Ion mirror for multi-reflecting mass spectrometers
11239067 · 2022-02-01
Assignee
Inventors
Cpc classification
International classification
Abstract
Improved ion mirrors (30) (FIG. 3) are proposed for multi-reflecting TOF MS and electrostatic traps. Minor and controlled variation by means of arranging a localized wedge field structure (35) at the ion retarding region was found to produce major tilt of ion packets time fronts (39). Combining wedge reflecting fields with compensated deflectors is proposed for electrically controlled compensation of local and global misalignments, for improved ion injection and for reversing ion motion in the drift direction. Fine ion optical properties of methods and embodiments are verified in ion optical simulations.
Claims
1. An ion mirror comprising: a plurality of electrodes and at least one voltage supply connected thereto that are configured to generate an electric field region that reflects ions in a first dimension (X-dimension), and wherein at least part of the electric field region through which ions travel in use has equipotential field lines that diverge, converge or curve as a function of position along a second, orthogonal dimension (Z-direction); and electrodes arranged on opposing sides of the ion mirror in a third dimension (Y-dimension) that is orthogonal to the first and second dimensions, wherein the ion mirror comprises one or more voltage supply configured to apply different voltages to different ones of these electrodes for generating said equipotential field lines that diverge, converge or curve; wherein said electrodes arranged on opposing sides of the ion mirror in a third dimension comprise one or more first electrode arranged on a first side of the ion mirror, in the third dimension, and a plurality of second electrodes arranged on a second opposite side of the ion mirror; wherein the ion mirror is configured to apply different voltages to different ones of the second electrodes for generating said equipotential field lines that diverge, converge or curve.
2. The ion mirror of claim 1, wherein said least part of the electric field region having equipotential field lines that diverge, converge or curve is configured to tilt the time front of ions being reflected in the ion mirror.
3. The ion mirror of claim 1, wherein said least part of the electric field region is arranged at or proximate an end of the ion mirror, in the second dimension, and wherein the equipotential field lines converge as a function of distance, in the second dimension, away from said end.
4. The ion mirror of claim 1, wherein said one or more first electrode and/or said plurality of second electrodes are arranged on a printed circuit board (PCB).
5. The ion mirror of claim 1, comprising a voltage supply and electrodes configured to apply a static electric field in an ion acceleration region adjacent to, in a direction in which the ions are reflected, said part of the electric field region having equipotential field lines that diverge, converge or curve said ion acceleration region having parallel equipotential field lines for accelerating the ions out of the ion mirror.
6. The ion mirror of claim 1, wherein the ion mirror has a first length in the second dimension that comprises said at least part of the electric field region having equipotential field lines that diverge, converge or curve, and a second length in the second dimension that includes only parallel equipotential field lines for reflecting ions.
7. The ion mirror of claim 1, wherein said electrodes arranged on opposing sides of the ion mirror in the third dimension are tuning electrodes and the one or more voltage supply configured to apply different voltages to different ones of the electrodes are configured to be adjustable so as to adjust the voltages applied to the tuning electrodes.
8. The ion mirror of claim 7, comprising electrodes that are tilted at an angle with respect to each other in a plane defined by the first and second dimensions (X-Z plane); and/or comprising one or more electrodes that are bent in a plane defined by the first and second dimensions (X-Z plane).
9. A method of mass spectrometry comprising: providing an ion mirror or mass spectrometer as claimed in claim 1; applying voltages to electrodes of the ion mirror so as to generate said electric field region having equipotential field lines that diverge, converge or curve as a function of position along the second dimension (Z-direction); and reflecting ions in the ion mirror in the first dimension (X-dimension).
10. A method of tuning an ion mirror comprising: providing an ion mirror as claimed in claim 7; and adjusting the voltage supplies as a function of time so as to vary the voltages applied to the tuning electrodes and the divergence, convergence or curvature of said equipotential field lines.
11. A mass spectrometer comprising: a time-of-flight mass analyser or electrostatic ion trap having at least one ion mirror and a pulsed ion accelerator for pulsing ion packets into the ion mirror; wherein the at least one ion mirror comprises a plurality of electrodes and at least one voltage supply connected thereto that are configured to generate an electric field region that reflects ions in a first dimension (X-dimension), wherein at least part of the electric field region through which ions travel in use has equipotential field lines that diverge, converge or curve as a function of position along a second, orthogonal dimension (Z-direction); and wherein the mass spectrometer is configured so that one of the ion mirrors receives ions from the ion accelerator with a time front that is tilted relative to the second, orthogonal dimension, and wherein said electric field region having equipotential field lines that diverge, converge or curve is configured to tilt the time front of the ions passing therethrough so as to at least partially counteract the tilt of the time front that the ions have when they are received at the ion mirror.
