High performance gridless ion mirrors for multi-reflection time-of-flight and electrostatic trap mass analyzers

International Journal of Mass Spectrometry 426 (2018) 1–11

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High performance gridless ion mirrors for multi-reflection time-of-flight and electrostatic trap mass analyzers Mikhail I. Yavor a,∗ , Timofey V. Pomozov a , Sergey N. Kirillov b , Yuri I. Khasin b , Anatoly N. Verenchikov b a b

Institute for Analytical Instrumentation RAS, 190103 St. Petersburg, Russian Federation MSC-CG D.O.O., 85000 Bar, Montenegro

a r t i c l e

i n f o

Article history: Received 25 November 2017 Received in revised form 18 December 2017 Accepted 7 January 2018 Available online 12 January 2018 Keywords: Flight time Mass analyzer Ion mirror Time focusing Aberrations Quasi-planar mirror

a b s t r a c t The paper summarizes original developments of gridless ion mirrors for high-resolution multi-reflection time-of-flight mass spectrometers (MR TOF MS). Optimized mirror geometries and electrostatic field distributions reach up to the 5th order isochronicity with respect to the energy spread and up to the 3rd order full isochronicity per energy, spatial and angular spreads of ion packets. Using a retarding focusing field at the mirror entrance doubles the ion transport energy at limited highest voltages. In planar analyzers with a zig-zag ion path, quasi-planar mirrors eliminate the 2nd order dependence of the flight time on the ion packet width in the drift direction. Improved MR TOF analyzers of 1 m size provide well over one million aberration limit at realistic ion packets parameters past orthogonal accelerators. Because of high order isochronicity the aberration limit rapidly grows with the analyzer size or when using narrower ion packets. In experiments, improved analyzers with one meter size demonstrate up to 300 000 mass resolving power at the full mass range and 500 000 at the restricted mass range. Improved ion mirrors with two-dimensional electrostatic fields are applicable for TOF MS, electrostatic traps and open electrostatic traps in planar and hollow cylindrical geometries. © 2018 Elsevier B.V. All rights reserved.

1. Introduction In 1956 Alikhanov [1] proposed reflecting ions in electrostatic fields to reduce the time per energy spread. Mamyrin [2] implemented a two-stage ion mirror in a time-of-flight (TOF) analyzer and demonstrated yet another advantages of ion mirrors – folding ion trajectories for a longer flight path and using strong ion accelerating fields for reducing the so-called “turn-around time” in ion sources. Since then an electrostatic ion mirror became a key ion-optical element in TOF mass spectrometers (MS). Mamyrin’s dual stage ion mirror with grid covered electrodes still remains very popular in commercially produced TOF MS. Grids have to be extremely fine to minimize the angular ion scattering and geometrical ion losses, which poses technological challenge in singly reflecting TOF MS and prevents their use in further described multireflecting time-of-flight (MR TOF) mass analyzers. To overcome grid limitations, multiple attempts were made to design gridless ion mirrors. First gridless mirrors were intended

∗ Corresponding author. E-mail address: [email protected] (M.I. Yavor). https://doi.org/10.1016/j.ijms.2018.01.009 1387-3806/© 2018 Elsevier B.V. All rights reserved.

for one-stage reflectron TOF MS and mostly tried to copy the field structure of a standard reflectron mirror [3–5]. After an MR TOF MS with multiple gridless mirrors was proposed by Wollnik [6], several ion mirror designs for such spectrometers have been developed [7–9]. However, up to a certain point gridless mirrors provided a limited set of ion-optical properties: a geometric focusing and the first order TOF focusing with respect to the ion energy spread. In alternative parabolic ion mirrors [10–13] with the quadratic distribution of the electrostatic potential the perfect time per energy focusing is negated by a spatial ion defocusing and a small spatial acceptance of ion mirrors. The ion-optical quality of gridless ion mirrors has been substantially improved in 2004 [14,15]. Authors proposed, simulated, and experimentally tested a high performance gridless planar ion mirror controlled by four electrode voltages. The mirror provides for the third-order TOF focusing with respect to the ion energy spread and for the overall and complete second-order TOF focusing with respect to the spatial, angular and energy ion spreads, which resulted in the energy acceptance of 6% and the spatial acceptance of 6 mm × 15 mrad at 30 mm mirror window height. The mirror has been developed for reaching the mass resolving power of R = 100 000 at the full mass range and for R = 200 000 at

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Fig. 1. Ion motion in MR TOF mass analyzers with different types of ion mirrors: (A) axially symmetric, (B) planar, (C) hollow cylindrical, and (D) pancake ones. In all drawings parts of the mirrors are cut out to show electrode sections. In case (B) an array of periodic 2D lenses, refocusing ions in the Z-direction, is shown between the mirrors.

