Patent Publication Number: US-8124930-B2

Title: Multipole ion transport apparatus and related methods

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to the guiding of ions which finds use, for example, in fields of analytical chemistry such as mass spectrometry. More particularly, the present invention relates to the guiding of ions in a converging ion beam. 
     BACKGROUND OF THE INVENTION 
     An ion guide (or ion transport apparatus) may be utilized to transmit ions in various types of ion processing devices, one example being a mass spectrometer (MS). The theory, design and operation of various types of mass spectrometers are well-known to persons skilled in the art and thus need not be detailed in the present disclosure. A commonly employed ion guide is based on a multipole electrode structure in which two or more pairs of electrodes are elongated in the direction of the intended ion path and surround an interior space in which the ions travel. Typically, the electrode structure is an RF-only electrode structure in which the ions passing through the ion guide are subjected to a two-dimensional, radio-frequency (RF) trapping field that focuses the ions along an axial path through the electrode structure. The paths of the ions are able to oscillate in radial directions in the transverse plane that is orthogonal to the axis of the electrode structure, but these oscillations are limited by the forces imparted by the RF electrical field being applied in the transverse plane. As a result, the ions are confined to an ion beam centered around the axis of the electrode structure (which typically is a geometrically centered axis). In the absence of the RF field, the ions would be widely dispersed in an unstable, uncontrolled manner. Few ions would actually be transmitted to a subsequent device from the ion exit of the ion guide; most ions would not reach the ion exit but instead hit the ion guide rods or escape from the electrode structure. Therefore, in an ion guide the ions need to experience a certain minimum amount of RF restoring force during their flight so as to be confined to an ion beam for efficient transmission to and beyond the ion exit at the axial end of the ion guide. 
     In a conventional ion guide, the applied RF electrical field is generally uniform along the axial direction from the ion entrance to the ion exit, disregarding fringe effects and other localized discontinuities. As a result, the ion beam is generally cylindrical at least in the sense that the cross-sectional area of the ion beam—generally representing the envelope in which radial excursions of the ions are limited in the two-dimensional plane—is uniform along the axis. The size of the cross-section of the ion beam generally depends on the nature of the RF field being applied. As examples, a set of four parallel electrodes may be utilized to generate a quadrupolar RF field, a set of six parallel electrodes may be utilized to generate a hexapolar RF field, etc. In a quadrupolar field, the ions are focused more strongly about the axis and hence the cross-section of the ion beam is smaller as compared to a hexapolar field. In all such conventional cases the RF field and therefore the cross-section of the ion beam are uniform. However, the conditions under which ions of a given mass-to-charge (m/z) ratio or range of m/z ratios can be admitted into the ion guide in an optimal manner are not necessarily the same as the conditions under which ions can be emitted from the ion guide in an optimal manner. Consequently, the dimensions of a uniform ion beam are often not optimal for both ion entry and ion exit, or even for either ion entry or ion exit alone, leading to less than optimal ion signal and instrument sensitivity. 
     Accordingly, there is a need for ion transport devices configured for providing optimized ion transmission conditions for ions of a wide range of m/z ratios. 
     SUMMARY OF THE INVENTION 
     To address the foregoing problems, in whole or in part, and/or other problems that may have been observed by persons skilled in the art, the present disclosure provides methods, processes, systems, apparatus, instruments, and/or devices, as described by way of example in implementations set forth below. 
     According to one implementation, an ion transport apparatus includes an ion entrance end, an ion exit end disposed at a distance from the ion entrance end along a longitudinal axis, an ion entrance section extending along the longitudinal axis from the ion entrance end toward the ion exit end, an ion exit section extending along the longitudinal axis from the ion exit end toward the ion entrance end, and a plurality of electrodes. The electrodes are arranged along the longitudinal axis wherein at least portions of the electrodes are disposed at a radial distance in a transverse plane orthogonal to the longitudinal axis. The plurality of electrodes includes a plurality of first electrodes circumscribing an interior space in the ion entrance section and a plurality of second electrodes circumscribing an interior space in the ion exit section. The plurality of electrodes is configured for applying an RF electrical field that varies along the longitudinal axis such that at the ion entrance end, the RF electrical field includes a first RF electrical field including a major first multipole component of 2n 1  poles where n 1 ≧3/2, and at the ion exit end the RF electrical field includes a second RF electrical field including predominantly a second multipole component of 2n 2  poles where n 2 ≧3/2 and n 2 &lt;n 1 . 
     According to another implementation, at least some of the electrodes have a cross-sectional area in a transverse plane orthogonal to the longitudinal axis wherein the cross-sectional area is different at the ion entrance end than at an opposite axial end of the at least some electrodes. 
     According to another implementation, a method is provided for transporting ions. The ions are admitted into an interior space of an ion transport apparatus at an axial ion entrance end thereof. The ion transport apparatus includes a plurality of electrodes arranged along a longitudinal axis from the axial ion entrance end toward an axial ion exit end, wherein the plurality of electrodes surrounds the interior space in a transverse plane orthogonal to the longitudinal axis. Radial motions of the ions in the transverse plane are constrained to a converging ion beam that extends along the longitudinal axis from a large ion beam cross-section at the ion entrance end to a small ion beam cross-section at the ion exit end. The converging ion beam is effected by applying an RF electrical field that varies along the longitudinal axis such that at the ion entrance end, the RF electrical field comprises a major first multipole component of 2n 1  poles where n 1 ≧3/2, and at the ion exit end the RF electrical field comprises predominantly a second multipole component of 2n 2  poles where n 2 ≧3/2 and n 2 &lt;n 1 . 
     Other devices, apparatus, systems, methods, features and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention can be better understood by referring to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. In the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1  is a simplified perspective view of an example of an ion transport apparatus according to certain implementations of the present disclosure. 
         FIG. 2  is a side (length-wise) view of another example of an ion transport apparatus according to other implementations of the present disclosure. 
         FIG. 3  is a schematic end view of an electrode set of an ion transport apparatus at its ion entrance end. 
         FIG. 4  is a schematic end view of the same electrode set illustrated in  FIG. 3  but at the opposite, ion exit end of the ion transport apparatus. 
         FIG. 5  is a cross-sectional side (length-wise) view of an example of an ion transport apparatus according to other implementations. 
         FIG. 6  is a cross-sectional side (length-wise) view of an example of another ion transport apparatus according to other implementations. 
         FIG. 7  is a group of plots illustrating the pseudo-potentials of a quadrupole, hexapole, and octopole RF field. 
         FIG. 8  is a group of plots illustrating ion distributions in a quadrupole, hexapole, and octopole RF field. 
         FIG. 9  is a perspective view of an example of ion transport apparatus according to other implementations. 
         FIGS. 10A ,  10 B and  10 C are schematic cross-sectional views of the electrode sets in the entrance section, intermediate section, and exit section, respectively. 
         FIG. 11  is a perspective view of an example of an ion transport apparatus according to other implementations. 
         FIGS. 12A and 12B  are schematic cross-sectional views of the electrode sets in the entrance section and exit section, respectively. 
         FIG. 13  is a side (length-wise) view of an example of ion transport apparatus according to other implementations. 
         FIG. 14  is a side (length-wise) view of an example of ion transport apparatus according to other implementations. 
         FIGS. 15A ,  15 B and  15 C are schematic cross-sectional views of the electrode sets in the entrance section, intermediate section, and exit section, respectively, of the ion transport apparatus illustrated in  FIG. 14 . 
         FIG. 16  is a side (length-wise) view of an example of ion transport apparatus according to other implementations. 
         FIG. 17  is a perspective view of an example of ion transport apparatus according to other implementations. 
         FIG. 18  is a perspective view of an example of an ion transport apparatus according to other implementations. 
         FIG. 19  is a perspective view of an example of an ion transport apparatus according to other implementations. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The subject matter disclosed herein generally relates to the transmission of ions and associated ion processing. Examples of implementations of methods and related devices, apparatus, and/or systems are described in more detail below with reference to  FIGS. 1-19 . These examples are described at least in part in the context of mass spectrometry (MS). However, any process that involves the transmission of ions may fall within the scope of this disclosure. 
       FIG. 1  is a simplified perspective view of an example of an ion transport apparatus (device, assembly, etc.)  100  according to certain implementations of the present disclosure. The ion transport apparatus  100  includes a plurality of electrodes  104 ,  108 ,  112 ,  116  arranged about a longitudinal axis  120 , which may be referred to as the z-axis. The electrodes  104 ,  108 ,  112 ,  116  are arranged so as to circumscribe an interior space within the ion guide  100  such that the interior space also is elongated along the longitudinal axis  120 . At least a portion of each electrode  104 ,  108 ,  112 ,  116  is disposed at a radial distance from the longitudinal axis  120  in the transverse or x-y plane that is orthogonal to the longitudinal axis  120 . Hence, the electrodes  104 ,  108 ,  112 ,  116  and the interior space have respective cross-sectional areas in the transverse plane and an axial dimension along the longitudinal axis  120 . The cross-sectional area of the interior space is generally bounded by the surfaces of the electrodes  104 ,  108 ,  112 ,  116  that face inward toward the interior space. The opposing axial ends of the electrodes  104 ,  108 ,  112 ,  116  respectively surround an axial ion entrance end  124  and an axial ion exit end  128  of the ion transport apparatus  100 . The ion guide  100  may generally include a housing or frame (not shown) or any other structure suitable for supporting the electrodes  104 ,  108 ,  112 ,  116  in a fixed arrangement along the longitudinal axis  120 . Depending on the type of ion processing system contemplated, the housing may provide an evacuated, low-pressure, or less than ambient-pressure environment. As appreciated by persons skilled in the art, upon the proper application of RF voltages to the electrodes  104 ,  108 ,  112 ,  116 , the electrodes  104 ,  108 ,  112 ,  116  generate a two-dimensional (x-y plane in the present example), multipolar, RF electrical restoring field that focuses ions generally along a path or ion beam directed along the longitudinal axis  120 , as described further below in conjunction with  FIG. 3 . The ions are constrained to motions in the transverse plane in the vicinity of the longitudinal axis  120 , such that the ion beam may be considered to be an ion cloud or ion-occupied transport region focused along the longitudinal axis  120  from the ion entrance end  124  to the ion exit end  128 . 
