The subject of this work is twofold. The main objective is to measure the βν angular correlation (aβν) in the β decay of the 6He+ at a 0.5% precision level as well as the associated shakeoff probability. Evidences of a discrepancy between the experimental value of a βν and the prediction in the Standard Model (SM) would mean the existence of a tensor current in the weak interaction. Consequently, it would question the V-A structure used to describe the weak interaction in the SM. A Paul trap is used to confine 6He+ ions almost at rest in a very small volume in order to provide a decay source as well defined as possible. The emitted β particle and recoil ion (RI) are detected in coincidence by detectors surrounding the trap. The setup is sensitive to the different charge states of the RIs and also allows the measurement of shakeoff probability. This latter and a βν are deduced from comparison with realistic Monte Carlo simulations of the time of flight spectra of the recoiling ions using Geant4 and Simion. The set of measured distributions enables to control the main systematic effects. The second part of this work is dedicated to the development of a new target ion source system (TISS) using a FEBIAD (Forced Electron Beam Induced Arc Discharge) and SPIRAL1 target in the framework of its upgrade. Several experiments have been performed to test the reliability of the TISS and to measure the yields of expected new beams. These tests led to an improved design of the TISS to be tested in December 2013. Within the framework of this upgrade, new beams should be available in 2016.
