Radiofrequency trapping of ions in a pure toroidal potential distribution

• Solutions of Laplace equation in toroidal coordinates allow analysis of toroidal ion traps.
• Ion trapping and stability diagram in a quadrupole-like potential in toroidal space.
• Comparison with conventional, Cartesian quadrupole devices.

Although toroidal ion traps are being used more widely in miniaturized mass spectrometers, there is a lack of fundamental understanding of how the toroidal electric field affects ion motion, and therefore, the ion trap's performance as a mass analyzer. Toroidal harmonics, which represent solutions to the Laplace equation in a toroidal coordinate system, may be useful to understand these devices. This paper reports on SIMION simulations of ion trapping and ion motion in a time-varying electric potential representing the symmetric, second-order toroidal harmonic of the second kind—the solution most analogous to the conventional, Cartesian quadrupole. Simulations show that this potential, which we call the toroidal quadrupole, is similar to that of the Cartesian quadrupole in its ability to trap ions. The stability diagram for the toroidal quadrupole shares similarities with that of both the quadrupole ion trap (QIT) and the quadrupole mass filter (QMF), but has several minor differences including a series of chasms and a portion of the boundary that is diffuse.

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