     The ion transport apparatus  100  may further include one or more ion entrance lenses  132  positioned at one or more axial distances before the ion entrance end  124 , and one or more ion exit lenses  136  positioned at one or more axial distances after the ion exit end  128 . The ion entrance lens  132  and the ion exit lens  136  may be any suitable structures, such as plates, disks, cylinders or grids with respective apertures. The ion transport apparatus  100  may include a device or means for generating one or more electrical fields utilized to control ion energy in the axial direction. These devices or means may be embodied in one or more DC voltage sources or signal generators. Thus, in the illustrated example, respective DC voltage sources  148 ,  152 ,  156  may be placed in electrical communication with the ion entrance lens  132 , the electrodes  104 ,  108 ,  112 ,  116 , and the ion exit lens  136  to generate axial DC potentials across the axial gap between the ion entrance lens  132  and the electrodes  104 ,  108 ,  112 ,  116  and across the axial gap between the electrodes  104 ,  108 ,  112 ,  116  and the ion exit lens  136 . In this manner, ions may be guided and urged into the ion transport apparatus  100  through the ion entrance end  124  and out from the ion transport apparatus  100  through the ion exit end  128 . It will be understood that the DC voltage sources  148 ,  152 ,  156  are schematically represented in  FIG. 1  and in practice may be implemented by various different types of physical circuitry or devices. As one alternative, an external axial DC field-generating device or devices (not shown) may be implemented, such as one or more other conductive structures (e.g., resistive traces, wires, etc.) positioned along the longitudinal axis  120 . 
     In various implementations, the ion transport apparatus  100  may include a plurality of ion transport sections. Each ion transport section may be distinguished from the other sections by the configuration of the electrodes  104 ,  108 ,  112 ,  116  or the composition of the RF multipole electrical field applied in that section. The ion transport apparatus  100  may include an ion entrance section (or first ion transport section)  160  extending from the ion entrance end  124  toward the ion exit end  128 , and an ion exit section (or second ion transport section)  164  extending from the ion exit end  128  toward the ion entrance end  124 . In some implementations, the ion transport apparatus  100  may further include one or more intermediate sections (or third ion transport section, fourth ion transport section, and so on)  168  interposed between the ion entrance section  160  and the ion exit section  164 . In  FIG. 1 , the ion entrance section  160 , ion exit section  164  and intermediate section  168  are schematically demarcated by dashed lines. No limitation is placed on the respective axial lengths of these ion transport sections  160 ,  164 ,  168  relative to each other. Some or all of the electrodes  104 ,  108 ,  112 ,  116  may extend through each section  160 ,  164 ,  168 . 
     In the example specifically illustrated in  FIG. 1 , the electrodes  104 ,  108 ,  112 ,  116  are provided in the form of a set of straight rods. In this case, the electrodes  104 ,  108 ,  112 ,  116  may be generally parallel to each other and to the longitudinal axis  120 , circumferentially spaced from each other about the longitudinal axis  120 , and elongated along the longitudinal axis  120 . In other implementations, examples of which are described below, the electrodes  104 ,  108 ,  112 ,  116  may have rectilinear, square or other polygonal cross-sections, or may be provided in the form of helices coiled around the longitudinal axis  120 , or may be provided in the form of a series or stack of rings axially spaced along the longitudinal axis  120 . Moreover, in general no limitation is placed on the number of electrodes  104 ,  108 ,  112 ,  116 , so long as the electrodes  104 ,  108 ,  112 ,  116  are configured to generate a two-dimensional RF electrical field in the interior space to control the ion beam in the manner disclosed herein. In some implementations, the electrode set includes at least two opposing pairs of electrodes corresponding to a quadrupolar arrangement of electrodes. Thus in  FIG. 1 , relative to the longitudinal axis  120 , one electrode  104  is located radially opposite to another electrode  108  (such as along the y-axis) and another electrode  112  is located radially opposite to yet another electrode  116  (such as along the x-axis). In other implementations, more than four electrodes may be provided as for example in hexapolar, octopolar, decapolar and dodecapolar arrangements, as well as arrangements including more than twelve electrodes. In still other implementations such as in the case of helical electrodes, as few as two electrodes may be utilized. 
       FIG. 2  is a side (length-wise) view of another example of an ion transport apparatus  200  according to other implementations of the present disclosure. For clarity, only a partial arrangement of radially opposing pairs of electrodes is illustrated. This ion transport apparatus  200  may be considered as comprising a series of multipole ion transport devices arranged along a longitudinal axis  220 , or as having a segmented electrode configuration. The ion transport apparatus  200  includes a first set  206  of electrodes corresponding to an ion entrance section  260  and a second set  210  of electrodes corresponding to an ion exit section  264 . The ion transport apparatus  200  may further include one or more other sets  214  of electrodes corresponding to one or more intermediate sections  268 . The interior space circumscribed by the first set  206  of electrodes may be referred to as an ion entrance region (or first ion transport region), the interior space circumscribed by the second set of electrodes  210  may be referred to as an ion exit region (or second ion transport region), the interior space circumscribed by the third set  214  of electrodes may be referred to as an intermediate region (or third ion transport region), and so on. The sets  206 ,  214 ,  210  of electrodes are separated by axial gaps in this example. One or more ion entrance lenses  232  and ion exit lenses  236  may also be included. As schematically depicted in  FIG. 2 , respective DC voltage sources  248 ,  250 ,  252 ,  254 ,  256  may be placed in electrical communication with the ion entrance lenses  232 , the electrode sets  206 ,  214 ,  210 , and the ion exit lenses  236 , to drive ions into, through and out from the ion transport apparatus  200 . 
       FIG. 3  is a schematic end view, in the transverse or x-y plane, of an electrode set of an ion transport apparatus  300  at its ion entrance end. The electrode set may correspond to the electrode set illustrated in  FIG. 1  or to the first electrode set  206  illustrated in  FIG. 2 . In this example, the electrode set includes a first pair of opposing electrodes  304 ,  308  and a second pair of opposing electrodes  312 ,  316 . Typically, the opposing pair of electrodes  304  and  308  is electrically interconnected, and the other opposing pair of electrodes  312  and  316  is electrically interconnected, to facilitate the application of appropriate RF voltage signals that drive the two-dimensional ion guiding field. Each electrode  304 ,  308 ,  312  and  316  is typically spaced at the same radial distance r 0  from a longitudinal z-axis  320  as the other electrodes  304 ,  308 ,  312  and  316 . Thus, the interior space of the ion transport apparatus  300  is generally bounded in the transverse plane by a circle of inscribed radius r 0 . The interior space of the ion transport apparatus  300 , and the ion guiding region in which two-dimensional (radial) excursions of the ions are constrained by the applied RF focusing field, are generally defined within this inscribed circle. 
     The ion transport device  300  includes a device or means for generating one or more two-dimensional RF electrical fields in one or more corresponding ion transport regions to constrain ions to a converging ion beam as described in more detail below. These devices or means may be embodied in one or more RF (or RF/DC) voltage sources or signal generators. Thus, in the illustrated example, to generate the ion focusing or guiding field(s), a radio frequency (RF) voltage of the general form V RF  cos(Ωt) is applied to opposing pairs of interconnected electrodes  304 ,  308  and  312 ,  316 , with the signal applied to the one electrode pair  304 ,  308  being 180 degrees out of phase with the signal applied to the other electrode pair  312 ,  316 . In  FIG. 3 , application of the RF energy is schematically depicted by an RF voltage source (+V RF )  362  in signal communication with the first pair of electrodes  304 ,  308  and another RF voltage source (−V RF )  366  in signal communication with the second pair of electrodes  312 ,  316 . In a segmented ion transport apparatus such as illustrated in  FIG. 2 , each electrode pair in each section may be interconnected and RF voltages applied thereto in a similar manner. In implementations where it is desired that the ion transport device  300  function as a mass filter or mass sorter, appropriate DC voltages (±U) may be superposed on the RF voltages (±V RF ) being applied. These DC voltages are not to be confused with the above-noted axial DC potentials utilized to create axial DC fields. The basic theories and applications respecting the generation of multipole RF fields for ion focusing, guiding or trapping, as well as for mass filtering, ion fragmentation, ion ejection, ion isolation and other related processes, are well known and thus need not be detailed here. 
     In the examples given in  FIGS. 1-3 , the electrode set consists of four electrodes arranged in parallel and in opposing, electrically interconnected pairs. If a two-dimensional RF confining field is conventionally applied to this electrode set, the result is a pure, symmetrical, quadrupolar RF field where the number of poles of the electrical field is 2n and n=2. In the present context, a “pure” or “predominant” quadrupolar RF field is taken to mean that no major (or significant) higher-order multipole RF fields are present (intentionally or unintentionally) in combination with the quadrupolar field. Examples of higher-order RF fields include, but are not limited to, hexapolar fields (n=3), octopolar fields (n=4), decapolar fields (n=5), and dodecapolar fields (n=6). Generally, the field strength of a higher-order multipole RF field or fields is “major” if it enables a larger ion beam cross-section to be maintained in a given space as compared to the ion beam cross-section that would result from a lower-order multipole RF field applied to the same space. 
     In the present context, “major” higher-order multipole RF fields may also be characterized as superimposing a substantial fraction of the field strength onto the lower-order (e.g., quadrupolar) field being applied in a particular ion transport region of the ion transport apparatus. As an example, consider that in a given ion transport region a composite RF field is present and is characterized as comprising a combination of a quadrupolar field component and one or more higher-order multipole field components. For the higher-order multipole field component or components to be major, the higher-order multipole RF field (or plurality of fields in a case where more than one type of higher-order multipole field is superposed) may have a strength that is 10% or greater of the strength of the quadrupolar field being applied. Therefore, in a pure or predominant quadrupolar RF field, if there are any higher-order multipole fields present, the collective strength of these higher-order multipole fields is less than 10% of the strength of the quadrupolar field. 
     For convenience, then, the term “pure” as used herein encompasses both “pure” (100% field strength) and “predominant” or “substantially pure” (greater than 90% field strength). The term “pure” also takes into account that in practical implementations, relatively weak (and sometimes very localized) higher-order multipole fields may be present unintentionally or unavoidably due to field faults, fringe effects or distortions resulting from machining and assembly imperfections, from the presence of apertures or other geometric discontinuities in the electrodes, from the necessarily finite size of the electrodes (i.e., real electrodes are truncated; their surfaces do not infinitely extend toward the asymptotic lines of the perfect hyperbolic geometry that would result in a purely quadrupolar electric field), from the use of electrodes having surfaces deviating from the ideal hyperbolic geometry (e.g., cylindrical rods, rectilinear bars or plates, etc.), space-charge effects, etc. 
     In a pure quadrupolar field, the ion beam is concentrated relatively tightly about the longitudinal axis about which the electrodes are arranged and thus is shaped approximately as an elongated cylinder. Moreover, again in a conventional quadrupole rod arrangement, the quadrupole RF field active in the interior space of the electrode set is generally uniform along the length of the electrode set (i.e., from ion entrance end to ion exit end). Thus, the cross-sectional area of the ion beam-i.e., the limits of the excursions of the ions in the transverse plane-is generally uniform or constant from the ion entrance end to the ion exit end. That is, the ion beam has a generally cylindrical shape of constant cross-sectional area as opposed to being conical or funnel-shaped. Stated yet another way, the cross-sectional area of the ion beam does not appreciably diverge or converge. Similarly, if a two-dimensional RF focusing field is conventionally applied to an electrode set consisting of six parallel rods, the result would be a hexapolar RF field. The resulting ion beam would again have a generally cylindrical shape of constant cross-sectional area from the ion entrance end to the ion exit end. However, the cross-sectional area of an ion beam in a hexapolar field will be larger than it would be in a pure quadrupolar field. Similar results obtain for yet higher-order RF fields. In all such conventional cases, the ion beam neither converges nor diverges. 
