Device geometries for controlling mass spectrometer pressures

Abstract

A mass spectrometer collision cell system, comprising: a gas containment vessel comprising an internal chamber having ion inlet and ion outlet ends and a cross-sectional area, A.sub.chamber; a gas inlet aperture; first and second gas outlet apertures that are disposed at or proximal to the ion inlet and outlet ends, respectively, and that have respective outlet aperture cross-sectional areas, A.sub.aperture1 and A.sub.aperture2, and an average outlet aperture cross-sectional area, A.sub.aperture.sup.ave; a longitudinal axis of the chamber extending from the ion inlet end to the ion outlet end and having a length, L.sub.chamber; and a set of multipole rod electrodes, at least a portion of each multipole rod electrode being within the chamber, wherein the values of A.sub.chamber, L.sub.chamber and A.sub.aperture.sup.ave are such that the combined gas conductance of the chamber and the gas outlet apertures is not greater than 95 percent of the gas conductance of the gas outlet apertures alone.

Claims

1. A mass spectrometer collision cell, cooling cell or reaction cell system, comprising: a gas containment vessel comprising an internal chamber having an ion inlet end and an ion outlet end, the chamber having a cross-sectional area, A.sub.chamber, transverse to the longitudinal axis; a gas inlet aperture for providing gas to the internal chamber; first and second gas outlet apertures disposed at or proximal to the ion inlet and ion outlet ends of the internal chamber, respectively, the first and second gas outlet apertures having respective outlet aperture cross-sectional areas, A.sub.aperture1 and A.sub.aperture2, and an average outlet aperture cross-sectional area, A.sub.aperture.sup.ave; a longitudinal axis of the chamber extending from the ion inlet end to the ion outlet end and having a length, L.sub.chamber; and a set of multipole rod electrodes, wherein at least a portion of each multipole rod electrode is disposed within the chamber, wherein the values of A.sub.chamber, L.sub.chamber and A.sub.aperture.sup.ave are such that the combined gas conductance of the chamber and the gas outlet apertures is less than or equal to 95 percent of the gas conductance of the gas outlet apertures alone.

2. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein the values of A.sub.chamber, L.sub.chamber and A.sub.aperture.sup.ave are such that the combined gas conductance of the chamber and the gas outlet apertures is less than or equal to 90 percent of the gas conductance of the gas outlet apertures alone.

3. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein the values of A.sub.chamber, L.sub.chamber and A.sub.aperture.sup.ave are such that the combined gas conductance of the chamber and the gas outlet apertures is less than or equal to 80 percent of the gas conductance of the gas outlet apertures alone.

4. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein the values of A.sub.chamber, L.sub.chamber and A.sub.aperture.sup.ave are such that the combined gas conductance of the chamber and the gas outlet apertures is less than or equal to 70 percent of the gas conductance of the gas outlet apertures alone.

5. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein each of the entrance aperture and the exit aperture comprises an opening in or a channel through an electrostatic lens.

6. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein each of the entrance aperture and the exit aperture is defined by a respective channel between portions of the multipole rods that extend outside of the chamber.

7. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein each of the entrance aperture and the exit aperture is defined by a respective channel between rod electrodes of a respective multipole device disposed outside of the chamber.

8. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein the longitudinal axis and the multipole rods are curved.

9. A mass spectrometer collision cell, cooling cell or reaction cell system as recited in claim 1, wherein d.sub.aperture is less than or equal to 5 millimeters.

10. A method of mass analyzing a sample comprising: generating a first plurality of ions derived from the sample and transmitting the plurality of ions into a chamber having an internal pressure, P.sub.1; transmitting the first plurality of ions through a first gas-restricting aperture into a second chamber having an internal pressure, P.sub.2, where P.sub.2>P.sub.1; either cooling the first plurality of ions within the chamber, reacting the first plurality of ions with gas in the chamber, or colliding the first plurality of ions with gas in the chamber to generate a plurality of product ions; transmitting either the cooled first plurality of ions or the plurality of product ions through a second gas-restricting aperture into a third chamber having an internal pressure, P.sub.3, where P.sub.2>P.sub.3; and mass analyzing either the cooled first plurality of ions or the plurality of product ions using a mass analyzer within the third chamber, wherein the combined gas conductance of the second chamber and the gas-restricting apertures is less than or equal to 95 percent of the gas conductance of the gas-restricting apertures alone.

11. A method of mass analyzing a sample as recited in claim 10, wherein the combined gas conductance of the second chamber and the gas-restricting apertures is less than or equal to 90 percent of the gas conductance of the gas-restricting apertures alone.

12. A method of mass analyzing a sample as recited in claim 10, wherein the combined gas conductance of the second chamber and the gas-restricting apertures is less than or equal to 70 percent of the gas conductance of the gas-restricting apertures alone.

