  The LPCTrap experiment uses an open Paul trap which was built to enable
precision measurements in the beta decay of radioactive ions. The initial goal
was the precise measurement of the beta-neutrino angular correlation
coefficient in the decay of 6He. Its geometry results from a careful
optimization of the harmonic potential created by cylindrical electrodes. It
supersedes previously considered geometries that presented a smaller detection
solid angle to the beta particle and the recoiling ion. We describe here the
methods which were used for the potential optimization, and we present the
measured performances in terms of trapping time, cloud size and temperature,
and space charge related limits. The properties of the ion cloud at equilibrium
are well reproduced by a simple numerical simulation using hard sphere
collisions, which additionally gives insights on the trapping loss mechanism.
The interpretation for the observed trapping liftetimes is further corroborated
by a model recently developed for ion clouds in Paul traps. The open trap shall
serve other projects. It is currently used for commissioning purpose in the
TRAPSENSOR experiment and is also considered in tests of the Standard Model
involving the beta decay of polarized $^{23}$Mg and $^{39}$Ca ion in the frame
of the MORA experiment. The latter tests require in-trap polarization of the
ions and further optimization of the trapping and detection setup. Based on the
results of the simulations and of their interpretations given by the model,
different improvements of the trapping setup are discussed.