       FIG. 3  schematically depicts the cross-sectional area  374  of an ion beam in a lower-order field such as a quadrupole in comparison to the cross-sectional area  378  of an ion beam in a higher-order field such as a hexapole, octopole, etc. It will be appreciated by persons skilled in the art that these dashed-line circles are provided to generally demarcate the envelope in which the ions of the ion beam travel in the transverse plane. In practice, the actual cross-sectional area of the ion beam may have a more elliptical shape, with the orientation of the ellipse varying in the x-y plane in accordance with the cycle of RF energy being applied. 
     In contrast to the above-described conventional RF field which has a generally constant composition along the longitudinal axis, in accordance with the present teachings, the electrode set and/or the means for applying the RF voltages to the electrode set are configured such that the RF field varies along the longitudinal axis. In various implementations described herein, the RF field varies from comprising a major higher-order multipole field component at the ion entrance end to comprising a predominantly lower-order multipole field component at the ion exit end. In the present context, the terms “higher” and “lower” are taken to be relative to each other. Thus, if the number of poles in the higher-order multipole field is taken to be 2n 1  and the number of poles in the lower-order multipole field component is taken to be 2n 2 , then n 1 &gt;n 2 . As a result of the axially varying RF field, the ion beam converges in the direction of the ion exit end and thus is generally cone-shaped or funnel-shaped. This convergence may be manifested in a gradual (e.g., tapering) manner, in a step-wise manner, or in a combination of both gradual and step-wise attributes. 
     The converging ion beam may be visualized by comparing  FIG. 3  to  FIG. 4 . For this purpose,  FIG. 3  may be considered as schematically depicting an ion beam of cross-sectional area  378  under the influence of a higher-order multipole RF field at the ion entrance end. At this axial position, the cross-sectional area  378  of the ion beam may be referred to as the ion entrance aperture or ion acceptance aperture.  FIG. 4  is a schematic end view, in the transverse or x-y plane, of the same electrode set illustrated in  FIG. 3  but at the opposite, ion exit end of the ion transport apparatus  300 .  FIG. 4  may be considered as depicting the same ion beam as in  FIG. 3 , but at the ion exit end where the ion beam now has a smaller cross-sectional area  374  due to the greater focusing influence of the lower-order multipole RF field at this axial position. At the ion exit end, the cross-sectional area  374  of the ion beam may be referred to as the ion exit aperture or ion emission aperture. 
     The converging ion beam may be further visualized in  FIG. 5 , which is a cross-sectional side (length-wise) view of an example of an ion transport apparatus  500  along its longitudinal axis  520 . For simplicity, a single pair of opposing electrodes  504 ,  508  is illustrated along with an ion beam  570  in the interior space between these electrodes  504 ,  508 . The ion beam  570  converges in the direction of ion transfer, from a relatively larger (or wider) ion acceptance aperture  578  to a relatively smaller (or narrower) ion emission aperture  574 . In this example, the ion beam  570  converges in a gradual or tapered manner from an ion entrance end  524  to an ion exit end  528 , and optionally through one or more distinct ion transport sections  560 ,  564 ,  568 . 
     By comparison,  FIG. 6  is a cross-sectional side (length-wise) view of an example of another ion transport apparatus  600  along its longitudinal axis  620 . In this example, electrodes of the ion transport apparatus  600  are segmented whereby the ion transport apparatus  600  includes an ion entrance section  660 , an ion exit section  664 , and optionally one or more intermediate sections  668 , each of which are axially spaced from the others. Also illustrated is an ion beam  670  that converges in the direction of ion transfer from a larger ion acceptance aperture  678  to smaller ion emission aperture  674 . In this example, the ion beam  670  converges in a step-wise manner. 
     Other implementations may include various combinations of the features or aspects described above and illustrated in  FIGS. 5 and 6 , depending on the configuration of the electrode set and/or the means for applying the RF field(s). Thus, for instance, the non-segmented electrode set shown in  FIG. 5  may apply the step-wise converging ion beam  670  shown in  FIG. 6 . Alternatively, the segmented electrode set shown in  FIG. 6  may apply the gradually converging ion beam  570  shown in  FIG. 5 . Moreover, while the size of step-wise ion beam  670  is illustrated in  FIG. 6  as being constant or substantially constant over the length of each ion transport section  660 ,  664 ,  668 , the ion beam may alternatively have a hybrid tapering/stepped convergence. For example, the cross-sectional area of the ion beam may taper down along the length of the first ion entrance section  660 , then step down to an even more reduced area at the beginning of the next ion transport section  668 , then taper down along the length of this section  668 , then down to an even more reduced area at the beginning of the next ion transport section  664 , and so on. Hence, the composition of the RF electric field applied to the electrode set in either  FIG. 5  or  FIG. 6  may be (substantially) uniform through a given ion transport section and only appreciably change in an adjacent ion transport section, or alternatively may vary gradually throughout the axial extent of two or more ion transport sections defined for the ion transport apparatus. 
     An axially varying RF field according to the present disclosure may be characterized as including at least a major higher-order RF multipole field at the ion entrance end (or in the ion entrance section) and a predominantly lower-order RF multipole field at the ion exit end (or in the ion exit section). Thus, for example, the RF field may include a major dodecapole field at the ion entrance end and may predominantly consist of a quadrupole field at the ion exit end. For many implementations disclosed herein, the applied two-dimensional RF electric field may be considered to be a composite of two or more multipole field components. Thus, for example, the RF field may include a major dodecapole field superposed on a quadrupole field at the ion entrance end, and may predominantly consist of a quadrupole field at the ion exit end. At the ion exit end, the dodecapole field—if it exists at all—is minor or insignificant. Other higher-order multipole field components may exist in any given ion transport section of the ion transport apparatus but such other fields are likewise insignificant. Generally, a higher-order multipole field is major if it is strong enough to maintain an enlarged ion beam cross-section in comparison to a lower-order multipole field. As described above, the significance of the higher-order multipole field may be quantified in one non-limiting example by stating that the strength of the higher-order multipole field is 10% or greater of the strength of the lower-order field being applied at the ion exit end. In addition to the major higher-order multipole field applied at the ion entrance end and any major higher-order multipole field applied at an intermediate ion transport section, other higher-order multipole field components may exist in any given ion transport section of the ion transport apparatus. Such other fields, however, may be insignificant (i.e., weak), generally meaning that they do not appreciably affect the intended varying cross-section of the ion beam. 
     The axially varying RF field giving rise to the converging ion beam may be realized by various combinations of multipole field components. As a few examples, the ion entrance section may include a dodecapole field while the ion exit section includes an octopole, hexapole or quadrupole field. As further examples, the ion entrance section may include an octopole field while the ion exit section includes a hexapole or quadrupole field. As another example, the ion entrance section may include a hexapole field while the ion exit section includes a quadrupole field. In other examples, the higher-order multipole field that is of significance at the ion entrance section may be of a higher order than dodecapole, i.e., n&gt;6. Additional variations are possible when the ion transport apparatus is partitioned so as to include one or more intermediate ion transport sections, whether by means of axial segmentation of the electrode set or by some other electrode configuration. As a few examples, the ion entrance section may include a dodecapole field, an intermediate section may include an octopole or hexapole field, and the ion exit section may include a quadrupole field. As another example, the ion entrance section may include an octopole field, an intermediate section may include a hexapole field, and the ion exit section may include a quadrupole field. As another example, the ion entrance section may include a dodecapole field, an intermediate section may include an octopole field, and the ion exit section may include a hexapole field. 
     In the above examples, the number of electrodes provided is a multiple of 2. Alternatively, however, the number of electrodes in the electrode set may be an odd number, e.g., 3, 5, 7, etc. Also in the above examples, the lowest-order field mentioned is the quadrupole field. However, the lowest-order field applied at the ion exit end (or in the ion exit section) may be a tripole, i.e., 2n=3 poles where n=3/2. A tripole field may be realized by any suitably configured electrode set. In one non-limiting example, three parallel electrodes are provided (not shown). The electrodes are elongated along the longitudinal axis and symmetrically spaced from each other in the transverse plane about the longitudinal axis, i.e., the electrodes are positioned 120° apart. The respective RF signals applied to the three electrodes differ in phase by 120°. 
     Accordingly, in some implementations in which the ion transport apparatus includes at least an ion entrance end and an ion exit end, the plurality of electrodes is configured for applying an RF electrical field that varies along the longitudinal axis such that at the ion entrance end (or in an associated ion entrance section), the RF electrical field comprises a major first multipole component of 2n 1  poles where n 1 &gt;3/2, and at the ion exit end (or in an associated ion exit section) the RF electrical field comprises predominantly a second multipole component of 2n 2  poles where n 2 &gt;3/2 and n 2 &lt;n 1 . In other implementations in which the ion transport apparatus additionally includes at least one intermediate ion transport section, the plurality of electrodes may be configured for applying an RF electrical field that varies along the longitudinal axis such that at the intermediate section, the RF electrical field comprises a major third multipole component of 2n 3  poles where n 3 &gt;n 2  and n 3 &lt;n 1  (n 1 &gt;n 3 &gt;n 2 ). 
     From the foregoing, it is evident that implementations of the present teachings may provide improved ion transmission efficiency and focusing for various applications entailing the processing of ions such as mass spectrometry. Advantages are achieved by increasing the ion acceptance aperture at the ion entrance end and decreasing the ion emission aperture at the ion exit end. As compared to conventional ion transport or guide devices, the increased ion acceptance aperture allows a higher number of ions to enter the device from an upstream device (e.g., an ion source, collision cell, etc.), and the decreased ion emission aperture allows the ions to be transferred to a downstream device (e.g., a mass analyzer, collision cell, etc.) with increased efficiency and higher ion signal. By means of the converging ion beam, an ion transport device as disclosed herein is able to direct and focus the dispersive ion beam entering the device into a well-confined ion stream that is optimized for transfer to the next device. Optionally, collisional cooling (or damping) may be utilized to further reduce the space volume taken up by the ion phase at the exit end, thereby further increasing ion transfer efficiency. Collisional cooling typically entails the introduction of an inert background gas (e.g., hydrogen, helium, nitrogen, xenon, argon, etc.) into the interior space of the device by any suitable means known to persons skilled in the art. The ion transport device may operate at atmospheric, near-atmospheric, or sub-atmospheric pressure levels (for example, down to about 10 −9  torr). 
     Implementations disclosed herein may be further explained by the following observations. The electric potential in multipole RF ion guide may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       ⁡ 
                       
