Mass analyser having extended flight path

Abstract

A time-of-flight or electrostatic trap mass analyzer is disclosed comprising: an ion flight region comprising a plurality of ion-optical elements (30-35) for guiding ions through the flight region in a deflection (x-y) plane. The ion-optical elements are arranged so as to define a plurality of identical ion-optical cells, wherein the ion-optical elements in each ion-optical cell are arranged and configured so as to generate electric fields for either focusing ions travelling in parallel at an ion entrance location of the cell to a point at an ion exit location of the cell, or for focusing ions diverging from a point at the ion entrance location to travel parallel at the ion exit location. Each ion-optical cell comprises a plurality of electrostatic sectors having different deflection radii for bending the flight path of the ions in the deflection (x-y) plane. The ion-optical elements in each cell are configured to generate electric fields that either (i) have mirror symmetry in the deflection plane about a line in the deflection plane that is perpendicular to a mean ion path through the cell at a point half way along the mean ion path through the cell, or (ii) have point symmetry in the deflection plane about a point in the deflection plane that is half way along the mean ion path through the cell. The ion-optical elements are arranged and configured such that, in the frame of reference of the ions, the ions are guided through the deflection plane in the ion-optical cells along mean flight paths that are of the same shape and length in each ion-optical cell.

Claims

1. A time-of-flight or electrostatic trap mass analyzer comprising: an ion flight region comprising a plurality of ion-optical elements for guiding ions through the flight region in a deflection (x-y) plane; wherein said ion-optical elements are arranged so as to define a plurality of identical ion-optical cells; wherein the ion-optical elements in each ion-optical cell are arranged and configured so as to generate electric fields for either focusing ions travelling in parallel at an ion entrance location of the cell to a point at an ion exit location of the cell, or for focusing ions diverging from a point at the ion entrance location to travel parallel at the ion exit location; wherein each ion-optical cell comprises a plurality of electrostatic sectors having different deflection radii for bending the flight path of the ions in the deflection (x-y) plane; wherein the ion-optical elements in each cell are configured to generate electric fields that either (i) have mirror symmetry in the deflection plane about a line in the deflection plane that is perpendicular to a mean ion path through the cell at a point half way along the mean ion path through the cell, or (ii) have point symmetry in the deflection plane about a point in the deflection plane that is half way along the mean ion path through the cell; and wherein the ion-optical elements are arranged and configured such that, in the frame of reference of the ions, the ions are guided through the deflection plane in the ion-optical cells along mean flight paths that are of the same shape and length in each ion-optical cell.

2. The analyser of claim 1, wherein the parallel-to-point focusing, or point-to-parallel focusing, is focusing to the first order approximation.

3. The analyser of claim 1, wherein said ion-optical elements are arranged and configured such that said ions travel through said ion-optical cells such that they are subjected to one or more cycle, wherein each cycle comprises either: (i) said parallel-to-point focusing by one of said cells and then said point-to-parallel focusing by another successive one of said cells; or (ii) said point-to-parallel focusing by one of said cells and then said parallel-to-point focusing by another successive one of said cells.

4. The analyzer of claim 3, wherein said ion-optical elements are arranged and configured such that said ions are subjected to an even, integer number of said cycles.

5. The analyzer of claim 1, wherein said ion-optical elements are arranged and configured such that, in use, said ions pass through each of said ion-optical cells in a spatially achromatic and/or energy isochronous mode to a first order approximation.

6. The analyzer of claim 1, wherein each of said ion-optical cells comprises at least three electrostatic sectors having at least two different deflection radii.

7. The analyzer of claim 1, wherein the ion-optical elements are arranged and configured in any given ion-optical cell such that for ions entering the cell as a parallel beam, the flight time of these ions through the cell is independent, to the second order approximation, of the distance of the ions from a beam ion-optic axis on entering the cell, at least in the deflection (x-y) plane.

8. The analyzer of claim 1, wherein the ion-optical elements are arranged and configured in any given ion-optical cell so as to provide second order focusing of ion flight time with respect to energy spread in ion bunches passing through the cell.

9. The analyzer of claim 1, comprising an ion accelerator for accelerating ions into the flight region and/or an ion detector for detecting ions exiting the flight region.

10. The analyzer of claim 1, comprising a drift electrode arranged and configured to cause ions to drift through the analyzer in a drift (z) dimension perpendicular to the deflection (x-y) plane as the ions travel through the ion-optical elements.

11. The analyzer of claim 10, wherein the ion-optical elements are arranged and configured to cause the ions to have a looped flight path in the deflection plane and to perform a plurality of loops in the deflection plane; and wherein the analyzer comprises one or more drift lens arranged in the flight region so that the ions pass through the one or more drift lens as the ions loop around the deflection plane, and wherein the one or more drift lens is configured to focus the ions in the drift (z) dimension so as to limit the divergence of the ions in said drift dimension as they drift along the drift dimension.

12. The analyzer of claim 11, wherein the analyzer comprises a plurality of said drift lenses spaced along said drift dimension.

13. The analyzer of claim 10, wherein said drift electrode is arranged on a first side, in the drift (z) dimension, of the ion-optical elements and the ion detector is arranged on a second opposite side, in said drift dimension, of the ion-optical elements.