12. The spectrometer of claim 11, wherein the time-of-flight mass analyser or electrostatic ion trap is a multi-pass time-of-flight mass analyser or electrostatic ion trap having said at least one ion mirror, and electrodes arranged and configured so as to provide an ion drift region that is elongated in a drift direction (z-dimension) and to reflect or turn ions multiple times in an oscillating dimension (x-dimension) that is orthogonal to the drift direction.
13. The spectrometer of claim 12, wherein: (i) the multi-pass time-of-flight mass analyser is a multi-reflecting time of flight mass analyser having two ion mirrors that are elongated in the drift direction (z-dimension) and configured to reflect ions multiple times in the oscillation dimension (x-dimension); or (ii) the multi-pass time-of-flight mass analyser is a multi-turn time of flight mass analyser having an ion mirror and at least one electric sector configured to reflect and turn ions multiple times in the oscillation dimension (x-dimension).
14. The spectrometer of claim 12, comprising an ion deflector configured to back-steer the average ion trajectory of the ions, in the drift direction, thereby tilting the angle of the time front of the ions, and wherein said electric field region having equipotential field lines that diverge, converge or curve is configured to tilt the time front of the ions passing therethrough so as to at least partially counteract a tilting of the time front by the ion deflector.
15. The spectrometer of claim 14, wherein the ion deflector is configured to generate a quadrupolar field for controlling the spatial focusing of the ions in the drift direction.
16. A multi-reflecting mass spectrometer comprising: (a) a pulsed ion source or a pulsed converter generating ion packets substantially elongated in the first Z-direction; (b) a pair of parallel gridless ion mirrors separated by a drift space; electrodes of said ion mirrors are substantially elongated in the Z-direction to form an essentially two-dimensional electrostatic field in an orthogonal XY-plane; said field provides for an isochronous repetitive multi-pass ion motion and spatial ion confinement along a zigzag mean ion trajectory lying within the XY symmetry plane; (c) an ion detector; (d) at least one electrically adjustable electrostatic deflector, arranged for steering of ion trajectories for angle ψ, associated with equal tilting of ion packets time front; (e) at least one electrode structure to form at least one electrically adjustable wedge electrostatic field with equipotential lines diverging or converging in said Z-direction in the retarding region of said ion mirror, followed by electrostatic acceleration in a flat field with equipotential lines parallel to said Z-direction; said at least one wedge field is arranged for the purpose of adjusting the time-front tilt angle γ of said ion packets, associated with steering of ion trajectories at much smaller (relative to said angle γ) inclination angle φ; (f) wherein said steering angles ψ and φ are arranged for either denser folding of ion trajectories, and/or for bypassing rims of said source or of said deflector or of said detector by ion packets, and/or for reverting ion drift motion; and (g) wherein said time-front tilt angle γ and said ion steering angles ψ are electrically adjusted for compensating the TIZ and/or T/ZZ time-of-flight aberrations at said detector.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) Various embodiments will now be described, by way of example only, and with reference to the accompanying drawings in which:
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
DETAILED DESCRIPTION
(10) Referring to
(11) Referring to
(12) In the example 20, to fit 14 reflections (i.e. L=7 m flight path) the source bias is set to U.sub.Z=9V. Parallel rays with an initial width in the z-direction of Z.sub.0=10 mm and no angular spread Δα=0 start hitting rims of OA 14 and of detector 17. In example 21, the top ion mirror is tilted by λ=1 mrad, representing the realistic overall effective angle of mirror tilt, accounting for built up faults of stack assemblies, standard accuracy of machining and moderate electrode bend by internal stress at machining. Every “hard” ion reflection in the top ion mirror then changes the inclination angle α by 2 mrad. The inclination angle α grows from α.sub.1=27 mrad to α.sub.2=41 mrad, gradually expanding the central trajectory. To hit the detector after N=14 reflections, the source bias has to be reduced to U.sub.Z=6V. The angular divergence is amplified by the mirror tilt and increase the ion packets width in the z-direction to Δ.sub.Z=18 mm, inducing ion losses on the rims. Obviously, slits in the drift space may be used to avoid trajectory overlaps and spectral confusion, however, at a cost of additional ionic losses.