                         ( 
                         
                           r 
                           , 
                           φ 
                         
                         ) 
                       
                     
                     = 
                     
                       V 
                       * 
                       
                         COS 
                         ⁡ 
                         
                           ( 
                           
                             Ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             r 
                             
                               r 
                               o 
                             
                           
                           ) 
                         
                         n 
                       
                       * 
                       
                         COS 
                         ⁡ 
                         
                           ( 
                           
                             n 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             φ 
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where r is a radial position in the RF electrical field relative to the longitudinal axis, 2r 0  is the distance between two opposite rods, 2n is the number of rods, V is the amplitude of RF voltage applied to rods, φ is the phase of the RF voltage, Ω is the angular frequency of the RF voltage, and t is time. 
     From equation (1), the pseudo-potential of the RF multipole electric field may be expressed as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         V 
                         p 
                       
                       ⁡ 
                       
                         ( 
                         r 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           z 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             n 
                             2 
                           
                           ⁢ 
                           
                             e 
                             2 
                           
                           ⁢ 
                           
                             V 
                             2 
                           
                         
                         
                           4 
                           ⁢ 
                           m 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Ω 
                             2 
                           
                           ⁢ 
                           
                             r 
                             o 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             r 
                             
                               r 
                               o 
                             
                           
                           ) 
                         
                         
                           
