D. Hilk

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 ar X iv :1 61 2. 00 26 2v 1 [ ph ys ic s. co m pph ] 1 D ec 2 01 6 Kassiopeia: A Modern, Extensible C++ Particle Tracking Package 2 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 algorithmswapping 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/Kassiopeia.

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.

Electric field simulations and electric dipole investigations at the KATRIN main spectrometer

This thesis deals with the development of high-accuracy electric field simulation methods and experimental background investigations with the electric dipole method for the KATRIN experiment. Both fields of work are of crucial importance to obtain the targeted background level of 10 mcps for the investigation of the absolute neutrino mass scale with a sensitivity of 200 meV/c² at 90% C.L.

Study of the Cox–Thompson inverse scattering method with a Coulomb potential

In order to learn more about the precision of the inversion by the Cox?Thompson method, we investigated the inversion of phase shifts of a singular potential, namely of a Coulomb potential. Using asymptotically Riccati?Bessel functions as reference functions, we could only approximately reproduce the singularity of the Coulomb potential at the origin. We also show uncertainties in the inverted potential due to different minima in the minimization solution of the nonlinear equations of the Cox?Thompson procedure. As a result, we conclude that one has to take much care with the inversion of experimental phase shifts suffering from measurement errors.