14. The analyzer of claim 10, wherein said drift electrode and ion detector are arranged on a first side, in the drift dimension, of the ion-optical elements and one or more reflector electrode is arranged on a second opposite side, in said drift dimension, of the ion-optical elements; wherein said reflector electrode is configured to reflect ions back in the drift dimension towards the detector.

15. The analyzer of claim 13, wherein one or more reflector electrode is arranged on each side, in the drift dimension, of the ion-optical elements and are configured to reflect the ions along the drift dimension as the ions pass through the ion-optical elements.

16. The analyzer of claim 1, wherein each of the electrostatic sectors is a cylindrical sector having its axis of cylindrical rotation aligned in the dimension orthogonal to the deflection (x-y) plane.

17. The analyzer of claim 1, wherein said analyzer is one of: (i) a time-of-flight mass analyzer comprising an ion accelerator for pulsing ions into said flight region and an ion detector, wherein said flight region is arranged between said ion accelerator and detector such that ions separate according to mass to charge ratio in the flight region; (ii) an open trap mass analyzer configured such that ions enter a first end of the flight region and exit the flight region at a second, opposite end; (iii) an electrostatic trap mass analyzer having an image current detector for detecting ions; or (iv) an electrostatic trap mass analyzer having an ion detector arranged for detecting only a portion of the ions passing the detector.

18. A mass spectrometer comprising an analyzer as claimed in claim 1.

19. A method of time of flight or electrostatic trap mass analysis comprising: transmitting ions through a flight region comprising a plurality of ion-optical elements that guide the ions in a deflection (x-y) plane; wherein said ion-optical elements are arranged so as to define a plurality of identical ion-optical cells; wherein the ion-optical elements in each ion-optical cell generate electric fields that either focus ions travelling in parallel at an ion entrance location of the cell to a point at an ion exit location of the cell, or focus ions diverging from a point at the ion entrance location to travel parallel at the ion exit location; wherein each ion-optical cell comprises a plurality of electrostatic sectors having different deflection radii that bend the flight path of the ions in the deflection (x-y) plane; wherein the ion-optical elements in each cell generate electric fields that either (i) have mirror symmetry in the deflection plane about a line in the deflection plane that is perpendicular to a mean ion path through the cell at a point half way along the mean ion path through the cell, or (ii) have point symmetry in the deflection plane about a point in the deflection plane that is half way along the mean ion path through the cell; and wherein the ion-optical elements guide the ions through the deflection plane in the ion-optical cells along mean flight paths that, in the frame of reference of the ions, are of the same shape and length in each ion-optical cell.

20. A mass analyzer comprising: an ion flight region comprising a plurality of ion-optical elements for guiding ions through the flight region in a deflection (x-y) plane; wherein said ion-optical elements are arranged so as to define a plurality of identical ion-optical cells; wherein the ion-optical elements in each ion-optical cell are arranged and configured so as to generate electric fields for either focusing ions travelling in parallel at an ion entrance location of the cell to a point at an ion exit location of the cell, or for focusing ions diverging from a point at the ion entrance location to travel parallel at the ion exit location; wherein each ion-optical cell comprises a plurality of electrostatic sectors having different deflection radii for bending the flight path of the ions in the deflection (x-y) plane; wherein the ion-optical elements in each cell are configured to generate electric fields that either (i) have mirror symmetry in the deflection plane about a line in the deflection plane that is perpendicular to a mean ion path through the cell at a point half way along the mean ion path through the cell, or (ii) have point symmetry in the deflection plane about a point in the deflection plane that is half way along the mean ion path through the cell; and wherein the ion-optical elements are arranged and configured such that, in the frame of reference of the ions, the ions are guided through the deflection plane in the ion-optical cells along mean flight paths that are of the same shape and length in each ion-optical cell.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Various embodiments will now be described, by way of example only, and with reference to the accompanying drawings in which:

(2) FIG. 1 shows an ion-optical scheme of a prior art sector based instrument in which the ions travel a substantially oval path;

(3) FIG. 2 shows an ion-optical scheme of another prior art sector based instrument in which the ions travel a figure-of-eight path;

(4) FIG. 3 shows a typical ion flight time dependence on the initial y-coordinate of the ions for the analyser of FIG. 2;

(5) FIGS. 4A and 4B show ion-optical schemes of sector based instruments according to embodiments of the present invention having second order focusing of the flight time with respect to spatial ion spread in the deflection plane;

(6) FIGS. 5A and 5B show simulated dependencies of the flight time on the initial y-coordinate of the ions and the angle b, respectively, for the analyser of FIG. 4A;

(7) FIG. 6A shows an ion-optical scheme of a sector based instruments according to an embodiment of the present invention having cylindrical sectors and periodic lenses for confining ions in the z-direction, and FIG. 6B shows an embodiment having an end deflector for reversing the direction of the ions in the z-direction;

(8) FIG. 7 shows a simulated time peak for an analyser according to FIG. 4A; and

(9) FIG. 8 shows an ion-optical scheme of an embodiment of the present invention having five sectors per cell; and

(10) FIG. 9 shows an ion-optical scheme of an embodiment of the present invention having three sectors and two lenses in each cell.

DETAILED DESCRIPTION

(11) As described above, folded flight path time of flight (TOF) mass spectrometers are known in which electrostatic sectors are used to bend the flight paths of the ions so that a relatively long TOF flight path can be provided in a relatively small instrument.

