Reducing ion reflections at the quadrupole pre-filter/mass filter boundary: Simulation and experiment.

This work presents the experimental evaluation of a digital tandem mass filter that is composed of two digitally operated low-resolution mass filters in series whose mass windows are shifted with respect to each other. The overlap of the mass windows allows the resolution (Δm) of ions to be narrowed to provide better resolving power, while the acceptance of the tandem mass filter is defined by the acceptance of the first low-resolution quadrupole. Our experiments show that digital operation fulfills the promise of the tandem mass filter for providing better ion transmission at the same or better resolving power as a single quadrupole mass filter. It allows the user to continuously adjust the resolving power and sensitivity to meet current needs. Most importantly, the observed resolving power/sensitivity characteristics are the same at any mass and m/z.

Mass filter operation in higher stability zones is known to provide better resolution. Unfortunately, for sine driven instruments, higher stability zone operation reduces the accessible mass range and increases the degenerative effects of fringe fields. Conversely, digitally driven mass filters do not suffer from loss of mass range, and the fringe field effects do not increase significantly by switching stability zones because the AC voltage is always constant and the DC voltage is always zero. This work catalogues 12 stability zones that are accessible with the new digital waveform generation technology. These zones have theoretical baseline resolving powers that range from 22 to 1 300 000 with pseudopotential well depths that range from 3.5 to 43 V. Operation in higher stability zones also has the advantage of aligned axial stability wells. That alignment maximizes the pseudopotential well depth for each higher stability zone, making them more than an order of magnitude greater than the standard ∼0.2 V well of a sine filter operating in the first stability zone at unit resolution. Increased pseudopotential well depth correlates with better ion transmission and sensitivity. Our theoretical examination suggests that the digital mass filter can obtain both high resolution and high sensitivity with essentially unlimited mass range.

The kinetic energy dependence of ions trapped in a radio-frequency (RF) hexapole ion trap has been calculated as a function of space charge, mean free path, mass, RF potential and charge. The average kinetic energy of the ions was found to increase with increasing space charge, mean free path and the ion charge state. For a trapped ion in a given coulombic field, the mass of the ion and the amplitude of the applied RF potential did not affect the average kinetic energy. The consequences for multipole-storage-assisted dissociation (MSAD), in which ions are accumulated for prolonged periods of time in the multipole ion trap of an electrospray ion source, are discussed. As a result of radial stratification inside the ion trap, MSAD can lead to the preferential excitation of ions with larger m/z values. Such discrimination would have negative consequences for the detection of labile non-covalent adducts, which are normally detected at higher m/z values than their constituent species.

Digital ion trap technology is an alternate method for driving quadrupole ion traps and mass filters using variable frequency, fixed amplitude RF square waves in place of variable amplitude, fixed frequency RF sine waves. This technique offers some advantages such as an increase in the high mass analysis range by varying frequency and lower overall voltage requirements. Here, we present a complex square waveform developed for resonant parametric excitation in a quadrupole linear ion trap. Unlike traditional resonance methods, the driving RF square wave and auxiliary square wave are coupled using the same digital circuitry without the need for transformer coupling. In this work, we use this complex waveform to selectively excite the first order parametric resonances of ion motion. The square parametric excitation method presented here employs a simple and repetitive circuit design consisting of a low-voltage waveform generator followed by a series of high-voltage MOSFET switches. This design allows for resonance methods to be easily implemented in the all-digital quadrupole. The complex square waveform can perform the same useful functions as sine wave auxiliary signals, such as selective mass elimination and mass isolation. We also demonstrate that the mass resolution performance and S/N of our digital mass spectrometer is improved by applying the complex square waveform during ion ejection.

A detailed study of the quadrupole mass filter

A theoretical method was proposed in this work to study space charge effects in quadrupole ion traps, including ion trapping, ion motion frequency shift, and nonlinear effects on ion trajectories. The spatial distributions of ion clouds within quadrupole ion traps were first modeled for both 3D and linear ion traps. It is found that the electric field generated by space charge can be expressed as a summation of even-order fields, such as quadrupole field, octopole field, etc. Ion trajectories were then solved using the harmonic balance method. Similar to high-order field effects, space charge will result in an "ocean wave" shape nonlinear resonance curve for an ion under a dipolar excitation. However, the nonlinear resonance curve will be totally shifted to lower frequencies and bend towards ion secular frequency as ion motion amplitude increases, which is just the opposite effect of any even-order field. Based on theoretical derivations, methods to reduce space charge effects were proposed.

Digitally driven mass filter analysis is an advancing field. This work presents a tutorial of digital waveforms, stability diagrams, and pseudopotential well plots. Experimental results on digitally driven mass filter analysis in stability zones A and B are also shown. This work explains duty cycle manipulation of the waveforms to axially trap and eject ions from linear quadrupoles and how to change and distort the stability diagrams to create mass filters and their effects on the pseudopotential well depth. It discusses the sensitivity and resolution that can be obtained and what limits these benchmarks. It reveals the advantages of mass filter operation without any added direct current potential between the quadrupole electrodes (a=0).

The current continuity equation is usually applied to solve DC electric field distribution when there is inhomogeneous material conductivity due to temperature gradient or multi‐layer dielectrics. However, in the presence of charge accumulation, which may result from the process of electrode injection, impurity ionisation or charge trapping, the material conductivity is in tangled relationship with local field strength, and the current continuity equation can be hardly applied due to the ignorance of conductivity distribution. Thus, quantitative analysis on the effect of space (surface) charge for DC apparatus with inhomogeneous material conductivity has been a difficult problem, which requires a complicated physical model to solve. This paper has proposed a simple method to compute the synergetic influence of inhomogeneous conductivity and the space charge on the DC field distribution; through assigning bulk (interface) charge as functions of local material conductivity and field strength, the effect of inhomogeneous conductivity can be incorporated in Gauss' law and the space charge accumulation can be further included in the equation. The effect of space (surface) charge on electric field distribution in DC apparatus with temperature gradient as well as multiple‐layer dielectrics is simulated through the proposed method, which shows that the method has offered a convenient approach for investigating the effect of charge accumulation on DC field distribution under various insulation structure and working conditions.

