4D phase-space acceptance of the quadrupole mass filter.

Simulations of the four-dimensional (4D) phase-space acceptance volume of a quadrupole mass filter (QMF) are discussed. The 4D acceptance is considered since the ion trajectories in the X and Y phase planes are dependent via the initial RF phase at ion entry into QMF. The QMF parameters are set up for resolution equal to the ion mass number M. For a wide range of ion masses, the acceptance is characterized by relatively large aperture with about 5% transmission, primarily defined by phase dependent ellipses. Contrary to expectations, the small-aperture central spot with 75% transmission accepts a very small portion, namely less than 1% of the passed through particles.

Modeling of a linear ion trap with driving rectangular waveforms.

We consider the operation of a digital linear ion trap with resonant radial ejection. A sequence of rectangular voltage pulses with a dipole resonance signal is applied to the trap electrodes. The periodic waveform is piecewise constant, has zero mean, and is determined by an asymmetry parameter d $$ d $$ : one value is taken on interval 0 dT $$ \left(0, dT\right) $$ and another on dT T $$ \left( dT,T\right) $$ , where T $$ T $$ is the RF period. Ion mass scanning is performed by varying the asymmetry parameter d $$ d $$ and amplitude of the negative pulse part with time. The ion oscillation frequencies and acceptance of the linear trap are calculated. The dependence of the ion mass to charge ratio m / z $$ m/z $$ on the parameter d $$ d $$ is m / z ~ d 2 $$ m/z\sim {d}^2 $$ . The maximum value is about m / z = 30 $$ m/z=30 $$  kDa for typical parameters of the linear trap: frequency 0.5 MHz, rod radius 4 mm, and negative pulse amplitude 1 kV. The dipolar excitation frequency is 0.125 MHz at which the LIT acceptance is maximal.

Modeling dipolar excitation for quadrupole mass filter.

The results of modeling AC and DC dipole excitation of ion oscillations in a quadrupole mass filter are presented. The simulation is done by numerical integration of the ion motion equations, ions' initial coordinates and velocities are distributed normally. For AC dipole excitation the instability bands on the (a, q) stability diagram follow along the isolines ßx/2 and ßy/2, creating regular dips on the transmission contour. We show that AC excitation at frequency Ω/2 makes it possible to control the resolution of the mass filter by either changing the AC amplitude or phase. Instability bands can be used for mass selective excitation in a linear ion trap. Options for the joint use of DC and AC dipole excitation to form the mass peak shape are considered.

Modelling of a linear ion trap operation in the second stability region.

Ion trajectory numerical simulation is used to find the linear ion trap excitation contour in the second stability region. The effects of initial conditions, the ejection Mathieu parameter, scan speed, dipole excitation voltage and gas damping are studied. Modeling shows that in the stability region center the resolution power is ≈ 200 000 (at full width half height of a peak, FWHM) at pressure 0.1 mTorr and 100 % excitation efficiency (not taking into account the space charge).

Stable X-islands of quadrupole mass filter.

Quadrupole mass filters are normally operated as narrow band pass filters by appropriate choices of rf and DC voltages corresponding to Mathieu a and q values near the apex of the first stability region. We add an auxiliary quadrupole excitation potential to the main drive voltage. As a result, stability islands appear on the (a,q) plane. The method of the islands mapping on the (a,q) plane is discussed in detail. The DC electric field's effect responsible for removing "shadowing" islands has been studied using a combination of analytic theory and computer modeling. We call a narrow stability region elongated along an iso-ßx line an X-island. Two such stability islands were found where operation is possible without mass spectra interference when the DC potential is used. Those islands are formed by quadrupole potentials with relative excitation frequencies ν=ß,ν=1±ß and ν=2±ß, where ß << 1. Many other stability X-islands are presented in detail and illustrated by their transmission contours. This data is necessary for experimental testing of the separation mode at those islands. The study demonstrates how to use X-islands to achieve relatively high resolution 4000-12,000 at the transmission of about 28-15%, respectively.