13. A method of mass analyzing a sample as recited in claim 10, wherein each gas-restricting aperture comprises a diameter, d.sub.aperture, that is less than or equal to 5 millimeters.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above noted and various other aspects of the present invention will become apparent from the following description which is given by way of example only and with reference to the accompanying drawings, not necessarily drawn to scale, in which:

(2) FIG. 1A is a schematic illustration of liquid chromatography and mass spectrometry (LCMS) analysis system that employs a conventional triple-quadrupole mass spectrometer system;

(3) FIG. 1B is a schematic illustration of gas chromatography and mass spectrometry (GCMS) analysis system that employs a conventional triple-quadrupole mass spectrometer system;

(4) FIG. 2 is a schematic transverse cross-sectional diagram of a known collision cell apparatus;

(5) FIG. 3A is a graph of the variation of the Clausing factor, shown as the variation of the probability of transmission gas or ion particles through a tube of length, L, and diameter, d, with changing ratio, L/d;

(6) FIG. 3B is a graph of the calculated cumulative probability density of reflection or scattering of particles off of a surface as a function of the angle of emission from the surface, in accordance with Lambertian reflection;

(7) FIG. 4A is a graph with a set of graphical plots, each plot representing a different collision cell tube length, of calculated average pressure in the collision cell at various ratios of tube diameter to aperture diameter, the values of each plot calculated for a steady-state flow of 0.248 mL/min of Argon gas at 300 K;

(8) FIG. 4B is a set of graphical plots of the same collision cell internal pressure information plotted in FIG. 4A, but with the ordinate showing the ratio of calculated pressure to the asymptotic minimum possible pressure.

(9) FIG. 5A is a schematic transverse cross-sectional diagram of a first collision cell apparatus in accordance with the present teachings;

(10) FIG. 5B is a schematic transverse cross-sectional diagram of a second collision cell apparatus in accordance with the present teachings;

(11) FIG. 6 is a graph with a set of graphical plots, each plot representing a collision cell tube length, of calculated gas conductance through the collision cell at various ratios of tube diameter to aperture diameter, the values of each plot calculated for a steady-state flow of 0.248 mL/min of Argon gas at 300 K, the graph also showing gas conductance values of six known conventional collision cells and the gas conductance values of the novel collision cells depicted in FIGS. 5A and 5B;

(12) FIG. 7 is a schematic longitudinal cross-sectional diagram of a third collision cell apparatus in accordance with the present teachings;

(13) FIG. 8A is a schematic longitudinal cross-sectional diagram of a fourth collision cell apparatus in accordance with the present teachings; and

(14) FIG. 8B is a schematic transverse cross-sectional diagram through a portion of the collision cell apparatus of FIG. 8A.

DETAILED DESCRIPTION

(15) The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the described embodiments will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiments and examples shown but is to be accorded the widest possible scope in accordance with the features and principles shown and described. To fully appreciate the features of the present invention in greater detail, please refer to FIGS. 1-7, 8A and 8B in conjunction with the following description.

(16) In the description of the invention herein, it is understood that a word appearing in the singular encompasses its plural counterpart, and a word appearing in the plural encompasses its singular counterpart, unless implicitly or explicitly understood or stated otherwise. Furthermore, it is understood that, for any given component or embodiment described herein, any of the possible candidates or alternatives listed for that component may generally be used individually or in combination with one another, unless implicitly or explicitly understood or stated otherwise. Moreover, it is to be appreciated that the figures, as shown herein, are not necessarily drawn to scale, wherein some of the elements may be drawn merely for clarity of the invention. Also, reference numerals may be repeated among the various figures to show corresponding or analogous elements. Additionally, it will be understood that any list of candidates or alternatives is merely illustrative, not limiting, unless implicitly or explicitly understood or stated otherwise.

(17) The Clausing factor, K, is often used for static molecular flow calculations (Clausing, Pieter. “Ober das Kosinusgesetz der Zurückwerfung als Folge des zweiten Hauptsatzes der Thermodynamik.” Annalen der Physik 396, no. 5 (1930): 533-566.). The Clausing Factor is a transmission probability correction factor that that ranges from zero to unity and that must be applied in order to correct calculations of gas flux through a theoretical aperture in an infinitely thin plane to real apertures of non-zero thickness, e.g., tubes of length, L. This factor takes into account the phenomenon that, when a tube has non-zero length, L, there are certain molecule trajectories that are excluded from passing out of the tube through the aperture because of angular restrictions. The original calculations of K were based on early Monte-Carlo simulations of molecular flow through tubes of different L/d ratios. Subsequently, the results of such calculations have been fit to empirical equations and tabulated. Clausing tables may also be used to gas conductance values and internal pressures for various types of tubes and chambers.

