Patent Publication Number: US-11049712-B2

Title: Fields for multi-reflecting TOF MS

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a national phase filing claiming the benefit of and priority to International Patent Application No. PCT/GB2018/052101, filed on Jul. 26, 2018, which claims priority from and the benefit of United Kingdom patent application No. 1712612.9, United Kingdom patent application No. 1712613.7, United Kingdom patent application No. 1712614.5, United Kingdom patent application No. 1712616.0, United Kingdom patent application No. 1712617.8, United Kingdom patent application No. 1712618.6 and United Kingdom patent application No. 1712619.4, each of which was filed on Aug. 6, 2017. The entire content of these applications is incorporated herein by reference. 
     FIELD OF INVENTION 
     The invention relates to the area of time of flight and multi-reflecting time-of-flight mass spectrometers (MRTOF) with pulsed sources orthogonal pulsed converters, and is particularly concerned with improved control over drift motion in OA-MRTOF. 
     BACKGROUND 
     Time-of-flight mass spectrometers (TOF MS) are widely used for their combination of sensitivity and speed, and lately with the introduction of multiple ion mirrors and multi-reflecting schemes, for their high resolution and mass accuracy. 
     Pulsed ion sources are used in TOF MS for intrinsically pulsed ionization methods, such as Matrix Assisted Laser Desorption and Ionization (MALDI), Secondary Ionization (SIMS), and pulsed EI. The first two ion sources have become more and more popular for mass spectral surface imaging, where a relatively large surface area is analyzed simultaneously while using mapping properties of TOF MS. Pulsed converters are used to form pulsed ion packets out of ion beams produced by intrinsically continuous ion sources, like Electron Impact (EI), Electrospray (ESI), Atmospheric pressure ionization (APPI), atmospheric Pressure Chemical Ionization (APCI), and Inductively coupled Plasma (ICP). 
     Most common pulsed converters are orthogonal accelerators (WO9103071) and radiofrequency ion traps with pulsed radial ejection, lately used for ion injection into Orbitraps. Two aspects of prior art ion sources and converters for TOFMS are relevant: (a) they employ pulsed accelerating fields; (b) they are spatially wide which complicates their bypassing. 
     Resolution of TOF MS instruments has been substantially improved in multi-reflecting TOFMS (MRTOF) instruments. MRTOF instruments have parallel gridless ion mirrors, separated by a drift space, e.g. as described in SU1725289, U.S. Pat. Nos. 6,107,625, 6,570,152, GB2403063, U.S. Pat. No. 6,717,132, incorporated herein by reference. Most of MRTOF employ two dimensional (2D) electrostatic fields in the XY-plane between mirror electrodes, substantially elongated in the drift Z-direction. The 2D-fields of ion mirrors are carefully engineered to provide for isochronous ion motion and for spatial ion packet confinement in the transverse XY-plane. Ion packets are injected at a small inclination angle to the X-axis to produce multiple reflections in the X-direction combined with slow ion drift in the drift Z-direction, thus producing zigzag ion path. The resolving power (also referred as resolution) of MR-TOF grows at larger number of reflections N by reducing effect of the initial time spread and of the detector time spread. 
     By nature, the electrostatic 2D-fields have zero component E Z =0 in the orthogonal drift Z-direction, i.e. have no effect on the ion packets free propagation and its expansion in the drift Z-direction. In OA-MRTOF, the inclination angle α of zigzag ion trajectory is controlled by ion beam energy U Z  and by MRTOF acceleration voltage U X , and the angular divergence Δα by the beam energy spread ΔU Z :
 
α=( U   Z   /U   X ) 0.5   ; Δα=α*ΔU   Z /2 U   Z   =ΔU   Z /2( U   Z   U   X ) 0.5   (eq. 1)
 
