Monitoring of the energy scale in the KATRIN neutrino experiment

The question of the absolute mass scale of neutrinos is of particular interest for particle physics, astrophysics, and cosmology. The KATRIN experiment (KArlsruhe TRItium Neutrino experiment) aims to address the effective electron antineutrino mass from the shape of the tritium $\beta$-spectrum with an unprecedented sensitivity of 0.2 eV/c$^2$. One of the major systematic effects concerns the experimental energy scale, which has to be stable at the level of only a few parts in a million. For its calibration and monitoring the monoenergetic electrons emitted in the internal conversion of $\gamma$-transition of the metastable isotope $^{83\mathrm{m}}$Kr will be extensively applied. The aim of this thesis is to address the problem of KATRIN energy scale distortions and its monitoring in detail. The source of electrons based on $^{83\mathrm{m}}$Kr embedded in a solid as well as the source based on gaseous $^{83\mathrm{m}}$Kr are studied. Based on the experimental results an approach for the continuous stability monitoring is proposed.