                             2 
                             ⁢ 
                             n 
                           
                           - 
                           2 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where m is the mass of the ion, the unit of charge e=1.602×10 −19 , and z is the number of the charge of the ions (Guo-Zhong Li and Joseph A. Jarrell,  Proc.  46 th    ASMS Conference on Mass Spectrometry and Allied Topics, Orlando, Florida,  1998,  p  491). 
       FIG. 7  is a group of plots illustrating the pseudo-potentials of a quadrupole, hexapole, and octopole RF field. From  FIG. 7 , it is clear that acceptance ellipse of a multipole ion guide with a higher number of rods is larger than that of a multipole ion guide with a lower number of rods.  FIG. 8  is a group of plots illustrating ion distributions in a quadrupole, hexapole, and octopole RF field, i.e., the radial ion density distributions when ions enter the RF electric field and reach equilibrium.  FIG. 8  reveals that the ion radial distribution in a quadrupole (n=2) RF electric field is closer to the central axis than that in a higher-order multipole (n≧3) RF electric field. Thus, the ion transferring efficiency from a lower RF electric field, such as quadrupole electric field, to mass analyzer will be higher than that from a higher RF electric field to the mass analyzer. The information presented in  FIGS. 7 and 8  indicate that optimal ion transmission through an ion transport apparatus may be attained by providing a higher-order multipole RF field at the ion entrance end and a lower-order multipole RF field at the ion exit end. 
     Further descriptions of the present teachings are given by way of additional examples set forth below. 
       FIG. 9  is a perspective view of an example of ion transport apparatus  900  according to some implementations. The ion transport apparatus  900  includes an ion entrance section  960 , an ion exit section  964 , and optionally one or more intermediate ion transport sections  968 . For simplicity, only one intermediate section  968  is illustrated and described. The ion entrance section  960  includes a first set of electrodes  906 , the ion exit section  964  includes a second set of electrodes  910 , and the intermediate section  968  if provided includes a third set of electrodes  914 . In this example, each section  960 ,  964 ,  968  includes the same number of electrodes. The number of electrodes and the manner in which they are structured, and the manner in which RF signals are applied to the electrodes, are such that the ion transport apparatus  900  generates a higher-order multipole RF field in the ion entrance section  960 , a lower-order multipole RF field in the ion exit section  964 , and another higher-order multipole RF field in the intermediate section  968  (if provided) that is of lower order than the electrical field in the ion entrance section  960  but higher order than the electrical field in the ion exit section  964 . By way of example and not by limitation in  FIG. 9 , each ion transport section  960 ,  964 ,  968  includes twelve electrodes, elongated along the longitudinal axis and circumferentially arranged about the longitudinal axis. 
       FIGS. 10A ,  10 B and  10 C are schematic cross-sectional views of the electrode sets  906 ,  914 ,  912  in the entrance section  960 , intermediate section  968 , and exit section  964 , respectively.  FIGS. 10A ,  10 B and  10 C also illustrate how the RF voltages are applied to the electrodes in each respective section  960 ,  968 ,  964 . One or more of the electrode sets  906 ,  914 ,  912  may be divided into groups of m electrodes. In the present example, the number of electrodes in each group  1080  of the first electrode set  906  is m 1 =1, the number of electrodes in each group  1084  of the second electrode set  912  is m 2 =3, and the number of electrodes in each group  1088  of the third electrode set  914  is m 3 =2. Thus, in the example of the twelve-electrode arrangement, the first electrode set  906  includes twelve groups  1080  of one electrode, the second electrode set  912  includes four groups  1084  of three electrodes, and the third second electrode set  914  includes six groups  1088  of two electrodes. Each electrode group  1080 ,  1084 ,  1088  is radially positioned in the transverse plane opposite to another electrode group. As indicated by the “+” and “−” signs on the electrodes, the RF voltage applied to each pair of opposing electrodes (or pair of opposing groups  1080 ,  1084 ,  1088  of electrodes) is 180° out of phase with the RF voltage applied to the adjacent electrodes (or groups  1080 ,  1084 ,  1088  of electrodes) on either side of that pair. The result in the illustrated example is that the first electrode set  906  applies a major dodecapole RF field in the ion entrance region  960 , the second electrode set  912  applies a predominant quadrupole RF field in the ion exit region  964 , and the third electrode set  914  applies a major hexapole field in the intermediate section  968 . The RF field thus varies in the axial direction from a dodecapole RF field to a quadrupole RF field. When the intermediate ion transport section  968  is provided, the RF field varies in the axial direction from a dodecapole RF field, to a hexapole RF field, and then to a quadrupole RF field. 
     As described in detail earlier in this disclosure, the ion transport apparatus  900  may be modified or configured as needed to generate other types of RF fields in any given ion transport section  960 ,  964 ,  968 . As an example, an eight-electrode set may be utilized to generate a strong octopole or quadrupole RF field depending on how the electrodes are grouped. As another example, a sixteen-electrode set may be utilized to generate a strong 16-pole, octopole or quadrupole RF field. It will also be understood that a converging ion beam may be realized without requiring that each ion transport section  960 ,  964 ,  968  apply a different RF field. As examples, the ion entrance section  960  and any intermediate section  968  adjacent to it could both apply a dodecapole field while the ion exit section  964  applies a quadrupole field, or the ion entrance section  960  could apply a dodecapole field while the ion exit section  964  and any intermediate section  968  adjacent to it could both apply a quadrupole field, and so on. 
       FIG. 11  is a perspective view of an example of an ion transport apparatus  1100  according to other implementations. The ion transport apparatus  1100  includes an ion entrance section  1160 , an ion exit section  1164 , and optionally one or more intermediate ion transport sections (not shown). The ion entrance section  1160  includes a first set  1106  of electrodes  1106  and the ion exit section  1164  includes a second set  1112  of electrodes. In this example, each section  1160 ,  1164  includes a different number of electrodes. The number of electrodes and the manner in which they are structured, and the manner in which RF signals are applied to the electrodes, are such that the ion transport apparatus  1100  generates a higher-order multipole RF field in the ion entrance section  1160  and a lower-order multipole RF field in the ion exit section  1164 . By way of example and not by limitation in  FIG. 11 , the electrodes in each ion transport section  1160 ,  1164  are elongated along the longitudinal axis and circumferentially arranged about the longitudinal axis. The ion entrance section  1160  includes twelve electrodes  1106  and the ion exit section  1164  includes four electrodes  1112 . One or more intermediate sections, if provided, could include a number of electrodes between four and twelve. 
       FIGS. 12A and 12B  are schematic cross-sectional views of the electrode sets  1106 ,  1112  in the ion entrance section  1160  and the ion exit section  1164 , respectively.  FIGS. 12A and 12B  also illustrate how the RF voltages are applied to the electrodes  1106 ,  1112  in each respective section  1160 ,  1164 . As in the previous example, the RF voltage applied to each pair of opposing electrodes is 180° out of phase with the RF voltage applied to the adjacent electrodes on either side of that pair. As a result, the first electrode set  1106  applies a major dodecapole RF field in the ion entrance region  1160  and the second electrode set  1112  applies a predominant quadrupole RF field in the ion exit region  1164 , and an ion beam through the ion transport apparatus  1100  will be convergent as described above. As in previous examples, one or more axially intermediate ion transport sections (not shown) could be added to apply one or more RF fields of an intermediate order relative to the RF fields applied in the ion entrance section  1160  and the ion exit section  1164 . As in the example illustrated in  FIGS. 9 to 10C , the ion transport apparatus  1100  is not limited to application of a dodecapole RF field and a quadrupole RF field; other types of RF fields may be utilized. Also as in the previous example, one or more electrode sets may be divided into groups of m electrodes. Thus, for example, the electrodes in first electrode set  1106  may be grouped so as to apply a hexapole field. 
