Computational Analysis of Quadrupole Mass Filters Employing Nontraditional Waveforms

Abstract

Abstract. Quadrupole mass filters using non-sinusoidal driving potentials present exciting opportunities for new functionality. Predicting figures of merit like resolving power and transmission efficiency helps characterize these emerging devices. To this end, matrix methods of solving the Hill equation of ion motion are employed to calculate stability diagrams and pseudopotential well depth maps in the a,q plane for arbitrary waveforms. The theoretical resolving power and well depth of digital, trapezoidal and sinusoidal mass filters are compared. Simplified expressions for digital mass filter operation are presented.

The pseudopotential for quadrupole fields up to q = 0.9080

“…0  q . Reilly and Brabeck [28,29] proposed to get the quadratic coefficient of a pseudopotential function directly from secular frequencies of MathieuHill equations using the numerically or analytically calculated trace of a monodromy matrix, in a way similar to that used in [27]. However, their formula is artificially modified in such a way that both the secular frequency and the pseudopotential well depth decrease to zero near the far end of the stability zone.…”

“…Sudakov [17,18], Douglas and coauthors [27], and Reilly and Brabeck [28,29] have suggested independently some modifications of the pseudopotential model which should return its validity for quadrupole rf fields over a wide range of q . These theories differ mathematically which is not a suspicious matter by itself.…”

“…Namely, both [17,18] and [28,29] state that the quadratic pseudopotential well depth increases from zero at the entry boundary of the stability zone (for example, at…”

“…However, [27] states that the quadratic pseudopotential grows monotonically and smoothly from zero at the entry boundary of the stability zone till the exit boundary of the stability zone where it has a positive maximum and an instant jump to some negative values corresponding to instability of ions. The theory of Reilly and coworkers [28,29] predicts that the secular frequency is zero at both boundaries of the stability zone and a maximum in-between, while [27] predicts that the secular frequency  grows monotonically from zero at the entry boundary to 2  at the eхit boundary (where  is the rf frequency). Both [17,18] and [28,29] state that the loss of stability is due to the fact that the quadratic pseudopotential changes its sign, the pseudopotential barrier smoothly changes its concave profile into a flat (zero) and a convex one at the far stability boundary (…”

“…The said qualitative description by the theories [17][18][19][20][21][22][23][24][25][26][27][28][29] which are modifying the Landau classical approach [1][2][3] specifically for quadrupoles applies to all zones of stability, not only to the first zone, and to arbitrary periodic radio signals, not necessarily only to sinusoidal waveforms. However, the differences between these theories are too serious to ignore.…”