a restricted mass range [16]. An axially-symmetric ion mirror with similar ion-optical design was also implemented into the shuttletype MR TOF MS at JLU Giessen [17,18]. For 133 Cs+ ions after a flight time of 49 ms the latter MR TOF MS experimentally achieved 600 000 mass resolving power. The present paper summarizes further original developments and improvements of high performance gridless ion mirrors for MR TOF MS. Further improved ion optical quality allows increasing the energy and spatial acceptance of the MR TOF mass analyzers, thus increasing their mass resolving power and/or sensitivity per analyzer size. In particular, a range of ion mirrors with the full third order isochronicity and up to the fifth order time per energy focusing has been proposed in Refs. [19,20]. The ion-optical quality of such mirrors has been verified in experimental tests, demonstrating the mass resolving power of 300 000 at the full mass range and up to 500 000 at a restricted mass range [21]. Ion mirrors discussed in the paper may be applied to a variety of isochronous electrostatic analyzers, such as time-of-flight mass spectrometers, open trap and electrostatic trap mass-spectrometers [21,22], constructed in a variety of topologies, corresponding to planar, coaxial, and hollow cylindrical ion mirrors.

2. Geometry types of gridless ion mirrors Historically first gridless ion mirrors [3,7] were designed as axially symmetric ones built of coaxial rings or round aperture electrodes. Two opposed coaxial mirrors are separated by a drift space to form an isochronous shuttle-type electrostatic trap for axial ion oscillations in the X-direction, as shown in Fig. 1A. Ions are pulsed injected and pulsed ejected through apertures in the cap electrodes [9,18,23]. Typically, both mirrors are identical, though different mirror geometries can be used [9]. Axially symmetric TOF mass analyzers have an advantage of providing equal spatial and TOF focusing properties in both transverse directions Y and Z. The main drawback is a closed ion motion cycle, so that only a narrow mass range can be accepted onto a TOF detector in order to prevent spectral confusion.

Planar ion mirrors [8,16] may be built of flat electrodes elongated in one (Z) direction, thus forming a two-dimensional 2D field in the XY plane with zero field in the Z-direction at sufficient distance from the mirror Z-boundaries, typically exceeding a couple of calibers. Planar ion mirrors allow organizing a periodic zig-zag ion motion by reflecting ions between mirrors in the X-direction and spatially focusing ions in the Y-direction while drifting ions in the Z-direction. In this case, ion trajectories are not closed into cycles, allowing non-interfering ion injection and ion detection, necessary for the mass analysis in the full mass range. Since planar mirrors do not possess any focusing properties in the drift Z-direction, achieving long ion flight paths with several tens of reflections requires using additional focusing means in the drift direction, such as 2D periodic lenses [24–26] as shown in Fig. 1B. A further variety of ion mirror geometries can be found in Ref. [22]. In particular, one can bend a planar mirror in the Z-direction this way closing it into a so-called hollow cylindrical mirror. To retain the ion optical quality, the curvature radius shall be much larger than the Y-width of the electrode window. Such a mirror provides much denser folding of ion trajectory per analyzer volume and eliminates boundary fields at the mirror Z-edges. The curvature of the electrostatic field equipotential lines in the Z-direction creates a force moving ions towards the center, so that ions, injected into the analyzer at small inclination angle to the X-axis, approximately follow a “mean” cylindrical surface between the mirror electrodes and thus perform a cylindrical zig-zag motion as shown in Fig. 1C. Alternatively, the planar mirror electrodes can be bent in the X-direction with a curvature radius much larger than the Y-width of the electrode window, forming a pancake mirror design rotationally symmetric about the Y-axis. If ions are injected into the pancake analyzer in the XZ-plane and miss the rotational symmetry axis, they form oscillating trajectories not closed into cycles as shown in Fig. 1D. A central lens [27] plays the role of periodic lens developed for planar analyzers. It is important to emphasize that the electrode sections and geometrical focusing properties in the XY-plane as well as TOF focusing properties of all above referred ion mirrors are very similar, so that

M.I. Yavor et al. / International Journal of Mass Spectrometry 426 (2018) 1–11

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Fig. 2. Section by the XY-plane through the electrodes and equipotential lines in a typical planar mirror forming different focusing modes A and B. Shown is also the axial electrostatic potential distribution and TOF dependence on ion energy for the mode B in case of the mean ion kinetic energy 4500 eV in the drift space outside the mirror field.

the process of ion mirror optimization is basically the same. For this reason, the paper describes advances in ion mirror design based on examples of planar ion mirrors. 3. Principles of the mirror design First gridless ion mirrors were designed with purely retarding and monotonically varying fields [3], but later it was found that an accelerating lens at the ion mirror entrance improves spatial ion focusing [28]. Ion optical properties of ion mirrors with an accelerating lens were further improved in our studies [14–16,19,20,25,26,29]. A typical electrode geometry and an electrostatic potential distribution in a planar mirror with an accelerating lens is shown in Fig. 2. Multiple reflections of ion packets between two identical mirrors can be considered as passing ions through a sequence of identical ion-optical cells corresponding to a single ion reflection from and to the middle plane. The conditions of a stable ion trajectory confinement in the direction Y of mirror focusing after multiple reflections is known from Refs. [30,31]: −1 < (Y |Y ) < 1

(1)

where (Y|Y) is the aberration coefficient of the Tailor expansion. Y1 = (Y |Y )Y0 + (Y |B)B0 + (Y |ı)ı + (Y |YY )Y02 +(Y |YB)Y0 B0 + (Y |BB)B02 + ... ,