(12) Various instrument geometries and ion flight paths of folded flight path TOF mass spectrometers will be described herein using Cartesian coordinates. The Cartesian coordinates are described herein such that the plane in which the electrostatic sectors bend the ion path are defined as the x-y plane, where x is the position along the ion optic axis (i.e. along the mean flight path of the ions), and y is perpendicular to this ion optic axis. The z-dimension is orthogonal to the x-y plane.

(13) FIG. 1 shows a schematic of the ion-optical scheme of part of a prior art folded flight path TOF mass spectrometer according to Sakurai et al (Nucl. Instrum. Meth. A427, 1999, 182-186). The spectrometer comprises ion-optical elements arranged so as to bend the ion path. The ion-optical elements comprise six electrostatic sectors 2-10 arranged so as to bend the ion path so that the ions are guided in a closed loop. A drift region is provided between each pair of adjacent sectors. Each sector is torroidal and the sectors have the same deflection radius. Electrostatic potentials are applied to the electrodes of each of the sectors so as to bend the flight paths of the ions so that the ions travel into the downstream electrostatic sector and continue around the closed path.

(14) As can be seen from FIG. 1, ions pass into the first electrostatic sector 2 along the ion optical axis x. The ions diverge in the y-direction as they travel towards the first sector 2. The first sector 2 bends the ion path and directs the ions into the second sector 4. The second sector bends the ion path and directs the ions into the third sector 6. The ions emerge from the third sector 6 and are focused in the y-direction to a point 14 before diverging again in the y-direction and entering the fourth sector 8. The fourth sector 8 bends the ion path and directs the ions into the fifth sector 10. The fifth sector 10 bends the ion path and directs the ions into the sixth sector 12. The ions emerge from the sixth sector 12 and are focused in the y-direction to a point 16 before diverging again in the y-direction and re-entering the first sector 2. It can therefore be seen that the use of sectors 2-12 enables the TOF path length to be relatively long within a relatively small instrument.

(15) However, as described in the Background section, conventional sector field folded flight path TOF mass spectrometers, such as that shown in FIG. 1, have limited spatial acceptance since they possess only first order TOF focusing with respect to the spatial spread of the ions in the plane that the sectors deflect the ions (i.e. the x-y plane). When such conventional instruments are described as having isochronous ion transport this actually means, in practice, first order isochronous ion transport at small spatial acceptance, as described by Sakurai et al (Int. J. Mass Spectrom. Ion Proc., 63, 1985, 273-287). This is because, unlike ion mirror-based folded flight path TOF mass spectrometers, sector field based instruments have a curved ion optic axis and so multiple geometrical conditions are required to be satisfied to reach first order isochronicity. The number of second order aberrations is even larger, when accounting for mixed geometrical-chromatic TOF aberrations, and ion optical designers have conventionally been unable to compensate for these aberrations.

(16) The analysis of aberrations can be assisted by considering the closed loop motion of the ions as periodic motion of the ions through a sequence of identical ion-optical cells, wherein each cell is considered to comprise a set of sector fields (and may optionally also comprise other ion optical elements such as ion lenses for focusing ions). For example, in FIG. 1 the three sectors 2-6 on the right side may be considered to form a first ion-optical cell and the three sectors 8-12 on the left side may be considered to form a second ion-optical cell. Each cell also has mirror symmetry about a line that is perpendicular to the mean ion path through the cell at the point half way along the mean ion path through the cell (in the x-y plane of deflection).

(17) Ion trajectory projections in the x-y deflection plane can be described at each coordinate x along the ion optic axis by position vectors {y, b, , }, where: b=dyldx=tan , being the inclination angle of ion trajectory projection to the ion optic axis; =(KK.sub.0)/K.sub.0, wherein is the relative deviation of the ion kinetic energy K component in the x-y deflection plane and the kinetic energy K.sub.0 component in the deflection plane for ions moving along the ion optic axis; and =tt.sub.0, where r is the difference between the flight time t of the considered ion and the flight time t.sub.0 of an ion moving along the optic axis or mean trajectory.

(18) The transformation between the position vectors performed by one cell extending from the point x=x.sub.0 and x=x.sub.1 can be described by a transfer matrix M.sup.(1): {y.sub.1, b.sub.1, .sub.1, .sub.1}=M.sup.(1){y.sub.0, b.sub.0, .sub.0, .sub.0}, where the components with the subscript 1 correspond to position x=x.sub.1 and the components with the subscript 0 correspond to position x=x.sub.0. In this case, the transport of ions through N cells is described by a product of cell transfer matrices, i.e. as follows:
M.sup.(N)=[M.sup.(1)].sup.N(1)

(19) It is important to emphasize that equation 1 above requires that all cells have identical electric field distributions to each other, as viewed by the ions. This requires that the mean path of the ions be bent in the same manner by each cell, as viewed from the frame of reference of the ions. For example, in FIG. 1 the first cell formed of sectors 2-6 causes the mean path of the ions to be bent to the right as the ions travel through the first cell (from the ions' frame of reference), and the second cell formed by sectors 8-12 also causes the mean path of the ions to be bent in the same manner to the right as the ions travel through the second cell (from the ions' frame of reference).