(18) FIG. 3A is a graph 101 of the variation of the Clausing factor, K, as calculated for a simple tube of length, L, and diameter, d, with changing ratio, L/d. It may be observed that the transmission probability drops as the L/d ratio increases; molecules are less likely to pass through a tube which has a large length-to-diameter ratio. A key phenomenon that contributes to the value of the Clausing factor is the fact that the rebound of gas molecules from internal surfaces within follows so-called Lambertian reflection, which is otherwise known as the Cosine Law.

(19) Lambertian reflection, as referred to herein, is analogous to Lambert's cosine law in the field of optics which states that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal. When molecules interact with a surface (metal, ceramic, plastic, etc), the molecular structure is rough relative to the size of a molecule. Molecules interact with this roughness and ultimately lose “memory” of the original angle of incidence. This phenomenon leads to desorption angles which are centered around normal to the surface and to the Cosine Law. With regard to this phenomenon, Rozanov (Rozanov, L. N. “Vacuum Technique” (2002) Hablanian, M. H. ed.) notes that a particularly relevant idea that emerges from Clausing's paper is that “the molecules leaving a surface at equilibrium consist of molecules having undergone, in general, various types of interaction with the surface: elastic scattering (specular reflection, diffraction in various channels), inelastic scattering (one or multiphonon annihilation or creation) or desorption (following adsorption). If more than one of these processes are effective, the distribution of the molecules leaving the surface, as a result of one of these processes, is in principle arbitrary even at equilibrium. The only constraint imposed by the presence of equilibrium is that the sum of all the distributions must be cosine.” FIG. 3B is a graph 111 of the calculated cumulative probability density of reflection or scattering of particles off of a surface as a function of the angle of emission from the surface, in accordance with Lambertian reflection.

(20) Based on the above considerations, the present inventors have recognized that the reason why molecules are generally prevented from escaping from a tube having a large L/d ratio is that, even when using the maximum diameter openings at the ends of the tube (i.e., apertures having the same diameter as the tube diameter), the average trajectories of molecules rebounding off of the tube interior surfaces are transverse to the longitudinal axis of the tube. As a result, there are relatively few internal pathways by which molecules rebound can off of the interior surfaces and still pass through an aperture immediately after the rebound. A consequence of the Lambertian reflection phenomenon is that, for a given constant diameter, d.sub.aperture, of gas-flow restricting apertures at the ends of a tube having length, L, and tube diameter, d, it is increasingly less likely for gas molecules to pass through the apertures as the ratio, L/d, increases (e.g., FIG. 3A). In such instances, an increase in L/d at a constant gas flow rate causes an increase in internal cell pressure.

(21) In order to exploit the phenomenon of Lambertian reflection, the inventors have studied how changing the geometry of a collision cell affects its internal gas pressure. Three different simple empty tubes with different inner diameters were fabricated by three-dimensional printing as listed in Table 1 below. The internal gas pressure of each tube under a flow of argon gas at 300 K was determined as the inlet pressure required to create a steady-state flow of 0.248 mL/min through the respective tube. Additionally, expected internal tube pressures were calculated from Direct Simulation Monte Carlo (DSMC) calculations [e.g., see G. A. Bird, “Molecular Gas Dynamics and the Direct Simulation of Gas Flows” (Oxford University Press, Oxford, 1994)] as well as by using the Clausing factor. The results of the experiments and calculations are shown in Table 1 below.

(22) TABLE-US-00001 TABLE 1 Experimental data from 3D printed tubes. 2.5 mm apertures, 125 mm total internal chamber length, L.sub.chamber (see FIG. 7). Cell Inner Pressure (mTorr) Pressure (mTorr) Pressure Diameter determined from determined from (mTorr) (mm) DSMC simulation Clausing Factor measured 40   5.5  4.1  3.9 24   5.8  4.2  4.3   2.50 40.3 67.3 78.1

(23) FIG. 7, which is discussed further in a subsequent paragraph, shows how the length, L, of the calculations and measurements of pressure in simple tubes relate to dimensions of a mass spectrometer collision cell, ion/gas reaction cell or cooling cell. Each simple tube comprises an inlet aperture and an outlet aperture that are at opposite ends of the tube. The inlet and outlet apertures of a simple tube are thus spaced apart by a distance, L, where L is just the length of the tube in question. However, in the mass spectrometer collision cell, ion/gas reaction cell or cooling cell, gas does not enter into the cell interior at one of the ends of the cell. Instead, gas is introduced into the cell interior chamber 53 of the cell through an ion inlet aperture 9 that is disposed approximately mid-way between the two end apertures 6. Each of the two end apertures 6 is a gas outlet end, even though one of the end apertures is an ion inlet end and the other end aperture is an ion outlet end. Thus, the effective cell length, L, that must be used for comparison to theoretical pressure calculations and simulations and for comparison to pressure measurements in simple tubes is one-half of the length, L.sub.chamber, of the cell interior chamber 53 as shown.

