Analytic expression for the ideal one-dimensional mirror potential yielding perfect energy focusing in TOF mass spectrometry

Flory, Curt A.; Taber, R. C.; Yefchak, George E.

doi:10.1016/0168-1176(95)04343-8

Cited by 8 publications

(8 citation statements)

References 5 publications

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“…In the arrangement where distances and the average ion energy are fixed, the minimum possible thickness of the ion packet (often referred to as 'focusing') on the detector can be provided by adjusting the electric fields in the ion mirror until the narrowest width of mass peaks recorded by the detector is achieved. The thickness of the ion packet in the image plane of an 'ideal' ion mirror17, 18 stays the same as it is in the source plane for a broad range of masses and does not depend on ion kinetic energy. In an ideal cylindrical or planar‐symmetry ion mirror having non‐linear potential distribution along its axis of symmetry, ion flight times are independent or almost independent of ion energy only when the ions travel in a very narrow space near the mirror axis (paraxial space).…”

mentioning

confidence: 86%

On the high‐resolution mass analysis of the product ions in tandem time‐of‐flight (TOF/TOF) mass spectrometers using a time‐dependent re‐acceleration technique

Kurnosenko

Moskovets

2009

Rapid Comm Mass Spectrometry

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The time-dependent reacceleration of product ions produced as a result of dissociation of a single precursor ion in a tandem time-of-flight mass spectrometer is considered for the first time. Analytical expressions for the shapes of electric pulses bringing all the kinetic energies of the product ions to the same value are derived for two cases: forward acceleration mode and deceleration, followed by re-acceleration in the reversed direction (reversed mode). Secondary time-of-flight focusing resulting from the re-acceleration in the reversed mode is shown to be mass-dependent and, when averaged over a wide mass range, the focusing is tight enough to provide mass resolution exceeding 10,000. After time-dependent re-acceleration, additional compression of the ion packet width leading to better mass resolution can be obtained by decelerating the ions in a constant field.

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mentioning

confidence: 86%

On the high‐resolution mass analysis of the product ions in tandem time‐of‐flight (TOF/TOF) mass spectrometers using a time‐dependent re‐acceleration technique

Kurnosenko

Moskovets

2009

Rapid Comm Mass Spectrometry

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“…In all previous work on the use of nonlinear fields for ideal space or velocity focusing, [9][10][11][12][13][14][15][16][17][18] a simplified TOF-MS design was considered which did not include many features normally present in any practical TOF-MS such as ion lenses, discrimination filters, a post-acceleration region before ion detection etc. In our recent work 19 we solved the problem of designing an ideal reflectron TOF-MS for initial velocity focusing in which the drift region may also include any other acceleration and/or deceleration regions in addition to a field-free region.…”

Section: -18mentioning

confidence: 99%

“…This became possible since in this ideal reflectron TOF-MS the minimum initial energy of ions to be focused is allowed to be larger than zero (a parabolic reflectron focuses ions of all energies starting from zero). The authors 13 obtained the most general solution for the field inside such an ideal reflectron, and the solutions for some special cases have also been reported using analytical 14 and numerical 15 approaches. A similar approach has been developed for ideal space focusing in TOF-MS using nonlinear extraction in combination with a field-free drift region.…”

Section: Introductionmentioning

confidence: 99%

Ideal Space Focusing in a Time-of-Flight Mass Spectrometer: An Optimization Using an Analytical Approach

Doroshenko

2000

Eur J Mass Spectrom (Chichester)

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An exact, analytical solution for an electric field in a nonlinear acceleration region of an ion source for the cases of linear and reflectron time-of-flight (TOF) mass spectrometers has been found to achieve universal temporal focusing of ions having an initial space distribution. The general solutions are valid for an arbitrary electric field distribution in the drift region (from the ion source to an ion detector) of a linear TOF mass spectrometer, and in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions of a reflectron TOF instrument. This may include, for example, electrostatic lenses commonly used after an ion source for angular focusing of ions onto the detector to increase the instrument sensitivity and additional acceleration of ions before their detection. Using analytical expressions obtained for an arbitrary case, convenient working formulae are derived for the widely used single-and dual-stage ion extraction schemes in the cases of linear and reflectron TOF mass spectrometers. The formulae are used in optimizing the TOF mass spectrometer design by decreasing the curvature of the nonlinear acceleration potential in the ion source. The relationship has been shown between the conditions for an ideal space focusing using an optimized curved extraction field and a finite-order space-focusing using a linear extraction field in an ion source. The results obtained are especially useful for designing miniature TOF mass spectrometers or instruments with large volume ion sources.

