4 showing the invariants added; 2 references and relating remarks adde