(2)

which expresses the coordinate Y1 after passing through the cell provided the initial ion coordinate Y0 , the initial trajectory angle B0 = dY/dX, and the relative deviation ı = (K − K0 )/K0 of the ion energy K from the mean ion kinetic energy K0 in the drift space. The best stability is achieved if every mirror reflection satisfies the condition: (Y |Y ) = 0

(3)

The condition of Eq. (3) means focusing of the parallel beam into a point in the linear approximation as shown for the mirrors of Fig. 2 in which spatial focusing is achieved by tuning the accelerating “lens” electrode #5. Note that the condition of Eq. (3) can be reached with different trajectory arrangements within the mirror field. Examples of different tunings of the same mirror are shown in Fig. 2. One tuning (A) provides the parallel-to-point focusing without ions intersecting the optic axis inside the mirror and the other (B) with intersection of the optic axis by ion trajectories near the ion turning point. The latter case is preferred because of much smaller ion beam Y-height in the vicinity of the turning point and consequently smaller TOF aberrations caused by the spatial ion spread. Note also that the condition of Eq. (3) means that after each two reflections the point-to-point focusing condition is satisfied, and in principle such an MR TOF analyzer can be turned into a stigmatic mass microscope similar to the sector field multi-turn mass analyzer MULTUM-IMG [32], but apparently with better imaging

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quality [33]. However, studies of imaging properties of MR TOF ion mirrors are beyond the scope of the present paper and deserve a separate publication. Ion optical properties and the basic principles of designing planar ion mirrors have been published elsewhere [14–16,31] and so are only briefly summarized below. For an example we refer to the mirror B of Fig. 2, in which the cap electrode #1 and the electrode #2 are electrically connected. By optimizing the voltages at the electrodes #2–#4 (or alternatively by optimization of the electrode lengths) the axial potential distribution inside the mirror can be tuned to eliminate certain low-order aberrations (T|ı), (T|ıı) etc. of the flight time T dependence on the ion energy given by the aberration power series expansion T − T0 = (T |ı)ı + (Tıı)ı2 + (T |ııı)ı3 + ... + (T |YY )Y02 +(T |YB)Y0 B0 + (T |BB)B02 + ... ,

(4)

where T0 is the flight time of the “reference” ion flying with the nominal mean kinetic energy along the optic axis. The mirror B of Fig. 2 has been optimized to perform the 3rd order TOF focusing with respect to the ion energy: (T |ı) = (T |ıı) = (T |ııı) = 0.

(5)

The relative deviation of the flight time on the ion energy in this case stays within 10−5 at the interval of 8% of the relative energy spread, as demonstrated by the graph in Fig. 2. The straight optic axis guarantees the absence of the first order dependence of the flight time on the Y-coordinate and on the angular parameter B = dY/dX, as well as of the 2nd order mixed chromatic aberrations: (T |Y ) = (T |B) = (T |Yı) = (T |Bı) = 0.

(6)

Then, due to the system symmetry in the analyzer with the identical pair of ion mirrors, reaching the condition of Eq. (3) automatically eliminates the mixed coordinate-angular TOF aberration after each two reflections: (T |YB) = 0.

E(X) = 2E0 (U1 , −X) + 2E0 (U2 , X) + E0 (−U2 , X − L2 ) +E0 (−U2 , X + L2 ) + E0 (U3 , X − L2 ) + E0 (U3 , X + L2 )

(7)

Moreover, the same geometric condition of Eq. (3) together with the intrinsic symmetry of the mirror cell leads to the proportionality of the two remaining geometric TOF aberrations: (T|BB) = (B|Y)2 (T|YY). Therefore, using only one more optimization parameter (electrode voltage, distance between the mirrors or electrode length) allows reaching the 2nd order TOF focusing with respect to the spatial spread in the ion packets: (T |YY ) = (T |BB) = 0.

calculation of aberration coefficients by integrating so-called differential algebra vectors instead of ion trajectories. This approach is a well formalized and convenient way to directly integrate differential equations for aberration coefficients, which considerably improves the accuracy of determining the aberrations. It is especially practically convenient for ion mirrors with planar or axial symmetry in which the field is fully defined by its distribution along the straight optic axis. For optimizing planar and axially symmetric mirrors we developed a home-made program based on the boundary element method for field calculation. The program performs pre-calculation of the axial field distribution and its derivatives along the optic axis, followed by DA simulation of aberration expansions. Unfortunately, using any numerical field calculation method is time-consuming which prevents optimizing electrode geometries at a real time scale. However, if an ion mirror is composed of flat and parallel electrodes with constant electrode window height (or ring electrodes with equal diameter) and if small gaps between adjacent electrodes can be neglected, simple analytical models exist for the axial field distributions which allow varying both voltages and electrode lengths at numerical optimization. Consider a model planar ion mirror consisting of one flat cap electrode (#1) with the surface coinciding with the plane X = 0, a set of (n − 1) electrodes (#2, #3, . . ., #n) elongated in the Z-direction, each electrode having a pair of flat surfaces at the planes Y = ±H/2, terminated in the X-direction by a long shielding electrode at the potential U = 0. An exemplar mirror with n = 5 is drawn in Fig. 2. The i-th electrode has the X-width Li and the potential Ui . The gaps between the electrodes are considered negligibly small. Similarly, a model axially symmetric mirror can be formed of the cap electrode, set of (n − 1) electrodes with cylindrical inner surfaces of the radius R, and a long shielding electrode of the same diameter. The electrostatic field strength distribution E(X) at the axis Y = 0 of such mirror can be expressed as a superposition:

