Commissioning of the vacuum system of the KATRIN Main Spectrometer

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. The strong magnetic field that guides the beta-electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips has been deployed and was tested during the commissioning of the spectrometer. In this paper the configuration, the commissioning with bake-out at 300{\deg}C, and the performance of this system are presented in detail. The vacuum system has to maintain a pressure in the 10^{-11} mbar range. It is demonstrated that the performance of the system is already close to these stringent functional requirements for the KATRIN experiment, which will start at the end of 2016

Solving Partial Differential Equations

The paper deals with solving the partial differential equations by the old and well known "analog" method of lines. This method is also suitable for digital computation and it can be directly used for solving the time depending equations as e.g. heat and wave equations. The aim of the paper is to show the nonstandard applications of the method of lines for solving the stationary problems. These problems may be described by the elliptic equations (Laplace's or Poisson's) or by some others linear or nonlinear equations. Keywords: Partial Differential Equations, Method of Lines 1 Introduction Partial differential equation (PDE) is one in which there appear partial derivatives of an unknown function with respect to two or more independent variables u(x 1 ; x 2 ; ::; x n ), (n 2). The order of an equation is given by highest-order partial derivative that occurs in this equation. The equations with unique solutions can be solved by computers only. It means that the boundary and initial con..