B. M. Retailleau

In the frame of the project MORA (Matter's Origin from the Radio Activity of trapped and oriented ions), a transparent axially symmetric radio-frequency ion trap (MORATrap) was designed in order to measure the triple correlation parameter $D$ in nuclear $β-$decay of laser-polarised ions. The trap design was inspired from the LPCTrap geometry, operated at GANIL from 2005 to 2013. In a real (non-ideal) Paul trap, the quadrupole electric potential is not perfect leading to instabilities in ion motion and therefore affecting the overall trapping efficiency. This paper presents a numerical method aiming to optimise the geometry of a trap. It is applied to MORATrap in order to improve the trapping efficiency and to enlarge the axial transparent solid angle compared to LPCTrap. In the whole optimisation process, numerical computation of electric potential and field was carried out using an electrostatic solver based on boundary element method (BEM). The optimisation consisted in minimising an objective function (fitness function) depending on higher order multipoles of the potential. Finally, systematic changes of trap dimensions and electrode displacements were applied to investigate geometrical effects on the potential quality.

The MORA (Matter's Origin from the RadioActivity of trapped and oriented ions) project aims at measuring with unprecedented precision the D correlation in the nuclear beta decay of trapped and oriented ions. The D correlation offers the possibility to search for new CP-violating interactions, complementary to searches done at the LHC and with Electric Dipole Moments. Technically, MORA uses an innovative in-trap orientation method which combines the high trapping efficiency of a transparent Paul trap with laser orientation techniques. The trapping, detection, and laser setups are under development, for first tests at the Accelerator laboratory, JYFL, in the coming years.

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.