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“…Enke et al 13,14 developed a method for designing ion mirrors capable of focussing large ranges of kinetic energies, given significant field-free regions between source and mirror and detector and mirror. Flory et al 15 obtained an analytical expression in the one-dimensional case for the potential within an ideal ion mirror. Following the method of Managadze and Shutyaev 11 , Doroshenko and Cotter 16 found an analytical solution in 1D for the field within a mirror providing ideal velocity focusing, notably for ions formed at a smooth surface.…”

Section: Introductionmentioning

confidence: 99%

“…The field in the ion mirror of Managadze and Shutyaev 11 has curvature, in the sense that the field is neither independent of distance as in a one-stage mirror nor linearly dependent on distance as in an ideal mirror. The best solutions for energycompensating fields from calculations by the methods of Enke et al 13,14 , Flory et al 15 and Doroshenko and Cotter 16,17 are curved, again in this sense of being neither wholly uniform nor wholly linear. The fields developed for high-resolution mass spectrometry by Wollnik 18 could be described as being curved.…”

Section: Introductionmentioning

confidence: 99%

Unveiling the Intricacies of the Curved-Field Ion Mirror

Maechler

Fillipov

Derrick

2015

Eur J Mass Spectrom (Chichester)

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In time-of-flight (ToF) mass spectrometry, non-linear ion mirrors, i.e. mirrors that produce a non-linear potential in which the ions fly, can focus ions exhibiting a very broad kinetic energy distribution. Besides the quadratic potential, the so-called curved field has been used in mirrors as a non-linear potential over the past 20 years. The curved field has, however, only been loosely defined. The focusing properties of the curved field appear to have never been mathematically investigated and explained. In this work, we put forward a rigid definition of the curved field and investigate the properties of it in terms of focusing and transmission. This rigid definition shows the curved field as a two-parameter function for a given mirror length and maximum potential, which can be optimized in terms of ToF distribution/resolution. Such an optimization was performed in one- dimension (1D) by solving the ToF integral equation numerically. The characteristics of optimized configurations arrived at through a comparison with mirrors with polynomial distance-potential relationships are assessed. These optimised solutions cannot be approximated in 1D by a common set of polynomial terms. There are optimised configurations affording ideal energy focussing, but on closer inspection, these potential distributions are found to be, in fact, quadratic potentials. There are other optimised solutions that afford good energy focussing in cases of there being significant field-free regions between the source/detector and the entrance to the mirror. Some of these configurations are approximated by a linear plus a quadratic term, others need higher-order terms to be approximated. To facilitate 3D investigation, the optimised solutions in 1D were used to set the initial voltages on electrodes in a rotationally symmetric mirror, which was modelled with the computer package SIMION 8.0. The SIMION ion-flight simulations revealed that the other optimised solutions with higher-order terms have the disadvantage of lowering the transmittance. That is to say, in 3D the configurations of the curved field, which give good resolution and transmittance with field- free regions between source/detector and mirror, can all be approximated by a potential consisting of a linear plus a quadratic term.

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Analytic expression for the ideal one-dimensional mirror potential yielding perfect energy focusing in TOF mass spectrometry

Cited by 8 publications

References 5 publications

On the high‐resolution mass analysis of the product ions in tandem time‐of‐flight (TOF/TOF) mass spectrometers using a time‐dependent re‐acceleration technique

On the high‐resolution mass analysis of the product ions in tandem time‐of‐flight (TOF/TOF) mass spectrometers using a time‐dependent re‐acceleration technique

Ideal Space Focusing in a Time-of-Flight Mass Spectrometer: An Optimization Using an Analytical Approach

Unveiling the Intricacies of the Curved-Field Ion Mirror

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