Electric potential and field calculation of charged BEM triangles and rectangles by Gaussian cubature

It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for the case of electric potential and field computation of charged triangles and rectangles applied in the boundary element method (BEM). Analytical potential and field formulas are rather complicated (even in the simplest case of constant charge densities), they have usually large computation times, and at field points far from the elements they suffer from large rounding errors. On the other hand, Gaussian cubature, which is an efficient numerical integration method, yields simple and fast potential and field formulas that are very accurate far from the elements. The simplicity of the method is demonstrated by the physical picture: the triangles and rectangles with their continuous charge distributions are replaced by discrete point charges, whose simple potential and field formulas explain the higher accuracy and speed of this method. We implemented the Gaussian cubature method for the purpose of BEM computations both with CPU and GPU, and we compare its performance with two different analytical integration methods. The ten different Gaussian cubature formulas presented in our paper can be used for arbitrary high-precision and fast integrations over triangles and rectangles.Comment: 28 pages, 13 figure

Focal-plane detector system for the KATRIN experiment

The focal-plane detector system for the KArlsruhe TRItium Neutrino (KATRIN) experiment consists of a multi-pixel silicon p-i-n-diode array, custom readout electronics, two superconducting solenoid magnets, an ultra high-vacuum system, a high-vacuum system, calibration and monitoring devices, a scintillating veto, and a custom data-acquisition system. It is designed to detect the low-energy electrons selected by the KATRIN main spectrometer. We describe the system and summarize its performance after its final installation

Background reduction at the KATRIN experiment by the shifted analysing plane configuration

The KATRIN experiment aims at measuring the electron neutrino mass with a sensitivity of 0.2 eV/c$^2$ after 5 years of data taking. Recently a new upper limit for the neutrino mass of 0.8 eV/c$^2$ (90% CL) was obtained. To reach the design sensitivity, a reduction of the background rate by one order of magnitude is required. The shifted analysing plane (SAP) configuration exploits a specific shaping of the electric and magnetic fields in the KATRIN main spectrometer to reduce the spectrometer background by a factor of two. We discuss the general idea of the SAP configuration and describe the main features of this novel measurement mode

Kassiopeia: A Modern, Extensible C++ Particle Tracking Package

The Kassiopeia particle tracking framework is an object-oriented software package using modern C++ techniques, written originally to meet the needs of the KATRIN collaboration. Kassiopeia features a new algorithmic paradigm for particle tracking simulations which targets experiments containing complex geometries and electromagnetic fields, with high priority put on calculation efficiency, customizability, extensibility, and ease of use for novice programmers. To solve Kassiopeia's target physics problem the software is capable of simulating particle trajectories governed by arbitrarily complex differential equations of motion, continuous physics processes that may in part be modeled as terms perturbing that equation of motion, stochastic processes that occur in flight such as bulk scattering and decay, and stochastic surface processes occuring at interfaces, including transmission and reflection effects. This entire set of computations takes place against the backdrop of a rich geometry package which serves a variety of roles, including initialization of electromagnetic field simulations and the support of state-dependent algorithm-swapping and behavioral changes as a particle's state evolves. Thanks to the very general approach taken by Kassiopeia it can be used by other experiments facing similar challenges when calculating particle trajectories in electromagnetic fields. It is publicly available at https://github.com/KATRIN-Experiment/Kassiopei

The 2010 very high energy gamma-ray flare & 10 years of multi-wavelength observations of M 87

Abridged: The giant radio galaxy M 87 with its proximity, famous jet, and very massive black hole provides a unique opportunity to investigate the origin of very high energy (VHE; E>100 GeV) gamma-ray emission generated in relativistic outflows and the surroundings of super-massive black holes. M 87 has been established as a VHE gamma-ray emitter since 2006. The VHE gamma-ray emission displays strong variability on timescales as short as a day. In this paper, results from a joint VHE monitoring campaign on M 87 by the MAGIC and VERITAS instruments in 2010 are reported. During the campaign, a flare at VHE was detected triggering further observations at VHE (H.E.S.S.), X-rays (Chandra), and radio (43 GHz VLBA). The excellent sampling of the VHE gamma-ray light curve enables one to derive a precise temporal characterization of the flare: the single, isolated flare is well described by a two-sided exponential function with significantly different flux rise and decay times. While the overall variability pattern of the 2010 flare appears somewhat different from that of previous VHE flares in 2005 and 2008, they share very similar timescales (~day), peak fluxes (Phi(>0.35 TeV) ~= (1-3) x 10^-11 ph cm^-2 s^-1), and VHE spectra. 43 GHz VLBA radio observations of the inner jet regions indicate no enhanced flux in 2010 in contrast to observations in 2008, where an increase of the radio flux of the innermost core regions coincided with a VHE flare. On the other hand, Chandra X-ray observations taken ~3 days after the peak of the VHE gamma-ray emission reveal an enhanced flux from the core. The long-term (2001-2010) multi-wavelength light curve of M 87, spanning from radio to VHE and including data from HST, LT, VLA and EVN, is used to further investigate the origin of the VHE gamma-ray emission. No unique, common MWL signature of the three VHE flares has been identified.Comment: 19 pages, 5 figures; Corresponding authors: M. Raue, L. Stawarz, D. Mazin, P. Colin, C. M. Hui, M. Beilicke; Fig. 1 lightcurve data available online: http://www.desy.de/~mraue/m87