(8)

In the particular ion mirror B of Fig. 2, the flight time deviation stays within 10−5 at the interval of ±10% of the mirror window Y-height and for the angular spread of ±0.5◦ in the ion packets. After those optimization steps, the quality of the TOF focusing of the mirror of Fig. 2 is mostly restricted by two major remaining aberrations: the 4th order aberration (T|ıııı)ı4 with respect to the ion energy spread and the mixed 3rd order aberrations (T|YYı)Y2 ı and (T|BBı)B2 ı, both reaching the relative level of 10−4 at the values of the coordinate and angular spreads mentioned above and at ±2.5% energy spread. Further mirror optimization and compensation of higher order aberrations will be discussed in Section 5. 4. Simulation methods Designing highly isochronous ion mirrors and reaching simultaneous compensation of multiple aberration coefficients requires optimizing electrode geometries and voltages. To do that, we used the differential algebra (DA) approach [34] which allows direct

+E0 (−U3 , X − L2 − L3 ) + E0 (−U3 , X + L2 + L3 ) +E0 (U4 , X − L2 − L3 ) + E0 (U4 , X + L2 + L3 ) + ...

(9)

+E0 (−Un , X − L1 − L2 − ... − Ln ) +E0 (−Un , X + L1 + L2 + ... + Ln ), where E0 (W,X) is the distribution at the axis Y = 0 of the electrostatic field created by two flat or cylindrical electrodes extended from X = 0 to X = −∞ and to X = +∞, with the potentials U = 0 and U = W, respectively. In case of planar electrodes the electrostatic potential distribution at the axis of the just described two-electrode system can be represented in the analytical form: (pl)

U0 (W, X) = (2W/) arctan(exp(X/H),

(10)

and so the electrostatic field strength E0 (W,X) is (pl)

(pl)

E0 (W, X) = −dU0 (W, X)/dX = −

2W exp(X/H) . H 1 + exp(2X/H)

(11)

In case of cylindrical electrodes one can use an approximate analytical representation for the axial potential distribution. A simple approximation is known from Ref. [35]: (ax)

U0

(W, X) = W (tanh(kX/R) + 1)/2,

(12)

where k = 1.318. The corresponding expression for the electrostatic field strength reads

M.I. Yavor et al. / International Journal of Mass Spectrometry 426 (2018) 1–11 (ax)

E0

=

(ax)

(W, X) = −∂U0

(W, X)/dX

−2kW . R[exp(2kX/R) + exp(−2kX/R) + 2]

(13)

However, the accuracy of the approximation of Eq. (13) is only about 10−2 which is too low for practical calculations. By multiple numerical experiments we found a more accurate analytical approximation for the axial distribution of the electrostatic field strength which reads (ax)

E0

(W, X) =

−2aW , R[exp(2bX/R) + exp(−2bX/R) + c]

(14)

where a = 1.05342, b = 1.22798 and c = 1.17519. The accuracy of the approximation of Eq. (14) is an order of magnitude higher than that of Eq. (13). Including realistic widths of the gaps between adjacent electrodes into the mirror optimization is possible within the same procedure by inserting additional segmented electrodes between main mirror electrodes. 5. Mirrors with higher order TOF focusing As we learned from our own experimental program, multireflecting analyzers can be brought to their aberration limit, and there is a strong demand in improving the ion optical quality of ion mirrors to reach yet higher resolutions and transmissions within compact instrumental packages. We were not yet satisfied with the 3rd order time per energy focusing and the full second order isochronicity of the ion mirrors of Fig. 2. Indeed, reducing the ion turn-around time in ion sources or pulsed converters requires applying a strong extraction field which inevitably causes a proportional increase of the ion energy spread. Higher energy spread increases not only TOF aberrations due to the pure energy spread but also the mixed geometric-chromatic aberrations (T|YYı)Y0 2 ı, (T|YBı)Y0 B0 ı and (T|BBı)B0 2 ı. Besides, the Y-orientation of the ion packets [36] is preferable for denser folding of ion trajectories in planar analyzers, and reduction of those cross aberrations would increase the Y-acceptance of the analyzer, so as the sensitivity of mass spectrometers. Increasing the energy acceptance of the ion mirror requires a more sophisticated optimization involving more optimization parameters, which can be additional electrode voltages or relations of electrode lengths. This way we could reach 4th and even 5th order TOF focusing with respect to energy: (T |ı) = (T |ıı) = (T |ııı) = (T |ıııı) = (T |ııııı) = 0 (15) The fifth order focusing of Eq. (15) allows enlarging the energy acceptance of the analyzer above 10%, as shown in Fig. 3A. Increasing the spatial mirror acceptance appears a more challenging task. While both 2nd and 3rd order mixed aberrations (T|YB)Y0 B0 and (T|YBı)Y0 B0 ı vanish due to the system symmetry after each pair of reflections in case of satisfying the geometric condition of Eq. (3), the other two mixed 3rd order aberrations in general remain non-vanishing though proportional to each other: (T|BBı) = (B|Y)2 (T|YYı). While examining various mirror configurations, we found out that increasing the order of time per energy focusing usually leads to increase of those two mixed aberrations, unless the length of the accelerating “lens” electrode of the mirror becomes larger and larger. As a matter of fact, substantial elongation of the lens electrode forms a field-free region inside the lens and creates a separate accelerating immersion lens field near the mirror entrance and far from the ion turning point. The elongation

