Geant4 Monte Carlo simulations for the LPCTrap setup

The LPCTrap setup at GANIL is fully operational since 2006. The first breakthrough was the detection of 100000 coincidences between the $ \beta$ particles and the recoil ions from the decay of ⁶He⁺ produced by the SPIRAL source. After preparation, the decaying nuclei are confined in a transparent Paul trap which is surrounded by a $ \beta$ -telescope made of a double-sided silicon strip detector followed by a scintillator, and by a micro-channel plate position-sensitive detector to record in coincidence the $ \beta$ particles and the recoil ions. Simulations of this system are needed in order to study possible systematic effects and extract with high accuracy the $ \beta$ - $ \nu$ angular-correlation coefficient. A code based on Geant4 is well suited for this purpose. In this contribution the results from the simulations compared with those from the experiment will be presented and discussed.