A Spatially Resolved Study Of The Katrin Main Spectrometer Using A Novel Fast Multipole Method

The Karlsruhe Tritium Neutrino (KATRIN) experiment is intended to make a sensitive (~ 200 meV) model-independent measurement of the neutrino mass through high precision electrostatic spectroscopy of the tritium /-decay spectrum. One of the principle components in this experiment is the main spectrometer which serves as an integrating MAC-E filter with 0(1) eV resolution. Thorough understanding of the transmission properties of the main spectrometer system is an inextricable challenge associated with this effort, and requires a very accurate and fast method for calculating the electrostatic fields created within its volume. To this end, the work described in this thesis documents the development of a novel variation on the Fast Multipole Method (FNM), which is a hybrid of the canonical algorithm and the Fast Fourier Transform on Multipoles (FFTM) method. This hybrid technique has been implemented to take advantage of scalable parallel computing resources and has been used to solve the Laplace boundary value problem using the Boundary Element Method with millions of degrees of freedom. Detailed measurements taken during the KATRIN main spectrometer commissioning phase are used to validate the fully three-dimensional electrostatic field calculation and the hybrid fast multipole method. Then, the hybrid method is used to greatly accelerate charged particle tracking in a high-statistics Monte Carlo simulation. The data from this simulation is then used to develop a spatially resolved model of the main spectrometer transmission function. This full transmission function model is then used to evaluate the performance of several of approximate transmission function models, the results of which show that a purely axially symmetric treatment of the main spectrometer is not sufficient. We conclude by addressing the appropriate level of measurement detail needed in order to reconstruct a realistic, non-axially symmetric transmission function model.