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3D SIMULATION OF QUADRUPOLE MASS FILTERS WITH OFFSET AND TILTED RODS

David Langridge

Waters Corporation, Wilmslow, UK

METHODS

SIMION 8.1 (with surface enhancement) [2] was used to

simulate a 3D system comprising a stacked ring ion guide, a

differential aperture, a quadrupole mass filter with pre- and

post-filters, and a detector plate. The ion guide is at an

elevated pressure relative to the quadrupole and a hard-

sphere collision model was used for the interaction with the

buffer gas. Gas flow through the differential aperture was

calculated using the DSMC method [3]. An ensemble of ions is

run at a range of RF/DC values to generate a mass spectrum.

For the offset rod calculations we consider a shift of the top

(+y) rod in either the x or y-axis (a +y offset moves the rod

away from the optic axis). Figure 1 shows the notation used

for an axial tilt applied to the top rod. For a positive tilt angle

the rod tilts inwards with increasing z. The y-axis separation of

the rod from the optic axis varies as a function of axial

position, giving an axial position dependent y-offset y(z).

RESULTS

The potential within a 2D quadrupole can be written as a sum of multipoles,

In a perfect quadrupole the only non-zero component is the A2

component. The positional offset of one of the rods breaks the symmetry of the system thus we observe additional non-zero

multipole components. Figure 2 plots the first three additional non-zero components for a range of y-offset values (note that

a +y offset moves the rod outward, normalised to +1/-1 V on the x/y rods respectively).

It is clear that over this range of rod offsets the multipole component amplitude is a linear function of the rod offset.

Figure 3 plots the same components for a tilted rod system over a range of axial positions. This example has a tilt angle of

0.0047° with y(L/2)=0) and y(0)/ y(L) = +/- 0.001*r0.

Examining the magnitudes of the components we see that at

any given z-position they are simply equal to an offset system with the offset equal to y(z).

References

1. D Langridge, Proc. 60th ASMS Conf., Minneapolis, USA, 2013.

2. SIMION 3D v8.1, Scientific Instrument Services Ltd.

3. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994).

4. S Taylor, J R Gibson, Prediction of the effects of imperfect construction of a QMS filter. J. Mass Spectrom. 43, 609–616 (2008)

We now consider calculations of mass peaks for a variety of

offset rod systems. Unless otherwise stated these calculations

are for singly charged positive ions of mass 556, the RF/DC

ratio is set to give a peak width of ~0.5 Da, and the axial ion

energy = 0.5eV. Note that the A0 component present in the y-

offset systems leads to a non-zero DC potential on the optic

axis. In these systems we adjust the DC offset of the

quadrupole to maintain the axial ion energy at 0.5eV. Intensity

is normalised relative to the unresolved transmission, while the

m/z scale is linear with applied volts and calibrated for the

unmodified system.

Figure 4 shows simulated peaks for a range of y-offset values

with positive resolving DC applied to the y-rods. While the

intensity and resolution are unchanged there is a peak position

shift to lower m/z that is linear with the rod offset. The rod is

offset inwards which leads to an increase in the A2 multipole

component, hence we expect the observed shift to lower m/z.

For the 0.001*r0 shift we see a 0.05% change in A0 and a 0.3

Da m/z shift which is ~0.05% of m/z 556. This demonstrates

that for small rod offsets the effects are linear (note we see a

0.05% change in A0 as we only offset one rod). In practice this

peak shift would be calibrated out.

Figure 5 shows the results when we apply negative resolving

DC to the y-rods. Again we observe shifts to lower m/z,

however the transmission is reduced and the peak shape

becomes increasingly distorted as we go to larger rod offsets,

with a precursor peak becoming apparent. A prior study in 2D

[4] observed this behaviour and attributed the precursor to

attenuation of the centre of the main peak, if we reconstruct

the full peak we observe the same peak position shifts as in

the +DC case. We have observed comparable qualitative

behaviour in 2D calculations however the initial normalised

transmission and the degree of transmission loss were

significantly different.

Figure 6 shows simulated peaks for a range of x-offset values

with negative resolving DC applied to the y-rods. In this case

we see no change in the simulated peaks at all. The small x

displacement of the y-rod gives a negligible change in the A2

component, hence we expect no m/z shift for the x-offset

system.

Figure 7 shows simulated peaks for a range of x-offset values

with positive resolving DC applied to the y-rods. As above

there is no peak position shift, however there are comparable

transmission and peak shape distortions to those seen for the

y-offset system with negative resolving DC on the y-rods.

CONCLUSION We present results for 3D simulation of

quadrupole mass filters with offset and tilted

rods.

The effects on the peak for an offset rod can be

interpreted in terms of the additional multipole

potential components.

