Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >

Particle-in-Cell Charged Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC

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Reaction cells and collision cells for ICP-MS: a tutorial review

Linear ion traps are finding new applications in many areas of mass spectrometry. In a linear ion trap, ions are confined radially by a two-dimensional (2D) radio frequency (RF) field, and axially by stopping potentials applied to end electrodes. This review focuses on linear ion trap instrumentation. Potentials and ion motion in linear multipole fields and methods of ion trapping, cooling, excitation, and isolation are described. This is followed by a description of various mass discrimination effects that have been reported with linear ion traps. Linear ion traps combined in various ways with three-dimensional (3D) traps, time-of-flight (TOF) mass analyzers, and Fourier transform ion cyclotron resonance mass spectrometers are then given. Linear ion traps can be used as stand alone mass analyzers, and their use for mass analysis by Fourier transforming image currents, by mass selective radial ejection, and by mass selective axial ejection are reviewed.

Linear ion traps in mass spectrometry.

The quadrupole ion trap (QIT) is constructed of three electrodes that, when held at appropriate potentials, cause the formation of a trapping pseudo-potential well so that charged particles, or gaseous ions, may be confined or stored for long periods of time. The two end-cap electrodes resemble saucers while the ring electrode resembles a napkin ring; all of the electrodes are of hyperbolic geometry. The ion trap itself functions as a mass spectrometer when the ion-confining conditions are modified such that ions are ejected mass-selectively from the trapping potential well. As ions of successive mass/charge ratios are ejected in turn from the ion trap, they impinge upon an external detector whereby ion signals are created in proportion to the ion number of each species; in this manner, a mass spectrum is generated. The QITMS (quadrupole ion trap mass spectrometer) is an extraordinary instrument in that it is physically small (the entire electrode assembly can be held in the palm of one's hand) compared with magnetic and electric sector instruments, it is relatively inexpensive, it is one of the most, if not the most, sensitive mass spectrometers and, since several mass-selective operations can be carried in succession, the ion trap can function as a tandem mass spectrometer. Tandem mass spectrometric operation is described as (MS)n. With the QITMS, (MS)n is carried out in time in the same volume of space whereas (MS)n in sector instruments is carried out in space. With sector instruments, the maximum value of n is n = 4 yet with the ion trap, (MS)n where n = 4–6 can be carried out routinely and n = 13 has been achieved. The QITMS shares several similarities with the ion cyclotron resonance mass spectrometer yet the cost of the former is about one-tenth that of the latter. One striking difference between the QITMS and all other mass spectrometers is that the QITMS operates at a pressure of 10−3 Torr compared with 10−6 to 10−9 Torr for other mass spectrometers.



The theory of ion confinement and ion trajectory manipulation in the QITMS has been explained relatively simply so far. Since the theory differs widely from those of sector instruments and ion cyclotron resonance mass spectrometry (ICR/MS), it will not be familiar to those who have not had the opportunity to examine ion motion in quadrupole fields. Optimum operation of the QITMS is effected by collisional focusing of the ion cloud to the center of the ion trap under the influence of helium buffer gas. Since the movement of ions confined in the ion trap is periodic, the trajectories of collisionally focused ions can be expanded by resonance excitation effected by the imposition of supplementary radio frequency (rf) potentials of low amplitude to the end-cap electrodes of the ion trap. This excitation operation permits isolation of selected ion species, by ejection of unwanted ion species, followed by selective ion/molecule reaction or by collision-induced dissociation (CID) with subsequent mass analysis of the product/fragment ions formed. Sample calculations are given of all of the relevant trapping parameters. Applications of the QITMS as a single stage mass spectrometer and as a tandem mass spectrometer are discussed. The operation of the QITMS for the identification of dioxins and furans co-eluting from a gas chromatograph is described. In addition, the application of chemical ionization (CI) for the identification of co-eluting polychlorinated biphenyl (PCB) congeners is discussed. The QITMS is an extraordinary instrument that is capable of great sensitivity, high mass range and high mass resolution. Since the QITMS is compatible with methods for generating ions externally, such as electrospray ionization (ESI), its continued growth in many areas of mass spectrometry (MS) is assured. The structural details of the glycoprotein and the optical spectroscopy of stored ions are applications of the QITMS combined with ESI, while the ion trap in combination with a metal-cluster aggregation source has been used for an electron diffraction study.

Quadrupole ion trap mass spectrometry

https://link.springer.com/content/pdf/10.1016%2FS1044-0305%2802%2900365-3.pdf

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

The influence of the ratio of the rod radius, r, to field radius, r(0), on the peak shape for a linear quadrupole mass filter constructed with round rods has been investigated. The expansion of the potential in multipoles, phi(N),Phi(x, y) = sum(infinity)(N=0)A(N)phi(N)/r(N)(0) has been considered, and the peak shape and resolution have been determined by numerical calculation of ion trajectories in quadrupoles with different ratios, r/r(0). Geometries that make the dodecapole term (A(6)) zero (r/r(0) = 1.14511) do not give the best performance because the contribution of the 20-pole term, A(10), must be considered. The optimum ratio is r/r(0) approximately 1.13. With this ratio the dodecapole term (A(6)) is ca. 1 x 10(-3), but its effects are partially compensated by the A(10) term which has similar magnitude, but opposite sign.

Influence of the 6th and 10th spatial harmonics on the peak shape of a quadrupole mass filter with round rods.

Excitation frequencies of ions confined in a quadrupole field with quadrupole excitation.

Quadrupole mass filter operation with auxiliary quadrupolar excitation: theory and experiment

The performance of quadrupole mass filters with added octopole fields in the range 2.0-4.0% has been investigated. The added fields are much greater than those normally added to conventional rod sets by mechanical tolerances or construction errors. Quadrupole rod sets with added octopole fields were constructed with round rods by making one pair of rods greater in diameter than the other pair. For positive ions, resolution at half height of only about 200 is possible if the negative direct current (dc) output of the quadrupole power supply is connected to the smaller rods. If the positive dc output of the quadrupole power supply is connected to the smaller rods, the resolution improves dramatically; a resolution at half height of 5800 has been observed with a rod set with 2.6% added octopole field. For negative ions the best resolution is obtained with the polarity of the dc reversed, i.e. with the negative dc applied to the smaller rods. These findings are unexpected in view of the literature that argues that to obtain high mass resolution with quadrupole mass filters, higher order multipoles must be kept as small as possible. Numerical simulations of peak shapes agree qualitatively with experiments. Simulation of the boundaries of the first stability region for positive ions shows that when the positive dc is applied to the smaller rods, the addition of a 2.0% octopole field causes the boundaries to shift slightly but the boundaries are well defined, and the tip of the stability region remains sharp. When the positive dc is applied to the larger rods, the boundaries of the stability region move out and become diffuse. For instruments that require a rod set that can be used both as a linear trap and a mass filter, these rod sets may offer improved trap performance while still being capable of providing conventional mass analysis.

N. V. Konenkov

Papers

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

Influence of the 6th and 10th spatial harmonics on the peak shape of a quadrupole mass filter with round rods.

Excitation frequencies of ions confined in a quadrupole field with quadrupole excitation.

Quadrupole mass filter operation with auxiliary quadrupolar excitation: theory and experiment

Quadrupole mass filters with octopole fields.