5

of the lens electrode allows ions to be focused to a smaller diameter bunch in the vicinity of the ion turning point which helps to reduce the contribution of the spatial ion Y-size and angular divergence into the TOF spread. However, at 5th order focusing condition of Eq. (15) the considered lens electrode tends to be unrealistically long. One solution of this problem is to create an additional lens at the entrance of the mirror by inserting one more electrode with an accelerating potential, as shown in Fig. 7. Then an immersion lens is created by the electrode #6 in Fig. 3B between the “standard” mirror and the drift space, and so finally two acceleration fields (created by the electrodes #5 and #6) help to simultaneously compensate two mutually proportional third order mixed aberrations: (T |YYı) = (T |BBı) = 0.

(16)

Accounting the compensated (T|YBı) aberration, earlier compensated high order time per energy aberrations, so as the absence of odd-order pure spatial or angular aberrations due to the system symmetry, reaching the condition of Eq. (16) accomplishes achieving the full third-order isochronicity, including all types cross-term aberrations between the energy, spatial and angular spreads up to the third order, which means advancing ion mirrors to the next level of ion optical quality. Fig. 4 compares three types of ion mirrors: with the 3rd order energy and the 2nd order spatial TOF focusing (A and B), with the 5th order energy and the 2nd order spatial TOF focusing (C and D), and with the 5th order energy and the 3rd order spatial TOF focusing (E and F). In all cases, the relative energy spread of ion packets is limited to 7%, and the maximal size of ion packets is limited to 2Y/H = 0.266, where H is the mirror window height, and accounts angular spreads. For calculations of peak shapes in the graphs B, D and F, ion packets time width is assumed limiting the mass resolving power to R(50%) = 300 000 by the turn around time produced in the ion source. As seen in the graph B, aberrations of the first ion mirror with the third order energy isochronicity do reduce R(50%) mass resolution to 225 000 and create long side tails. Contrary, a high quality ion mirror with the high order energy isochronicity and the full third-order TOF focusing does not add any spreading to the peak shape in the graph F, defined by the turn around time in the ion source. TOF aberrations of those three ion mirrors (not accounting source spreading) are plotted versus ion energy and at individual vertical scales: 5 × 10−5 in graph A, 8 × 10−6 in graph C and 1 × 10−6 in graph E. As seen from graph E, time spread of high quality ion mirror stays well under 10−6 , meaning that low flight time aberrations of the mirror theoretically allow reaching over 1 000 000 level of the mass resolving power of an MR TOF MS at the peak base. Note that for MR TOF analyzers with planar (or hollow cylindrical) mirrors this goal also requires eliminating 2nd order TOF aberrations with respect to the Z-spread in ion bunches, caused by periodic lenses shown in Fig. 1B. A way to solve this problem is discussed in Section 7 below. 6. Ion mirrors with a retarding lens field Increasing the ion energy is another resource for improving the MR TOF MS performance. First, increasing the ion energy in TOF analyzers allows increasing the extraction field strength in the pulsed ion source or converters, thus increasing the mass resolving power proportionally to the square root of the ion energy [31]. A higher ion energy reduces the ion angular spread, thus, reducing analyzer aberrations and improving its transmission. Finally, the space charge capacity of MR TOF MS is expected to improve at higher ion energies. Typically ions in the source are formed at about ground electrostatic potential, so that the maximum reachable ion kinetic energy

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Fig. 3. (A) Comparison of the energy acceptance of the ion mirror with 5th-order TOF focusing with respect to energy and the acceptance of the mirror of Fig. 2. (B) Section by the XY-plane through the electrodes of a planar mirror with two accelerating lens fields and the axial electrostatic potential distribution in case of the mean ion kinetic energy 4500 eV in the drift space outside the mirror field.