     In attempts to increase MRTOF resolution by denser folding of the ion trajectory, the injection angle α (to axis X) of ion packets shall be reduced, thus, requiring much lower U Z  of the injected continuous ion beam, in turn, increasing the spread of injection angles Δα. Ion packets start hitting rims of the orthogonal accelerator (OA) and detector, and may produce trajectories that overlap, thus confusing spectra. For trap converters, similar problems occur at bypassing of the trap and of the detector rims. Most importantly, the scheme appears highly sensitive to unintentional misalignments of MRTOF components, either ruining MRTOF isochronicity or requiring extremely tight precision requirements. 
     To address those problems, multiple complex solutions have been proposed to define the ion drift advance per reflection, to prevent or compensate the angular divergence of ion packets, and to withstand various distortions, such as stray fields and mechanical distortions of analyzer electrodes: U.S. Pat. No. 7,385,187 proposed periodic lens and edge deflectors for MRTOF; U.S. Pat. No. 7,504,620 proposed laminated sectors for MTTOF; WO2010008386 and then US2011168880 proposed quasi-planar ion mirrors having weak (but sufficient) spatial modulation of mirror fields; U.S. Pat. No. 7,982,184 proposed splitting mirror electrodes into multiple segments for arranging E Z  field; U.S. Pat. No. 8,237,111 and GB2485825 proposed electrostatic traps with three-dimensional fields, though without sufficient isochronicity in all three dimensions and without non-distorted regions for ion injection; WO2011086430 proposed first order isochronous Z-edge reflections by tilting ion mirror edge combined with reflector fields; U.S. Pat. No. 9,136,101 proposed bent ion MRTOF ion mirrors with isochronicity recovered by trans-axial lens. Though prior art solutions do solve the problem of controlling Z-motion, however, they have several drawbacks, comprising: (i) technical complexity; (ii) additional time aberrations, affecting resolution; (iii) limited length of ion packets and limited duty cycle and charge capacity of pulsed converters; and most importantly, (iv) fixed arrangement with low tolerance to manufacturing faults. Those drawbacks become devastating when trying to construct a compact and low cost MRTOF instruments for higher resolutions. 
     Making larger analyzers raises the manufacturing cost close to the cubic power of the instrument size. It is desirable to keep instrument size at about 0.5 m, which becomes a limiting factor on the flight time TOF and mass resolution R TOF/2DET, where the practical limit for DET=1.5-2 ns if using non-stressed data systems. On the other hand, to resolve isobaric interferences, R=80-100,000 are desired, thus triggering the search for MRTOF schemes with yet denser trajectory folding, longer flight times TOF and longer flight paths L. 
     SUMMARY 
     From a first aspect the present invention provides a multi-reflecting time-of-flight mass spectrometer comprising: 
     (a) a pulsed ion emitter having a pulsed acceleration region and a static acceleration region to accelerate ions substantially along an X-direction; said pulsed ion emitter configured to emit ion packets at an inclination angle α 0  to said X-direction; 
     (b) a pair of parallel gridless ion mirrors separated by a drift space; wherein electrodes of said ion mirrors are substantially elongated in a Z-direction that is orthogonal to said X-direction so as to form a substantially two-dimensional electrostatic field in the XY-plane orthogonal to said Z-direction; 
     (c) a time-of-flight detector; 
     (d) at least one electrostatic ion deflector arranged for deflecting ion trajectories by angle ψ in the XZ plane; and 
     (e) at least one electrode structure configured to form a local wedge electrostatic field having equipotential field lines that are tilted with respect to the Z-direction, arranged either in said pulsed accelerating region and/or in an ion retarding region of one or both of said ion mirrors, followed by an electrostatic acceleration field having equipotential field lines that are parallel to the Z-direction; said at least one electrode structure being arranged to adjust the time front tilt angle γ of said ion packets in the XZ plane, and to steer the ion trajectories by inclination angle ϕ in the XZ plane; 
     (f) wherein said angles ψ and ϕ are arranged for: (i) denser folding of the ion trajectories at inclination angle α to the X-direction that is smaller than said angle α 0 , (ii) and/or for causing ions to bypass rims of said pulsed ion emitter or ion deflector, (iii) and/or for reversing ion drift motion in said Z-direction; 
     (g) wherein said time front tilt angle γ and said ion deflecting angle ψ are set for compensation of the ion packets time front tilt angle induced by the ion deflector 
     In step (g), the time front tilt angle γ and ion steering angles ψ may be electrically adjusted or selected for local mutual compensation of the ion packets time front tilt angle induced by the ion deflector. The local compensation may be performed within at most a pair of ion mirror reflections. 
     Electrodes of the electrode structure may be connected to an adjustable voltage supply for adjusting the voltages applied to these electrodes so as alter said wedge electrostatic field and hence the angle of the time front tilt caused by said electrode structure. 
     One or more electrodes of the ion deflector may be connected to an adjustable voltage supply for adjusting the voltage(s) applied to these electrodes so as alter the ion deflecting angles ψ. The ion deflector introduces a time front tilt angle to the ion packets. The adjustable voltages may be adjusted to alter the time front tilt caused by the electrode structure and the deflecting angle of the ion deflector so that the time front tilt caused by the ion deflector is at least partially compensated for. 
     The time front tilt angle and ion steering angle ψ may be electrically adjusted or set for the global mutual compensation at the detector face of the ion packets time front tilt angle induced by misalignments of an ion source, and/or of said ion mirrors and/or of said detector. 
     The ion emitter may comprise a continuous ion source, generating an ion beam at mean specific energy U Z  in the Z-direction and an orthogonal accelerator in the form of said pulsed ion emitter for pulsed ion acceleration substantially along the X-direction to specific energy U X , thus forming ion packets emitted at said inclination angle α 0 =(U Z /U X ) 0.5  to said X-direction. 
     The ion emitter may comprise a transverse ion confinement device selected from the group of: (i) a radiofrequency rectilinear multipolar ion guide; (ii) an electrostatic quadrupolar ion guide with ion beam compression and/or confinement in the X-direction; (iii) an electrostatic periodic lens; and (iv) an electrostatic ion guide having a quadrupolar field that is spatially alternated along the Z-direction. 
     A quadrupolar field may be formed within said at least one ion deflector along the Z-direction, optionally by at least one electrode structure of the group of: (i) Matsuda plates; (ii) a gate shaped deflecting electrode; (iii) side shields of the deflector with an aspect ratio under 2; (iv) toroidal sector deflection electrodes; and (v) an electrode curvature within a trans-axial wedge deflector. 
     Said quadrupolar field may be adjustable for at least one purpose selected from the group of: (i) controlling the spatial focusing or defocusing of ion packets; (ii) arranging telescopic compression of the ion packets; (ii) compensating the second order time aberrations per Z-width in ion packets T|ZZ=0, either locally and/or globally. 
     The wedge field may be located within said pulsed accelerating region and may be arranged by an electrode structure selected from the group of: (i) a tilted pull, ground or push plate electrode; (ii) a tilted ion guide for spatial confinement of the ion beam within an ion storage region of the pulsed ion emitter; (iii) an auxiliary electrode around electrodes forming an ion storage region of the pulsed ion emitter for forming a non-equally penetrating fringing field through a window, or a mesh, or a gap into the ion storage region. 
     Said wedge field may be located within said ion retarding region of at least one of the ion mirrors and may be arranged by an electrode structure selected from the group comprising: (i) a wedge-shaped slit oriented in the ZY-plane and located between mirror electrodes; (ii) at least one printed circuit board with discrete electrodes aligned in the Z-direction, connected via a resistive divider and located between mirror electrodes; (iii) a locally tilted portion of at least one electrode of said ion mirror; and (iv) at least one split portion of at least one electrode of said ion mirror, connected to a separate potential. 
     At least one of the following may be provided: (i) said at least one deflector may be located to receive ions after a first ion mirror reflection and optionally before a second ion mirror reflection; (ii) a lens or a trans-axial lens may be provided at the exit of said pulsed ion emitter and at least one ion deflector may be provided that is configured for ion packet defocusing, so as to provide telescopic compression of said ion packets; (iii) a lens may be located proximate one of said ion mirrors and arranged to receive ions reflected by that ion mirror in one mirror reflection and also after a second subsequent reflection from that ion mirror; (iv) a dual ion deflector may be arranged proximate said detector for causing the ions to bypass the detector&#39;s rim; and (v) a dual ion deflector with a spatially focusing quadrupolar field may be provided for reversing the ion drift motion in the Z-direction and compensating a tilt of the ion packet time front. 
     The spectrometer may further comprise at least one printed circuit board, located between electrodes of at least one of said mirrors; said board having discrete electrodes, connected to each other via a resistive chain and to a voltage supply for forming a wedge or arc shaped electrostatic field within the ion retarding region of the ion mirror for altering the ion packet time-front tilt. 
     Electrodes of at least one of said ion mirror may be made of one or more printed circuit boards having conductive pads; optionally having a rib mounted thereto for maintaining the flatness thereof. 
     The present invention also provides a method of multi-reflecting time-of-flight mass spectrometry comprising: 
     providing a spectrometer as described hereinabove; 
     pulsing ions along the X-direction with the pulsed ion emitter so as to emit ion packets at said inclination angle α 0 ; 
     oscillating ions in the X-direction between the mirrors as the ions drift in the Z-direction; and 
     deflecting the ion trajectories by angle ψ in the XZ plane using the ion deflector; 
     wherein the time front tilt angle γ of the ion packets is adjusted, and the steering angle of the ion trajectories is adjusted by inclination angle ϕ, in the XZ plane, using said wedge electrostatic field and electrostatic acceleration field so as to (i) more densely fold the ion trajectories at inclination angle α to the X-direction that is smaller than said angle α 0 , (ii) and/or to cause ions to bypass a rim of said pulsed ion emitter or ion deflector, (iii) and/or to reverse ion drift motion in said Z-direction. 
     The method may comprise adjusting one or more voltages applied to the ion deflector and/or pulsed ion emitter so as to adjust the ion deflecting angle ψ and/or time front tilt angle γ so as to at least partially compensate for a time front tilt angle induced by the ion deflector. 
     The wedge field may be arranged in at least one of said ion mirrors and so as to extend in the Z-direction by a distance such that ions reflected by that mirror between 2 and 4 times pass through the wedge field. 
     The method may comprise forming a wedge-shaped or curved electric field within the reflecting region of at least one ion mirror and along substantially the entire ion path in the Z-direction, optionally for compensating the isochronicity of ion motion related to the ion packet Z-width. 
     The method may comprise adjusting voltages applied to the spectrometer so as to spatially vary the wedge-shaped or curved electric field. 
     Said compensating of the tilt angle of the ion packets time front may comprise monitoring the resolution of the spectrometer whilst adjusting said deflecting angle and/or steering angle and/or ion beam energy at the entrance of said pulsed ion emitter. 
     The deflecting angle and/or steering angle and/or ion beam energy may be varied until the resolution is optimised, and then these parameters may then be fixed. 
     This technique may account for mechanical inaccuracies or misalignments of said ion emitter, of said ion mirrors, of said wedge field structures, or of said ion detector. 
     The method may comprise at least one step of the following group: (i) providing said at least one ion deflector downstream of the first ion mirror reflection; (ii) telescopically compressing said ion packets using a lens or a trans-axial lens at the exit of said pulsed ion emitter and setting said at least one deflector to an ion defocusing state; (iii) focusing ion packets using a lens located in proximate one of said ion mirrors and arranged to receive ions reflected by that ion mirror in one mirror reflection and also after a second subsequent reflection from that ion mirror; (iv) displacing the ion trajectory using a dual ion deflector arranged in proximate said detector so that ions bypass the detector&#39;s rim; and (v) reversing of the ion drift motion in the Z-direction at compensated tilt of the ion packet time front with a dual deflector having a spatially focusing quadrupolar field. 
     There are proposed herein several ion optical elements and solutions which are novel at least for MRTOF field: 
     I. A combination of wedge reflecting fields or wedge accelerating fields with “flat” post-acceleration. Such optical element, further referred as “amplifying wedge field” appears a powerful, flexible and electrically adjustable tool for tilting time fronts of ion packets while introducing very minor ion ray steering; 
     II. An electrically controlled wedge field near retarding equipotential of ion mirrors for compensation of time-front parasitic tilts introduced by mechanical unintentional misalignments of accelerators, ion mirror electrodes and detector; 
     III. A compensated deflector, incorporating quadrupolar field, in most simple example produced by Matsuda plates. The compensated deflector overcomes the over-focusing of conventional deflectors in MRTOF, so as provides an opportunity for controlled ion packet focusing and defocusing; 
     IV. A set of compensated deflectors for flexible controlling of both time-front tilt angle and ion ray steering angle. 
     Further, it has been realized that applying a combination of compensated deflectors with amplifying wedge fields to MRTOF allows reaching the desired combination of: (a) elevated energies of ion beams at the entrance of orthogonal accelerators for improved sensitivity and for reduced angular divergence Δα of ion packets; (b) dense folding of ion rays at small inclination angles for higher resolution of MPTOF; (c) spatial ion packet focusing Z|Z=0 onto detector; and (d) mutual compensation of multiple aberrations, including (i) first order time-front tilt T|Z, (ii) chromatic angular spread α|β and, accounting analyzer properties, most of Y-related time-of-flight aberrations. 
     Most of the proposed schemes and embodiments were tested and are presented herein in ion optical simulations, which have verified the stated ion optical properties, including flexible tuning and compensation of misalignments; so as confirmed an ability of reaching substantially improved combination of resolution and sensitivity within compact MPTOF systems. As an example,  FIG. 11  illustrates a compact 250×450 mm MRTOF system reaching resolution over 80,000. 
     Embodiments of the present invention provide a multi-reflecting time-of-flight mass spectrometer comprising:
     (a) A pulsed ion emitter having pulsed acceleration region and static acceleration region with field strengths directed substantially along the X-direction; said pulsed source periodically emits ion packets at an inclination angle α 0  to said X-direction;   (b) A pair of parallel gridless ion mirrors separated by drift space; electrodes of said ion mirrors are substantially elongated in the Z-direction to form a substantially two-dimensional electrostatic field in the 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) A time-of-flight detector;   (d) At least one electrically adjustable electrostatic deflector, numbered as n along the ion path and arranged for steering of ion trajectories for angles ψ n , associated with equal tilting of ion packets time front;   (e) At least one, numbered as m along the ion flight path, electrode structure to form an adjustable local wedge electrostatic field with equipotential lines tilted with respect to the Z-direction either in said pulsed accelerating region and/or in the retarding region of said ion mirror, followed by electrostatic acceleration in Z-independent (flat) field; said at least one wedge field is arranged for the purpose of adjusting the time front tilt angle γ m  of said ion packets, associated with steering of ion trajectories at much smaller (relative to said angle γ m ) inclination angle ϕ m ;   (f) Wherein said steering angles ψ 1  and ϕ 1  are arranged for either denser folding of major portion of ion trajectories at inclination angles α being smaller than said angle α 0 , and/or for bypassing rims of said accelerator or deflector, and/or for reverting ion drift motion within said analyzer this way extending ion flight paths and resolutions;   (g) Wherein said time front tilt angles γ m  and said ion steering angles ψ n  are electrically adjusted for local mutual compensations of ion packets time front tilt angle induced by individual n-th deflector, said local compensation occurring within at most pair of ion mirror reflections; and   (h) Wherein said time front tilt angles γ m  and said ion steering angles ψ n  are electrically adjusted for the global mutual compensation at the detector face of ion packets time front tilt angle induced by misalignments of said ion source, of said ion mirrors and of said detector.   