(20) The transformation of components of the position vector by one cell can be represented by aberration expansions, as follows:
y.sub.1=Y.sub.yy.sub.0+Y.sub.bba.sub.0+Y.sub.b.sub.0+Y.sub.yyy.sub.0.sup.2+Y.sub.yby.sub.0b.sub.0+Y.sub.bbb.sub.0.sup.2+Y.sub.yy.sub.0.sub.0+Y.sub.bb.sub.0.sub.0+Y.sub..sub.0.sup.2+ . . . , b=B.sub.yy.sub.0+B.sub.bb.sub.0+B.sub..sub.0+B.sub.yyy.sub.0.sup.2+B.sub.yby.sub.0b.sub.0+B.sub.bbb.sub.0.sup.2+B.sub.yy.sub.0.sub.0+B.sub.bb.sub.0.sub.0+B.sub..sub.0.sup.2+ . . . , .sub.1=T.sub.yy.sub.0+T.sub.bb.sub.0+T.sub..sub.0+T.sub.yyy.sub.0.sup.2+T.sub.yby.sub.0b.sub.0+T.sub.bbb.sub.0.sup.2+T.sub.yy.sub.0.sub.0+T.sub.bb.sub.0.sub.0+T.sub..sub.0.sup.2+ . . . , .sub.1=.sub.0.

(21) The transformation up to a particular order of aberration expansion can be expressed by the transfer matrix of this order, which is expressed through the aberration coefficients up to the same order. The general form of the second order transfer matrix is presented in the book Optics of charged particles by H. Wollnik (Acad. Press, Orlando, 1987).

(22) It is relatively easy to select the combination of sector fields and the drift intervals between them so as to eliminate the first order dependence of time of flight on ion energy (i.e. T.sub.=0). In order to make a cell first order isochronous (T.sub.y=T.sub.b=0) it is also required to make the cell symmetric, either by mirror symmetry or point symmetry. The above-mentioned three conditions for first order focusing are satisfied in prior art sector based instruments. Note that due to the so-called symplectic conditions, a first order isochronous cell is always first order spatially achromatic: Y.sub.=B.sub.=0, and vice versa.

(23) Referring back to the prior art instrument of FIG. 1, the arrangement shows sector fields and sample ion trajectories with different initial y-coordinates and different energies. The ions follow a closed oval path in the analyzer by passing through identical 180-degree deflecting cells. The geometric condition after each cell is Y.sub.b=0, but the flight time focusing is performed only in the first order approximation and the aberration coefficients T.sub.yy and T.sub.bb remain.

(24) FIG. 2 shows a schematic of the ion-optical scheme of a prior art folded flight path TOF mass spectrometer according to MULTUM II by Toyoda et al (J. Mass Spectrom. 38, 2003, 1125-1142). The instrument comprises ion-optical elements arranged so as to guide ions in a figure-of-eight flight path. More specifically, the instrument comprises four electrostatic sectors 22-28 and drift regions between adjacent pairs of sectors, arranged so as to guide ions in a figure-of-eight flight path. Each sector has a 157-degree deflecting toroidal sector field. The arrangement of sector fields and sample ion trajectories for ions having different initial y-coordinates and different energies are shown. The motion of the ions will now be described in ions' frame of reference. As can be seen from FIG. 2, ions pass into the first electrostatic sector 22 along the ion optical axis x. The ions travel parallel, rather than diverging in the y-direction, as they travel towards the first sector 22. The first sector 22 bends the ion path to the right and directs the ions into the second sector 24. The second sector 24 bends the ion path to the left and directs the ions into the third sector 26. The ions emerge from the second sector 24 and are focused in the y-direction to a point 23 before diverging again in the y-direction and entering the third sector 26. The third sector 26 bends the ion path to the left and directs the ions into the fourth sector 28. The fourth sector 28 bends the ion path to the right. The ions emerge from the fourth sector 28 travelling parallel to each other, rather than diverging or converging in the y-direction, and then re-enter the first sector 22.

(25) As will be described in more detail below, the inventors have recognized that it is necessary for each cell to perform parallel-to-point (or point-to-parallel) of the ion beam in order to avoid certain aberrations. Accordingly, the first sector 22 and second sector 24 may be considered to form a first ion-optical cell that provides parallel-to-point focusing of the ions in the x-y deflection plane, thus eliminating aberration coefficients Y.sub.y=B.sub.b=0. The third sector 26 and fourth sector 28 may be considered to form a second ion-optical cell that provides point-to-parallel divergence of the ion beam in the x-y deflection plane. However, as described above, equation 1 requires that all ion-optical cells have identical electric field distributions to each other, as viewed by the ions. In the analyzer of FIG. 2, the ions cannot be considered as passing through consecutive identical cells that meet the requirements of equation 1 above (and each having point-to-parallel or parallel-to-point focusing), because the orientation of the coordinate frame reverses after each cell. That is, in the frame of reference of the ions, the first cell consisting of sectors 22 and 24 causes the mean path of the ions to be bent firstly to the right and then to the left; whereas in contrast the second cell consisting of sectors 26 and 28 causes the mean path of the ions to be bent firstly to the left and then to the right. The ions are therefore guided in different manners by the first and second cells. Therefore, the cell symmetry condition described above in relation to equation 1 is violated and the second order flight time aberrations cannot be eliminated, even if ions are passed along the full figure-of-eight like path once or several times. Furthermore, in each zigzag cell (i.e. the combination of sectors 22 and 24, or the combination of sectors 26 and 28) the second order flight time aberrations T.sub.yy and T.sub.bb are not eliminated.