       FIG. 13  is a side (length-wise) view of an example of ion transport apparatus  1300  according to other implementations. The ion transport apparatus  1300  may include an ion entrance section  1360 , an ion exit section  1364 , and optionally one or more intermediate ion transport sections  1368 , all axially positioned along a longitudinal axis  1320 . The ion transport apparatus  1300  includes a plurality of electrodes elongated along the longitudinal axis  1320  and circumferentially arranged about the longitudinal axis  1320 . For simplicity, only three electrodes are illustrated. The electrodes  1304 ,  1308 ,  1316  begin at an ion entrance end  1324  and extend through the sections to an ion exit end  1328 . The number of electrodes and the manner in which they are structured, and the manner in which RF signals are applied to the electrodes, are such that the ion transport apparatus  1300  generates a higher-order multipole RF field at the ion entrance end  1324  (or in the ion entrance section  1360 ), a lower-order multipole RF field at the ion exit end  1328  (or in the ion exit section  1364 ), and another higher-order multipole RF field in the intermediate section  1368  (if provided) that is of lower order than the electrical field at the ion entrance end  1324  but higher order than the electrical field at the ion exit end  1328 . In this example, the axially varying RF field is attained by some of the electrodes  1304 ,  1308  being of variable radius and hence variable cross-section. The reduction in cross-sectional area may be accomplished gradually in a tapered manner in the axial direction toward the ion exit end  1328 . Thus, the cross-sectional areas of the tapered electrodes  1304 ,  1308  (in the transverse plane) are larger at the ion entrance end  1324  than at the ion exit end  1328 . The reduction in cross-sectional area may alternatively be accomplished in a step-wise manner rather than gradual tapering, or a combination of tapered and stepped features may be implemented. At the ion entrance end  1324 , the cross-sectional areas of the varying-radius electrodes  1304 ,  1308  may be the same as those of the constant-radius electrodes  1316 . 
       FIG. 14  is a side (length-wise) view of an example of ion transport apparatus  1400  according to other implementations. The ion transport apparatus  1400  may include an ion entrance section  1460 , an ion exit section  1464 , and one or more intermediate ion transport sections  1468 , all axially positioned along a longitudinal axis  1420 . The ion transport apparatus  1400  includes a plurality of electrodes elongated along the longitudinal axis  1420  and circumferentially arranged about the longitudinal axis  1420 . For simplicity, only three electrodes  1404 ,  1408 ,  1416  are illustrated. The electrodes  1404 ,  1408 ,  1416  begin at an ion entrance end  1424  and extend through the sections toward an ion exit end  1428 . The number of electrodes and the manner in which they are structured, and the manner in which RF signals are applied to the electrodes, are such that the ion transport apparatus  1400  generates a higher-order multipole RF field at the ion entrance end  1424  (or in the ion entrance section  1460 ), a lower-order multipole RF field at the ion exit end  1428  (or in the ion exit section  1464 ), and another higher-order multipole RF field in the intermediate section  1468  (if provided) that is of lower order than the electrical field at the ion entrance end  1424  but higher order than the electrical field at the ion exit end  1428 . In this example, the axially varying RF field is attained by some of the electrodes  1404 ,  1408  having varying cross-sectional areas that are reduced, such as by gradual tapering and/or in a step-wise manner, at one or more points in the axial direction toward the ion exit end  1428 . Moreover, some or all of the varying-radius electrodes  1404 ,  1408  are shorter than the uniformly-sized electrodes  1416 . Thus, both the uniformly-sized electrodes  1416  and the varying-radius electrodes  1404 ,  1408  begin at the ion entrance end  1424 , but only the uniformly-sized electrodes  1416  may actually extend fully to the ion exit end  1428 . The axial ends of the varying-radius electrodes  1404 ,  1408  opposite to the ion entrance end  1424  may be located, for example, at the end of the intermediate ion transport section  1468  as illustrated in  FIG. 14 . In this manner, the varying-radius electrodes  1404 ,  1408  exert no influence on the RF field applied to the ion exit section  1428 . Alternatively, the varying-radius electrodes  1404 ,  1408  may extend partially (not shown) into the ion exit section  1464 . In either case, the varying-radius electrodes will not contribute to the RF field at the ion exit end  1428 . 
       FIGS. 15A ,  15 B and  15 C are schematic cross-sectional views of the electrode sets in the entrance section  1460 , intermediate section  1468 , and exit section  1464 , respectively, of the ion transport apparatus  1400  illustrated in  FIG. 14 .  FIGS. 15A ,  15 B and  15 C also illustrate how the RF voltages are applied to the electrodes in each respective section  1460 ,  1464 ,  1468 . In this example, there are twelve electrodes. Two opposing pairs of constant-radius electrodes (e.g.,  1416 ,  1512 ) are positioned 90° from each other. Four opposing pairs of varying-radius electrodes (e.g.,  1404 ,  1408 ) are positioned between the constant-radius electrodes  1416 ,  1512 , such that two varying-radius electrodes are located circumferentially on either side of each constant-radius electrode. In the present example, cross-sectional areas of both the constant-radius electrodes  1416 ,  1512  and the varying-radius electrodes  1404 ,  1408  are equal at the ion entrance end, as shown in  FIG. 15A . As shown in  FIG. 15B , the cross-sectional areas of the varying-radius electrodes  1404 ,  1408  are less than cross-sectional areas of the constant-radius electrodes  1416 ,  1512  in the intermediate section  1468 . As shown in  FIG. 15C , the varying-radius electrodes  1404 ,  1408  are terminated before the ion exit section  1464  (or in other implementation, at least before the ion exit end), such that only the constant-radius electrodes  1416 ,  1512  are present in the ion exit section  1464  (or at least at the ion exit end). In this example, as indicated by “+” and “−” signs, the RF voltage applied to any given electrode, whether of constant or varying radius, is 180° out of phase with the RF voltage applied to the adjacent electrode on either side of that particular electrode. As a result of this configuration, the RF field applied will axially vary from a dodecapole field, to a multipole of intermediate order (e.g., hexapole), to a quadrupole. 
     In other implementations, the electrode set in the ion entrance section  1460  ( FIG. 15A ) and/or the intermediate section  1468  ( FIG. 15B ) may be grouped to apply other types of RF fields, as described above. 
     In the case of the ion transport apparatus  1300  illustrated in  FIG. 13 , the arrangement of electrodes and corresponding RF voltages may be similar to  FIG. 15A  at the ion entrance end  1324  and  FIG. 15B  at the ion exit end  1328 . The RF will axially vary from a higher-order field (e.g., dodecapole) to a lower-order field (e.g., hexapole). At the ion exit end  1328 , the radii of the varying-radius electrodes  1304 ,  1308  may, however, be small enough that a quadrupole field predominates at the ion exit end  1328  as in the case of the ion transport apparatus  1400  illustrated in  FIG. 14 . 
       FIG. 16  is a side (length-wise) view of an example of ion transport apparatus  1600  according to other implementations. The ion transport apparatus  1600  includes an ion entrance section  1660 , an ion exit section  1664 , and optionally one or more intermediate ion transport sections  1668 , all axially positioned along a longitudinal axis  1620 . The ion transport apparatus  1600  includes a plurality of electrodes, including first electrodes  1606  in the ion entrance section  1660 , second electrodes  1610  in the ion exit section  1664 , and third electrodes  1614  in the intermediate section  1668  if provided. The electrodes  1606 ,  1610 ,  1614  are arranged circumferentially about the longitudinal axis  1620  such that at least a portion of the electrodes  1606 ,  1610 ,  1614  are disposed at a radial distance from the longitudinal axis  1620  in the transverse plane. The first electrodes  1606  are spaced from each other by a first axial distance  1690  relative to the longitudinal axis  1620 , and the second electrodes  1610  are spaced from each other by a second axial distance  1694  that is greater than the first axial distance  1690 . The third electrodes  1614  (if provided) are spaced from each other by a third axial distance  1698  that is greater than the first axial distance  1690  but less than the second axial distance  1694 . Accordingly, each section  1660 ,  1664 ,  1668  of the ion transport apparatus  1600  is characterized by electrodes of different axial spacing as compared to the other sections  1660 ,  1664 ,  1668 . In the example specifically illustrated in  FIG. 16 , the axial spacing between electrodes in any given section  1660 ,  1664 ,  1668  is uniform over the extent of that section  1660 ,  1664 ,  1668 . Alternatively, the axial spacing between the electrodes in one or more of the sections  1660 ,  1664 ,  1668  may vary as well, e.g., the axial spacing in a given section may increase in the direction through that section toward the ion exit end  1628 . 
     In the example given in  FIG. 16 , the electrodes are provided in the form of helices coiled about the longitudinal axis  1620 . Thus in this example, the axial spacing  1690 ,  1694 ,  1698  between electrodes corresponds to the helical pitch of the electrodes. Thus, the helical pitch increases in the direction of the ion exit end  1628  from one section to another and/or through individual sections. The helical pitch may be varied gradually or in steps. With the inner diameter of the helices fixed, the pseudo-potential well of the ion transport apparatus  1600  is varied gradually or in steps via the varying of the pitch in the direction toward the ion exit end  1628 . In the present example, each section  1660 ,  1664 ,  1668  respectively includes two electrodes  1606 ,  1610 ,  1614  to which RF voltages are applied 180° out of phase. More than two electrodes, however, may be provided in a given section. By the illustrated configuration, the ion transport apparatus  1600  generates a higher-order multipole RF field in the ion entrance section  1660 , a lower-order multipole RF field in the ion exit section  1664 , and a second higher-order multipole RF field in the intermediate section  1668  (if provided) that is of lower order than the electrical field in the ion entrance section  1660  but higher order than the electrical field in the ion exit section  1664 . As in other implementations described herein, the axially varying RF field results in a converging ion beam. 