     Preferably, said ion emitter may comprise a continuous ion source, generating an ion beam at mean specific energy U Z  in the Z-direction and an orthogonal accelerator for pulsed ion acceleration substantially along a second orthogonal X-direction to specific energy U X , thus forming ion packets emitted at an inclination angle α 0 =(U Z /U X ) 0.5  to said X-axis; 
     Preferably, said ion emitter may comprise one mean of transverse ion confinement of the group: (i) a radiofrequency rectilinear multipolar ion guide; (ii) an electrostatic quadrupolar ion guide with ion beam compression in the X-direction; (iii) an electrostatic periodic lens; and (iv) an electrostatic ion guide with quadrupolar field being spatially alternated along the Z-axis. 
     Preferably, an additional quadrupolar field may be formed within said at least one deflector by at least one electrode structure of the group: (i) Matsuda plates; (ii) gate shaped deflecting electrode; (iii) side shields of the deflector with the aspect ratio under 2; (iv) toroidal sector deflection electrodes; and (v) additional electrode curvature within a trans-axial wedge deflector. 
     Preferably, said additional quadrupolar field may be adjusted for the at least one purpose of the group: (i) controlling spatial focusing or defocusing of ion packets; (ii) arranging telescopic compression of ion packets; (ii) compensating second order time aberrations per Z-width in ion packets T|ZZ=0, either locally and/or globally. 
     Preferably, said accelerating wedge field within said emitter may be arranged with one electrode structure of the group: (i) a tilted pull, ground or push plate; (ii) a tilted ion guide for spatial confinement of said ion beam within said ion storage region; (iii) an auxiliary electrode around electrodes of said accelerator forming a non equally penetrating fringing field through a window, or a mesh, or a gap. 
     Preferably, said reflecting wedge field within ion retarding region of at least one ion mirror may be arranged with one electrode structure of the group: (i) a wedge slit oriented in the ZY-plane and located between mirror electrodes; (ii) at least one printed circuit board with discrete electrodes aligned in the Z-direction, connected via resistive divider and located between mirror electrodes; (iii) a locally tilted portion of at least one electrode of said ion mirror; and (iv) at least one split portion of at least one electrode of said ion mirror, connected to a separate potential. 
     Preferably, said spectrometer may further comprise at least one means of the group: (i) said at least one deflector is located after first ion mirror reflection or first ion turn; (ii) a lens or a trans-axial lens at the exit of said emitter in combination with setting of at least one deflector for ion packet defocusing, this way providing for telescopic compression of said ion packets; (iii) a lens located in close vicinity of said ion mirror and arranged to surround two adjacent ion trajectories; (iv) a dual deflector arranged in close vicinity of said detector for improved bypassing of the detector&#39;s rim; and (v) a dual deflector with spatially focusing quadrupolar field for reversing of the ion drift motion at compensated tilt of the ion packet time front. 
     Preferably, for the purpose of electrically compensating the ion packet time front tilting by unintentional minor inaccuracy of misalignments of said ion mirrors, said spectrometer may further comprise at least one printed circuit board, located between said mirror electrodes; said board forms discrete electrodes, connected via resistive chain to form a wedge or an arc shaped electrostatic wedge field within the ion retarding region of at least one ion mirror; said compensation is arranged both locally (within one or two adjacent ion mirror reflections) and/or globally for the entire ion path. 
     Preferably, said ion mirror electrodes may be made of printed circuit boards with conductive pads; wherein the flatness of said electrodes is improved by at least one attached orthogonal rib; and wherein the straightness and flatness of the electrode assembly is improved by milling slots in said electrodes for compensating the uneven thickness of the boards. 
     Embodiments of the present invention provide a method of multi-reflecting time-of-flight mass spectrometry comprising the following steps:
     (a) Arranging pulsed acceleration region and static acceleration region with field strengths directed substantially along the X-direction within a pulsed ion emitter for periodically emitting ion packets at an inclination angle α 0  to said X-direction;   (b) Forming a two dimensional electrostatic field in an XY-plane, substantially elongated in first Z-direction within parallel ion mirrors electrodes separated by a drift space; 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, but without affecting ion drift motion in the Z-direction;   (c) Detecting ions on a time-of-flight detector;   (d) Steering of ion trajectories for electrically adjustable angles ψ n , associated with equal tilting of ion packets time front within at least one electrostatic deflector, numbered as n along the ion path;   (e) Forming at least one electrically adjustable local wedge electrostatic field with equipotential lines tilted with respect to the Z-direction, numbered as m along the ion flight path, either in said ion pulsed accelerating region of said orthogonal accelerator and/or in the ion retarding region of said ion mirror, followed by electrostatic acceleration in a Z-independent (flat) field; said at least one wedge field is arranged for the purpose of adjusting the time front tilt angle γ m  of said ion packets, associated with steering of ion trajectories at much smaller (Vs said angle γ m ) inclination angle ϕ m ;   (f) Wherein said steering angles ψ 1  and ϕ 1  are arranged for either denser folding of major portion of ion trajectories at inclination angles α being smaller than said angle α 0 , and/or for bypassing rims of said accelerator or deflector, and/or for reverting ion drift motion within said analyzer this way extending ion flight paths and resolutions;   (g) Wherein said time front tilt angles γ n  and said ion steering angles ψ n  are electrically adjusted for local mutual compensations of ion packets time front tilt angle induced by individual n-th deflector, said local compensation occurring within at most pair of ion mirror reflections; and   (h) Wherein said time front tilt angles γ, and said ion steering angles W are electrically adjusted for the global mutual compensation at the detector face of ion packets time front tilt angle induced by misalignments of said ion source, of said ion mirrors and of said detector.   