in MR TOF analyzers with the mirrors of Figs. 2 and 3 is limited by the limited voltages at their accelerating “lens” electrodes. With a typical limit of 15 kV to minimize risks of a current leakage and discharges and to keep voltages highly stable this restricts the specific kinetic ion energy per charge by the level of 7.5 kV, as shown in Fig. 5A. A way to overcome such limitation is to replace the accelerating lens by a decelerating one. We found out, however, that in order to provide for high order focusing properties similar to one described in Section 5, this retarding lens field should be not integrated in the mirror reflecting field as it was done in Ref. [3] but rather separated from this field. In other words, the dependence of the electrostatic potential at the mirror optic axis should be non-monotonic and ions should be re-accelerated after the retarding lens region, for example to the drift space energy, before entering the reflecting

mirror field. An example of such mirror and electrode voltages is shown in Fig. 5B. With the described configuration of the mirror field the largest accelerating potential in the analyzer becomes the drift space one, so that using ion mirrors with a retarding lens field allows operating MR TOF analyzers at about twice higher specific energies (15 kV) as compared to the mirrors with accelerating lens fields. 7. Quasi-planar mirrors As was mentioned in Section 2, in MR TOF analyzers based on planar mirrors, at long flight paths with multiple reflections additional ion-optical elements are needed to maintain ion packet confinement in the drift Z-direction. Periodic 2D lenses located between the mirrors shown in Fig. 1B fulfill this task but inevitably

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Fig. 4. Time-energy phase space volumes (A, C, E) and simulated peak shapes (B, D, F) in planar analyzers, in which ion mirrors have the 2nd order spatial isochronous condition and the 3rd order TOF energy focusing (A, B); 2nd order spatial isochronous condition and 5th order TOF energy focusing (C, D); and 3rd order spatial isochronous condition and 5th order TOF energy focusing (E, F). In all cases time peaks were calculated for 2 ns turn-around time and the path length was chosen such that to provide in the ideal case (without taking mirror aberrations into account) the FWHM mass resolving power of 300 000 and the resolving power at 5% peak level of 140 000. The aberration limits RA of the mass resolving power are indicated for given initial ion beam parameters.

induce 2nd order TOF aberrations (T|ZZ)Z0 2 with respect to the initial coordinate spread ±Z0 and (T|AA)A0 2 due to the corresponding angular spread ±A0 , where A = dZ/dX. The mixed aberration (T|ZA)Z0 A0 can be eliminated after a pair of parallel-to-point focusing cells at which the condition (Z|Z) = 0 is satisfied, similarly as it is done with 2nd order TOF aberrations with respect to the spatial spread in the Y-direction. Due to well-known properties of the electrostatic 2D lenses the aberration coefficients (T|ZZ) and (T|AA) are always positive. When high performance ion mirrors of Section 5 are used, aberrations of periodic lenses become the dominating factor limiting the mass resolving power of the MR TOF MS at the level of about 500 000 for MR TOF analyzers of 1 m size and at ion packet emittance of orthogonal accelerators. An alternative to periodic lenses is integration of Z-focusing elements into ion mirrors as was proposed by the authors of the present paper [37] and independently by Ristroph and Flory [38]. An example is shown in Fig. 6 where thin periodic mask electrodes are inserted in both (or one) mirrors between two adjacent electrodes in the vicinity of the ion turning points. The potential at the mask electrode is chosen such that in the symmetry plane Y = 0 of the mirror the electrostatic field is perturbed to focus ions reflected from curved equipotential lines. Instead of the mask one can use shaped mirror electrodes [37]. The principal difference between periodic lenses in the drift space and periodic field structures in the “quasi-planar” mirrors is that the latter field structures can provide not only for positive but also for negative or zero aberration coefficients (T|ZZ) and (T|AA), depending on the sign of the curvature gradient of the equipotential lines in the X-direction. This property is analogous to the control over ion mirrors aberrations (T|YY) and (T|BB) in the vertical Ydirection (see Eq. (8)). In the Y-direction, the properly designed ion

mirror creates a negative aberration (T|YY)Y0 2 near the ion turning point in order to compensate for a positive aberration created by the “lens” field at the mirror entrance. Absolutely similarly, a quasi-planar field structure in the Z-direction is designed to compensate for the positive aberration (T|ZZ)Z0 2 created by periodic lenses. Using quasi-planar mirrors one can achieve the full 2nd order TOF focusing with respect to the spatial spread in ion packets in the entire MR TOF analyzer. Numerical simulations show that this allows overcoming the limit of the mass resolving power of Rm = 500 000 in MR TOF MS with periodic lenses and gives a realistic hope for exceeding the level of Rm = 1 000 000 resolving power in TOF mass spectrometry at 1 m size MR TOF analyzers and extending well beyond at larger analyzer sizes. 8. Experimental Based on the theoretical studies presented in Section 5, an MR TOF mass analyzer was designed and built with planar ion mirrors driven by five power supplies. The mirrors provide for the time per energy focusing of the 4th order and of the “almost 3rd order” with respect to the spatial spread of ions in the Y-direction. Stability of the ion motion and spatial focusing in the drift Z-direction was provided with a periodic array of 23 two-dimensional lens. The last lens was also used for static reversal of the ion Z-motion after passing through the analyzer [26], thus doubling the flight path in the full mass range mode. The cap-to-cap distance between the mirrors is 1 m, and so with 46 mirror reflections the flight path length is about 40 m and the flight time is 950 ␮s for singly charged ions of the mass 500 a.m.u. at 6 keV mean energy. Ions are injected into the analyzer from an orthogonal accelerator using the “double orthogo-