(24) As stated in the Background section of this document, the inventors have identified a need in the mass spectrometry art for collision cell designs that are able to attain the highest possible internal pressure possible while, at the same time, reducing the flow rate of collision gas to the collision cell. The ratio of gas flow rate to pressure is known as conductance, which may be stated in units of liters per second as follows:

(25) $\mathrm{Conductance}\left[\frac{L}{s}\right]=12.67\times \frac{\mathrm{Flow}\mathrm{Rate}\left[\mathrm{atm}\frac{\mathrm{mL}}{\min }\right]}{\mathrm{Pressure}\left[\mathrm{mTorr}\right]}$
Thus, the above-identified need in the art may be satisfied by making cell conductance as small as possible. As a result of the observed close correspondence between measured pressures and pressures that are calculated using the Clausing factor (Table 1), it is possible to predict the internal pressures will be developed, under steady-state gas flow, in tube-like collision cells of other sizes and then calculate the conductance. More generally, it is possible to measure conductance for any tentative collision cell design. It is then possible to calculate a quantity which is herein referred to as “relative conductance”, which is the ratio of the conductance for a complete collision cell system (including the interior chamber and the its gas inlet and gas outlet apertures) to the theoretical conductance of the apertures by themselves. The theoretical gas conductance, C.sub.aperture, of an aperture (or “theoretical aperture conductance”) is herein defined as the limiting conductance of a circular-bore tube of inner diameter, d, as tube length, L, approaches zero. Generally, for any tube of finite length, C.sub.tube=νκ.sub.tubeA.sub.tube/4, where ν is the average molecular velocity, κ.sub.tube is the Clausing factor of the tube and A.sub.tube is the cross-sectional area of the tube. Similarly, C.sub.aperture=νκ.sub.apertureA.sub.aperture/4 where κ.sub.aperture and A.sub.aperture are the Clausing factor and cross-sectional area of the aperture, respectively. The above procedure gives a ratio of how much lower the conductance of the complete collision cell geometry is compared to the conductance of the apertures in isolation. This procedure also normalizes out the molecular velocity and temperature of the gas.

(26) For example, FIG. 4A is a graph of the calculated pressure within simple tubes having various lengths, inner diameters and inlet and outlet aperture diameters. The values of each plot of FIG. 4A are calculated for a steady-state flow of 0.248 mL/min of Argon gas at 300 K. Plot 121 of FIG. 4A pertains to a series of tubes having inner diameters ranging from 39.5 mm to 2.5 mm, all tubes 250 mm long and positioned adjacent to an outlet aperture having a 2.5 mm aperture diameter. Plot 122 pertains to a series of tubes having inner diameters ranging from 39.5 mm to 2.5 mm, all tubes 125 mm long and positioned adjacent to an outlet aperture having a 2.5 mm aperture diameter. Plot 123 pertains to a series of tubes having inner diameters ranging from 79.0 mm to 5.0 mm, all tubes 125 mm long and positioned adjacent to an outlet aperture having a 5.0 mm aperture diameter.

(27) The asymptotic values (i.e., baseline values) of pressure that are approached at the right-hand side of the graph of FIG. 4A represent the pressures that are developed in a collision cell within which the conductance is determined only by the diameter of the inlet and outlet apertures. In FIG. 4B, the data of FIG. 4A is migrated to a common baseline. Thus, the plots 131, 132 and 133 represent the same data as graphed in plots 121, 122 and 123, respectively and represent the ratio of the calculated pressures in each tube cell to the respective baseline value. In many instances, the length, L, of the collision cell and the diameter, d.sub.aperture, are not free to vary as a result of external constraints. The plots of FIG. 4B demonstrate that, under conditions where the aperture diameter is constrained, an advantageous gain in pressure can be achieved at constant gas flow rate by reducing the tube diameter and thereby reducing the conductance of the apparatus.

