The second stability region of quadrupole mass filter with square wave shape power supply.

We consider the operation of a digital linear ion trap with resonance radial ejection and mass selective instability modes. Periodic wave shape has a positive part with amplitude and duration and negative part with amplitude and duration , where T is the period. The mapping of the stability diagram, calculations of the well's depth and ion oscillations spectra are presented. The process of resonant excitation of ion oscillations by a dipole sinusoidal signal is studied, as well as ion ejection at the stability boundary. The trajectory method is used for this purpose. It is shown that the mass selectivity of dipole excitation is twice as large for rectangular wave shape compared to sinusoidal wave shape. Increasing the diameter of the round rods of the linear trap gives an increase in the resolving power. The possibility of DIT operation in mass-selective instability mode at the boundary point is discussed.

There are multiple metrics used in research and industry to describe the visibility of temporal light modulation (TLM), colloquially referred to as ‘flicker’. However, the metrics are not straightforward to calculate, and the values sometimes vary according to sampling rates. This work addresses the vagaries in processing TLM waveform data and calculating the metrics. For each TLM metric, its sensitivity to sampling rate is presented, followed by recommendations for improving the reliability and consistency of calculated metrics. Appropriate sampling rates are proposed according to the nature of the waveform and metric. The analyses of this paper are based on ideal waveforms without noise or instability, but the effects of sampling rate also apply to real-world waveforms. Some metrics, such as the Stroboscopic Visibility Measure, were relatively stable (i.e. produced the same value regardless of sampling rate) – within the ranges for which they are defined – for sinusoidal and/or rectangular TLM waveforms. In contrast, short-term flicker indicator [Formula: see text] and perceived modulation [Formula: see text] values exhibited greater variability based on sampling rate. Metric values from sinusoidal waveforms were generally more stable than those from rectangular waveforms, although [Formula: see text] showed inconsistency even with sinusoidal TLM.

The process of nonlinear resonant excitation of ion oscillations in a linear trap is studied. There is still no detailed simulation of the resonance peak in the literature. We propose to use the excitation contour to describe the collective ion resonance. The excitation contour is a resonant mass peak obtained by the trajectory method with the Gaussian distribution of the initial coordinates and velocities. The following factors are considered: excitation time, low order hexapole and octopole harmonics with amplitudes A3 and A4, the depth of the initial ion cloud position. These multipoles are used for selective ion ejection from linear ion trap. All these factors affect the ion yield and the shape of the contours. Obtained data can be useful for control of such processes as ion fragmentation, ion isolation, ion activation, and ion ejection. Simulated resonance peaks are important for the theoretical description of the ion collective nonlinear resonances.

The first completely digital quadrupole mass filter was recently introduced. There is now a need to understand and demonstrate the benefits of digital operation and compare them to the commercial standards. Our work to date has demonstrated that sine and square wave operation are very similar because of their similar stability diagrams and because they use a direct current (DC) potential between the electrode pairs to narrow and limit the mass range. In contrast, rectangular wave-operated digital mass filters and ion traps narrow and limit the stable mass range with the waveform duty cycle without the need for a DC potential. To understand and compare the differences between rectangular and sinusoidal modes of operation, our group has developed new spreadsheet tools that permit calculation of the m/z versus frequency space stability diagrams with the application of a DC potential between the electrode sets for rectangular and sine waveforms, and plots of the pseudopotential well depth against the entire range of stable m/zs for rectangular and sine waveforms. Our spreadsheets were used to make comparisons between fixed-frequency variable-voltage and fixed-voltage variable-frequency modes of operation. They provide a comprehensive companion tool for operating in the laboratory frame and are tunable to the instrument. This manuscript introduces these tools as it compares sine and rectangular wave modes of operation and provides a basis for understanding the advantages and disadvantages of digital operation relative to conventional technology.

In this paper, the electromagnetic performance of switched reluctance machines (SRMs) with unipolar and bipolar excitations, either sinusoidal or rectangular current waveforms, is investigated in terms of torque capability and torque ripple, iron loss etc. By employing a cost effective standard 3-phase full bridge inverter, both rectangular and sinusoidal bipolar excitations are implemented. Compared with unipolar and rectangular bipolar excitations, the torque ripple and iron loss are significantly reduced with sinusoidal bipolar excitation, albeit with reduced torque capability. Experiments on a prototype 6/4 SRM are carried out to demonstrate the advantages of sinusoidal bipolar excitation.

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 ≈200000 (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).

