Second-order space-time transfer matrix of the two-stage electrostatic mirror

Ioanoviciu, D.; Yefchak, George E.; Enke, Christie G.

doi:10.1016/0168-1176(89)80049-7

Cited by 13 publications

(4 citation statements)

References 13 publications

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“…This is related to the ion final velocity ui in the spectrometer reference plane by: u,, = ui cos a, while ui = u(l +a). The initial velocity components of the ions, ula along the packet direction and, uyo normal to it, both in the spectrometer reference plane, contribute by second-and higherorder terms to the velocity spread u, together with the contribution of potential energy differences due to the ion starting points: a=6/2-62/8+63/16with 6 = s l d + ( u~+ u $ ) l u 2 (4) 6 is therefore the sum of the initial potential and kinetic energy difference of a particular ion, divided by the reference particle energy.…”

Section: Flight Timesmentioning

confidence: 99%

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Complete third‐order resolution formulae for time‐of‐flight mass spectrometers incorporating reflectrons

Ioanoviciu

1993

Rapid Comm Mass Spectrometry

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The resolution of single-and double-stage, homogeneous electric mirror time-of-flight mass spectrometers can be calculated with the derived formulae for detectors located normally to the ion flight direction or parallel to the mirror face. These formulae account for contributions to the peak width from ion initial velocity and position in the source ('turn around' time included), from ion-packet longitudinal and transverse size at the source h a l grid, as well as due to the angular ion spread. Third-order terms are included for beam size, angular aperture and velocity spread, the incidence angle being small. The field-free space needed to obtain energy focusing in time is connected with the length of the accelerating space inside the source.Since the first use of electrostatic mirrors,' their theory has been developed by Gohl et al.,' the resolution of time-of-flight mass spectrometers employing this device being increased to 35Formulae to calculate resolution for single-and double-stage homogeneous electric-field mirror reflectrons have been previously derived in Ref. 4. The second-order components of the detected ion-packet length were accounted for, oblique incidence being assumed. However, flight time inside the ion source and the initial velocity effect (leading to the so-called 'turn around' time) were disregarded. They apply for detectors located parallel to the mirror face.Perturbative effects of the slightly tilted grids or detectors have been simulated by Riggi.' The resolution limitations introduced by wire meshes were calculated in Refs 6 and 7. The results obtained are difficult to include in an analytical resolution formula.The flight time inside the accelerating gap of a singlefield ion source has been given in Ref. 8. Recently, second-order fringing field effects were calculated for single-stage electrostatic mirrors.' A fringing field with plane symmetric structure was assumed, that is unusual for reflectrons.Because in two-stage electrostatic mirror time-offlight mass spectrometers the second-order time aberration coefficient of the energy spread is cancelled, the third-order term becomes relevant. Also cross terms may contribute significantly to the detected packet length.We derive third-order resolution formulae and compare, for various source types and mass spectrometer geometries, the resolution values obtained when thirdorder terms are accounted for and also when they are neglected. FLIGHT TIMESThe flight time, t, through a homogeneous electric field may be calculated with the formulae of Ref. 10 rewritten in the form: t = (ud-uzi)ml(eE) where m , e, uzi, uZf are respectively the ion mass, its electric charge, the velocity components along the direction of the electric field (E), at the ion entry and exit, h being the distance between the field-limiting planes (Fig. 1). E is positive if ions are accelerated. When E < 0 and uzf= 0, Eqn (1) gives half of the 'turn around' time of ions in that field.We define: (1) the source reference plane, located in the ionization region normal to the ion-...