(28) In order to take advantage of the above insights, the inventors have developed new collision cell designs that can achieve higher internal pressures than can be achieved within conventional collision cells without an increase in gas flow relative to conventional designs. Accordingly, each of FIG. 5A and FIG. 5B is a schematic transverse cross-sectional diagram of a collision cell, cooling cell or reaction cell apparatus 34b, 34c in accordance with the present teachings. The cross sections shown in FIGS. 5A-5B are taken transverse to a longitudinal axis of the respective apparatus. In similarity to the collision cell 34a depicted in FIG. 2, each of the apparatuses 34b, 34c comprises a set of four quadrupole rods 4 that are elongated parallel to the longitudinal axis of the respective apparatus 34b, 34c. Within each apparatus, the quadrupole rods are disposed within a central chamber 7 of a housing structure 5. Gas is provided into the chambers 7 through a gas inlet tube 35 (see FIGS. 1A, 1B) that is not depicted in FIGS. 5A-5B but that passes through the housing 5 within a transverse cross section other than the cross sections shown in FIGS. 5A-5B. In each of FIGS. 5A-5B, the outlet aperture 6 is shown as a projection onto the plane of the drawing. An axial field may be generated within each cell 34b, 34c by means of pluralities of electrodes printed onto each of the circuit boards 1. Each of the collision, cooling or reaction cell apparatuses 34b, 34c that are depicted in FIGS. 5A-5B employs a modified design in which the ratio between the cross-sectional area of the central chamber 7 and the cross-sectional area of the aperture 6 is greatly reduced relative to the similarly calculated ratio for the conventional cell 34a (FIG. 2). Specifically, the ratio of chamber cross-sectional area to aperture cross-sectional area of the conventional cell 34a is approximately 103 but the similarly calculated ratios of the novel cells 34b and 34c are approximately 22 and 9, respectively.

(29) FIG. 6 is a graph that compares measured relative gas conductance values of several commercially-available collision-induced dissociation cells to the measured conductance of the novel collision-induced dissociation cell shown in FIG. 5A. All data shown in FIG. 6 were obtained using a gas flow rate of 0.248 mL/min of argon at 300 K. The relative conductance values are plotted against ordinate values determined as the ratio of an average inner diameter, d.sub.average, of an internal chamber of a collision cell to the diameter, d.sub.aperture, of the bounding gas-constricting apertures. For purposes of comparison between two different physical collision cell structures, the quantity d.sub.average should be calculated consistently. In simple cases, the cross section of the internal chamber may be circular, in similarity to the cross section depicted in FIG. 2, with diameter, d.sub.tube. In such cases,
d.sub.average=d.sub.tube.
Otherwise, if the cross section is a rectangle with height, h and width, w, then one may approximate d.sub.average as

(30) $d_{average}=2\sqrt{\frac{hw}{\pi }}.$
If the tube or chamber in question is long and narrow, then, instead of estimating relative conductance values by comparing diameters or cross-sectional areas (as above), it is preferable to calculate the conductance directly using rectangular duct Clausing factors or DSMC calculations.

(31) The Clausing factor for a rectangular duct can be calculated using the tables in Santeler, D. J.; Boeckmann, M. D. “Molecular Flow Transmission Probabilities of Rectangular Tubes”, Journal of Vacuum Science Technology A, 1991, 9(4), 2378-2383. The conductance of the rectangular chamber is then calculated as
C.sub.chamber=(νκ.sub.chamberA.sub.chamber)/4
where A.sub.chamber=hw is the cross-sectional area of the rectangular chamber and k.sub.chamber is the Clausing factor of the rectangular chamber.

(32) For tubes or chambers having more complex cross-sectional shapes, one may compare different chamber designs or to compare estimated chamber conductance to aperture conductance by comparing cross sectional areas instead of comparing average diameters. For example, one may determine the cross sectional area, A.sub.chamber, of the chamber by graphical integration and then compare A.sub.chamber to A.sub.aperture (where, in general, A.sub.aperture=πr.sub.aperture.sup.2) or else compare A′.sub.chamber, relating to the cross sectional area of a first collision cell structure, to A″.sub.chamber relating to a the cross sectional area of a second collision cell structure to which the first cell structure is being compared.

(33) Plotted point 144c on FIG. 6 pertains to the instance of the cell design shown in FIG. 2. Plotted point 145a pertains to the novel cell design shown in FIG. 5A. Plotted point 145b pertains to the novel cell design shown in FIG. 5B. Plotted points 144a, 144b, 144d, 144e, and 144f pertain to other known cell designs. For comparison, curves 141, 142 and 143 depict calculated relative conductance values of various tube and aperture combinations. The abscissa value of each plotted point of FIG. 6—either on one of the curves 141-143 or plotted individually—represents a ratio between the conductance of an elongated internal volume relative to the theoretical aperture conductance of just the bounding apertures that are adjacent to the ends of the elongated internal volume. As noted above, the theoretical conductance of an aperture (or “theoretical aperture conductance) is herein defined as the limiting conductance of a circular-bore tube of inner diameter, d, as tube length, L, approaches zero. Curve 141 pertains to a circular-bore tube having a length, L, of 250 mm and variable inner diameter, d.sub.tube, together with a bounding aperture having a diameter of 2.5 mm. Curve 142 pertains to a circular-bore tube having a length, L, of 125 mm and variable inner diameter, d.sub.tube, together with a bounding aperture having a diameter of 5.0 mm. Curve 143 pertains to a circular-bore tube having a length, L, of 125 mm and variable inner diameter, d.sub.tube, together with a bounding aperture having a diameter of 2.5 mm.

