Thermal Analysis of EPOS components

We present a simulation study of the thermal behaviour of essential parts of the electron-positron converter of the positron source EPOS at the Research Center Dresden-Rossendorf. The positron moderator foil and the upper tube element of the electrostatic extraction einzellens are directly exposed to the primary electron beam (40 MeV, 40 kW). Thus, it was necessary to prove by sophisticated simulations that the construction can stand the evolving temperatures. It was found that thin moderator foils (< 20...40 µm) will not show a too strong heating. Moreover, the temperature can be varied in a wide range by choosing an appropriate thickness. Thus, the radiation-induced lattice defects can at least partly be annealed during operation. The wall of the extraction lens which is made from a stainless steel tube must be distinctly thinned to avoid damage temperatures. The simulations were performed time dependent. We found that the critical parts reach their final temperature after less than a minute

dS-AdS structures in the non-commutative Minkowski spaces

We consider a family of non-commutative 4d Minkowski spaces with the signature (1,3) and two types of spaces with the signature (2,2). The Minkowski spaces are defined by the common reflection equation and differ in anti-involutions. There exist two Casimir elements and the fixing of one of them leads to non-commutative "homogeneous" spaces $H_3$, $dS_3$, $AdS_3$ and light-cones. We present the quasi-classical description of the Minkowski spaces. There are three compatible Poisson structures - quadratic, linear and canonical. The quantization of the former leads to the considered Minkowski spaces. We introduce the horospheric generators of the Minkowski spaces. They lead to the horospheric description of $H_3$, $dS_3$ and $AdS_3$. The irreducible representations of Minkowski spaces $H_3$ and $dS_3$ are constructed. We find the eigen-functions of the Klein-Gordon equation in the terms of the horospheric generators of the Minkowski spaces. They give rise to eigen-functions on the $H_3$, $dS_3$, $AdS_3$ and light-cones.Comment: 31 pages, LateX, typos corrected, references adde