Method and apparatus to increase ionization efficiency in an ion source

A method and an apparatus for collecting ions in which ions are produced from a sample in an ion source. An electric field is provided that is more uniform in an area adjacent the sample than in an area adjacent an inlet to the ion transfer device or that is larger in field strength at the sample than at a point removed from the sample towards the inlet of the ion transfer device. Ions are received into the electric field and transferred through the ion transfer device to a sampling orifice of the mass spectrometer. The apparatus includes an ion transfer device coupled to a sampling orifice of a mass spectrometer. The ion transfer device has an inlet with a surface that extends in a direction from an axis of the ion transfer device. The ion transfer device can extend a distance of at least 10 times an inner diameter of a sampling orifice of the mass spectrometer.

CROSS-REFERENCE TO RELATED DOCUMENTS

This application is related to U.S. application Ser. No. 10/367,917 entitled “Method and Apparatus for Efficient Transfer of Ions into a Mass Spectrometer,” filed on Feb. 19, 2003, the entire contents of which is incorporated herein by reference. This application is related to U.S. application Ser. No. 09/795,108 entitled “Capillary ion delivery device and method for mass spectroscopy,” filed on Mar. 1, 2001, the entire contents of which is incorporated herein by reference. This application is related to U.S. Pat. No. 5,965,884 entitled “Atmospheric Pressure Matrix-Assisted Laser Desorption,” issued Oct. 12, 1999, the entire contents of which is incorporated herein by reference.

DISCUSSION OF THE BACKGROUND

1. Field of the Invention

This invention relates in general to ion sources, and in particular to MALDI mass spectrometry ion sources especially with pulsed dynamic focusing.

2. Background of the Invention

Ionization of chemical species can be accomplished by a variety of methods including matrix-assisted laser desorption/ionization (MALDI), atmospheric pressure (AP)-MALDI, electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI), field ionization, electron ionization, discharge and photoionization. These ionization techniques, when combined with an appropriate mass analyzer or ion mobility spectrometer, yield chemical and structural information about the molecules ionized. One goal of combining an ion source with an instrumental analyzer is to achieve a low limit of detection for a chemical species of interest (i.e., high sensitivity). Another goal is to acquire such information in the fastest time possible (i.e., high throughput).

One combination of ion source and spectrometer is an AP-MALDI mass spectrometry as described by Laiko et al. in Anal. Chem. 2000, 72:652–657; 72:5239–5243; and described in U.S. Pat. No. 5,965,884, the entire contents of which are incorporated herein by reference. As shown inFIG. 1, AP-MALDI system2uses a pulsed laser4for ionization, at ambient pressures, to create ions for analysis in a mass spectrometer6. A capillary8is used in conventional AP-MALDI MS configurations to transfer ions from the sample target plate10(i.e., the ion source) to the mass spectrometer6.

FIG. 2Ais a diagram depicting an enlarged view of an AP-MALDI sampling interface configuration showing a tapered capillary8, which is itself interfaced to the mass spectrometer6by a sampling orifice9bto an inlet flange9. The numbers depicted on the figures represent typical values for the dimensions used, and are not intended to specifically restrict the present invention. Capillaries (as shown for example inFIG. 1andFIG. 2A) can be tapered.

Further, as shown inFIG. 2B, the sampling orifice9bcan utilize sharp tips. However, other sampling inlets9, as shown inFIGS. 2C and 3, have been used, including arrangements as inFIG. 3in which a non-parallel sample plate10is adjacent to the inlet flange9. The non-parallel configuration permits laser irradiation to be aligned on-axis with the sampling interfaces, and illustrates one problem overcome by the use of extended capillaries, such as for example capillary8shown inFIG. 1, to provide better sample access.

Traditionally, samples were mounted on sample plates10and placed close to the inlet flange9of the mass spectrometer6. However, pragmatic considerations such as line-of-sight for laser desorption and imaging drove the development of extended capillary delivery systems such as shown inFIG. 1, in which more space is obtained permitting flexibility in sampling and the sampling from multiple sample plates into one mass spectrometer unit.