(34) The data depicted in FIG. 6 highlights the somewhat counterintuitive fact that, in all cases in which the collision cell gas chamber diameter—either d.sub.tube for chambers having circular cross sections or d.sub.average otherwise—is greater than the aperture diameter, d.sub.aperture, the gas conductance of the collision cell decreases as the diameter of the collision cell chamber decreases. When the collision cell diameter is much greater than the diameter of the surrounding gas-restricting apertures (i.e., greater by a factor of 7 or more (see FIG. 6), the gas conductance of the collision cell system (i.e., collision cell and apertures) is predominantly controlled by the diameter of the apertures. However, as the collision cell diameter decreases, the Clausing factor of the chamber exerts an increasing level of influence over the conductance value of the system, since the collision cell has non-trivial length, L. Therefore, the conductance of the collision cell system decreases—and, correspondingly, the constant-flow-rate pressure increases—as the collision cell diameter decreases down to the diameter of the apertures. Therefore, for a given flow rate, the internal pressure increases as the collision cell diameter decreases down to the size of the bounding apertures.

(35) As a specific example of how a decrease in collision gas chamber diameter increases internal pressure, the inventors have compared the known collision cell 34a of FIG. 2 (represented by point 144c in FIG. 6) with the novel collision, cooling or reaction cell 34c of FIG. 5B (represented by point 145b of FIG. 6). Using identical cell lengths, aperture diameters and gas flow rates, it is found that the average pressure within the interior chamber 7 of the apparatus 34c (FIG. 5B) is 6.7 mTorr as compared to a pressure of 4.2 mTorr within the internal chamber 53 of the collision cell 34a (FIG. 2). This sixty percent increase in pressure is attributable, at least in part, to the smaller ratio, in cell 34c as compared to cell 34a, between the cross-sectional area, A.sub.chamber, of the respective internal chamber (i.e., of chamber 7 as shown in FIG. 5B as compared to chamber 53 as shown in FIG. 2) and the area, A.sub.aperture, of the respective gas outlet apertures 6. For instance, the ratio of the cross-sectional area of chamber 53 to the cross-sectional area of outlet aperture 6 is approximately 103 for the apparatus 34a (FIG. 2) whereas the ratio between the ratio of the cross-sectional area of chamber 7 to the cross-sectional area of outlet aperture 6 is approximately 8.9 for the apparatus 34c (FIG. 5B). It should also be noted, from comparison of curve 142 (length, L, equal to 125 mm) with 141 (length, L, equal to 250 mm), the collision cell pressure could be significantly further increased, with the same cell and aperture diameters, by increasing (e.g. doubling) the length of the collision cell. Increasing the length decreases the Clausing factor of the chamber which therefore decreases the conductance and increases the pressure.

(36) As another specific example of how a decrease in collision gas chamber diameter increases internal pressure, the inventors have compared the known collision cell 34a of FIG. 2 (represented by point 144c in FIG. 6) with the novel collision, cooling or reaction cell 34b of FIG. 5A (represented by point 145a of FIG. 6). Using identical cell lengths, aperture diameters and gas flow rates, it is found that the average pressure within the interior chamber 7 of the apparatus 34b (FIG. 5A) is 4.8 mTorr as compared to a pressure of 4.2 mTorr within the internal chamber 53 of the collision cell 34a (FIG. 2). This fourteen percent increase in pressure is attributable, at least in part, to the smaller ratio, in cell 34b as compared to cell 34a, between the cross-sectional area, A.sub.chamber, of the respective internal chamber (i.e., of chamber 7 as shown in FIG. 5A as compared to chamber 53 as shown in FIG. 2) and the area, A.sub.aperture, of the respective gas outlet apertures 6. For instance, the ratio of the cross-sectional area of chamber 53 to the cross-sectional area of outlet aperture 6 is approximately 103 for the apparatus 34a (FIG. 2) whereas the ratio between the ratio of the cross-sectional area of chamber 7 to the cross-sectional area of outlet aperture 6 is approximately 22 for the apparatus 34b (FIG. 5A). It should also be noted, from comparison of curve 142 (length, L, equal to 125 mm) with 141 (length, L, equal to 250 mm), the collision cell pressure could be significantly further increased, with the same cell and aperture diameters, by increasing (e.g. doubling) the length of the collision cell. Increasing the length decreases the Clausing factor of the chamber which therefore decreases the conductance and increases the pressure.