(13) In example 21, the inclination of ion mirror introduces yet another and much more serious problem—the time-front 15 of the ions becomes tilted by angle γ=14 mrad in-front of the detector. The total ion packet spreading in the time-of-flight X-direction ΔX=ΔZ*γ=0.3 mm limits mass resolution to R<L/2ΔX=11,000 at L=7 m flight path, being low even for a regular TOF and too low for MRTOF. To avoid the limitation, the electrode precision has to be brought to non-realistic levels: λ<0.1 mrad, translated to better than 10 um accuracy and straightness of individual electrodes.
(14) Summarizing the problems of prior art MRTOF, attempts of increasing flight path require much lower specific energies U.sub.Z of continuous ion beam and larger angular divergences Δα of ion packets, which induce ion losses on component rims and may produce spectral overlaps. Most important, small mechanical imperfections strongly affect MRTOF resolution and require unreasonably high precision.
(15) Embodiments of the present invention propose to arrange wedge-shaped electrostatic fields with equipotential lines diverging in the Z-direction in the reflecting region of electrostatic gridless ion mirrors of either MRTOF or E-traps for effective and electrically adjustable control over the ion packets time-front tilt angle γ.
(16) Referring to
(17) Flat field 38 has equipotential lines arranged parallel to the Z-axis within potential boundaries corresponding to mean energies K.sub.0 and K.sub.1 of the ions, where K.sub.0>K.sub.1. Model wedge field 35 may be arranged with uniformly diverging equipotential lines in the XZ-plane, where the field strength E(z) is independent on the X-coordinate, and within the ion passage Z-region the field E(z) is reverse proportional to the Z-coordinate: E(z)˜1/z. Wedge field 35 starts at equipotential corresponding to K=K.sub.1 and continues at least to the ion retarding equipotential 36 (K=0), tilted to Z-axis at λ.sub.0 angle. This arrangement causes the time-front of the ion packet to be tilted by angle γ relative to the Z-axis, and the average trajectory of the ion packet (relative to the X-dimension) to be altered by steering angle ϕ.
(18) While applying standard mathematics a non-expected and previously unknown result was arrived at: in ion mirror 30 with wedge field 35, the time-front tilt angle γ and the ion steering angle ϕ are controlled by the energy factor K.sub.0/K.sub.1 as:
γ=4λ.sub.0*(K.sub.0/K.sub.1).sup.0.5=4λ.sub.0*u.sub.0/u.sub.1
ϕ=4λ.sub.0/3*(K.sub.1/K.sub.0).sup.0.5=4λ.sub.0/3*u.sub.1/u.sub.0
i.e. γ/ϕ=3K.sub.0/K.sub.1>>1
(19) where K.sub.1 and K.sub.0 are the mean ion kinetic energies at the exit of the wedge field 35 (index 1) and at the exit of flat field 38 (index 0) respectively, and u.sub.1 and u.sub.0 are the corresponding mean ion velocities. The angle ratio γ/ϕ=3K.sub.0/K.sub.1 may be practically reaching well over 10 or 30 and is controlled electronically.
(20) At K.sub.0/K.sub.1=1 (i.e. without acceleration in the field 38), the wedge field already provides twice larger time front tilt γ compared to fully tilted ion mirrors (γ=4λ.sub.0 Vs γ=2λ.sub.0), while producing a smaller steering angle (ϕ=4/3λ.sub.0 Vs ϕ=2λ.sub.0). The angle ratio γ/ϕ further grows with the energy factor as K.sub.0/K.sub.1 because the angles are transformed with ion acceleration in the field 38: both flight time difference dT and z-velocity w are preserved with the flat field 38, where the time front tilt dT/u grows with ion velocity u and the steering angle dw/u decreases with ion velocity u. By arranging larger K.sub.0/K.sub.1 ratio, the combination of wedge field with post-acceleration provides a convenient and powerful tool for adjustable steering of the time fronts of ion packets, accompanied by negligibly minor steering of ion rays.
(21) Again referring to
(22) A simulated ion optical model for a realistic ion mirror with wedge electrode W of embodiment 31 is illustrated by icons 32 and 33, where icon 32 shows the electrode structure (C, W and E1) around the ion reflection region and also shows equipotential lines in the XY-plane at one particular Z-coordinate. Icon 33 illustrates a slight bending of retarding equipotential 36 in the XZ-middle plane at strong disproportional compression of the picture in the Z-direction, so that the slight curvature of the line 36 can be seen. Dark vertical strips in icon 33 correspond to ion trajectories, arranged at relative energy spread δ=0.05, so that angled tips illustrate the range of ion penetration into the mirror. Icon 33 shows that the wedge field 35 is spread in the Z-direction in the region for several ion reflections, which helps distributing the time-front tilting at yet smaller bend and smaller displacement of equipotential 36.