To increase ion collection efficiencies in the above shown configurations, electric field extraction techniques were developed. An applied electric field serves to draw ions produced from the sample toward the capillary8or the sampling orifice9bof the mass spectrometer6. A further enhancement to the electric field extraction techniques has been the application of a pulsed dynamic focusing (PDF) technique which removes the electric field in the sample-to-inlet region, just prior to ions entering the capillary8or the sampling orifice9b. The PDF technique reduces ion losses due to collisions of ions with walls of the capillary8or the sampling orifice9b. This PDF technique as described in U.S. patent application Ser. No. 10/367,917, the entire contents of which are incorporated herein by reference, is often referred to as “timed-extraction” and has also been recently described by Tan et al. in 2004, Anal. Chem., the entire contents of which are incorporated herein by reference.

In brief, the PDF technique permits the use of off-axis ion production techniques from the sampling interface8, such as for example off-axis laser irradiation, to generate ions from regions not directly in front of the capillary8or the inlet flange9. The PDF technique increases analytical throughput when laser spot sizes are increased. Improvements in throughput with PDF have been demonstrated using AP-MALDI ion trap MS systems with both capillary and conical sampling interfaces. In addition to the higher throughput afforded by the PDF technology, sensitivity was found to be positively correlated with electric field strength.

Ion trajectories and kinetics have been recently modeled for the conventional PDF techniques. Ion simulation typically apply a boundary element method on user-defined geometries, voltage settings and gas flow rates to determine electric field, gas dynamic flow, and ion trajectories. The ion trajectories can be determined based on ion mobility calculations. Such simulations made for example for the configuration shown inFIG. 1with a tapered extended capillary8show that, in a static electric field, ions off-axis from the sampling interface are lost to the walls12and tip14of the sampling interface (seeFIG. 4). Simulations further showed that when PDF was applied to AP-MALDI, off-axis ions are more efficiently collected, since the electric field being terminated before the ions arrive at the walls12and tip14of the sampling interface does not force the ions onto the walls. Rather, upon termination of the electric field, the ions are entrained in the gas flow entering the mass spectrometer6.

Further simulations to include ion recombination kinetics to study the relative ion yield associated with different configurations and electric field strengths have determined that the electric field strength directly affects ion signal intensity (seeFIG. 5). One possible theory to explain this phenomenon is that positive and negative ions ejected from the sample surface by the laser pulse initially occupy a narrow layer near the target plate. The applied electric field causes these positive and negative ions to move in opposite directions, minimizing ion losses that can result from gas-phase ion recombination and neutralization. From this theory higher electric fields at the site of ionization would improve ionization efficiency and hence sensitivity, as the positive and negative ions are more rapidly separated thus reducing the number of gas-phase ion recombination events.

One potential drawback with the sampling interface designs discussed above is that the electric field may not be optimized at the location of irradiation (i.e. the location of ion generation). Thus, a significant fraction of the ions can recombine or be neutralized. While applying higher voltages to the sample target plate could raise the electric field, arcing and discharge at the higher voltages can limit the upper bound to which the electric field can be adjusted. Furthermore, the electric field in the sampling interface designs may be limited to a range of effectiveness about the sampling interface.

SUMMARY OF THE INVENTION

One object of the present invention is to provide a mechanism for generating higher electric field strength at and/or near the ionization location.

A further object of the present invention is to increase the electric field strength about areas around the sampling orifice to facilitate ion collection from large ionization areas and improve off-axis ionization.

Still a further object of the present invention is to increase the ionization efficiency of a MALDI ion source as well as an atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) source.

Accordingly, a further object of the present invention is to create near the sample surface a greater extraction electric field.

Various of these and other objects are provided in one embodiment of the present invention by a method for collecting ions in which ions are produced from a sample in an ion source, an electric field is provided that is more uniform in an area adjacent the sample than in an area adjacent an inlet to the ion transfer device or that is larger in field strength at the sample than at a point removed from the sample towards the inlet of the ion transfer device. In this embodiment, ions are received into the electric field and transferred through the ion transfer device to a sampling orifice of the mass spectrometer.

