Radio-frequency (RF) linear multipole traps have been shown to be very sensitive to mis-positioning of their electrodes, which results in a symmetry breaking and leads to extra local minima in the trapping potential as shown in Pedregosa-Gutierrez etal (2018 J. Mod. Opt. 65 529) disturbing the operation of the trap. In this work, we analytically describe the RF-potential of a realistic octupole trap by including lower order terms to the well-established equation for a perfectly symmetric octupole trap. We describe the geometry by a combination of identified defects, characterized by simple analytical expressions. A complete equation is proposed for a trap with any electrode deviation relying on a combination of the simple cases where the defects are taken individually. Our approach is validated by comparison between analytical and numerical results for defect sizes up to 4% of the trap radius. As described in Pedregosa-Gutierrez etal (2018 Rev. Sci. Instrum. 89 123101), an independent fine-tuning of the amplitude of the RF voltage applied on each electrode can be used to mitigate the geometrical defects of a realistic trap. In a different way than in Pedregosa-Gutierrez etal (2018 Rev. Sci. Instrum. 89 123101), the knowledge of an analytical equation for the potential allows to design the set of RF-voltages required for this compensation, based on the experimental measurement of the ion positions in the trap, without information concerning the exact position of each electrode, and with a small number of iterations. The requirements, performances and limitations of this protocol are discussed via comparison of numerical simulations and analytical results.

射频 (RF) 线性多极阱已被证明对其电极的错误定位非常敏感，这会导致对称性破坏并导致捕获电位的额外局部最小值，如 Pedregosa-Gutierrez等人(2018 J) 所示. Mod. 选项 65529）扰乱陷阱的运作。在这项工作中，我们通过将低阶项包含到完美对称八极陷阱的完善方程中，分析地描述了现实八极陷阱的 RF 电位。我们通过识别缺陷的组合来描述几何形状，以简单的分析表达式为特征。为具有任何电极偏差的陷阱提出了一个完整的方程，依赖于单独获取缺陷的简单情况的组合。我们的方法通过对缺陷尺寸高达陷阱半径 4% 的分析和数值结果进行比较来验证。如 Pedregosa-Gutierrez等人(2018 Rev. Sci. Instrum. 89) 所述123101），对施加在每个电极上的射频电压幅度的独立微调可用于减轻现实陷阱的几何缺陷。与 Pedregosa-Gutierrez等人(2018 Rev. Sci. Instrum. 89 123101) 不同，电位分析方程的知识允许根据实验测量设计此补偿所需的一组射频电压离子在陷阱中的位置，没有关于每个电极的确切位置的信息，并且迭代次数很少。该协议的要求、性能和局限性通过数值模拟和分析结果的比较进行了讨论。