The effects of space charge and lens aberrations on a 5-keV, 80–200-mA electron beam focused by a solenoid lens are investigated theoretically and experimentally. A third-order radial trajectory equation is derived with space charge added in the form of discrete annular current elements. This equation is numerically solved for the trajectories of focused electrons in a short solenoid lens. Trajectories launched near the axis are ‘‘reflected’’ from the axis at the waist due to space charge, and trajectories launched farther from axis, cross the axis. The resulting discontinuity is best illustrated in a transverse phase-space plot where it may be described as a ‘‘tearing’’ of the electron distribution. Due to the combined action of the nonlinear lens forces and the space charge, the initially uniform radial current density distribution becomes markedly nonuniform (hollow or peaked depending on distance) downstream from the lens. Detailed experimental measurements of the density profiles at different positions are found to be in very good agreement with computations.

Study on feature profile evolution for chlorine etching of silicon in an RF biased sheath

A versatile method of simulation of the operation of ion trap mass spectrometers

Since its introduction a few years ago, the linear ion trap Orbitrap (LTQ Orbitrap) instrument has become a powerful tool in proteomics research. For high resolution mass spectrometry measurements ions are accumulated in the linear ion trap and passed on to the Orbitrap analyzer. Simultaneously with acquisition of this signal, the major peaks are isolated in turn, fragmented and recorded at high sensitivity in the linear ion trap, combining the strengths of both mass analyzer technologies. Here we describe a next generation LTQ Orbitrap system termed Velos, with significantly increased sensitivity and scan speed. This is achieved by a vacuum interface using a stacked ring radio frequency ion guide with 10-fold higher transfer efficiency in MS/MS mode and 3–5-fold in full scan spectra, by a dual pressure ion trap configuration, and by reduction of overhead times between scans. The first ion trap efficiently captures and fragments ions at relatively high pressure whereas the second ion trap realizes extremely fast scan speeds at reduced pressure. Ion injection times for MS/MS are predicted from full scans instead of performing automatic gain control scans. Together these improvements routinely enable acquisition of up to ten fragmentation spectra per second. Furthermore, an improved higher-energy collisional dissociation cell with increased ion extraction capabilities was implemented. Higher-collision energy dissociation with high mass accuracy Orbitrap readout is as sensitive as ion trap MS/MS scans in the previous generation of the instrument.

Computation of the space charge effect within an ion trap may cost a few days to even years in clusters. Here, we report a statistical algorithm that can compute the space charge effect within a few minutes via a personal computer, without scarifying the accuracy. The key technology developed here was an effective electric field extracted from the statistics of N ions to replace the time-consuming computation of ion-ion Coulombic interactions, therefore reducing the computational burden from ∼N2 to ∼N; then, the burden was further reduced by shrinking the sampling size to Nsim = 500. For a linear ion trap (LIT) with an ion capacity N = 1 × 10 5∼1 × 106, this indicated an improved efficiency of N2/Nsim , i.e., 20 million∼2 billion-fold. Using the algorithm, space charge effects under different trapping conditions were explored, and the acquired knowledge enabled the spectral correction of the mass shift and peak broadening due to the effect in a miniature dual-LIT mass spectrometer.

We developed a simulation technique to study the effect of space charge interaction between trapped ions in the electrostatic ion beam trap (EIBT). The importance of space charge is demonstrated in both the dispersive and the self-bunching regime of the ion trap. The simulation results provide an estimate for the space charge effect on the trapping efficiency. They also allow for a better understanding of the enhanced diffusion and the self-bunching effect and provide a better characterization of the EIBT as a mass spectrometer, where peak coalescence is important. The numerical results reproduce all experimental data, demonstrating the critical importance of including space charge effects, even at low ion density, to understand the ion trap dynamics.

Ions stored in an electrodynamic ion trap can be forced from the center of the ion trap to regions of higher radio frequency (RF) electric fields by exposing them to a dipolar DC (DDC) potential applied across opposing electrodes. Such ions absorb power from the trapping RF field, resulting in increased ripple motion at the frequency of the trapping RF. When a bath gas is present, ions undergo energetic collisions that result in "RF-heating" sufficient to induce fragmentation. DDC is therefore a broad-band (i.e., mass-to-charge-independent) means for collisional activation in ion traps with added bath gas. Under appropriate conditions, the internal energy distribution of an ion population undergoing dissociation can be approximated with an effective temperature, Teff. In such cases, it is possible to determine thermal activation parameters, such as Arrhenius activation energies and A-factors, by measuring dissociation kinetics. In this work, the well-studied thermometer ion, protonated leucine enkephalin, was subjected to DDC activation under rapid energy exchange conditions and in two separate bath gases, N2 and Ar, to measure Teff as a function of the ratio of DDC and RF voltages. As a result, an empirically derived calibration was generated to link experimental conditions to Teff. It was also possible to quantitatively evaluate a model described by Tolmachev et al. that can be used to predict Teff. It was found that the model, which was derived under the assumption of an atomic bath gas, accurately predicts Teff when Ar was used as the bath gas but overestimates Teff when N2 was the bath gas. Adjustment of the Tolmachev et al. model for a diatomic gas resulted in an underestimate of Teff. Thus, use of an atomic gas can provide accurate activation parameters, while an empirical correction factor should be used to generate activation parameters using N2.