(26) FIG. 3 is a graph showing a typical time dependence on the initial y-coordinate of the ion for the prior art analyzer of FIG. 2, as simulated by the computer program SIMION 8.0. The calculated value of the second order coefficient is (T|yy)/t.sub.0=29.6 m.sup.2 which is in reasonable agreement with the data given by Toyoda et al (J. Mass Spectrom. 38, 2003, 1125-1142). This shows that the prior art arrangement of FIG. 2 does not suffers from higher order aberrations.

(27) Therefore, it will be appreciated that the prior art instruments provide first order focusing only and that second order aberration coefficients are not able to be fully eliminated.

(28) The inventors have recognized that using a special combination of symmetry and focusing conditions in sector field based folded flight path TOF mass spectrometers, and simultaneously using electrostatic sectors with different radii, allows the ion flight time to be independent of spatial coordinates as well as independent of mixed spatial-chromatic terms in the sector field deflection plane (i.e. the x-y plane) in the second order approximation, thus considerably increasing spatial acceptance of the instrument in this plane.

(29) Various embodiments of the present invention will now be described, which allow full independence of ion flight time from spatial coordinates in the x-y deflection plane, i.e. to eliminate all second order coefficients for the flight time expansion except for T.sub..

(30) As in the prior art instruments described above, it remains important for the analyzers according to the embodiments of the present invention to fulfill first order isochronicity. As described above in relation to equation 1, the sectors of the analyzers according to the embodiments of the present invention are arranged such that the motion of the ions in the x-y deflection plane can be considered to be a motion through a sequence of identical ion-optical cells.

(31) Each cell is symmetric with respect to its middle, and the symmetry may be mirror symmetry such that the transfer matrix M.sup.(1) obeys the relationship:
M.sup.(1)=P[M.sup.(1)].sup.1P(2a)
where P is the reversing operator: P{y, b, , }={y, b, , }.

(32) Alternatively, the symmetry may be point symmetry such that the transfer matrix M.sup.(1) obeys the relationship:
M.sup.(1)=RP[M.sup.(1)].sup.1PR(2b)
where R is the rotating operator: R{y, b, , }={y, b, , }.

(33) The sectors are arranged and configured such that each cell is first order isochronous, as in prior art instruments, such that:
T.sub.=T.sub.y=T.sub.b=0(3)

(34) The electrostatic fields in each cell are tuned such that, in the first order approximation, ions entering the cell as a parallel beam will be focused to a point at the exit (i.e. parallel-to-point focusing). As a result of the cell symmetry given by equations 2a or 2b above, this also means that the electrostatic fields in each cell are tuned such that, in the first order approximation, ions entering the cell that diverge from a point will be focused to a parallel beam at the exit (i.e. point-to-parallel focusing).

(35) As each cell provides parallel-to-point focusing in the first order approximation (for ions entering the cell as a parallel beam), this leads to:
Y.sub.y=0(4)

(36) As each cell provides point-to-parallel focusing in the first order approximation (for ions diverging from a point and entering the cell), this leads to:
B.sub.b=0(5)

(37) The condition of equation 4 also leads to stable, indefinite ion confinement of ions in the x-y plane, since it satisfies the stability condition 1<Y.sub.y<1. Note that some prior art sector systems such as that of FIG. 1 violate the stability condition since Y.sub.y=1.

(38) The inventors have recognized that in sector based instruments the compensation of at least one second order aberration (e.g. fulfilling the condition T.sub.yy=0) can be reached by adding another degree of flexibility, such as by using a cell in which there are sector fields with two different deflection radii. As it is required for each cell to be symmetric, a cell having sectors of two different deflection radii must comprise at least three sectors.

(39) FIGS. 4A and 4B show ion-optical schemes of embodiments of the present invention with second order focusing of the flight time with respect to spatial ion spread in the x-y deflection plane. These instruments are capable of compensating for the second order time-of-flight aberration T.sub.yy such that:
T.sub.yy=0(6)

(40) The ion-optical elements in the analyzer of FIG. 4A comprise six electrostatic sectors 30-35 arranged so as to bend the ion path so that the ions are guided in a substantially oval closed loop. A drift region is provided between each pair of adjacent sectors. Electrostatic potentials are applied to the electrodes of each of the sectors so as to bend the flight paths of the ions so that the ions travel into the downstream electrostatic sector and continue around the closed path. The motion of the ions will now be described in the frame of reference of the ions. As can be seen from FIG. 4A, ions pass as a parallel ion beam into the first electrostatic sector 30 along the ion optical axis x. The first sector 30 bends the ion path to the right and directs the ions into the second sector 31. The second sector 31 bends the ion path to the right and directs the ions into the third sector 32. The ions emerge from the third sector 32 and are focused in the y-direction to a point 36 before diverging again in the y-direction and entering the fourth sector 33. The fourth sector 33 bends the ion path to the right and directs the ions into the fifth sector 34. The fifth sector 34 bends the ion path to the right and directs the ions into the sixth sector 35. The ions emerge from the sixth sector 35 as a parallel beam and re-enter the first sector 30. It can therefore be seen that the use of sectors 30-35 enables the TOF path length to be relatively long within a relatively small instrument.

