On the relationships between resolution, dimensionless stability, pseudopotential well depth, acceptance, and transmission in mass filters

The relationships between resolution, stability, pseudopotential well depth, acceptance aperture, and transmission for sinusoidal quadrupole mass filters are examined graphically and mathematically. Simple linear or power relationships are revealed. Comparison of these quantities plotted against resolving power show that the pseudopotential well depth correlates well with the mass filter transmission. Pseudopotential well depth is directly proportional to the product of dimensionless stability well depth and the AC voltage. This relationship extends to all quadrupoles regardless of operational zone because it is rooted in stability. Ion transmission and sensitivity scale directly with the pseudopotential well depth. Resolving power and pseudopotential well depth increase when operating in higher stability zones for all types of mass filters. Unfortunately, for fixed frequency sine wave mass filters, the increased resolving power and pseudopotential well depth are accompanied by a significant reduction of the mass range and increased in fringe field effects. For these reasons, sine mass filter operation in higher stability zones has been reported but not commercially produced. In contrast, for rectangular wave mass filter operation, there is no mass range limitation in any stability zone. The fringe field does not increase because the AC voltage is constant and does not change within a single stability zone or between them. A DC voltage is also unnecessary to access any zone. The high resolution and sensitivity of rectangular wave mass filters that can be gained by operation in higher stability zones without mass limit and limited fringe field restrictions suggest a bright and expansive future for this technology.