Various of these and other objects are provided in one embodiment of the present invention by a novel apparatus. The apparatus includes an ion transfer device configured to connect to a sampling orifice of a mass spectrometer. The ion transfer device has an inlet configured to accept ions, and the inlet has a surface that extends in a direction from an axis of the ion transfer device. In this embodiment, the ion transfer device extends a distance of at least 10 times an inner diameter of the sampling orifice of the mass spectrometer.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designate identical, or corresponding parts throughout the several views, and more particularly toFIG. 6,FIG. 6depicts one embodiment of the present invention as applied to an AP-MALDI ion source. Instead of a tapered capillary as shown inFIG. 1,FIG. 6depicts an ion collection device in one embodiment of the present invention including an ion transfer device (e.g., extended capillary8) and an end member (e.g., disk18), in which the end member forms a sampling surface16extending parallel to the sample target plate10. As shown, in this embodiment, the ion transfer device extends a distance from the mass spectrometer inlet flange9. The extension distance is preferably a distance of at least 10 times an inner diameter of a sampling orifice9bof the mass spectrometer6. Details of extended capillary lengths suitable for various embodiment of the present invention are described in the above noted U.S. Serial application Ser. No. 09/795,108 entitled “Capillary ion delivery device and method for mass spectroscopy,” filed on Mar. 1, 2001, the entire contents of which has been incorporated herein by reference. In the embodiment of the present invention shown inFIG. 6, a disc18(e.g., provided by a 4 mm O.D. “washer” attachment) forms an area preferably parallel to the sample target plate to create a more uniform electric field over a larger area than would be present from a tapered capillary. A magnified view of the ion collection device is shown inFIG. 7A.

Other embodiments of the present invention utilizing an extended capillary8as an ion collection device are shown inFIGS. 7B–7C. Each of these embodiments provide more uniform electric fields over larger areas. The extended capillary8, as to be discussed later, provides flexibility in sampling ions generated from the sample.

The present inventors have employed models to simulate the electric field in the present invention, and have compared the resultant electric field with the electric field present around tapered capillaries. (seeFIG. 8). The present invention at the same voltage effectively applies a higher electric field at the sample surface in comparison to when a tapered capillary is used. As shown inFIG. 8, for a background device, the field strength in an area adjacent the sample is ˜5,050 V/cm as compared to a peak field strength of ˜14,000 V/cm. In one example of the present invention, the field strength in an area adjacent the sample is 9,000 V/cm as compared to a peak field strength of ˜9,900 V/cm. Thus, in the present invention as shown inFIG. 8, the field strength in an area adjacent the sample is at least 50% of the peak field strength between the sample and the inlet.

Referring toFIGS. 7A–7C, in these embodiments of the present invention, a sampling surface16is provided at the end of the capillary8opposite the mass spectrometer6or opposite the mass spectrometer inlet flange9(e.g., opposite the sampling orifice9b). In one embodiment of the present invention, the sampling surface16is preferably a surface planar to the sample plate10. The dimensions shown onFIGS. 7A–7Dare used as illustrative dimensions. As shown inFIG. 7B, the ion collection device of the present invention can, in one embodiment, be an extended capillary8having a thick end wall (in a range of at least three times a diameter of the capillary opening). The thick end wall serves as the end member16. As shown inFIG. 7C, the ion collection device of the present invention can, in one embodiment, be an extended capillary8having a non-concentric capillary opening or gas passage. In this embodiment, the area of the end wall serves as the end member16. In this embodiment, the thickness of the wall16bis in a range of 2–5 times a diameter of the capillary opening.

FIG. 7Drepresents another embodiment of the present invention. In this embodiment, an extended capillary8is not used. Rather to provide the sampling surface16, a disk18is attached to the mass spectrometer inlet flange9. Attachment of the disk18to the inlet flange9(or to the capillary8in other embodiments of the present invention) can occur by welding, solder, adhesive, or mechanical attachment. InFIG. 7D, the disk18serves to provide the sampling surface16which, as previously noted, preferably is parallel to the sample plate10.