     Preferably, said step of emitting ion packets may comprise a step of generating a continuous ion beam at mean specific energy U Z  in the Z-direction and a step of pulsed ion acceleration substantially along a second orthogonal X-direction to specific energy U X , thus forming ion packets emitted at an inclination angle α 0 =(U Z /U X ) 0.5  to said X-axis; Preferably, said step of ion emitting may further comprise a step of transverse ion confinement by one field of the group: (i) a quadrupolar radiofrequency field; (ii) an electrostatic quadrupolar field with ion beam compression in the X-direction; (iii) an electrostatic periodic focusing field of periodic lens; and (iv) an electrostatic quadrupolar field, spatially alternated along the Z-axis. 
     Preferably, at the step of ion packet steering may further comprise a step of forming an additional quadrupolar field for the at least one purpose of the group: (i) controlling spatial focusing or defocusing of ion packets; (ii) arranging telescopic compression of ion packets; (ii) compensating second order time aberrations per Z-width in ion packets T|ZZ=0, either locally and/or globally. 
     Preferably, said step of forming an electrically adjustable reflecting wedge field in at least one ion mirror field may comprise a step of spreading said wedge field within a region extended in the Z-direction for several but few (between 2 and 4) ion reflections; said region being located either in the region of ion injection past said orthogonal accelerator, or in the region of ion reverting their drift motion. 
     Preferably, for the purpose of globally compensating isochronicity of ion motion related to the ion packet Z-width, affected by unintentional minor inaccuracy of misalignments of said ion mirror fields, said accelerator field, or with non parallel installation of said detector, the method may further comprise a step of forming electrically adjustable global (on the entire Z-width of ion path) wedge and/or arc field within reflecting region of at least one ion mirror. 
     Preferably, said step of global compensating of the tilt angle γ of ion packets time-front on the detector may further comprise a step of linked adjustments of said steering angles, and of ion beam energy at the entrance of said ion emitter while monitoring resolution of said method, this way accounting a given and occurred mechanical inaccuracy or misalignment of said ion emitter, of said ion mirrors, of said wedge field structures, or of said ion detector. 
     Preferably, the method may further comprise at least one step of the group: (i) improving the deflector bypassing by locating at least one deflector after first ion mirror reflection or after first ion turn; (ii) telescopically compressing said ion packets by a lens or a trans-axial lens at the exit of said orthogonal accelerator combined with setting of said at least one deflector to a defocusing state; (iii) focusing of ion packets by a lens located in close vicinity of said ion mirror and arranged to surround two adjacent ion trajectories; (iv) displacing ion trajectory with a dual deflector arranged in close vicinity of said detector for improved bypassing of the detector&#39;s rim; and (v) reversing of the ion drift motion at compensated tilt of the ion packet time front with a dual deflector with spatially focusing quadrupolar field. 
     Embodiments of the present invention provide a low cost means for controlling drift ion motion in planar MRTOF. 
     Embodiments provide a means and method for electronically adjusted compensation of unintentional misalignments of MRTOF components. 
     Embodiments provide a compact (say, 0.5 m) and low cost instrument with sufficiently high resolution R&gt;80,000 for separating major isobaric interferences, yet without stressing requirements of the detection system and not affecting peak fidelity, while operating at reasonably high energy of continuous ion beams for improved ion beam admission into the orthogonal accelerator. 
     For the avoidance of doubt, the time front of the ions may be considered to be a leading edge/area of ions in the ion packet having the same mass to charge ratio (and which may have the mean average energy). 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Various embodiments will now be described, by way of example only, and with reference to the accompanying drawings in which: 
         FIG. 1  shows prior art U.S. Pat. No. 6,717,132 planar multi-reflecting TOF with gridless orthogonal pulsed accelerator OA, 
         FIG. 2  illustrates problems of dense trajectory folding and limitations set by mechanical precision of the analyzer; 
         FIG. 3  shows a deflector according to an embodiment of the present invention, compensated by an additional quadrupolar field for controlled spatial focusing and shows a telescopic arrangement with a pair of compensated deflectors; 
         FIG. 4  shows an amplifying accelerating wedge field and wedge accelerator according to an embodiment of the present invention, designed for flexible control over the tilt angle of ion packets&#39; time front; 
         FIG. 5  shows a balanced ion injection mechanism according to an embodiment of the present invention employing the balanced deflector of  FIG. 3  and wedge accelerator of  FIG. 4  for controlling the inclination angle of ion packets while compensating the time-front tilt; 
         FIG. 6  shows numerical examples, illustrating ion packet spatial focusing within MRTOF with the injection mechanism of  FIG. 5 , and presents an ion optical component according to an embodiment of the present invention—i.e. a beam expander for bypassing detector rims, and demonstrates improved parameters of the exemplary compact MRTOF with a resolution R&gt;40,000; 
         FIG. 7  shows a numerical example with unintentional ion mirror misalignment—a tilt of the ion mirror by 1 mrad, and illustrates how the novel injection mechanism of  FIG. 5  helps compensate the misalignment with the electrical adjustment of the instrument tuning; 
         FIG. 8  shows a novel amplifying reflecting wedge field according to an embodiment of the present invention used for electrically adjustable tilting of ion packets time-front, shows one embodiment of the novel mirror wedge, achieved with a wedge slit, and presents results of ion optical simulations to illustrate the field structure and the bend of the retarding equipotential within the mirror wedge; 
         FIG. 9  shows another embodiment of the present invention for implementing the amplifying wedge mirror field of  FIG. 8 , here arranged with a printed circuit board auxiliary electrode for either electrically controlled tilt of the ion packet time front or for compensation of the unintentional misalignment of ion mirror electrodes; 
         FIG. 10  illustrates a novel arrangement according to an embodiment of present invention, using amplifying wedge mirror fields for either a compensated mechanism of ion injection into MRTOF analyzer or for a compensated far-end reflection of ion packets; 
         FIG. 11  shows numerical examples, illustrating ion packet spatial focusing at far-end reflection with the amplifying mirror wedge and deflector of  FIG. 10  and demonstrates improved parameters with resolution R&gt;80,000 within the exemplary compact MRTOF; and 
         FIG. 12  illustrates a novel method of the far-end ion packet steering in MRTOF with deflectors having quadrupolar focusing and defocusing fields of Matsuda plates. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , a prior art multi-reflecting TOF instrument  10  according to U.S. Pat. No. 6,717,132 is shown having an orthogonal accelerator (i.e. an OA-MRTOF instrument). The MRTOF  10  comprises: an ion source  11  with a lens system  12  to form a substantially parallel ion beam  13 ; an orthogonal accelerator (OA)  14  with a storage gap to admit the beam  13 ; a pair of gridless ion mirrors  16 , separated by a field-free drift region, and a detector  17 . Both the OA  14  and mirrors  16  are formed with plate electrodes having slit openings, oriented in the Z-direction, thus forming a two dimensional electrostatic field, symmetric about the s-XZ symmetry plane. Accelerator  14 , ion mirrors  16  and detector  17  are parallel to the Z-axis. 
     In operation, ion source  11  generates a continuous ion beam. Commonly, ion sources  11  comprise gas-filled radio-frequency (RF) ion guides (not shown) for gaseous dampening of ion beams. Lens  12  forms a substantially parallel continuous ion beam  13 , entering OA  14  along the Z-direction. An electrical pulse in OA  14  ejects ion packets  15 . Packets  15  travel in MRTOF at a small inclination angle α to the X-axis, controlled by the ion source bias U Z . 
     Referring to  FIG. 2 , simulation examples  20  and  21  illustrate multiple problems of the prior art MRTOF  10 , if pushing for higher resolutions and denser ion trajectory folding. Exemplary MRTOF parameters are: D X =500 mm mirror cap-cap distance; D Z =250 mm wide portion of non-distorted XY-field (from the leading edge of the OA region from which ions are pulsed to the downstream edge of the detecting surface); acceleration potential is U X =8 kV, OA rim=10 mm and detector rim=5 mm. 
     In the example  20 , to fit 14 reflections (i.e. L=7 m flight path) the source bias is set to U Z =9V. Parallel rays with initial ion packet width Z 0 =10 mm and no angular spread Δα=0 start hitting rims of the OA  14  and detector  17 . 
     In example  21 , the top ion mirror is tilted by λ=1 mrad, representing a realistic overall effective angle of mirror tilt, accounting for built up faults of the stack assemblies, standard accuracy of machining and moderate electrode bend due to 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 1 =27 mrad to α 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 Z =6V. The angular divergence is amplified by the mirror tilt and increases the ion packets width to ΔZ=18 mm, inducing ion losses on the rims. Obviously, slits in the drift space may be used to avoid trajectory overlaps, however, at a cost of additional ionic losses. 
     In example  21 , the inclination of the ion mirror introduces yet another and much more serious problem—the time-front  15  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&lt;L/2ΔX=11,000 at L=7 m flight path, which is too low compared to, for example, a desired R=80,000. To avoid the limitation, the electrode precision has to be brought to a non-realistic level: λ&lt;0.1 mrad, which translates to better than 10 um accuracy and straightness of individual electrodes. 
     Summarizing problems of prior art MRTOFs, attempts of increasing flight path require much lower specific energies U Z  of the 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. 
     With a complex electrode structure and tight requirements on the parallelism of analyzer electrodes in MPTOF, it is desirable to keep instrument size at about 0.5 m. Electrodes stability and vacuum chamber sagging under atmospheric pressure limit the analyzer width to under 300-350 mm. Making larger analyzers raises the manufacturing cost close to the cubic power of the instrument size. 
     The ideal MPTOF is expected to provide a significant gain in resolution, while not pushing the data system and detector time spreading (at peak base) under DET=2 ns, thus, not requiring ultra-fast detectors with strong signal ringing, or without artificially sharpening resolution by “centroid detection” algorithms, mining mass accuracy and merging mass isobars. To resolve practically important isobars at mass resolution R=TOF/2DET, the peak width shall be less than the isobaric mass difference, hence requiring longer flight time TOF and longer flight path L (calculated for 5 kV acceleration), all shown in Table 1 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Replacing 
                 Mass defect, 
                 Resolution &gt; 
                 TOF&gt;, 
                 Flight Path 
               
               
                 elements 
                 mDa 
                 (μ = 1000) 
                 us 
                 L&gt;, m 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 C for H 12   
                 94 
                 10,600 
                 42 
                 1.33 
               
               
                 O for CH 4   
                 38.4 
                 26,000 
                 104 
                 3.3 
               