(37) Line 147 of FIG. 6 represents a five percent decrease in collision cell system conductance, relative to the conductance of just the gas-restricting apertures of the system. Such a reduction in conductance would correspond to an approximate five percent increase in internal collision cell pressure, at constant gas flow rate. However, according to the available data, none of the known collision cell designs achieves this level of reduction of conductance, relative to the conductance of the apertures. However, the novel collision cell design of the apparatus 34c shown in FIG. 5B achieves an approximate 35-37 percent reduction in relative conductance, which corresponds to an approximate 56-58 percent increase in collision cell pressure, at constant flow rate. Stated differently, the value of the gas conductance of the apparatus 34c is approximately 63-65 percent of the value of the gas conductance of the apparatus 34a, yielding a constant-flow-rate pressure, in the apparatus 34c, that is approximately 1.55-1.59 times the pressure that is developed within the apparatus 34a, at the same gas flow rate. The results of FIG. 6 suggest that, in order to achieve a five percent decrease in relative conductance, the known collision cell systems would need to be modified by either decreasing the circular cross-section diameter, d.sub.chamber, by an amount such that the ratio d.sub.chamber/d.sub.aperture≤7 or by increasing (e.g. doubling) the length, L, of the collision cell or by some combination of decreasing d.sub.chamber and increasing L.

(38) The total conductance of gas flowing out of a collision cell involves gas flow from the gas inlet 9, 35 at the center (FIGS. 1 and 7), through a “half-tube” of length, L, that is one-half of the total length, L.sub.chamber of the cell (e.g., see FIG. 7), and through the aperture 6. This half-tube conductance must be multiplied by 2 since there are two parallel paths out of the chamber, one towards the entrance aperture and one towards the exit aperture. Thus, the conductance of the cell, C.sub.cell, can be approximated as:

(39) $C_{\mathrm{cell}}=\frac{2}{\frac{1}{C_{aperture}}+\frac{1}{C_{\mathrm{halftube}}}}.$
where C.sub.aperture is the conductance of each aperture and C.sub.halftube is the conductance from the center of the tube at the gas inlet to the aperture. Equations in Haefer, R. A.; Vacuum 1980 30 217, p. 217 and p. 221 can be used to sum more complex structures. For a large cross section tube, C.sub.halftube becomes very large compared to C.sub.aperture and the above equation reduces simply to C.sub.cell=2C.sub.aperture. However, as the cross section of the tube becomes smaller and/or the chamber length becomes longer, the resulting conductance C.sub.halftube decreases. A smaller cross section reduces the area and a longer distance reduces the Clausing factor. These trends lead to the inequality C.sub.cell<2C.sub.aperture which results in the desired higher pressure for a given flow of gas.

(40) As an example, if we have 2.5 mm diameter apertures in plates that are 0.75 mm thick, the conductance out of each such aperture will be 0.377 L/s for argon at 300 K. For a large inner diameter tube, there is no significant obstruction to the flow of gas. Therefore, in this instance, the conductance of the cell is approximately equal to 2C.sub.aperture=0.76 L/s. With a 125 mm total cell length, the conductance of the half tube drops as the inner diameter is reduced. Once the inner diameter is reduced to approximately 40 mm, the conductance of the tube itself becomes a restriction for the gas to reach the apertures. At an inner diameter of approximately 20 mm, the conductance of the cell has dropped to approximately 0.96 that of the two apertures by themselves. At an inner diameter of approximately 10 mm, the conductance of the cell has dropped to approximately 0.77 that of the two apertures by themselves. The conductance of the half-cell is 1.26 L/s. This makes the total cell conductance 0.58 L/s which is 0.77 times the conductance of the apertures by themselves, 0.76 L/s. This results in a lower conductance out of the cell. This in turn, gives a higher pressure in the cell for a given flow rate.

(41) These equations can be used for cells which are not symmetric, in other words where the gas inlet is not at the center of the device. These equations can also be used for cells which do not have identical apertures on each end. The conductance from the gas inlet to each of the two apertures are calculated, C.sub.halftube1 and C.sub.halftube2. Then the conductance of the two apertures are calculated, C.sub.aperture1 and C.sub.aperture2. The total cell conductance is

(42) $C_{\mathrm{cell}}\frac{1}{\frac{1}{C_{ape\mathrm{rture}1}}+\frac{1}{C_{halftube1}}}+\frac{1}{\frac{1}{C_{\mathrm{aperture}2}}+\frac{1}{C_{h\mathrm{alftube}2}}}.$
For more complex geometries, DSMC can be used to calculate the total conductance of the cell. This can then be compared to the conductance of the apertures by themselves. This could include curved cells (e.g. 90°, 180°, or anything else). The conductance of cell geometries with other internal shapes which are not simply round or rectangular can be calculated by simulation. This also includes cell geometries with internal parts which make the actual conductance different from that of a simple round or rectangular tube.

