Influence of octupole field on quadrupole mass filter performance in the second stability zone

TL;DR

This work addresses how controlled radial asymmetry, introduced by displacing a diagonally opposite rod pair in a quadrupole mass filter, affects operation in the second stability zone. By deriving the radially asymmetric potential and scaling the Mathieu parameters with a geometric factor $p$, the authors show an apex shift $q' = p q$ and reveal an octupole term with amplitude $A_4$ that grows with asymmetry and depends on DC polarity. Transmission and resolution are quantified via RK45-based stability maps and SIMION simulations, demonstrating that maximum resolution occurs at $\gamma_x = +0.04$ with displaced rods biased at $+U$ (and equivalently at $-0.04$ with reversed polarity), while outward displacement can enhance transmission due to a larger effective aperture. The results provide a practical method to tailor the resolution–transmission trade-off in second-zone QMFs by tuning radial asymmetry and DC polarity, with implications for high-resolution mass spectrometry and peak-shape control.

Abstract

Radial asymmetry in a quadrupole mass filter (QMF), introduced by symmetric displacement of a diagonally opposite rod pair, modifies the confinement potential and alters the ion stability characteristics. In this work, the influence of such radial asymmetry on QMF operation in the second stability zone is investigated through simulations. Using an existing potential formulation for a radially asymmetric QMF, the stability diagram in the second stability zone is extracted for the first time, revealing a systematic shift of the stability apex with the asymmetry parameter. Radial asymmetry introduces additional multipole components, notably an octupole term whose magnitude scales with the asymmetry parameter and whose sign depends on the DC polarity applied to the displaced rods. Transmission simulations show that the transmission peak shifts in accordance with the displaced stability apex, while the resolution exhibits a strong dependence on both the asymmetry parameter and the DC polarity. Comparable maximum resolution is obtained for inward and outward displacements under suitable polarity configurations, with outward displacement providing higher transmission efficiency due to an increased effective aperture. These results demonstrate that controlled radial asymmetry provides an effective means to tailor the resolution and transmission characteristics of QMFs operating in the second stability zone.

Figures (11)

• Figure 1: (a) Schematic of the linear QMF with circular rods. (b) Cross-sectional ($xy$ plane) view of the QMF with electrical connections, and illustrating diagonally opposite electrodes displaced from their normal positions.
• Figure 2: Second stability region of radially asymmetric QMFs for $\gamma_x=\pm0.06$, $\pm0.04$, $\pm0.02$ in comparison to a symmetric QMF ($\gamma_x=0$) as obtained from RK45 integration of the normalized equations of motion (eq. \ref{['eq5']}) in the $(a,q)$ plane. Dashed line shows the scan parameter $\lambda = 0.00182$ with which the transmission performances were simulated.
• Figure 3: Transmission characteristics of symmetric QMF for (a) different $\eta$ at a fixed $\lambda = 0.00182$, and (b) different scan parameter ($\lambda$) at a fixed $\eta=1.13$ in the second stability zone.
• Figure 5: Transmission profile for $\pm U$ applied to the displaced rod pair in the asymmetric configuration of (a) $\gamma_x=+0.04$ and (b) $\gamma_x=-0.04$.
• Figure 6: Resolution $R$ (solid lines) and peak transmission (dotted lines) as a function of the radial asymmetry parameter $\gamma_x=0, \pm0.02, \pm0.04, \pm0.06$. $R$ is determined using a 15% transmission window around the peak, where the middle transmission level serves as the reference while the upper and lower bounds define the uncertainty in $T_{max}$. The full width at half maximum is evaluated at 50% of each transmission level, and the resulting spread in resolution determines the error bar in $R$.