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

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

Data processing apparatus is disclosed for receiving recognition data from a speech recognition engine and its corresponding dictated audio data where the recognition data includes recognised words or characters. A display displays the recognised words or characters and the recognised words or characters are stored as a file together with the corresponding audio data. The recognised words or characters can be processed and link data is formed to link the position of the words or characters in the file and the position of the corresponding audio component in the audio data.

Method and apparatus for processing the output of a speech recognition engine

The use of linear quadrupoles in mass spectrometry as mass filters and ion guides is reviewed. Following a tutorial review of the principles of mass filter operation, methods of mass analysis are reviewed. Discussed are extensions of quadrupole mass filters to higher masses, scanning with frequency sweeps of the quadrupole waveform, operation in higher stability regions, and operation with rectangular or other periodic waveforms. Two relatively new methods of mass analysis the use of "islands of stability" and "mass selective axial ejection" are then reviewed. The optimal electrode geometry for a quadrupole mass filter constructed with round rods is discussed. The use of collisional cooling in quadrupole ion guides is discussed along with ion guides that have axial fields. Finally, mass analysis with quadrupoles that have large distortions to the geometry and fields is discussed. An Appendix gives a brief tutorial review of definitions of electrical potentials and fields, as well as the units used in this article.

Linear quadrupoles in mass spectrometry.

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.

Quadrupole mass filters with octopole fields.

https://link.springer.com/content/pdf/10.1016/j.jasms.2005.02.006.pdf

Ion Excitation in a Linear Quadrupole Ion Trap with an Added Octopole Field

https://link.springer.com/content/pdf/10.1016%2Fj.jasms.2006.03.013.pdf

Linear Quadrupoles with Added Hexapole Fields

A method and apparatus for manipulating ions using a two­dimensional substantially quadrupole field, and a method of manufacturing an apparatus for manipulating ions using a two-dimensional substantially quadrupole field are described. The field has a quadrupole harmonic with amplitude A2, an octopole harmonic with amplitude A4, and higher order harmonics with amplitudes A6 and A8. The amplitude A8 is less than A4. The A4 component of the field is selected to improve the performance of the field with respect to ion selection and ion fragmentation. The selected A4 component can be added by selecting a degree of asymmetry under a 90° rotation about a central axis of the quadrupole. The degree of asymmetry is selected to be sufficient to provide the selected A4 component.

Geometry for generating a two-dimensional substantially quadrupole field

A method and apparatus for manipulating ions using a two­ dimensional substantially quadrupole field, and a method of manufacturing and operating an apparatus for manipulating ions using a two-dimensional substantially quadrupole field are described. The field has a quadrupole harmonic with amplitude A2 and a hexapole harmonic with amplitude A3. The amplitude A3 of the hexapole component of the field is selected to improve the performance of the field with respect to ion selection and ion fragmentation.

Chuan-Fan Ding

Papers

Quadrupole mass filters with octopole fields.

Ion Excitation in a Linear Quadrupole Ion Trap with an Added Octopole Field

Linear Quadrupoles with Added Hexapole Fields

Geometry for generating a two-dimensional substantially quadrupole field

Method and apparatus for providing two-dimensional substantially quadrupole fields having selected hexapole components