(43) FIG. 7 is a schematic longitudinal cross-sectional diagram of a third collision cell, cooling cell or reaction cell apparatus 34d in accordance with the present teachings. The collision, cooling or reaction cell 34d comprises a set of multipole rod electrodes 74 which are employed, in operation, to contain ions within an ion channel 73. Entrance lens 71a and exit lens 71b are used to control the introduction of ions into cell 34d and to control the flow of ions through the cell along the ion channel 73. The collision cell 34d differs from conventional collision cell apparatuses in that the conventional entrance end lenses are replaced by specialized einzel lenses in which the apertures of the plate electrodes composing each lens progressively decrease in size in a direction towards the cell interior. Accordingly, entrance lens 71a comprises the three plate electrodes 78a, 78b and 78c, with the outermost plate electrode 78a having the aperture with the greatest diameter and the innermost electrode 78c having the aperture with the smallest diameter. At the ion outlet end of the apparatus, the exit lens 71b comprises the three plate electrodes 79a, 79b and 79c, with the outermost plate electrode 79a having the aperture with the greatest diameter and the innermost electrode 79c having the aperture with the smallest diameter. The apertures in plates 78c and 79c are the gas-flow-restricting inlet and outlet apertures, respectively. These apertures are smaller in diameter—or, more generally, have a smaller cross-sectional area—than the apertures of conventional einzel lenses. Accordingly, the Lambertian reflection phenomenon, it is probabilistically less likely for gas molecules to pass through the apertures in plates 78c and 79c than it is for gas molecules to pass through the apertures of conventional einzel lenses, thus leading to greater internal cell pressures, assuming constant gas flow rate.

(44) FIG. 8A is a schematic longitudinal cross-sectional diagram of a fourth collision cell, cooling cell or reaction cell apparatus 34e in accordance with the present teachings. FIG. 8B is a schematic transverse cross-sectional diagram of the apparatus along section C-C′. In contrast to the apparatus 34d that is shown in FIG. 7, the apparatus 34e (FIGS. 8A-8B) does not utilize end lenses. Instead, the ion focusing properties that are otherwise provided by end lenses are provided, in the apparatus 34e, by extensions of the multipole rod electrodes outside of the gas containment vessel 38. One such extension, of length, ΔL, is indicated in FIG. 8A. As shown in the transverse cross section of FIG. 8B, one or more insulative bodies 72, which form gas-flow barriers between pairs of rod electrodes, cause the gas flow out of each end of the gas containment vessel 38 to be limited to within a short channel 6 that functions as the gas-restricting aperture and that is centered between the rod electrode extensions. The one or more insulative bodies 72 may comprise, without limitation, either: spacers that support the rod electrodes, gaskets that are fitted between the electrodes or vacuum “feed-through” components that are affixed to the walls of the ion containment vessel.

(45) In alternative embodiments, the portions of the internal rod electrodes that extend through the wall of the gas containment vessel 38 (FIG. 8A) may be replaced by a separate set of short “stub” electrodes (not shown) that are partially disposed outside of the containment vessel 38 and that are separated from the internal rod electrodes 74 by gaps. In such embodiments, each aperture 6 is a short channel that is centered between the stub electrodes. Each set of stub electrodes—one set at the inlet end of the apparatus 34e and/or or a separate set at the ion outlet end of the apparatus—comprises a separate quadrupole or multipole device. Accordingly, a power supply (not shown) is configured to provide RF voltages to the stub electrodes. The power supply may also be configured to supply DC voltage differences between the internal rod electrodes and each set of stub electrodes in order to urge ions into and out of the apparatus 34e.

(46) The discussion included in this application is intended to serve as a basic description. The present invention is not intended to be limited in scope by the specific embodiments described herein, which are intended as single illustrations of individual aspects of the invention. Functionally equivalent methods and components are within the scope of the invention. As but one example, collision cells and ion cooling cells that have been used in the examples herein have been described above as having linear longitudinal axes. However, the principles described herein may also be applied more broadly to collision cells and ion cooling cells that are not straight. Thus, collision cells ion cooling cells and reaction cells that have rod electrodes that are curved along their lengths and that have curved longitudinal axes are also contemplated. Such curved multipole devices are described, for example, in U.S. Pat. Nos. 8,461,524, 9,543,136 and 6,576,897. The curvature is beneficial for the separation of uncharged molecules, which follow straight line trajectories in the absence of collisions, from ions, the trajectories of which are largely constrained to follow a pseudopotential well surrounding the curved longitudinal axis. In such instances, the chamber length, L.sub.chamber, (which equals 2 L) should be taken as the total length of the curved longitudinal axis, from an entrance aperture to an exit aperture. Various other modifications of the invention, in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description and accompanying drawings.