Simulations of ion trap devices based on finite element analysis method
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摘要: 利用有限元程序ANSYS，开展潘宁离子俘获装置的电场模拟计算。基于电场数据，结合Runge_Kutta_Fehlberg方法进行潘宁装置在多种模式下的离子俘获过程模拟工作，得到了准确的离子俘获结果。并对实际条件下具有偏离理想情况电极分布的俘获装置进行了优化计算及电场分析，同样实现了离子俘获过程的准确模拟。有限元方法用于离子俘获装置的电场计算以及后续离子俘获过程模拟流程的建立，为类似的电势阱离子俘获装置建造运行提供有效的技术支持。Abstract: Using the constructed electric field trap, Penning ion trap devices can constrain ions and are already applied in some research fields such as nuclear physics in which the mass of ions can be measured exactly and quantum computing in which the Penning traps can be a tool to story quantum bits. ANSYS, a finite element analysis (FEA) program, was employed to do the electric field calculations for Penning traps. And then, with the electric field from FEA program, we used the method of Runge_Kutta_Fehlberg to do simulations for the ion trapping process, and finally got the accurate results of ion tracking. Additionally, we carried out tracking simulations for practical traps which have ring electrodes with shapes different from the ideal Penning traps, and achieved similar simulation results. The way of the electric field calculation by FEA method, and the workflow for ion tracking will help a lot to build and run Penning traps and similar devices.
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图 3 潘宁装置间隙区域电场等电势分布结果图（1/4结构）
Figure 3. Contour of equal potential for the electric field in the gap of the Penning trap (1/4 of the whole plane)
图 4 理想潘宁装置离子中运动轨迹图（初始位置x=0.1 cm，y=0，z=0.2 cm）
Figure 4. Tracking results for an ion moving in an ideal Penning trap (start from x=0.1 cm, y=0 and z=0.2 cm)
图 5 充气He气体后，潘宁装置中离子运动轨迹图（初始位置x=0.1 cm，y=0 cm，z=0.2 cm）
Figure 5. The tracking results for an ion moving in the Penning trap, with Helium gas filled in (start from x=0.1 cm, y=0 and z=0.2 cm)
图 6 环形电极四极场激励电势施加方法
Figure 6. The way to apply the quadrupole excitation potential on the ring electrodes
图 7 潘宁装置中充入He气体加四极场激发时离子运动轨迹图（
$\omega = {\omega _{\rm{c}}}$ ）（初始位置x=0.1 cm，y=0，z=0.2 cm）Figure 7. Tracking results for an ion moving in the Penning trap, with helium gas filled in and quadrupole electric potential applied (start from x=0.1 cm, y=0 and z=0.2 cm), here
$\omega = {\omega _{\rm{c}}}$ 
图 8 环形电极施加激发±10 V电势时所产生电场的等电势分布图
Figure 8. Equal potential distribution when the excitation potential of ±10 V applied on the ring electrodes
图 9 气隙区域不同半径范围内真实电势分布与理想四极场的偏离情况
Figure 9. Relative error between the real distribution of the potential of the gap and the ideal quadruapole distribution, varying with different radii
图 10 优化的离子俘获装置环形电极结构平面图
Figure 10. Diagram of the ring electrodes for an optimized Penning trap
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