               
                 ClH for C 3   
                 24 
                 41,600 
                 167 
                 5.3 
               
               
                 N for CH 2   
                 12.4 
                 80,600 
                 320 
                 10 
               
               
                   
               
            
           
         
       
     
     The table presents the most relevant and most frequent isobaric interferences of first isotopes. In case of LC-MS, the required resolution is over 80,000. In case of GC-MS, where most ions are under 500 amu, the required resolution is over 40K. 
     Embodiments of the present invention provide the instrument with sufficiently high resolution R&gt;80,000 for separating major isobaric interferences, yet without stressing requirements of the detection system and not affecting peak fidelity. 
     Referring to  FIG. 3 , there is proposed a compensated deflector  30  to steer ion rays while overcoming the over-focusing effects of conventional deflectors by incorporating a quadrupolar field E Q =2U Q z/H 2  in addition to deflection field E Z =U/H. The exemplary compensated deflector  30  comprises a pair of deflection plates  32  with side plates  33  at different potential U Q , known as Matsuda plates for sectors. The additional quadrupolar field provides the first order compensation for angular dispersion of conventional deflectors. The compensated deflector  30  is capable of steering ions by the same angle ψ regardless of the Z-coordinate, tilts time front by angle γ=−ψ, is capable of compensating the over-focusing (F→∞) while avoiding bending of the time front  34  (typical for conventional deflectors), or alternatively is capable of controlling the focal distance F independently of the steering angle ψ.
 
 rψ=D/ 2 H*U/K ; γ=−ψ=const( z )  (Eq. 3)
 
     Alternatively, compensated deflectors may be trans-axial (TA) deflectors, formed by wedge electrodes. Embodiments of the invention propose using a first 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. 
     Compensated deflectors 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  30  without any significant TOF aberrations. 
     Again referring to  FIG. 3 , an embodiment  35  is shown with a pair of compensated deflectors  36  and  37 , each comprising: a single deflecting plate  32 , a shield  38  at drift potential and Matsuda plate  33 . Deflectors  36  and  37  are spaced by one ion reflection in an ion mirror  16 . In other words, the ions may undergo only a single ion mirror reflection between passing through deflector  36  and deflector  37 . Since Matsuda plates allow achieving both focusing and defocusing, a pair of deflectors  36  and  37  may be arranged for telescopic compression of ion packets  31  to  39  with the factor of compression being given by ΔZ 1 /ΔZ=C1, achieved at mutual compensation of the time front steering angle γ=0, equivalent to T|Z=0 if adjusting steering angles as ψ 1 =ψ 2 *C1. The pair of deflectors  36  and  37  may provide for parallel-to-parallel ray transformation, which provides for mutual compensation of the time-front curvature, equivalent to T|ZZ=0. Then the compression factor of the second deflector  37  may be considered as C2=1/C1. Use of arrangement  35  is exampled by ion packet displacement in  FIG. 6  and by reversing of ion drift motion in  FIG. 12 . 
     Referring to  FIG. 4 , a novel orthogonal accelerator (OA)  40  according to an embodiment of the present invention is proposed, incorporating a wedge accelerating field in the area of stagnated ion packets, combined with a flat accelerating fields, thus forming an “amplifying wedge field”. The amplifying wedge field allows electronically controlling the tilt angle γ of ion packets&#39; time-front at substantially smaller steering angle θ of ion rays. 
     Exemplary orthogonal accelerator  40  OA comprises: a region of pulsed wedge field  45 , arranged between tilted push electrode  44  and ground plate  47  aligned with the Z-axis; and a straight DC accelerating field  48  formed by electrodes parallel to the Z-axis. Field  48  may have accelerating and decelerating regions for producing low time spread and spatial ion focusing of ion packets in the XY-plane, however, all equipotential lines of field  48  stay parallel to the Z-axis. 
     In operation, continuous ion beam  41  enters OA along the Z-axis at specific ion energy U Z , e.g. defined by voltage bias of an upstream RF ion guide. Preferably ion beam angular divergence, spatial expansion and beam initial position are controlled by some radial confinement means, e.g. of the group: (i) a radiofrequency rectilinear multipolar ion guide; (ii) an electrostatic quadrupolar ion guide with ion beam compression in the X-direction; (iii) an electrostatic periodic lens; and (iv) proposed in a co-pending application, an electrostatic ion guide with quadrupolar field being spatially alternated along the Z-axis. An electrical pulse is applied periodically to push plate  44 , ejecting a portion of the beam  41  through an aperture in electrode  47 , thus forming an ion packet with starting time-front  42 , which crosses a starting equipotential  46 , tilted at the angle λ 0 . Ions start with zero mean energy in the X-direction K=0. At the exit of wedge field  45  ions gain specific energy K 1  and at the exit of the DC field  48  the ions have energy K 0 . Assuming a small angle λ 0  of equipotential  46  (in further examples 0.5 deg), a beam thickness of at least ΔX&gt;1 mm and a moderate ion packet length (examples use Z 0 =10 mm), the λ o  tilt of starting equipotential  46  produces negligible corrections on energy spread ΔK of ion packet  49 . 
     While applying trivial mathematics a non-expected and previously unknown result was arrived at: in accelerator  40  with amplifying wedge accelerating field, the time-front tilt angle relative to the z-axis (γ) and the ion steering angle θ introduced by the wedge field are controlled by the energy factor K 0 /K 1  as:
 
γ=2λ*( K   0   /K   1 ) 0.5 =2λ* u   0   /u   1  
 
ϕ=2λ/3*( K   1   /K   0 ) 0.5 =2λ/3* u   1   /u   0  
 
i.e. γ/ϕ=3 K   0   /K   1 &gt;&gt;1
 
     where K 1  and K 0  are mean ion kinetic energies at the exit of the wedge field  45  (index 1) and at the exit of flat field  48  (index 0) respectively, and u 1  and u 0  are the corresponding mean ion velocities. 
     Thus, novel accelerators with amplifying wedge field allow (i) operating with continuous ion beams introduced along the Z-axis, which allows convenient instrumental arrangements; (ii) tilting ion packets time-front by substantial angles γ, which may then be used for compensation of the time-front tilt in ion deflectors; (iii) controlling the tilt angle electronically, either by adjusting the pulse potential or by minor steering of continuous ion beam between various starting equipotential lines. 
     Again referring to  FIG. 4 , similar embodiment  40 TR is proposed for an ion trap converter, having the same (as  40  OA) reference numbers for accelerator components. The trap may be arranged for ion through passage or for ion trapping in the Z-direction, where  41  is either an ion beam or an ion cloud correspondingly. In both cases it is anticipated using one of the same (as in  40  OA) means for radial ion confinement, for example: (i) a radiofrequency rectilinear multipolar ion guide; (ii) an electrostatic quadrupolar ion guide with ion beam compression in the X-direction; (iii) an electrostatic periodic lens; and (iv) proposed in a co-pending application, an electrostatic ion guide with quadrupolar field being spatially alternated along the Z-axis. 
     Ion injection into MRTOF may be improved by using higher energy continuous ion beams for improving the ion beam admission into an orthogonal accelerator (OA) and for reducing angular divergence of ion packets in the MRTOF. For higher MRTOF resolution, ion trajectories may be compact folded by using back steering of ion packets, achieved with an ion deflector. To compensate for the time-front tilt produced by the deflector, it is proposed to use an amplifying wedge accelerating field in the OA. 
     Referring to  FIG. 5 , there is shown an ion injection mechanism for an MRTOF according to an embodiment  50  of the present invention comprising: a planar ion mirror  53  with a 2D XY-field, extended in the Z-direction; an orthogonal accelerator  40  with a “flat” DC acceleration field  48  aligned with the Z-axis and a wedge accelerating field  45  produced by tilted push plate  44 ; and a compensated deflector  30 , located along the ion path and after the first ion mirror reflection. Deflector  30  is similar to that in  FIG. 3  and accelerator  40  to that in  FIG. 4 . 
     The operation of embodiment  50  is illustrated by simulation example  51 , showing time fronts  54  and  55  crossing ion rays. Continuous ion beam  41  at specific energy U Z =57V propagates along the Z-axis to cross starting (K=0) equipotential  46 , which is tilted at the angle λ 0 =0.5 deg by push plate  44  being tilted by 1 deg to the Z-axis. Pulsed wedge field  45  accelerates ions to mean energy K 1 =800V, and flat field  48  to K 0 ==8 kV, thus producing an amplifying factor K 0 /K 1 ≅10. The amplifying wedge tilts the ion packets time front  54  at a large angle γ=2λ 0 *(K 0 /K) 0.5 ≈6λ 0 , while having a small effect on the rays angle α 1 =α0−ϕ=4.7 deg at ϕ≅0.2 deg, i.e. ion rays are inclined almost at the natural inclination angle α 0 =(U Z /U X ) 0.5 =4.9 deg. After the first ion mirror reflection, deflector  30  steers ion rays by ψ=−γ=−3.2 deg, thus reducing the inclination angle to α 2 =α 1 −ψ1.5 deg, while aligning the ion packets time front  55  with the Z-axis, i.e. γ=0. Much higher specific energies of the ion beam (U Z =57V Vs 9V in to prior art 20) improve the ion admission into the OA and reduce the angular divergence Δα of ion packets for denser folding of ion trajectories at smaller inclination angles, here at α 2 =α1−ψ=1.5 deg Vs natural inclination angle α 0 =4.9 deg. 
     Table 2 below summarizes equations for angles within individual deflector  30  and wedge accelerator  40 . Table 3 below presents conditions for compensation of the first order time front tilt and of the chromatic spread of Z-velocity. It is of significant importance that both compensations are achieved simultaneously. This is new finding in the field. The pair of wedge accelerator  40  and deflector  30  work nicely for MRTOF  50 —it compensates multiple aberrations, including the first order time front tilt, the chromatic angular spread and, accounting focusing properties of gridless ion mirrors in example  51 , the angular and spatial spreads of ion packets in the Y-direction. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                 Chromatic  
               