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Fig. 5. Typical electrode potentials in planar ion mirrors in case of the ground potential at the position of the ion source (pulsed converter) and the maximal negative voltage of −15 kV at the mirror electrodes (for positive ions): (A) ion mirror with an accelerating lens field, (B) ion mirror with a retarding lens field.

nal” scheme of Ref. [36]. The initial parameters of ion bunches are: the Y-height is 8 mm, the Z-width is 1.5 mm, the relative energy spread is 5%. Fig. 7 presents the mass spectra of the standard test compound PFTBA, obtained in the full mass range mode with an electron impact ion source, and a peak shape for an exemplar mass. The resolving power in the time-to-digital converter (TDC) mode is 340 000 for m/z = 264 a.m.u. Fig. 7 also presents plots of the measured mass accuracy and the FWHM mass resolving power of full mass range spectra. The scatter of mass measurements is calculated as 0.04 ppm. This unusually high level of the mass precision for TOF MS at limited ion statistics is obtained primarily due to the high mass resolving power, where the peak width itself is few ppm only. The mass resolving power, acquired both with the analog to digital converter (ADC) and with the TDC, improves at higher mass-tocharge ratios due to a smaller impact of the detector time width. The resolving power saturates at higher m/z range at approximately 250 000 and 350 000, respectively. In a simplified model, the overall resolving power is limited by three major factors, added as squares, each being expressed by individual resolution limits: the aberration limit of the analyzer RA , the turn around time limit RTAT , and the detector time spreading RDET . For presented spectra those factors are estimated as: RA = 500 000, RTAT = 700 000, RDET = 700 000 for m/z = 500 a.m.u. for ADC spectra and RDET = 1 000 000 for TDC spectra. The aberration limit of the mass resolving power RA has been tested in the so-called “zoom-in” mode [26], in which the first lens of the periodic lens array is switched to the deflection mode after an ion injection, thus providing for a repetitive ion passage through the whole analyzer back and forth in the Z-direction N times before

releasing ion packets onto the detector by switching off the deflection by the first lens. In Fig. 8 the dependence of the experimentally recorded FWHM mass resolving power is shown as function of N for two ion masses, acquired in the ADC mode. The prolonged flight path in the zoom-in mode diminishes the effects of RTAT and RDET , while leaving RA as a major limiting factor. In the zoom-in mode the mass resolving power of over 500 000 was recorded after N = 5 repetitive full ion passes through the analyzer for the ion mass 502 a.m.u. Fig. 8 also shows the mass spectrum of the isobaric cluster of the GC column bleed compound (C5 13 C2 H21 O4 Si4 ), ionized with an electron impact source and recorded after N = 5 repetitive passages. The high resolving power of 500 000 allows separating the fine isotopic structure, i.e. isobars with mass difference of less than 1 mDa. The shown experimental results confirm theoretical prediction that the aberration limit of the mass resolving power of MR TOF analyzers based on high performance ion mirrors in combination with periodic lenses exceeds 500 000. Experimental tuning of ion mirror voltages has demonstrated a remarkably accurate coincidence with predicted voltage values, with predicted analyzer tuning curves, and with achieved analyzer parameters, thus building confidence in the simulated quality of the ion mirrors. 9. Mirror scaling as way for further advance in resolving power With highly isochronous ion mirrors of Sections 5 and 7, the remaining non-eliminated aberration coefficients are of 4th and higher orders in the Y-direction, including pure geometric ones

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Fig. 6. MR TOF analyzer with quasi-planar ion mirrors having mask electrodes at a position close to the ion turning points.

(T|YYYY), (T|YYYB), etc, mixed ones (T|YYıı), (T|YBıı), (T|BBıı), etc, and chromatic ones (T|ıııııı), etc, as well as 3rd and higher order in the Z-direction, including (T|ZZı), (T|AAı), etc. Therefore, the mass resolving power rapidly scales at larger analyzer sizes. This means, that designing analyzers with the X-size over 1 m will rapidly improve aberration limits, already being over one million range for 1 m long analyzers. Besides, the resolving power also rapidly grows with reducing ion packet spreads, in particular the spatial spread relative to the analyzer size. As an example, unless dealing with heavy protein ions, the emittance of MALDI ion packets is roughly estimated by authors being ten times smaller compared to emittance of ion packets past double orthogonal accelerators. With strongly reduced effects of analyzer aberrations onto MR TOF analyzer isochronicity, the initial paradigm of multi-reflecting analyzers becomes valid again. With use of advanced analyzer schemes like quasi-planar mirrors or larger analyzer sizes, or reduced ion packet emittances, the TOF MS resolution is still expected being primarily limited by the first-order turn around

time, originating in the ion source. The resolution limit is then defined by the relation of Ref. [25]: Rm < (LV/lv)ı, where L is the flight path, V the ion velocity, l and v are the initial size and velocity spreads in ion packets and ␦ is the relative energy spread, tolerated at the resolution Rm , earlier shown to be within 5–7% range for Rm = 500 000. We predict that further extension of reflection numbers and of the ion path length, in particularly practical for hollow cylindrical MR TOF analyzer geometries, is expected to increase the mass resolving power at a scale exceeding millions, while retaining the advantage of parallel all-mass analysis, fast spectral acquisition and detection of individual ions, intrinsic for TOF MS. With implementation of various multiplexing methods, as described in Ref. [21], extension of the flight path shall not affect the MR TOF MS sensitivity.