(23) Simulations have confirmed that: (i) adjustments of the amplifying factor of 4(K.sub.0/K.sub.1).sup.0.5 allows strong tilting of the time-front at small wedge angles λ.sub.0, thus not ruining the structure of electrical fields, which are optimized for reaching overall isochronicity and spatial focusing of ion packets; (ii) the time front tilt angle can be electronically adjusted from, for example, from 0 to 6 degrees if using wedge W in both opposite ion mirrors; (iii) the compensation of the time-front tilting for deflectors (see
(24) Referring to
(25) To produce a desired curvature or bend of the ion retarding equipotential 46, the PCB 41 carries multiple conductive pads, connected via surface mounted resistive chain 42, energized by several power supplies U.sub.1 . . . U.sub.j 43. Preferably, absolute voltages of supplies 43 are kept low, say under 1 kV, which is to be achieved at ion optical optimization of the mirror electrode structure. The net of resistors 42 and power supplies 43 allows adjusting the voltage distribution on PCB 41 flexibly and electronically, thus generating a desired tilt or curvature of retarding equipotential 46, either positive or negative, either weak or strong, either local or global, as illustrated by dashed lines 45. Flexible electronic control over tilt and curvature of the retarding line 46 is a strong advantage of the PCB wedge embodiment 40.
(26) Again referring to
(27) Some practical aspects of using and tuning of PCB wedge are considered. Optionally, PCB electrodes 41 may be used at manufacturing tests only. The occurred inaccuracy of ion mirrors may be determined when measuring the required PCB compensation at recovered MRTOF resolution, which in turn could be used for calibrated mechanical adjustment of individual ion mirrors. Alternatively, the number of regulating power supplies 43 may be potentially reduced and the strategy of analyzer tuning may be optimized for constant use. It is expected that a pair of auxiliary power supplies may be used for simultaneous reaching of: creating preset wedge fields at far and near Z-edge, compensating electrodes faulty tilts, and compensating electrodes faulty bends. Indeed, all wedge fields may produce the same action—they tilt the time front of ion packets, and it is expected that a generic distribution of PCB potential may be pre-formed for each mirror, while controlling overall tilt and bow of wedge fields by a pair of low voltage power supplies 43.
(28) Compared to wedge slit W in
(29) The proposed compensation mechanism of
(30) Referring to
(31) It is important that compensating PCB 57 is used to form an electronically controlled wedge reflecting field (e.g. as described in
(32) The internal edge of window 54 is made conductive, similarly to standard PCB vias (usually made electrolytic). The preferred coating is Nickel, referred to in PCB industry as soft gold. The conductive rim may be at least three times wider than the gaps between electrodes 51 to minimize the insulator exposure and to avoid field effects of charged surfaces.
(33) The tracking distance of uncoated PCB is arranged at outer sides of PCB 51 to reduce surface gradient to under 300-500V/mm, where surface discharges are known to start at 1 kV/mm. Yet a larger tracking distance may be obtained if avoiding direct contact between edges of electrode 51 and base plate 55.
(34) Though base support 55, stiffing ribs 56 or stiffing supports 59 may be made of any mechanically stable material, preferably, we propose PCB material for matching the thermal expansion coefficient (TCE) of electrodes 51, e.g. being 4-5 ppm/C for wide spread FR-4 PCB material. Otherwise, large thermal variations (specified from −50 to +50 C) at instrument transportation may ruin the ion mirror precision and flatness. Optionally, one may use more expensive materials with close TCE, say Titanium or ceramics, however, authors are not aware of any low cost material with matching TCE, except G-10 (equivalent of FR-4 PCB), which is far less preferable for reasons of generating dust and chips. Moreover, PCB supports and ribs allow convenient soldering. Slits in supports 55 are aligned with electrode ribs 52, so that ribs could be soldered at outer sides of PCB 55.
(35) Embodiment 50 may be designed to compensate for the expected moderate PCB flexing. PCB electrodes 51 are stiff in the X- and Y-direction. Multiple aligning ribs 52 are soldered to slits in the base support 55, providing stiffness in the Z-direction. Flexing of base PCB plate 55 in the Y-direction (harmful at precision assembly) is compensated by attaching stiffing PCB ribs 56, or stiffing supports 59. Supports 59 may be metal (say aluminium) if using a hole and slit mounting to overcome TCE mismatch. Thus, PCB flexing is prevented in the fully assembled ion mirror in all three directions, where initial parallelism before soldering may be improved by technological jigs.