(41) The projection of the ion optic axis to the xy-plane forms a closed substantially oval path. Ion motion through the analyzer can be considered as the transport of ions through a sequence of identical cells, each cell deflecting the mean ion path by 180 degrees. More specifically, sectors 30-32 can be considered to form a first cell and sectors 33-35 can be considered to form a second cell. The sectors in each cell are arranged and configured to perform parallel-to-point focusing of the ions (or point-to-parallel focusing). Each cell also has mirror symmetry about a line that is perpendicular to the mean ion path through the cell at the point half way along the mean ion path through the cell (in the x-y plane of deflection).

(42) In order to compensate for at least one second order aberration, each cell comprises sectors having different deflection radii. Considering the first cell, the radius of the optic axis in the second sector 31 is 1.55 times larger than the radius of the optic axis in each of the first and third sectors 30,32. The ion deflecting angle of each of the first and third sectors 30,32 is 49 degrees. The ion deflecting angle of the second sector 31 is 82 degrees. Similarly, in the second cell, the radius of the optic axis in the fifth sector 34 is 1.55 times larger than the radius of the optic axis in each of the fourth and sixth sectors 33,35. The ion deflecting angle of each of the fourth and sixth sectors 33,35 is 49 degrees. The ion deflecting angle of the fifth sector 34 is 82 degrees. The ion deflecting angles, deflection radii, and lengths of drift spaces between the sectors are chosen such that in each cell the ion-optical conditions of equations 3-5 above are satisfied, i.e. Y.sub.y=B.sub.b=0 and T.sub.y=T.sub.b=T.sub.6=0. Additionally, the use of sectors having different deflection radii in each cell enables the system to compensate for the second order aberration of equation 6 above, i.e. T.sub.yy=0.

(43) FIG. 4B shows an embodiment that substantially corresponds to that of FIG. 4A, except that the sectors in FIG. 4B have different lengths, deflection radii and deflection angles. Like elements have been given the same reference numbers in FIGS. 4A and 4B. Considering the first cell in FIG. 4B, the radius of the optic axis in each of the first and third sectors 30,32 is 2.4 times larger than the radius of the optic axis the second sector 31. The ion deflecting angle of each of the first and third sectors 30,32 is 25 degrees. The ion deflecting angle of the second sector 31 is 130 degrees. Similarly, in the second cell, the radius of the optic axis in each of the fourth and sixth sectors 33,35 is 2.4 times larger than the radius of the optic axis in the fifth sector 34. The ion deflecting angle of each of the fourth and sixth sectors 33,35 is 25 degrees. The ion deflecting angle of the fifth sector 34 is 130 degrees. The ion deflecting angles, deflection radii, and lengths of drift spaces between the sectors are chosen such that in each cell the ion-optical conditions of equations 3-5 above are satisfied, i.e. Y.sub.y=B.sub.b=0 and T.sub.y=T.sub.b=T.sub.6=0. Additionally, the use of sectors having different deflection radii in each cell enables the system to compensate for the second order aberration of equation 6 above, i.e. T.sub.yy=0.

(44) Although two specific examples have been described in relation to FIGS. 4A and 4B, it will be appreciated that embodiments of the present invention may have other values of deflection radii ratio and/or deflection angles.

(45) The inventors have realized that the parallel-to-point (and point-to-parallel) geometric focusing described above in relation to equations 4 and 5 within a symmetric cell according to equations 2a or 2b has the important consequence that two second order aberration coefficients for the flight time expansion are proportional to each other, i.e. that:
T.sub.yy=B.sub.y.sup.2T.sub.bb(7)
Thus, the compensation of one second order aberration T.sub.yy=0 as described in relation to equation 6 automatically compensates for another proportional second order aberration such that:
T.sub.bb=0(8)

(46) Accordingly, it has been recognized that each identical cell of the system is now able to be first order isochronous in accordance with equation 3, provide parallel-to-point focusing (or point-to-parallel focusing) according to equations 4 and 5, and is able to compensate for two second order aberrations according to equations 6 and 8.

(47) The inventors have also recognized that fulfilling the above three conditions automatically allows the elimination of the rest of the second order time of flight aberrations (except for T.sub.) after passing the ions through a number of the cells. This can be shown by calculating geometric and time of flight coefficients of aberration expansions after several cells by using multiplication of the cell transfer matrices. Indeed, considering equations 4 and 5 for a single cell, the multiplication of transfer matrices as in equation 1 above gives the following first order geometric transfer matrix coefficients after two cells:
Y.sub.y.sup.(2)=B.sub.b.sup.(2)=1,B.sub.y.sup.(2)=Y.sub.b.sup.(2)=0(9)

(48) The same multiplication for the time of flight coefficients shows that all of the elimination conditions of equations 3, 6 and 8 above, which are achieved for a single cell, also remain valid after two cells, i.e.:
T.sub..sup.(2)=T.sub.y.sup.(2)=T.sub.b.sup.(2)=T.sub.yy.sup.(2)=T.sub.bb.sup.(2)=0(10)

(49) Also, due to the conditions of equations 4 and 5 above, the mixed geometric aberration coefficient T.sub.yb is eliminated after the ions pass through two identical cells. i.e.:
T.sub.yb.sup.(2)=0

(50) By multiplying two identical second order transfer matrices for two cells, it is also apparent that all time of flight coefficients that are eliminated after the ions pas through two cells (see equations 10 and 11) remain eliminated after the ions pass through four cells, i.e.:
T.sub..sup.(4)=T.sub.y.sup.(4)=T.sub.b.sup.(4)=T.sub.yy.sup.(4)=T.sub.bb.sup.(4)=T.sub.yb.sup.(4)=0(12)

(51) Also, due to the conditions in equation 9, the mixed geometric-chromatic aberration coefficients are also eliminated after the ions pass through each 4 cells, i.e.:
T.sub.y.sup.(4)=T.sub.b.sup.(4)=0.(13)

(52) Thus, it is clear from equations 12 and 13 that after ions pass through four successive cells all second order aberration coefficients for the flight time expansion, except for T.sub., are eliminated.