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Fig. 7. Mass spectrum of PFTBA at the full mass range, acquired with TDC data systems, with a shape of an exemplar mass peak; presented are also mass deviations and resolving powers in mass spectra of PFTBA as functions of ion mass-to-charge ratio, acquired at the full mass range with ADC and TDC data systems.

Fig. 8. Dependence of the FWHM mass resolving power on the repetition index N, and an exemplar recorded spectrum of the isotopic cluster of the GC column bleed compound (C7 H21 O4 Si4 ), ionized with electron impact source, at N = 5.

High mass resolving powers of over 200 000 have been shown to improve mass accuracy to tens of ppb level. At predicted Rm > 1 000 000 level we expect mass accuracy being in low ppb range for intense TOF peaks while being under 1 ppm for TOF peaks presented by very few ions. In other words, high mass accuracy may be obtained in a wide dynamic range.

10. Conclusion Theoretical and experimental studies confirm that MR TOF MS are capable of reaching a high level resolving power in the order of multiple hundred thousands. Presented improvements bring gridless ion mirrors to the new level of ion optical quality, including

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reaching higher order TOF focusing with respect to the energy and spatial ion spreads, doubling the ion energy by using a retarding mirror lens field, and eliminating the 2nd order spatial aberrations of periodic lenses in quasi-planar mirrors. Improved MR TOF analyzers of 1 m length can provide well over one million aberration limit at realistic ion packets parameters past orthogonal accelerators. In experiments, an analyzer of 1 m length demonstrates 300 000 mass resolving power at the full mass range and up to 500 000 in the restricted mass range. Because of a high order isochronicity, the aberration limit of MR TOF analyzers rapidly grows the with analyzer size or when using narrower ion packets, and we predict appearance of MR TOF MS with resolving power above 1 000 000 at low ppb mass accuracy, combined with all advantages, intrinsic for TOF MS, like rapid acquisition of panoramic spectra and detection of single ions, while sensitivity at more rarified pulsing may be recovered by numerous multiplexing methods. Improved ion mirrors are applicable for TOF MS, electrostatic traps, and open electrostatic traps in planar and cylindrical geometries. Acknowledgments The authors are thankful to the staff of the company MSC-CG for engineering support and of the Institute for Analytical Instrumentation RAS for scientific collaboration. This work was supported within joint instrumentation development program of companies Mass Spectrometry Consulting, Bar, Montenegro, Leco Corporation, St. Joseph, MI, USA, and Micromass Waters Corporation, Wilmslow, UK. References [1] S.G. Alikhanov, A new pulse method of measuring the masses of ions, Sov. Phys. JETP 4 (1956) 452–453. [2] B.A. Mamyrin, V.I. Karataev, D.V. Shmikk, V.A. Zagulin, The mass-reflectron, a new non-magnetic time-of-flight mass spectrometer with high resolution, Sov. Phys.–JETP 37 (1973) 45–48. [3] R. Frey, E.W. Schlag, Time of Flight Mass Spectrometer Using an Ion Reflector, Patent US4731532, 1988. [4] E.I. Kerley, R.E. Haufler, Reflectron Time-of-Flight Mass Spectrometer, Patent US5955730, 1999. [5] E. Kawato, Time-of-Flight Mass Spectrometer, Patent US6384410, 2002. [6] H. Wollnik, Time-of-Flight Mass Spectrometer, Patent DE3025764, 1982. [7] R. Kutscher, R. Grix, G. Li, H. Wollnik, A transversally and longitudinally focusing time-of-flight mass spectrometer, Int. J. Mass Spectrom. Ion Process. 103 (1991) 117–128. [8] L.M. Nazarenko, L.M. Sekunova, E.M. Yakushev, Time-of-Flight Mass Spectrometer with Multiple Reflection, Patent SU1725289, 1992. [9] H. Wollnik, A. Casares, An energy-isochronous multi-pass time-of-flight mass spectrometer consisting of two coaxial electrostatic mirrors, Int. J. Mass Spectrom. 227 (2003) 217–222. [10] Y. Yoshida, Time of Flight Mass Spectrometer, Patent US4625112, 1984. [11] D.C. Hamilton, G. Gloeckler, F.M. Ipavich, R.A. Lundgren, R.B. Sheldon, D. Hovestadt, New high-resolution electrostatic ion mass analyzer using time of flight, Rev. Sci. Instrum. 61 (1990) 3104–3106. [12] R.D. Knight, Storage of ions from laser-produced plasmas, Appl. Phys. Lett. 38 (1981) 221–223. [13] L.N. Gall, Y.K. Golikov, M.L. Alexandrov, E.E. Pechalina, N.A. Holin, Time-of-Flight Mass Spectrometer, Patent SU1247973, 1986.

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