(36) Referring to
(37) Again referring to
(38) Preferably, external edge and ribs 52 are milled simultaneously with internal window 54 to ensure their parallelism, specified at 0.1 mm in PCB industry, while typically being better. Yet preferably, simultaneously machined aligning holes 53 may serve for better alignment of the windows in the electrodes 51 windows.
(39) Again referring to
(40) Electrodes of ion mirror 64 are formed as follows. Plates 65 have multiple conductive coated strips 66, which are separated by slits 67 with partially conductive edges. To arrange electrical separation of adjacent electrodes, slits 67 are made partially conductive, for example by initially making fully conductive edges with PCB vias technology, and then disrupting the coating by making additional holes at far Z-edges of slits 67.
(41) Without going into further details, the inventors claim that embodiment 64 also satisfies all measures of embodiment 60 for compensating deficiencies of standard PCB technology.
(42) The inventors believe that known methods of making PCB ion optical components were missing most of those steps and could not provide precision, sufficient for ion mirrors.
(43) Referring to
(44) Again referring to
E.sub.Z=U/H−E.sub.Q*z/H,
ψ=D/2H*U/K;γ=−ψ
1/F=2ψ.sup.2/D−K/U.sub.QD=1/D(2ϕ.sup.2−K/U.sub.Q)
(45) where K is the mean energy of ion packets.
(46) Compensated deflectors 71 nicely fit MRTOF. The quadrupolar field in the Z-direction generates an opposite focusing or defocusing field in the transverse Y-direction. Below simulations prove that the focal properties of MRTOF analyzers are sufficient to compensate for the Y-focusing of deflectors 71 without any significant TOF aberrations.
(47) Alternatively, compensated deflectors may be trans-axial (TA) deflectors, formed by wedge electrodes. The invention proposes using a second order correction, produced by an additional curvature of TA-wedge. Controlled focusing/defocusing may be also generated by combination of the TA-wedge and TA-lens, arranged separately or combined into a single TA-device. For a narrower range of deflection angles, the compensated deflector may be arranged with a single potential while selecting the size of Matsuda plates or with a segment of toroidal sector.
(48) Again referring to
(49) View 74 illustrates the method of compensated ion injection. Ion injection mechanism into MRTOF of the embodiments of the present invention comprises: a “flat” orthogonal accelerator (OA) 14 aligned with the Z-axis; an ion mirror with a “flat” field 38 at higher ion energies; a reflecting wedge field 35 with retarding equipotential 36 tilted at λ.sub.0 angle; and a compensated deflector 71, preferably located along the ion path and after first ion mirror reflection.
(50) Ion beam 13 propagates along the Z-axis at elevated (compared to
(51) Again referring to
(52) Similar time front compensation occurs in-front of the detector 17. Ions arrive at the inclination angle α.sub.2, deflector 71F steers ion rays and tilts time front, since deflector 71F is set static and it was set in deflecting state at the ion injections stage 74. Wedge field 35 with flat post-acceleration field 38 tilts the time front to compensate for the tilt at ray steering. The resulting time front 79 is then set parallel to the Z-axis, which simplifies the detector installation.
(53) Alternatively, the front deflector 71F may be pulsed for trapping ion packets for multiple Z-passages, this way increasing the ion flight time and flight path with the purpose of increased resolution.
(54) Table 2 below presents formulas for time front tilt angles γ, for ray steering angles ϕ and for chromatic dependence d(Δw)/dδ of the Z-component of ion velocity w induced by wedge ion mirror and by deflectors. Table 3 below shows conditions for compensating the time front tilt and the chromatic dependence of the Z-velocity in the combined system, which may be achieved simultaneously.
(55) TABLE-US-00001 TABLE 2 Chromatic dependence of Time-front Rays Z-velocity Tilt Angle Steering Angle d(Δw)/dδ Wedge Mirror
(56) TABLE-US-00002 TABLE 3 Condition for Condition for the 1st order Compensating Time-front Tilt Chromatic Spread Compensation of Z-velocity Wedge Mirror + Deflector
(57) Overall, accounting for all above described methods of compensated ion steering, embodiment 70 allows: (i) a more efficient ion injection at higher energies; (ii) dense folding of ion rays for multiple reflections; (iii) reversal of ion rays for doubling ion path; (iv) compensating additional time-of-flight aberrations associated with steering of elongated (in the Z-direction) ion packets; (v) compensating chromatic angular spreads for reduced ion packet divergence; and (vi) compensating Y-related TOF and spatial aberrations of deflectors by spatial and isochronous properties of ion mirrors. Below described simulations do confirm those claimed positive effects.
