Influence of End Cap Structure on the Axial Geometric Parameter of the Linear Paul Trap

Through finite-element simulation, the axial potential distribution of the ion trap is analyzed. The effects of the central hole diameter of the end cap and the spacing between the two end caps on the axial geometric parameters of the ion trap are investigated. Based on these findings, a set of linear Paul traps is designed by selecting suitable end caps and quadrupoles. Stable trapping of calcium ions (Ca${}^{+}$) is successfully achieved, and these ions are subsequently laser-cooled into ionic Coulomb crystals. In the experiment, secular motion excitation of the Ca${}^{+}$ ion Coulomb crystal is performed, yielding an axial geometric parameter of 0.115(1) for the ion trap. This value aligns well with the simulation result of 0.114(2). The precise determination of the axial geometric parameter provides a solid foundation for subsequent high-precision optical or mass spectrometry measurements.