(53) In order to illustrate the ability of an embodiment of the present invention to compensate for aberrations, Table 1 below is presented. Table 1 shows the aberration coefficients after the ions pass through one, two and four cells in the instrument of FIG. 4A. The passage of ions through two sectors is one loop around the instrument shown in FIG. 4A. The unit for the coordinate y is metres and the flight path length per loop is 1.95 m.

(54) TABLE-US-00001 TABLE 1 Coefficient 1 cell (half loop) 2 cells (one loop) 4 cells (two loops) Y.sub.y 0 1 1 Y.sub.b 0.091 0 0 B.sub.y 11.0 1 1 B.sub.b 0 0 0 T.sub.y/t.sub.0 0 0 0 T.sub.b/t.sub.0 0 0 0 T.sub./t.sub.0 0 0 0 T.sub.yy/t.sub.0 0 0 0 T.sub.yb/t.sub.0 4.60 0 0 T.sub.bb/t.sub.0 0 0 0 T.sub.y/t.sub.0 4.82 0.025 0 T.sub.b/t.sub.0 0.434 0.436 0 T.sub./t.sub.0 0.084 0.084 0.084

(55) It can be seen from Table 1 that the only non-vanishing second order aberration after the ions pass through four successive cells is T.sub./t.sub.0, and even then the value of this aberration is about 3 times smaller than in the prior art analyzer of FIG. 2.

(56) The system of FIG. 4B is also first order isochronous and second order spatially isochronous, meaning that all of the aberration coefficients listed in Table 1 are zero, except T.sub./t.sub.0, which is 0.276.

(57) FIG. 5A is a graph showing the simulated flight time dependence on the initial y-coordinate of the ion for the analyzer of FIG. 4A. The relative time deviation /t.sub.0 is within 10.sup.6 in the intervals y=3.5 mm. The dependence t(y) is dominated by a 4.sup.th order term. It can be seen by comparing FIG. 5A to FIG. 3 that the flight time dependence on the initial y-coordinate is improved for the analyzer of FIG. 4A over the analyzer of FIG. 2.

(58) FIG. 5B is a graph showing the simulated flight time dependence on the angle =arctan (b) for the analyzer of FIG. 4A. The relative time deviation /t.sub.0 is within 2 degrees. The dependence t(b) is dominated by a 3.sup.rd order term.

(59) In the embodiments described above, the ions may be pulsed into the analyzer and guided along a flight path defined by the sectors. The sectors bend the flight path and hence allow a relatively long flight path to be provided in a relatively small space. When the ions have travelled a desired flight path length, e.g. when the ions have travelled through a desired number of cells of the analyzer, the ions are directed onto a detector. The duration of time between an ion being pulsed into the analyzer and the ion being detected at the detector can be used to determine the mass to charge ratio of that ion, as in conventional TOF mass analyzers. As the instruments of the present invention have a relatively long flight path length, the mass resolution of the instrument may be relatively high. The configuration of the sectors increases the flight path length per unit size of the instrument, whilst eliminating second order aberrations that would otherwise deteriorate mass analysis.

(60) The motion of the ions around the analyzer has only been described in the x-y deflection plane. When the ions have travelled the desired flight path length they may be deflected, e.g. in a direction perpendicular to the mean flight path, onto the detector. Alternatively, the ions may be caused to drift in a direction perpendicular to the x-y plane (i.e. the z-direction) as they pass around the analyzer in the x-y plane. The ion detector may be arranged at a position in the z-direction such that after a predetermined flight path (e.g., after a predetermined number of loops in the x-y place) the ions have travelled a distance in the z-direction such that the ions impact on the ion detector.

(61) FIG. 6A shows a perspective view of a schematic in which ions travel in the x-y plane and also travel in the z-direction. The analyser is of substantially the same form as that described in relation to FIGS. 4A-4B and like elements have been given like reference numbers. However, FIG. 6A also illustrates that the ions may drift in the z-direction as they loop around the analyser through the cylindrical sectors. Ions are pulsed into the first sector 30 along axis 60. Ions may be pulsed into the sector 30 at an angle such that they drift in the z-direction, or a drift electrode may be provided that urges the ions in the z-direction. The first sector 30, second sector 31 and third sector 32 form a first cell that bends the flight path of the ions, in the same manner described in relation to FIGS. 4A-4B. The fourth sector 33, fifth sector 34 and sixth sector 35 form a second cell that bends the flight path of the ions, in the same manner described in relation to FIGS. 4A-4B. The ions then re-enter the first sector 30 and continue around the analyser in the x-y plane for another loop. This looping in the x-y plane is repeated as the ions drift along the z-direction until the ions exit the fifth sector 35 along exit axis 62 and impact on ion detector 64.

