Quantitative evaluation of space charge effects of laser-cooled three-dimensional ion system on a secular motion period scale

In this paper, we introduce a method of quantitatively evaluating and controlling the space charge effect of a laser-cooled three-dimensional (3D) ion system in a linear Paul trap. The relationship among cooling efficiency, ion quantity, and trapping strength is analyzed quantitatively, and the dynamic space distribution and temporal evolution of the 3D ion system on a secular motion period time scale in the cooling process are obtained. The ion number influences the eigen-micromotion feature of the ion system. When trapping parameter q is similar to 0.3, relatively ideal cooling efficiency and equilibrium temperature can be obtained. The decrease of axial electrostatic potential is helpful in reducing the micromotion heating effect and the degradation in the total energy. Within a single secular motion period under different cooling conditions, ions transform from the cloud state (each ion disperses throughout the envelope of the ion system) to the liquid state (each ion is concentrated at a specific location in the ion system) and then to the crystal state (each ion is subjected to a fixed motion track). These results are conducive to long-term storage and precise control, motion effect suppression, high-efficiency cooling, and increasing the precision of spectroscopy for a 3D ion system.