For an axially tilted rod the peak position shifts

can be approximated as due to an average of the

rod offset.

The peak shape effects for a tilted rod show

complex behaviour that will require further

investigation to be fully understood.

Figure 8 plots ion motion in the x and y axis for an ion near

the tip of the stability diagram, and for an ion unstable in the x

and y axis (positive resolving DC applied to the x-rods). The

motion of the ion is markedly different in the two axes,

reflecting the different instability conditions. In the x-axis ions

have a high secular frequency, unstable ions gain amplitude

resonantly before being lost to the x-rods (RF ejection). In the

y-axis ions have a low secular frequency, unstable ions

undergo a gradual increase in y-axis position with micro-

motion superimposed (DC ejection).

For the y-rod offset case the most significant additional

multipole components (B1 and B3) are odd powers of y. We

would expect odd y-terms to enhance the drift ejection seen in

8d but not the oscillatory ejection of 8c, hence for the y-rod

offset system we see additional ion losses when we have

negative DC applied to the y-rods. This additional ejection is

seen predominantly on the low mass side of the peak, leading

to the apparent low mass precursor. With positive DC applied

to the y-rods the RF ejection is not enhanced by the additional

multipole components, hence the lack of peak distortion.

The x-offset rod case can be analysed in the same manner.

The additional multipole components are odd powers of x,

hence in this case the peak distortion is seen with negative

resolving DC applied to the x-rods.

OVERVIEW

We present a theoretical investigation of the

effects of mechanical misalignments on the

performance of quadrupole mass filters.

The method comprises 3D simulation of a gas

cell, differential aperture and quadrupole mass

filter.

Rod misalignments studied include an x or y

axis offset and an axial tilt.

Multipole component analysis of the potential is

used to explain the peak position and peak

shape effects of the various misalignments.

INTRODUCTION

The performance of a quadrupole mass filter (QMF) depends on the accuracy to which it is manufactured. Defects in the

machining or positioning of the rods will introduce non-quadrupolar potential components which can result in poor

peak shapes and reduced resolution / transmission.

The majority of previous calculations of quadrupole mass filter performance have been performed in 2D. While 2D simulations

are computationally less demanding they rely on an approximation of the initial ion beam distribution, and cannot

correctly model the fields at the entrance and exit of the

quadrupole. Furthermore, there are mechanical imperfections that are impossible to simulate in 2D, for example a rod with

an axial tilt. Recent advances in computing power and numerical methodology have made full 3D simulation of QMFs

practical [1], in this poster we extend this method to examine the effects of imperfectly constructed rods on QMF

performance.

Figure 1. Plan (y-z) view of the geometry used for a tilted rod

system.

Figure 3. Plot of the A0, B1 and B3 multipole potential compo-

nents for a tilted rod system over a range of axial positions.

(1)

Figure 4. Simulated peaks for varying top rod y-offsets, posi-

tive resolving DC applied to the y-rods.

Figure 5. Simulated peaks for varying top rod y-offsets, nega-

tive resolving DC applied to the y-rods.

Figure 7. Simulated peaks for varying top rod x-offsets, posi-

tive resolving DC applied to the y-rods.

Figure 6. Simulated peaks for varying top rod x-offsets, nega-

tive resolving DC applied to the y-rods.

Figure 9 shows simulated peaks for a tilted rod system, with

r0 correct at the prefilter and a tilt of +/- 0.0047°. This leads

to a y-offset of 0.002*r0 at the end of the rods, with the

positive tilt moving the rod inwards

We see peak position shifts of ~0.3 Da. This corresponds to

the peak shift for a 0.001*r0 rod offset, which is equal to the

offset for the tilted system averaged over the length of the

rods. Thus, in terms of the peak position shift, we can

approximate the tilted system as an average of the offset.

The peak shape behaviour shows significant differences

between the positive and negative tilt angles. With the positive

tilt angle we see ~35% transmission loss and a slight change

in the peak shape. We see little dependence on the DC polarity

applied to the y-rods in this case.

For the negative tilt angle we see ~15% transmission loss with

the +DC applied to the y-rods. With –DC on the y-rods we see

~60% transmission loss and a large distortion in the peak

shape with a low mass precursor visible. It is not clear why the

peak shape effects show such a disparity between the positive

and negative tilt angles, further investigation of tilted rod

systems is required to understand this behaviour.

Figure 2. Plot of the A0, B1 and B3 multipole potential compo-

nents for a range of y-offset values.

Figure 9. Simulated peaks for +/- 0.0047° tilted rod system,

with +/- resolving DC applied to the y-rods.

Figure 8. Plots of ion motion in the x (a) and y (b) axes near

the tip of the stability diagram, with +DC applied to the x-rods. (c) and (d) show the motion of an ion that is unstable in the x

and y axes, respectively.