The HITRAP project at GSI: trapping and cooling of highly-charged ions in a Penning trap

A decelerator will be installed at GSI in order to provide and study heavy nuclei without or with only few electrons at very low energies or even at rest. Highly-charged ions will be produced by stripping at relativistic energies. After electron cooling and deceleration in the Experimental Storage Ring (ESR) the ions are ejected out of the storage ring at 4 MeV/u and further decelerated in a combination of linear accelerator structures operated in reverse. Finally, they are injected into a Penning trap where the ions are cooled to 4 K by electron cooling in combination with resistive cooling. From here, the ions can be transferred in a quasi DC or in a pulsed mode to different experimental setups. This article describes the technical concepts of this project focused on the Penning trap.      

A competitive algorithm in searching for many edges in a hypergraph

We give a competitive algorithm to identify all d defective edges in a hypergraph with d unknown. Damaschke did the d=1 case for 2-graphs, Triesch extended the d=1 case to r-graphs, and Johann did the general d case for 2-graphs. So ours is the first attempt to solve the searching for defective edges problem in its full generality. Further, all the above three papers assumed d known. We give a competitive algorithm where d is unknown.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

Kinetics of reduction of ruthenium(III) by sodium tetrahydroborate

Summary The kinetics of reduction of ruthenium(III) by sodium tetrahydroborate in aqueous acidic medium have been studied. The effect of variation in the concentration of substrate (RuCl₃·3H₂O), pH, and reductant (BH₄ ^–1) has been studied. The activation parameters were evaluated. Based on a one-electron transfer, the mechanism involves the reduction of ruthenium(III) by hydrogen.     

Notes on symmetric g-functions

A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable. The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China.     

The categoricity of the group of all computable automorphisms of the rational numbers

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations. Supported by a Scheme 2 grant from the London Mathematical Society. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007.     

Modeling of single- and multimode photonic-crystal planar waveguides with the plane-wave admittance method

One-foil targets emit most transition radiation (TR) power in storage ring synchrotrons. Such one-foil TR emitting targets (OFTRTs) are optimized, with respect to the foil material and the foil thickness, for use as X-ray lithography (XRL) sources. The best possible elemental material and the foil thickness of OFTRTs for XRL are determined for our storage ring synchrotrons MIRROIRCLE-20SX and MIRRORCLE-6X, which operate with electrons accelerated to 20 MeV and 6 MeV, respectively. It is shown that the XRL efficiency of a OFTRT, with an optimum thickness, increases when the elemental foil material has a lower atomic number Z. The best elemental OFTRT, for performing XRL by MIRRORCLE-20SX, should contain one Be foil with a thickness of d≅240 nm, while the second best OFTRT should be made of one C foil with d≅220 nm. The best elemental OFTRT, for performing XRL by MIRRORCLE-6X, should contain one C foil with d≅35 nm, while the second best OFTRT should be made of one Be foil with d≅100 nm, because there are no thinner Be foils. The XRL efficiency of a C-foil OFTRT increases when a higher-density foil is used. A OFTRT containing one foil of a given material with optimum thickness, in MIRRORCLE-20SX, has approximately 100 times larger XRL efficiency in comparison with such a target in MIRRORCLE-6X. PACS 41.50.+h; 29.25.-t; 81.16.Nd; 41.60.Ap; 29.20.Dh