       FIG. 17  is a perspective view of an example of an ion transport apparatus  1700  according to other implementations. The ion transport apparatus  1700  includes an ion entrance section  1760 , an ion exit section  1764 , and optionally one or more intermediate ion transport sections  1768 , all axially positioned along a longitudinal axis  1720 . The ion transport apparatus  1700  includes a plurality of electrodes, including first electrodes  1706  in the ion entrance section  1760 , second electrodes  1710  in the ion exit section  1764 , and third electrodes  1714  in the intermediate section  1768  if provided. The electrodes  1706 ,  1710 ,  1714  are arranged circumferentially about the longitudinal axis  1720  such that at least a portion of the electrodes  1706 ,  1710 ,  1714  are disposed at a radial distance from the longitudinal axis  1720  in the transverse plane. The first electrodes  1706  are spaced from each other by a first axial distance  1790  relative to the longitudinal axis  1720 , and the second electrodes  1710  are spaced from each other by a second axial distance  1794  greater than the first axial distance  1790 . The third electrodes  1714  (if provided) are spaced from each other by a third axial distance  1798  that is greater than the first axial distance  1790  but less than the second axial distance  1794 . Accordingly, each section  1760 ,  1764 ,  1768  of the ion transport apparatus  1700  is characterized by electrodes of different axial spacing as compared to the other sections  1760 ,  1764 ,  1768 . In the example specifically illustrated in  FIG. 17 , the axial spacing between electrodes in any given section  1760 ,  1764 ,  1768  is uniform over the extent of that section  1760 ,  1764 ,  1768 . Alternatively, the axial spacing between the electrodes in one or more of the sections  1760 ,  1764 ,  1768  may vary as well, e.g., the axial spacing in a given section may increase in the direction through that section toward the ion exit end  1728 . 
     In the example given in  FIG. 17 , the electrodes are provided in the form of a series or stack of rings coaxially disposed about the longitudinal axis  1720  in the transverse plane. Thus in this example, the axial spacing  1790 ,  1794 ,  1798  between electrodes corresponds to the axial distance between adjacent rings. Thus, the axial distance increases in the direction of the ion exit end  1728  from one section to another and/or through individual sections. The axial distance may be varied gradually or in steps. With the inner diameter of the rings fixed, the pseudo-potential well of the ion transport apparatus  1700  is deepened gradually or in steps, and the ion radial distribution moves toward the longitudinal axis  1720 , via the varying of the axial distance in the direction toward the ion exit end  1728 . In the present example, each section  1760 ,  1764 ,  1768  respectively includes two electrodes  1706 ,  1710 ,  1714  to which RF voltages are applied 180° out of phase. More than two electrodes, however, may be provided in a given section. By the illustrated configuration, the ion transport apparatus  1700  generates a higher-order multipole RF field in the ion entrance section  1760 , a lower-order multipole RF field in the ion exit section  1764 , and a second higher-order multipole RF field in the intermediate section  1768  (if provided) that is of lower order than the electrical field in the ion entrance section  1760  but higher order than the electrical field in the ion exit section  1764 . As in other implementations described herein, the axially varying RF field results in a converging ion beam. 
       FIG. 18  is a perspective view of an example of an ion transport apparatus  1800  according to other implementations. The ion transport apparatus  1800  includes a plurality of electrodes elongated along a longitudinal axis  1820  and circumferentially spaced about the longitudinal axis  1820 . In the illustrated example, the electrode set includes an opposing pair of first electrodes  1804 ,  1808  and an opposing pair of second electrodes  1812 ,  1816 . The first electrodes  1804 ,  1808  and the second electrodes  1812 ,  1816  extend along the longitudinal axis  1820  from an ion entrance end  1824  to an ion exit end  1828 . The first electrodes  1804 ,  1808  each include a first cross-sectional area  1805  in the transverse plane, and the second electrodes  1812 ,  1816  each include a second cross-sectional area  1813  in the transverse plane. The respective cross-sectional areas  1805 ,  1813  of the first electrodes  1804 ,  1808  and the second electrodes  1812 ,  1816  vary along the longitudinal axis  1820  either gradually (e.g., in a tapering manner, as in the illustrated example) or step-wise, or by a combination of tapering and stepped features. Thus, for the first electrodes  1804 ,  1808  the sizes of the first cross-sectional areas  1805  are different at the ion entrance end  1824  than at the ion exit end  1828 , and for the second electrodes  1812 ,  1816  the sizes of the second cross-sectional areas  1813  are likewise different at the ion entrance end  1824  than at the ion exit end  1828 . In the example specifically illustrated in  FIG. 18 , the first cross-sectional areas  1805  are larger at the ion entrance end  1824  than at the ion exit end  1828 , and the second cross-sectional areas  1813  are smaller at the ion entrance end  1824  than at the ion exit end  1828 . At the ion entrance end  1824 , the first cross-sectional areas  1805  are greater than the second cross-sectional areas  1813 . At the ion exit end  1828 , the first cross-sectional areas  1805  may be equal or substantially equal to the second cross-sectional areas  1813 . The RF voltages applied to the first electrodes  1804 ,  1808  are 180° out of phase with the RF voltages applied to the second electrodes  1812 ,  1816 . By this configuration, the ion transport apparatus  1800  generates an RF field that varies from a major higher-order multipole RF field at the ion entrance end  1824  to a predominant quadrupole multipole RF field at the ion exit end  1828 . As in other implementations described herein, the axially varying RF field results in a converging ion beam. 
     While in the above-described implementation the ion transport apparatus  1800  includes two pairs of opposing electrodes, other implementations may include additional electrodes, some or all of which having varying cross-sections. While in the above-described implementation the ion transport apparatus  1800  may be considered as including a single set of electrodes extending from the ion entrance end  1824  to the ion exit end  1828 , other implementations may include additional sets of electrodes in distinct, axially spaced ion transport sections, with one or more electrodes in one or more of the ion transport sections having varying cross-sections. While in the above-described implementation the cross-sections  1805 ,  1813  of the electrodes are rectilinear in shape, in other implementations the cross-sections  1805 ,  1813  may have other types of polygonal or prismatic shapes or may be rounded (e.g., circular, elliptical, hyperbolic, etc.). 
       FIG. 19  is a perspective view of an example of an ion transport apparatus  1900  according to other implementations. The ion transport apparatus  1900  in  FIG. 19  may be considered as variation of the ion transport apparatus  1800  in  FIG. 18 , but where the RF field varies from higher-order multipoles to a purer lower-order multipole over multiple segments or sets of electrodes (or multiple ion transport sections). The ion transport apparatus  1900  includes a first ion transport section (or ion entrance section)  1960  and a second ion transport section (or ion exit section)  1964  axially spaced from the first ion transport section  1960 . Optionally, the ion transport apparatus  1900  additionally includes one or more intermediate sections (not shown) axially interposed between the first ion transport section  1960  and the second ion transport section  1964 . The first ion transport section  1960  longitudinally extends from a first ion entrance end  1924  to a first ion exit end  1925 , and the second ion transport section  1964  longitudinally extends from a second ion entrance end  1927  to a second ion exit end  1928 . The first ion transport section  1960  includes a plurality of first electrodes and the second ion transport section  1964  includes a plurality of second electrodes, all of which are elongated along a longitudinal axis  1920  and circumferentially spaced about the longitudinal axis  1920 . The first electrodes extend along the longitudinal axis  1920  from the first ion entrance end  1924  to the first ion exit end  1925 , and the second electrodes extend along the longitudinal axis  1920  from the second ion entrance end  1927  to the second ion exit end  1928 . In the illustrated example, the first electrode set includes an opposing pair of first electrodes  1906  and an opposing pair of second electrodes  1907 , and the second electrode set includes an opposing pair of third electrodes  1910  and an opposing pair of fourth electrodes  1911 . In the transverse plane, the first electrodes  1906  each include a first cross-sectional area, the second electrodes  1907  each include a second cross-sectional area, the third electrodes  1910  each include a third cross-sectional area, and the fourth electrodes  1911  each include a fourth cross-sectional area. 
