[en] Research in fundamental physics with the free neutron is one of the key tools for testing the Standard Model at low energies. Most prominent goals in this field are the search for a neutron electric dipole moment (EDM) and the measurement of the neutron lifetime. Significant improvements of the experimental performance using ultracold neutrons (UCN) require reduction of both systematic and statistical errors.The development and construction of new UCN sources based on the superthermal concept is therefore an important step for the success of future fundamental physics with ultracold neutrons. Significant enhancement of today available UCN densities strongly correlates with an efficient use of an UCN converter material. The UCN converter here is to be understood as a medium which reduces the velocity of cold neutrons (CN, velocity of about 600 m/s) to the velocity of UCN (velocity of about 6 m/s).Several big research centers around the world are presently planning or constructing new superthermal UCN sources, which are mainly based on the use of either solid deuterium or superfluid helium as UCN converter.Thanks to the idea of Yu.Pokotilovsky, there exists the opportunity to build competitive UCN sources also at small research reactors of the TRIGA type. Of course these smaller facilities don't promise high UCN densities of several 1000 UCN/cm³, but they are able to provide densities around 100 UCN/cm³ for experiments.In the context of this thesis, it was possible to demonstrate succesfully the feasibility of a superthermal UCN source at the tangential beamport C of the research reactor TRIGA Mainz. Based on a prototype for the future UCN source at the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRMII) in Munich, which was planned and built in collaboration with the Technical University of Munich, further investigations and improvements were done and are presented in this thesis. In parallel, a second UCN source for the radial beamport D was designed and built. The commissioning of this new source is foreseen in spring 2010. At beamport D with its higher thermal neutron flux, it should be possible to increase the available UCN densities of 4 UCN/cm³ by minimum one order of magnitude. (orig.)