(62) The analyser may also comprise periodic drift lenses 66 for confining ions in the z-direction. The drift lenses 66 focus ions in the z-direction and thus maintain the ion packets at a desired x-position as they loop around the analyzer in the x-y plane. The electric fields of the periodic lenses 64 may not focus or disperse the ions in the x-y plane but, e.g. by inducing an accelerating or retarding field, allow tuning a position of the final time focus at the detector 64. Note that in contrast to periodic lenses used in ion mirror based multi-reflecting time of flight mass spectrometers, in sector field instruments ions can pass through periodic lenses only once per loop. Although z-direction periodic lenses 66 are only shown between sectors 32 and 33 it is contemplates that these lenses, or additional such lenses, may be arranged between any other pair of sectors such as between sectors 30 and 35. Periodic lenses may be arranged between more than one pair of sectors so as to provide for tighter ion confinement in the z-direction. The periodic lenses may produce a two-dimensional focusing field, may be coaxial lenses, or may have an adjustable quadrupolar field component for adjustments of ion trajectories in the x-y plane.

(63) FIG. 6B shows an embodiment that is substantially the same as that shown in FIG. 6A, except that it additionally has a reflecting electrode 68 for reflecting the ions back in the z-direction. The ions are pulsed into the analyser along path 60, travel around the x-y plane and along the z-direction in the same manner as described in relation to FIG. 6A. However, rather than striking ion detector 64 at the z-end of the device, the ions are reflected back in the z-direction by reflecting electrode 68. As the ions drift back along the device in the x-direction they continue to loop around the x-y plane until they exit the analyser along path 62 and impact on ion detector 64. It will be appreciated that this embodiment doubles the ion flight path length as compared to the embodiment of 6A, without increasing the physical dimensions of the instrument or restricting mass range.

(64) FIG. 7 shows a simulated time peak after 20 loops of ions in an analyser of FIG. 4A having a 1.95 m long path per loop, i.e. a full path length of 39 m. The ion packet was simulated as a Gaussian profile having a 2 ns initial time FWHM width, y=2 mm, b=1 deg, a 35 mmmrad phase space in the X-Y deflection plane, a m/z=1000 amu, a mean kinetic energy of K=6 keV, and an energy spread K=30 eV. After passing 20 loops the packet time width increases from 2 ns to 2.75 ns, i.e. a mass resolving power R=200 000 is achieved. Comparative simulation shows that achieving the same resolving power in prior art sector-based spiral flight path instruments would require reducing the phase space in the x-y plane by an order of magnitude. Thus, embodiments of the present invention are able to provide at least an order of magnitude improved product of phase space acceptance and resolving power. Also, an order of magnitude higher spatial acceptance means at least an order of magnitude higher space charge tolerance of the analyzer, since ion packets are known to expand spatially under own space charge.

(65) At a simulated resolving power of R=200,000, embodiments of the present invention have an acceptance over 30 mm x mrad, while prior art sector based instruments have an acceptance of less than 3 mm x mrad. The embodiments of the present invention therefore accommodate ion sources having relatively great emittances, such as SIMS and DE MALDI sources, which tend to have emittances between 3 and 10 mm x mrad. The embodiments are also able to accommodate radio-frequency linear ion traps well, which tend to have larger emittances, e.g., emittances of at least 10 mm x mrad. The embodiments also have a relatively high tolerance to space charge effects (the analyzer tolerates ion packets spatial expansion), and an ability to reach higher resolving powers for ion sources with limited emittance. Compact analyzers or ion guides may also be used to match an ion sources emittance with the analyzer acceptance.

(66) FIG. 8 shows an ion-optical scheme according to an embodiment of the present invention with second order focusing of the flight time with respect to both energy and spatial ion spread in the x-y deflection plane. The analyser is substantially the same as that shown and described in relation to FIG. 4A, except that the ion-optical elements in the first cell comprise five cylindrical sectors 80-84 rather than three sectors, and the ion-optical elements in the second cell comprise five cylindrical sectors 85-89 rather than three sectors. The deflection angle of each of sectors 82 and 87 is 64 degrees, and the deflection angle of each of the other sectors is 29 degrees. The deflection radius of each of sectors 82,87 is 1.9 times larger than the deflection radius of each of sectors 80,84,85,89. The deflection radius of each of sectors 81,83,86,88 is 2.1 times larger than of each of sectors 80,84,85,89.

(67) FIG. 9 shows another ion-optical schemes according to an embodiment of the present invention with second order focusing of the flight time with respect to both energy and spatial ion spread in the x-y deflection plane. The analyser is substantially the same as that shown and described in relation to FIG. 4A, except that the ion-optical elements comprise sectors and 2D lenses. In each cell the three sectors are arranged between a pair of 2D lenses for focussing the ions in the x-y plane. More specifically, in the first cell the three sectors 91-93 are arranged between 2D lenses 90 and 94, and in the second cell the three sectors 96-98 are arranged between 2D lenses 95 and 99. In this embodiment, the angle of deflection of each of the sectors 91, 93, 96 and 98 is 50 degrees, and the angle of deflection of each of sectors 92,97 is 80 degrees. The deflection radius of each of sectors 92,97 is 1.2 times larger than the deflection radius of each of sectors 91, 93, 96 and 98.

(68) Although the present invention has been described with reference to preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the scope of the invention as set forth in the accompanying claims.