     In the example given in  FIG. 19 , the respective cross-sectional areas of the electrodes may be uniform or substantially uniform along the longitudinal axis  1920  in a given ion transport section. However, the cross-sectional areas of some electrode pairs may differ from the cross-sectional areas of other electrode pairs. Thus, in the example specifically illustrated, the first cross-sectional areas (first electrodes  1906 ) are larger than the second cross-sectional areas (second electrodes  1907 ), and the first cross-sectional areas are larger than the third cross-sectional areas (the third electrodes  1910 ). The second cross-sectional areas are smaller than the fourth cross-sectional areas (fourth electrodes  1911 ). The third cross-sectional areas may be equal or substantially equal to the fourth cross-sectional areas. The RF voltages applied to the first electrodes  1906  are 180° out of phase with the RF voltages applied to the second electrodes  1907 , and the RF voltages applied to the third electrodes  1910  are 180° out of phase with the RF voltages applied to the fourth electrodes  1911 . By this configuration, the ion transport apparatus  1900  generates an RF field that varies from a major higher-order multipole RF field at the first ion entrance end  1924  (or in the first ion transport region  1960 ) to a predominant quadrupole multipole RF field at the second ion exit end  1928  (or in the second ion transport region  1964 ). As in other implementations described herein, the axially varying RF field results in a converging ion beam. 
     In other implementations, the respective cross-sectional areas of one or more electrodes in the first ion transport section  1960  and/or the second ion transport section  1964  may vary along the longitudinal axis  1920  either gradually (e.g., in a tapering manner) or step-wise or by a combination of tapering and stepped features, in a manner similar to that illustrated in  FIG. 18 . While in the above-described implementation the ion transport apparatus  1900  includes two pairs of opposing electrodes in each section  1960 ,  1964 , other implementations may include additional electrodes, some or all of which having varying cross-sections. While in the above-described implementation the cross-sections of the electrodes are rectilinear in shape, in other implementations the cross-sections may have other types of polygonal or prismatic shapes or may be rounded (e.g., circular, elliptical, hyperbolic, etc.). 
     In other implementations, an ion transport apparatus may include various combinations of features and aspects described in conjunction with  FIGS. 1-19 . Moreover, the ion transport apparatus illustrated in any of  FIGS. 1-19  may represent a portion or section of a larger ion transport apparatus (not shown) that includes one or more additional sections positioned upstream and/or downstream of the illustrated ion transport apparatus. These additional ion transport sections may also be configured according to any of the implementations described above, but alternatively may be configured according to conventional designs without converging ion beams. 
     In the various implementations described above and illustrated in  FIGS. 1-19 , the ion transport apparatus is discussed primarily in the context of an RF-only ion guide, with axial DC potentials added as needed to modulate ion kinetic energy in the axial direction. It will be understood, however, that the ion transport apparatus may function as other types of ion processing apparatus. For example, the ion transport apparatus may be utilized as a collision cell for fragmenting ions, such as by directing an appropriate background gas to the convergent ion beam in the interior space circumscribed by the electrodes. As another example, the ion transport apparatus may be utilized as a mass filter or sorter that passes only ions within a desired range of mass-to-charge (or m/z) ratios, such as by superposing an appropriate DC voltage U on the RF voltage V that drives the two-dimensional RF field. 
     An ion transport apparatus provided in accordance with any of the implementations disclosed herein may form a part of an ion processing system that includes other ion-processing devices. For example, the ion processing system may generally include one or more upstream devices and/or one or more downstream devices. The ion processing system may be a mass spectrometry (MS) system (or apparatus, device, etc.) configured to perform a desired MS technique (e.g., single-stage MS, tandem MS or MS/MS, MS n , etc.). Thus, as a further example, the upstream device may be an ion source and the downstream device may be an ion detector, and additional devices may be included such as ion storage or trapping devices, mass sorting or analyzing devices, collision cells or other fragmenting devices, ion optics and other ion guiding devices, etc. Thus, for example, the ion guide may be utilized before a mass analyzer (e.g., as a Q0device), or itself as an RF/DC mass analyzer, or as a collision cell positioned after a first mass analyzer and before a second mass analyzer. Accordingly, the ion guide may be evacuated, or may be operated in a regime where collisions occur between ions and gas molecules (e.g., as a Q0 device in a high-vacuum GC/MS, or a Q0 device in the source region of an LC/MS, or a Q2 device, etc.). 
     In the various implementations described above and illustrated in  FIGS. 1-19 , the electrodes of the ion transport apparatus have been configured to provide an ion-guiding interior space elongated along a straight longitudinal axis, thereby resulting in a straight (albeit converging) ion beam. It will be understood, however, that the longitudinal axis need not be a straight axis but rather may be a curved axis. This may be accomplished by configuring the electrodes appropriately. A curved, converging ion beam is realized as a result. Generally, a curved ion guide is one in which the ion axis along which the ions pass is a curved path rather than a straight path. A curved ion guide is often desirable for implementation in ion processors such as mass spectrometers because the curved ion guide can improve the sensitivity and robustness of the mass spectrometer. A primary advantage of the curved ion guide in such a context is that it provides a line-of-sight separation of the neutral noise, large droplet noise, or photons from the ions, thereby preventing the neutral components from reaching the more sensitive parts of the ion optics and ion detector. Moreover, the curved ion guide enables the folding or turning of ion paths and allows smaller footprints in the associated instruments. 
     As an example, a curved ion transport apparatus may impart a smooth 90° turn to the ion path. One or more additional curved ion transport sections may be added to further modify the ion path. These additional ion transport sections may also be configured as circular sectors but alternatively may follow linear paths or other types of non-circular paths. Thus, one or more ion transport sections may be utilized to provide any desired path for an ion beam focused thereby. Thus, in another non-illustrated example, the ion transport apparatus may be shaped so as to provide a 180-degree turn in the focused ion path, i.e., a U-shaped ion path, with the use of one or more appropriately shaped ion transport sections. In another example, the “legs” of the U-shaped path may be extended by providing linear ion guide sections adjacent to the ion inlet and the ion outlet of the U-shaped ion guide. In another example, two 90-degree ion transport sections may be positioned adjacent to one another to realize the 180-degree turn in the ion path. In another example, two similarly shaped ion transport sections may be positioned adjacent to one another such that the radius of curvature of one section is directed oppositely to that of the other ion section, thereby providing an S-shaped ion path. Persons skilled in the art will appreciate that various other configurations may be derived from the present teachings. 
     It will be understood that the methods and apparatus described in the present disclosure may be implemented in an ion processing system such as an MS system as generally described above by way of example. The present subject matter, however, is not limited to the specific ion processing systems illustrated herein or to the specific arrangement of circuitry and components illustrated herein. Moreover, the present subject matter is not limited to MS-based applications, as previously noted. 
     In general, terms such as “communicate” and “in . . . communication with” (for example, a first component “communicates with” or “is in communication with” a second component) are used herein to indicate a structural, functional, mechanical, electrical, signal, optical, magnetic, electromagnetic, ionic or fluidic relationship between two or more components or elements. As such, the fact that one component is said to communicate with a second component is not intended to exclude the possibility that additional components may be present between, and/or operatively associated or engaged with, the first and second components. 
     It will be understood that various aspects or details of the invention may be changed without departing from the scope of the invention. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation-the invention being defined by the claims.