               
                   
                   
                   
                 dependence of 
               
               
                   
                 Time front 
                 Rays Steering 
                 Z-velocity 
               
               
                   
                 Tilt Angle 
                 Angle 
                 d(Δw)/dδ 
               
               
                   
               
             
            
               
                 Wedge Accelerator 
                 
                   
                     
                       
                         
                           γ 
                           0 
                           
                             ( 
                             OA 
                             ) 
                           
                         
                         = 
                         
                           2 
                           ⁢ 
                           
                             λ 
                             0 
                           
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           φ 
                           
                             ( 
                             OA 
                             ) 
                           
                         
                         ≈ 
                         
                           
                             + 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   λ 
                                   0 
                                 
                               
                               3 
                             
                           
                           ⁢ 
                           
                             
                               
                                 K 
                                 1 
                               
                               
                                 K 
                                 0 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           λ 
                           0 
                         
                         ⁢ 
                         
                           u 
                           0 
                         
                         ⁢ 
                         
                           
                             
                               K 
                               0 
                             
                             
                               K 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 Deflector 
                 −ψ 0   
                 ψ 0   
                 
                   
                     
                       
                         
                           - 
                           
                             1 
                             2 
                           
                         
                         ⁢ 
                         
                           u 
                           0 
                         
                         ⁢ 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Condition for the 1st  
                 Condition for  
               
               
                   
                 order Time-front 
                 Compensating Chromatic  
               
               
                   
                 Tilt Compensation 
                 Spread of Z-velocity 
               
               
                   
               
             
            
               
                 Wedge Accelerator + Deflector 
                 
                   
                     
                       
                         
                           2 
                           ⁢ 
                           λ 
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                         = 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           2 
                           ⁢ 
                           λ 
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                         = 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Referring back to  FIG. 5 , an alternative embodiment  52  differs from  50  by tilting DC acceleration field by angle λ 0  to the Z-axis for aligning ion beam  41  with starting equipotential line  46  parallel to the Z-axis. The angles are shifted, however, the above described compensations still survive. 
     Referring to  FIG. 6 , the compensated mechanism  50  of ion injection into MRTOF has been verified in ion optical simulations  60 ,  62 ,  64  and  66 . An exemplary MRTOF comprises an ion mirrors  53  with mirror cap-cap distance D X =450 mm and useful width D Z =250 mm, operating at acceleration potential U X =8 kV. The examples of  FIG. 6  employ the compensated deflector  30  with Matsuda plates of  FIG. 3 , amplifying wedge accelerator  40  of  FIG. 4 , a dual deflector  30 D with Matsuda plates, and TOF detector  17 , assumed having DET=1.5 ns Gaussian signal spread. Similar to example  51 , a continuous ion beam of μ=1000 amu with ΔX=1 mm width and 2 deg full angular divergence enters wedge OA at U Z =57V specific (per charge) energy and ΔU Z =0.5V energy spread. 
     Example  60  illustrates spatial focusing of ion rays  61  for Z=10 mm long ion packets (the initial length of the ion packet along the Z-axis), while not accounting angular spread of ion packets (Δα=0 at ΔU Z =0) and not accounting relative energy spread of ion packets (δ=ΔK/K=0 at ΔX=0). The chosen position of deflector  30  improves the ion packets bypassing of the deflector  30 . The Matsuda plate voltage of the deflector  30  is electrically adjusted for geometrical focusing of ion packets onto the detector, which allows a denser folding of ion rays in MRTOF at α 2 =1.5 deg. 
     Example  62  illustrates the angular divergence of ion rays  63  at ΔU Z =0.5V, while not accounting for the ion packets width Z 0 =0 and energy spread δ=0. Dual compensated deflector  30 D (another novel component for MRTOF) helps spreading ion rays in front of the detector  17  for bypassing the detector rims (here 5 mm). 
     Example  64  illustrates the (predicted by Table 4 below) simultaneous compensation of chromatic angular spread α|δ=0 and first order time front tilt γ=0 at δ=0.05, ΔU Z =0, and Z 0 =0 (dark intervals show positions of ions of different energies at fixed time steps, in particular demonstrating energy focusing at the detector and after each reflection). 
     Example  66  illustrates the overall mass resolution R M =47,000 achieved in a compact 450×250 mm analyzer while accounting for all realistic spreads of ion beam and ion packets, so as DET=1.5 ns time spread. The embodiment satisfies the previously set goal R&gt;40,000 for resolving major isobars presented in Table 1 for μ=m/z&lt;500 in GC-MS instruments. 
     The injection mechanism  50  has a built-in and not yet fully appreciated virtue—an ability to compensate for mechanical imperfections of MRTOF by electrical tuning of the instrument, including adjustment of ion beam energies U Z , pulse voltage on push plate  44 , deflector  30  steering, or steering of continuous ion beam  41  to fit different equipotential lines  46 . 
     Referring to  FIG. 7 , there is presented a simulation example  70 , employing the MRTOF analyzer of  FIG. 6  with D X =450 mm, D Z =250 mm, and U X =8 kV. The example  70  is different from  60  by introducing Φ=1 mrad tilt of the entire top mirror  71 , representing a typical non-intentional mechanical fault during manufacturing. If using the tuning settings of  FIG. 6 , the resolution drops to 25,000 as shown in the graph  74 . The resolution may be partially recovered to R=43,000 as shown in icon  75  by increasing the source bias and specific energy of continuous ion beam from U Z =57V to U Z =77V, and by retuning deflectors  30  and  30 D. Example  70  shows ion rays after the compensation when accounting for all realistic ion beam and ion packet spreads, similar to  FIG. 6 . Thus, the proposed injection scheme  50  into compact MRTOF still allows reaching the goal of R=40,000 for GC-MS. 
     Embodiments of the invention propose to arrange wedge fields in the reflection region of parallel ion mirrors for effective and electrically tuned control over the inclination angle of ion packets in the MRTOF. Referring to  FIG. 8 , a model gridless ion mirror  80  according to an embodiment of the present invention comprises a wedge reflecting field  85  and a flat post-accelerating field  88 . An ion packet  84  (formed with any pulsed converter or ion source) is initially aligned with the Z-axis, as shown by a line for the time-front. Ion packet  84  has mean (average) ion energy K 0  and energy spread ΔK (in the X-direction). Ion packet  84  enters the model wedge ion mirror at an inclination angle α (to the X-direction). 
     Flat field  88  has equipotential lines parallel to the Z-axis within boundaries corresponding to mean energies K 0  and K 1 , where K 0 &gt;K 1 . Model wedge field  85  is arranged with uniformly diverging equipotentials in the XZ-plane, where the field strength E(z) is independent of the X-coordinate, and within the ion passage Z-region the field E(z) is inversely proportional to the Z-coordinate: E(z)˜1/z. Wedge field  85  starts at an equipotential corresponding to K=K 1  and continues at least to the ion turning equipotential  86  (K=0), which is tilted to the Z-axis at λ 0  angle. 
     While applying standard mathematics a non expected and previously unknown result was arrived at: in ion mirror  80  with wedge field  85 , the time-front tilt angle γ and the ion steering angle ϕ are controlled by the energy factor K 0 /K 1  as:
 