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Section: Flight Timesmentioning

confidence: 99%

“…4. The second-order components of the detected ion-packet length were accounted for, oblique incidence being assumed.…”

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confidence: 99%

Complete third‐order resolution formulae for time‐of‐flight mass spectrometers incorporating reflectrons

Ioanoviciu

1993

Rapid Comm Mass Spectrometry

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“…The ion mirror in a TOF mass spectrometer (sometimes referred to as reflectron or re‐TOF) serves the purpose of time‐of‐flight focusing by compensating for the initial velocity spread of the ions emerging from the ion source. Using an analogy with a spherical mirror in optics, the operation of an ion mirror can be described as the translation of a thin packet of ions moving with the same average energy from one plane (source plane) in a field‐free region to another one (image plane or detector plane) in the same region 15, 16. 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.…”

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confidence: 99%

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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“…For a quadratic field ion mirror, the oblique incidence, in a specific case, induced flight time changes of the order of ppm. 4 Oblique-incidence effect for homogeneous, electric reflectron time-of-flight mass spectrometers can be determined with the formulas derived by Ioanoviciu et al 5 We determined the time of flight through the cylindrical mirror of an obliquely incident ion ( Fig. 1).…”

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Aberrations of the cylindrical mirror time‐of‐flight mass spectrometers with oblique incidence

Ioanoviciu

Cună

et al. 2005

J. Mass Spectrom.

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Aberrations of the cylindrical mirror time-of-flight mass spectrometers with oblique incidence † Classical reflectron time-of-flight mass spectrometers create ion packets and focus them in time by plane grid electrodes. 1 There are no focusing forces to act on ions directing them back to the packet axis. A substantial sensitivity increase can be expected by focusing the ion packets laterally. An ion source from three cylindrical electrodes can be combined with a cylindrical reflectron, with all the electrode surfaces having a common symmetry axis. 2 The idealized calculations assume the ion source and detector as being coincident (or at least collinear) for this geometry as well as for plane electrode reflectrons. Except linear reflectrons, 3 the real-world reflectron time-of-flight mass spectrometers are so assembled that ion paths before the mirror do not interfere with those after reflection. This is achieved by the oblique incidence of ion packet with respect to the mirror entry limit. The effect of the oblique incidence has often been neglected, as the angle of incidence is usually less than a few degrees. For a quadratic field ion mirror, the oblique incidence, in a specific case, induced flight time changes of the order of ppm. 4 Oblique-incidence effect for homogeneous, electric reflectron time-of-flight mass spectrometers can be determined with the formulas derived by Ioanoviciu et al. 5 We determined the time of flight through the cylindrical mirror of an obliquely incident ion (Fig. 1). We used the Euler-Lagrange equations in cylindrical coordinates r, ϕ, and z to derive t mirror :The following symbols were used: r 0 is the radius of the cylindrical earthed electrode, v ref is the velocity of the reference ion, D ln r max /r 0 where r max is the r-coordinate of the farthest point on the reference ion trajectory, Â is the incidence angle. For the double, longitudinal (time) and lateral focusing case, r max /r 0 D 1.339.The ion entering the mirror at ϕ i leaves it at ϕ f :We accounted also for the changes of the ion coordinate on entry into and exit from the mirror due to the angular spread of the packet as well as to the effect of the field-free spaces. 6 Finally, the ion packet is lengthened because of the oblique incidence, initial width and angular spread by t packet :Here x i and˛i are the ion distance to and angle with the packet axis, at the ion source longitudinal focus, while Â 0 is the packet-axis incidence angle. As the ion packets have the coordinates distributed between x i and Cx i and between angles ˛i and C˛i, the real resolution R cyl expressed by R normal , the ideal resolution, is: classical, homogeneous electric field, two-stage reflectrons, R class , for selected normal-incidence resolution values, R normal .As a comparison, the Á angle of Fig From the above results, we conclude that the double-focusing, cylindrical reflectron time-of-flight mass spectrometers are more sensitive to the incidence angle than the homogeneous electric field reflectrons. This fact is easy to explain as ...

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Second-order space-time transfer matrix of the two-stage electrostatic mirror

Cited by 13 publications

References 13 publications

Complete third‐order resolution formulae for time‐of‐flight mass spectrometers incorporating reflectrons

Complete third‐order resolution formulae for time‐of‐flight mass spectrometers incorporating reflectrons

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

Aberrations of the cylindrical mirror time‐of‐flight mass spectrometers with oblique incidence

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