PACS. 02.40.Sf -Manifolds and cell complexes. PACS. 61.25.Em -Molecular liquids. PACS. 61.30.Cz -Theory and models of liquid crystal structure.Abstract. -We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, continuous and interwoven sub-volumes. The construction gives helical windings of disjoint graphs on triply periodic hyperbolic surfaces, whose universal cover in the hyperbolic plane consists of packed, parallel trees. The simplest tri-, quadra-and octa-continuous morphologies consist of three (8, 3) − c, four (10, 3) − a and eight (10, 3) − a interwoven networks, respectively. The quadraand octa-continuous cases are chiral. A novel chiral bicontinuous structure is also derived, closely related to the well-known cubic gyroid mesophase. EUROPHYSICS LETTERS

Thallium-compound bulk lenses have the highest ability to focus relativistic electron beams (REBs, 0.87 kA, duration time of some nanoseconds) among the high-temperature superconducting Y-, Bi-, and Tl-compound bulk lenses (Supertrons). The REBs were focused to a diameter of less than 2 mm, the narrowest diameter ever achieved with Supertrons. The current densities on the beam axes were higher than 350 kA/mm2. A revised figure of merit was proposed to evaluate the superconducting lenses.

The structure of a jig is reported, which is useful to form gently tapered high-temperature superconductor tubes.

To confirm a model for operation of powder-pressed bulk superconductor lenses (Supertrons), Y-based quench-melt-growth (QMG) bulk superconductors were used to focus intense electron beams (340 keV, ∼1 kA, and 5∼10 ns). The lens focused the beams much less effectively than any of the Y-, Bi-, and Tl-based powder-pressed bulk lenses and even worse than a copper-made lens. These facts support the validity of the model in which powder-pressed bulk superconductors behave like ferrite cores at frequencies of some hundred MHz.

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