γ=4λ 0 *( K   0   /K   1 ) 0.5 =4λ 0   *u   0   /u   1  
 
ϕ=4λ 0 /3*( K   1   /K   0 ) 0.5 =4λ 0 /3* u   1   /u   0  
 
i.e. γ/ϕ=3 K   0   /K   1 &gt;&gt;1
 
     where K 1  and K 0  are mean ion kinetic energies at the exit of the wedge field  85  (index 1) and at the exit of flat field  88  (index 0) respectively, and u i  and u o  are the corresponding mean ion velocities. The angle ratio γ/ϕ=3K 0 /K 1  may in practice reach well over 10 or 30 and is controlled electronically. 
     At K 0 /K 1 =1 (i.e. without acceleration in the field  88 ), the wedge field already provides a twice larger time front tilt γ compared to fully tilted ion mirrors (γ=4λ 0 Vs γ=2λ 0 ), while producing a smaller steering angle (ϕ=4/3λ 0  Vs ϕ=2λ 0 ). The angles ratio γ/ϕ further grows with the energy factor as K 0 /K 1  because the angles are transformed with ion acceleration in the field  88 : both flight time difference dT and z-velocity w are preserved with the flat field  88 , where the time-front tilt dT/u grows with ion velocity u and the steering angle dw/u drops with ion velocity u. By arranging larger K 0 /K 1  ratio, the combination of wedge field with post-acceleration becomes a convenient and powerful tool for adjustable steering of time fronts, accompanied by negligibly minor steering of ion rays. 
     Again referring to  FIG. 8 , one embodiment  81  of an ion mirror with amplifying reflecting wedge field is shown comprising a regular structure of parallel mirror electrodes, all aligned in Z-direction, where C denotes the mirror cap electrode, and E 1  is the 1st mirror frame electrode (usually, there are 4 to 8 such frame electrodes). Mirror  81  further comprises a thin wedge electrode W, located between cap C and 1st frame electrode E 1 . Wedge electrode W has a constant thickness in the X-direction and is aligned parallel with the Z-axis, however, it has wedge window in the YZ-plane for variable attenuation of cap electrode C potential. Such a wedge window appears sufficient for minor curving of the reflecting equipotential  86  in the XZ-plane, while having minor effect on the structure and curvatures of the XY-field. 
     An ion optical model for the wedge electrode W of embodiment  81  is illustrated by icons  82  and  83 , where Icon  82  shows the electrode structure (C, W and E 1 ) around the ion reflection region and also shows equipotential lines in the XY-plane at one particular Z-coordinate. Icon  83  illustrates a slight bending of the retarding equipotential  86  in the XZ-middle plane, at strong disproportional compression of the picture in the Z-direction so that the slight curvature of the line  86  can be seen. Dark vertical strips in icon  83  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  83  shows that the wedge field  85  is spread in the Z-direction in the region for several ion reflections, which helps distributing the time-front tilting at yet smaller bend of equipotential  86 . 
     Simulations have shown that: (i) adjustments of the amplifying factor of 4(K 0 /K 1 ) 0.5  allows strong tilting of the time-front at small wedge angles λ 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 0 to 6 degrees if using wedge W in both opposite ion mirrors; (iii) the compensation of the time front tilting for deflectors is reached simultaneously with compensation of chromatic dependence of the Z-velocity, as illustrated in  FIG. 10 . 
     Referring to  FIG. 9 , yet another embodiment  90  of an ion mirror with an amplifying wedge reflecting field is shown comprising conventional ion mirror electrodes C, E 1  (and optionally further frame electrodes, E 2 , etc) and further comprising a printed circuit board  91 , placed between cap C and first frame electrode E 1 . Exemplary PCB  91  is either composed of two parallel PCB plates or may be one PCB with a constant (z-independent) window size. 
     To produce a desired curvature or bend of the ion retarding equipotential  96 , the PCB  91  carries multiple electrode segments, connected via resistive chain  92 , preferably surface mounted SMD resistors, energized by at least one additional power supply, or by several power supplies U 1  . . . U j    93 . Preferably, absolute voltages of supplies  93  are kept at low, say under 1 kV, which is to be achieved at ion optical optimization of the mirror electrode structure. The net of resistors  92  and power supplies  93  may be used for generating electronically controlled amplifying wedge mirror fields. Exemplary retarding equipotential  96  has wedges at both the near and far Z-ends for the purpose of compensated deflection according to  FIG. 10 . The Z-range, the amplitude and the sign of the wedge field angle are variable electronically as indicated by dashed line  95 . 
     Realistic instruments may have a slight mechanical inaccuracy in parallelism of the orthogonal accelerator electrodes, ion mirror electrodes and of the detector. One mechanism of compensating misalignments was presented in  FIG. 7 , where mirror tilt was compensated by adjusting the ion beam energy and steering angle in deflectors. Here, an alternative compensation method is presented comprising an electronically controlled ion mirror wedge. 
     Again referring to  FIG. 9 , an exemplary embodiment  94  illustrates the case of mirror cap C being unintentional tilted by angle  2   c , which is expected to be a fraction of 1 mrad at a realistic accuracy of mirror manufacturing. A printed circuit board  91  may be used for recovering the straightness of the reflecting equipotential  97 , primarily designed for compensation of time-front tilting by unintentional mirror faults. Similarly, a second (opposing) ion mirror may have another PCB for providing a quadratic distribution of PCB potentials for electronically controlled correction of unintentional overall bend of ion mirror electrodes. Exemplary retarding equipotentials  98  and  99  illustrate an ability of forming a compensating wedge or curvature, designed for compensating unintentional electrode misalignments. 
     Optionally, PCB electrodes  91  may be used at manufacturing tests only for measuring the occurred inaccuracy of ion mirrors 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  93  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-edges, compensating electrode faulty tilts, and compensating electrode faulty bends. Indeed, all wedge fields produce the same action—to tilt the time front of ion packets, and it is expected that a generic distribution of PCB potentials may be pre-formed for each mirror, while controlling the overall tilt and bow of wedge fields by a pair of low voltage power supplies  93 . 
     Compared to tilted push plate  44  in  FIG. 4  or wedge slit W in  FIG. 8 , PCB wedge mirrors  90  and  91  look more attractive for being more flexible. Adjusting potentials allows adjusting amplitude and changing the sign of the bend or tilt of the reflecting equipotential  96 . Electronically controlled PCB wedge mirrors may be also used for improved injection or in other methods of compensated ion packet steering. 
     As described in a co-pending application, the proposed compensation mechanism of  FIG. 9  may allow using lower cost technologies of ion mirror making, characterized by lower precision. The compensation shifts the precision requirements in the range of 0.1-0.3 mm. Embodiments of the invention propose making mirror electrodes from printed circuit board electrodes, so as to use the PCB for electrode mounting, e.g. by soldering. To avoid insulator charging and to avoid surface discharges at up to 5-10 kV voltages, PCB elements may have machined slots. While slots can be metal coated as vias and may be milled precisely, the biggest obstacle of applying the PCB technology to ion mirrors is related to the uneven thickness of the boards, usually specified as up to 5% of the PCB thickness and rarely controlled at PCB manufacturing. Embodiments of the invention propose an improvement of PCB electrode flatness and positioning by the following steps: using at least one attached orthogonal PCB rib with a precisely machined edge; milling slots in the PCB having electrodes for attaching those ribs with a face surface of said electrodes being pressed against a hard and flat surface. 
     Referring to  FIG. 10 , embodiments  100  of an ion injection mechanism into MRTOF are shown comprising: a “flat” orthogonal accelerator  102 , having push plate  44  and “flat” acceleration field  48 —both aligned with the Z-axis; an ion mirror with a “flat” field  88  at ion mirror entrance (along X) and with a reflecting wedge field  85 , characterized by a tilted retarding equipotential  86  at λ 0  angle to the Z-axis; and a compensated deflector  30  of  FIG. 3 , located along the ion path and after first ion mirror reflection. 
     Ion beam  41  propagates along the Z-axis at elevated (compared to  FIG. 11 ) energies (e.g. 20-50V) and enters accelerator  102 . Pulsed ejected ion packets have time-front  103  being parallel to the Z-axis while traveling at an inclination angle α 1  of several degrees. After reflection with the wedge mirror field  85  and after post-acceleration in the flat field  88 , the ion packets&#39; time-front  104  becomes tilted at angle γ&gt;&gt;λ 0 . Ion rays are steered back by angle ψ=−γ with compensated deflector  30  so that the inclination angle α 2 =α 1 −ψ is substantially reduced for denser trajectory folding in MRTOF, while orientation of the time-front  105  is recovered for γ=0. 
     Again referring to  FIG. 10 , an embodiment of back-end steering mechanism  101  in MRTOF is shown comprising a similar wedge ion mirror with “flat” entrance field  88 , a wedge reflecting field  85 , and with a “reflecting” or “retarding” equipotential line  86  tilted at an angle λ 0 . Ion packets  106  arrive to the far Z-end after multiple reflections in MRTOF, where they traveled at an inclination angle α 2  and with the time front  106  being parallel to the Z-axis, i.e. γ=0. After ion reflection in mirror wedge field  85  and after post-acceleration in flat field  88 , ion packets time-front  107  becomes tilted by a relatively large (say, 3 deg) angle γ=2α 2 . Ion rays are steered back by angle γ=−γ=2α 2  by compensated deflector  30 R, so that the inclination angle becomes −α 2 , while orientation of the time front  105  is recovered for γ=0. As a result, ion drift motion in the Z-direction is reversed without tilting of the time-front, which helps to achieve about twice denser folding of ion rays in MRTOF as shown below in  FIG. 11 . 
     Table 4 below presents formulae for time front tilt angles γ, for ray steering angles θ and for chromatic dependence d(Δw)/dδ of the Z-component of ion velocity w induced by wedge ion mirror and by deflectors. 
     Table 5 below shows conditions for compensating the time front tilt and the chromatic dependence of the Z-velocity in the combined system, apparently achieved simultaneously. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                   
                 Chromatic  
               