(58) The above described methods allow minor compensation of components (OA, mirrors detector) misalignments by adjusting ion injection energy, steering angles and strength of wedge fields. Wedges 35 may be combined with global compensation of ion mirror misalignment 44 of
(59) Referring to
(60) Example 80 illustrates spatial focusing of ion rays 81 for Z.sub.0=10 mm long ion packets, while not accounting angular spread of ion packets Δα=0 at ΔU.sub.Z=0 and not accounting relative energy spread of ion packets δ=ΔK/K=0 at ΔX=0. The chosen position of deflector 71F improves the ion packets bypassing of the deflector 71F and of detector 17 rim. Matsuda plates' voltages of the deflectors 71F and 71R are electrically adjusted for moderate spatial focusing of initially parallel rays onto detector 17, while being balanced for achieving optimal focusing in other examples of
(61) Example 82 illustrates angular divergence of ion rays 83 at ΔU.sub.Z=0.5V, while not accounting ion packets width Z.sub.0=0 and energy spread δ=0. Matsuda plate of the reversing deflector 71R is adjusted (being the same for all examples of
(62) Example 84 illustrates ion rays at all accounted spreads of ion beam. Though trajectories look filling most of the drift space, apparently, simulated ion losses are within 10%.
(63) Example 86 presents the overall mass resolution R.sub.M=82,000 achieved in compact 450×250 mm analyzer while accounting all realistic spreads of ion beam and ion packets, so as DET=1.5 ns time spread. The outstanding performance and low level of analyzer aberrations prove the entire concept and confirms the claimed low TOF and spatial aberrations of MRTOF with the novel wedge ion mirror.
(64) Yet higher resolutions are expected at larger size instruments, since the flight path L grows as product of instrument dimensions: L=2D.sub.X*D.sub.Z/L.sub.Z, where L.sub.Z is the ion advance per reflection. Note that the dense packing became available with the novel mechanism of compensated ion injection of the present invention.
Annotations
(65) Coordinates and Times:
(66) x,y,z—Cartesian coordinates;
(67) X, Y, Z—directions, denoted as: X for time-of-flight, Z for drift, Y for transverse;
(68) Z.sub.0—initial width of ion packets in the drift direction;
(69) ΔZ—full width of ion packet on the detector;
(70) D.sub.X and D.sub.Z—used height (e.g. cap-cap) and usable width of ion mirrors
(71) L—overall flight path
(72) N—number of ion reflections in mirror MRTOF or ion turns in sector MTTOF
(73) u—x-component of ion velocity;
(74) w—z-component of ion velocity;
(75) T—ion flight time through TOF MS from accelerator to the detector;
(76) ΔT—time spread of ion packet at the detector;
(77) Potentials and Fields:
(78) U— potentials or specific energy per charge;
(79) U.sub.Z and ΔU.sub.Z—specific energy of continuous ion beam and its spread;
(80) U.sub.X— acceleration potential for ion packets in TOF direction;
(81) K and ΔK—ion energy in ion packets and its spread;
(82) δ=ΔK/K—relative energy spread of ion packets;
(83) E—x-component of accelerating field in the OA or in ion mirror around “turning” point;
(84) μ=m/z—ions specific mass or mass-to-charge ratio;
(85) Angles:
(86) α—inclination angle of ion trajectory relative to X-axis;
(87) Δα—angular divergence of ion packets;
(88) γ—tilt angle of time front in ion packets relative to Z-axis
(89) λ—tilt angle of “starting” equipotential to axis Z, where ions either start accelerating or are reflected within wedge fields of ion mirror
(90) θ—tilt angle of the entire ion mirror (usually, unintentional);
(91) φ—steering angle of ion trajectories or rays in various devices;
(92) ψ—steering angle in deflectors
(93) ε—spread in steering angle in conventional deflectors;
(94) Aberration Coefficients
(95) T|Z, T|ZZ, T|δ, T|δδ, etc;
(96) Indexes are within the text
(97) Although the present invention has been describing with reference to preferred embodiments, it will be apparent to those skilled in the art that various modifications in form and detail may be made without departing from the scope of the present invention as set forth in the accompanying claims.