Search for non Standard Model physics in nuclear-$\beta$ decay with the WITCH experiment

In this work the WITCH experiment, which primarily aims for precision measurements of the beta-neutrino-angular correlation coefficient, is presented in detail. First a theoretical description of the beta-decay process is presented and it was shown how measurements of correlation coefficients can reveal the exact nature of the weak interaction. Although many experiments have already been conducted in this field, there is still considerable room for additional phenomena that are not included in the Standard Model. At WITCH the beta-neutrino-angular correlation coefficient will be obtained from precision measurements of the energy spectrum of the nuclei that recoil after beta-decay, thus avoiding the need to observe the neutrino. To enable a measurement of the recoiling ions, the setup uses a combination of two electromagnetic Penning traps and a retardation spectrometer. This allows one to construct the scattering free radioactive source that is needed as the recoiling ions have only a very small kinetic energy. To obtain good efficiency when transporting the beam to the Penning traps a new set of diagnostics detectors was developed and their properties were studied in detail. Before the radioactive ions that are obtained from ISOLDE through REXTRAP, can be injected into the Penning traps, they are first slowed down by means of a pulsed drift cavity. The behavior of this system was also researched in detail both experimentally and through the use of simulations. The behavior of single ions and ion clouds in the Penning traps is discussed in detail both through analytical calculations and Monte Carlo simulations. These simulations will finally have to provide the necessary input that is needed to analyze the experimental data that will be obtained with the setup. The first ever measurement of recoil ions in the system is presented and the available data are thoroughly analyzed. Although not all effects are under control yet, this measurement proves that the principle of the experiment is sound and that data contributing to the present physics knowledge can be obtained with this system. Additionally these first data allowed for the first time to deduce the charge state distribution after the decay of initially charged particles that are in addition not alkali metal nor noble gas elements. Several alternative measurements are also suggested. A possible search for the contribution of a heavy neutrino to the weak eigenstate of the electron-neutrino through a measurement of the recoil ion energy spectrum from an electron capture decay, is discussed in detail and the feasibility of such measurement is shown.