               
                   
                   
                   
                 dependence 
               
               
                   
                 Time-front 
                 Rays Steering 
                 of Z-velocity  
               
               
                   
                 Tilt Angle 
                 Angle 
                 d(Δw)/dδ 
               
               
                   
               
             
            
               
                 Wedge Mirror 
                 
                   
                     
                       
                         
                           γ 
                           0 
                           
                             ( 
                             M 
                             ) 
                           
                         
                         = 
                         
                           4 
                           ⁢ 
                           
                             λ 
                             0 
                           
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           φ 
                           
                             ( 
                             M 
                             ) 
                           
                         
                         ≈ 
                         
                           
                             + 
                             
                               
                                 4 
                                 ⁢ 
                                 
                                   λ 
                                   0 
                                 
                               
                               3 
                             
                           
                           ⁢ 
                           
                             
                               
                                 K 
                                 1 
                               
                               
                                 K 
                                 0 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           λ 
                           0 
                         
                         ⁢ 
                         
                           u 
                           0 
                         
                         ⁢ 
                         
                           
                             
                               K 
                               0 
                             
                             
                               K 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 Deflector 
                 −ψ 0   
                 ψ 0   
                 
                   
                     
                       
                         
                           - 
                           
                             1 
                             2 
                           
                         
                         ⁢ 
                         
                           u 
                           0 
                         
                         ⁢ 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                 Condition for the 1st  
                 Condition for  
               
               
                   
                 order Time-front 
                 Compensating Chromatic 
               
               
                   
                 Tilt Compensation 
                 Spread of Z-velocity 
               
               
                   
               
             
            
               
                 Wedge Mirror + Deflector 
                 
                   
                     
                       
                         
                           4 
                           ⁢ 
                           λ 
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                         = 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           4 
                           ⁢ 
                           λ 
                           ⁢ 
                           
                             
                               
                                 K 
                                 0 
                               
                               
                                 K 
                                 1 
                               
                             
                           
                         
                         = 
                         
                           ψ 
                           0 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Referring to  FIG. 11 , there are presented results of ion optical simulations of MRTOF  110  with the compensated ion reversal  101  of  FIG. 10 . The compact MRTOF  110  comprises: parallel ion mirrors with a mirror cap-cap distance D X =450 mm and useful length D Z =250 mm, separated by a drift space at U X =−8 kV acceleration voltage; an ion source (not shown) generating an ion beam  41  along Z-axis at U Z =57V specific energy with ΔU Z =0.5V spread; an orthogonal accelerator  40  having a tilted push electrode; a deflector  30  with compensating Matsuda plates; a reversing deflector  30 R, a wedge electrode W at far Z-end; and a detector  17  at near Z-end. 
     Example  110  illustrates spatial focusing of ion rays  111  for Z 0 =10 mm long ion packets, while not accounting for angular spread of ion packets Δα=0 at ΔU Z =0 and not accounting for relative energy spread of ion packets δ=ΔK/K=0 at ΔX=0. The chosen position of deflector  30  improves the ion packets bypassing of the deflector  30  and of detector  17  rim. Matsuda plates&#39; voltages of the deflectors  30  and  30 R 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  FIG. 11 . 
     Example  112  illustrates the angular divergence of ion rays  113  at ΔU Z =0.5V, while not accounting for ion packets width Z 0 =0 and energy spread δ=0. The Matsuda plate of the reversing deflector  30 R is adjusted (being the same for all examples of  FIG. 11 ) for spatial focusing of initially diverging rays onto detector  17 . 
     Example  114  illustrates ion rays at all accounted spreads of ion beam. Though trajectories look like they are filling most of the drift space, apparently, simulated ion losses are within 10%. 
     Example  116  illustrates the overall mass resolution R M =83,000 achieved in a compact 450×250 mm analyzer while accounting for all realistic spreads of ion beam and ion packets, so as DET=1.5 ns time spread. The embodiment satisfies the previously set goal R&gt;80,000 for resolving major isobars presented in Table 1 for μ=m/z&lt;1000 in LC-MS instruments. N=28 reflections correspond to 14 m flight path and TOF=328 us flight time for μ=1000. Thus, the far-end compensated deflector provides almost twice denser folding of ion trajectory. 
     Yet higher resolutions are expected at larger size instruments, since the flight path L grows as product of instrument dimensions: L=2D X *D Z /L Z , where L Z  is the ion advance per reflection. Embodiments of the invention provide methods of compensated steering, shown in  FIGS. 5, 10 and 11  for keeping low L Z  at dense trajectory folding, suitable for a wide range of the analyzer dimensions D X  and D Z . 
     Referring to  FIG. 12 , an embodiment and simulation example of MRTOF  120  of the present invention is shown, also illustrated by zoom view  121 , and comprising: ion mirrors  122 , separated by a drift space and extended in the Z-direction; an orthogonal accelerator  40  ( 40 OA) of  FIG. 4 , a compensated deflector  30  of  FIG. 3 ; and a pair of compensated deflectors  124  and  125 , similar to  30 , however having different voltage settings of their Matsuda plates for telescopic focusing. 
     In operation, continuous ion beam  41  propagates along the Z-axis at elevated specific energy U Z  (expected from 20 to 50V). A compensated ion injection mechanism is arranged with a wedge accelerator  40  (OA) and compensated deflector  30 , similar to injection mechanism  50 , described in  FIG. 5 . Accelerator  40  with amplifying wedge accelerating field tilts the time front  129  of ion packets to compensate for the time-front tilt of the downstream deflector  30 , thus arranging dense trajectory folding at small inclination angles α 2  while using relatively higher injection energies U Z . Ion packets bypass the OA  40  at larger angle α and then advance in the drift Z-direction within MRTOF along a zigzag ion trajectory at reduced inclination angle α 2 . 
     Embodiment  120  presents yet another novel ion optical solution—a compensated reversing of ion trajectories. The reversing mechanism is arranged with a pair of focusing and defocusing deflectors  124  and  125 , best seen in zoom view  121 , expanded in the Z-direction. Ion packets reach far Z-end of the sector analyzer at an inclination angle α 2 . Deflector  124  with Matsuda plates is set for increasing the inclination angle to α 3  while focusing the packet Z-width within deflector  125 . Deflector  125  is set to reverse ion trajectory with deflection for −2α 3  angle and defocuses the packet from Z 3  to Z 2  by using Z-defocusing quadrupolar field of Matsuda plates in deflector  125 . The focusing factor Z 3 /Z 2  and deflection angles are arranged as 2Z 3 *α 3 =Z 2 (α 3 −α 2 ) to mutually compensate for the time front tilts, as illustrated with simulated dynamics of the time front  129 . 
     Annotations 
     x, y, z—Cartesian coordinates; 
     X, Y, Z—directions, denoted as: X for time-of-flight, Z for drift, Y for transverse; 
     Z 0 —initial width of ion packets in the drift direction; 
     ΔZ—full width of ion packet on the detector; 
     D X  and D Z —used height (e.g. cap-cap) and usable width of ion mirrors 
     L—overall flight path 
     N—number of ion reflections in mirror MRTOF or ion turns in sector MTTOF 
     u—x-component of ion velocity; 
     w—z-component of ion velocity; 
     T—ion flight time through TOF MS from accelerator to the detector; 
     ΔT—time spread of ion packet at the detector; 
     U— potentials or specific energy per charge; 
     U Z  and ΔU Z —specific energy of continuous ion beam and its spread; 
     U X —acceleration potential for ion packets in TOF direction; 
     K and ΔK—ion energy in ion packets and its spread; 
     δ=ΔK—relative energy spread of ion packets; 
     E—x-component of accelerating field in the OA or in ion mirror around “turning” point; 
     μ=m/z—ions specific mass or mass-to-charge ratio; 
     α—inclination angle of ion trajectory relative to X-axis; 
     Δα—angular divergence of ion packets; 
     γ—tilt angle of time front in ion packets relative to Z-axis 
     λ—tilt angle of “starting” equipotential to axis Z, where ions either start accelerating or are reflected within wedge fields of ion mirror 
     θ—tilt angle of the entire ion mirror (usually, unintentional); 
     φ—steering angle of ion trajectories or rays in various devices; 
     ψ—steering angle in deflectors 
     ε—spread in steering angle in conventional deflectors; 
     T|Z, T|ZZ, T|δ, T|δδ, etc; Indexes are defined within the text 
     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.