Ion motion in a periodic radio frequency (RF) quadrupole electric field is analysed theoretically by the matrix method and direct trajectory calculation. General properties of the ion motion: stability condition, oscillation spectrum and secular frequency are derived analytically from the elements of the transformation matrix. Stability diagrams for ion motion in the Paul ion trap are presented for rectangular waveforms with different duty cycles (duration of pulse over period). Calculation of the secular frequencies of the ion motion in the ion trap is performed for the first time. The relation of radial and axial secular frequencies along the RF scan line was found to be practically identical in both the square waveform and harmonic voltage cases. Pulse shape distortions, due to resistive-inductive-capacitive filtering in real devices, are considered. Stability diagrams of ion motion in the ion trap with distorted voltage waveforms are calculated. Distortion of the waveform is shown to introduce minor changes in the diagram shape with respect to the diagram for an ideal square wave. Within the first stable region, distortion of the waveform does not lead to any auxiliary parametric resonances of the ion motion. Ion trapping with a pure random pulsed voltage is investigated by means of direct trajectory simulations. It is shown that, in this case, the ion motion can be conditionally stable for a considerable length of time.

Effect of hull geometry on parametric resonances of spar in irregular waves

The effects of the FOPI controller and time delay on stability region of the fuel cell microgrid

Capillary effect on the sloshing of a fluid in a rectangular tank submitted to sinusoidal vertical dynamical excitation

Dual pathway sequential DC shocks reduce energy requirements for internal defibrillation. Our purpose was to determine if dual pathway shocks similarly reduce energy requirements or improve shock success in transthoracic (external) defibrillation. We studied 39 closed-chest anesthetized mongrel dogs. The dual pathways used were left chest to right chest and left chest to posterior. In eight dogs we also assessed dual shock pathways oriented orthogonally, left lower chest to right upper chest and left upper chest to right lower chest. Four different dual pathway groups were studied: group 1: simultaneous shocks, sinusoidal waveform; group 2: sequential shocks, sinusoidal waveform, 100-msec shock separation, orthogonal shock pathways; group 3: sequential shocks, sinusoidal waveform, 100 msec shock separation; and group 4: sequential shocks, rectangular waveform (sequential shocks: 2 pulses, 2.5 msec each, 0.1-msec separation; single shock: 1 pulse, 5 msec). Shocks were given at 50 (J) joules, 100 J and 150 J and curves of energy versus success compared for dual pathway shocks versus single shocks. We found that the highest mean success rates (96 +/- SD 9%) were achieved by simultaneous sinusoidal waveform dual pathway shocks at 100 J; this was identical to results achieved by the single pathway sinusoidal waveform comparison shocks at 100 J. Sequential dual pathway sinusoidal shocks separated by 100 msec achieved a mean success rate of 79 +/- 31% at 150 J; the comparison single pathway mean success rate was similar: 81 +/- 22% at 150 J. Thus, dual pathway sequential or simultaneous transthoracic shocks did not demonstrate clear superiority over single pathway shocks.

Using transfer function approach, expressions have been derived for the irradiance distribution in the diffraction images of truncated one dimensional periodic triangular wave gratings. Assuming the use of incoherent illumination, the effect of amplitude filters on the images of such objects formed by a circular aperture has been studied. Results have also been obtained for the objects with sine and rectangular wave form and a comparison has been made. The value of minimum number of cycles for which the object acts effectively as an infinite periodic object has been given.

Variations in the spectral composition of ion oscillations within several stability regions of a quadrupole mass filter were studied. The frequency spectrum was shown to consist of two line systems. Side lines ωn=nω0±βω0/2 were observed in the oscillation spectrum near harmonics nω0 (n=0, 1, 2,...), where ω0 is the circular frequency of an RF field and β is the stability parameter. Near the boundaries of the stability regions, the oscillations took the form of beatings. For even values of the stability parameter, β=2k (k=1, 2,...), the beat frequency coincides with the fundamental frequency ω0 and, for β=2k−1, the main beat frequencies are ω0/2 and 3ω0/2.

Stability of ion motion in the quadrupole ion trap driven by rectangular waveform voltages

Linear quadrupole traps are employed in a wide range of applications. Here a linear quadrupole superimposed by a static transverse magnetic field in the x or y direction is considered. The magnetic field effect on the stability regions and performance of a linear quadrupole is surveyed. The equations of motion of particles in the trap with a static transverse magnetic field are calculated analytically. Subsequently, an applied magnetic field changes equations and stability parameters. The stability diagrams of a linear quadrupole trap with and without a static transverse magnetic field are compared. A static transverse magnetic field applied to a linear quadrupole trap reshapes stability regions causing their area and position to change. Stability region reshapes caused by a static transverse magnetic field applied to a linear quadrupole trap are calculated analytically.