The disk18inFIG. 7D, similar to that illustrated specifically inFIG. 8, causes the applied electric field to be more uniform in an area adjacent the sample than in a an area adjacent the sampling orifice9bof the mass spectrometer.

Various embodiments of the present invention have been demonstrated on a Quadrupole Time-of-Flight (QTOF) mass spectrometer (QTOF-II; Waters/Micromass) with a Z-Spray interface and an AP/MALDI source (Model 411, MassTech, Inc.) with PDF (MassTech, Inc.). The sampling cone in the standard Z-Spray interface was replaced with a capillary8, and the inlet end of the capillary was modified with the different inlet geometries such as shown inFIGS. 6–7C. The PDF module20(as shown for example inFIG. 9A) employed in these exemplary demonstrations was a MassTech Inc., Model 1×2 modified for the QTOF-MS system to accommodate a 173 V applied voltage. The PDF module20switched the applied HV electric field to zero, 10 μs after the laser irradiation pulse.

Samples used in the demonstrations were prepared on AP/MALDI target plates using a mixture of 4 peptides (Angiotensin I, II, Bradykinin, Fibrinopeptide A) at a 1 pmol level with an alpha-cyanno-4-hydroxycinnamic acid (CHCA) matrix. Each sample was spotted with 1 μL of peptide-matrix solution (peptides were made to a concentration of 1 pmol/μL each) and operated with AP/MALDI's spiral motion option. The laser spot size used was varied between 0.25 to 1.1 mm2. The laser energy per pulse was varied from 50 to 200 μJ/pulse.

FIG. 9Bshows a tapered capillary configuration. The taper angle of 45° is less sharp than in other designs where typically a 20° angle is applied.FIG. 9Cshows the capillary configuration utilized for the comparative work here. Comparisons between these two configurations demonstrate the improvements provided by one embodiment of the present invention. Further improvements would be expected for comparisons between the embodiment shown inFIG. 9Cand tapered capillary designs having even sharper capillary designs (e.g., 20° vs. 45°) than the configuration inFIG. 9B. Moreover, further improvements beyond the configuration inFIG. 9Care expected when, as inFIG. 7A, the area of the sampling surface16is increased.

Comparison of the results between the sampling interface configurations shown inFIGS. 9B and 9C, as applied to AP-MALDI PDF on a QTOF mass spectrometer, are summarized inFIG. 10. Ion signal intensities obtained inFIG. 10(and inFIGS. 11–16) were for the base peak (1538 Da—Fibrinopeptide A) acquired after summation of the signal over 1 minute. These results are representative and not limiting of the present invention. The results inFIG. 10were obtained at a constant laser fluence of 200 μJ/mm2over different irradiation areas to investigate sensitivity and throughput improvements. The results show that with PDF applied, the capillary design of the present invention shown inFIG. 9C, with no taper, yielded statistically better ion signal intensity than the configuration inFIG. 9B, using a tapered capillary. A higher signal intensity, as can be seen inFIG. 10, was present for all irradiation areas tested. When PDF was not applied, the results were not statistically different. The absence of an improvement without PDF can be explained by the fact that higher electric fields, although enhancing ionization efficiency, force the extracted ions into the surface of the sampling inlet where these ions are lost.

The improvement factor of the planar capillary design over the tapered capillary configuration with PDF applied is quantified (for exemplary purposes) inFIG. 11. At a 0.25 mm2laser irradiation area, an improvement of 2.7 times can be seen. As the laser spot gets larger, the improvement is still present but declined, possibly due to the limited area over which the higher electric field strength is applied. Thus, a 2.7 times enhancement or greater in sensitivity is possible in one embodiment of the present invention.

In terms of throughput differences between conventional and the ion collection devices of the present invention, with PDF on,FIG. 12shows that ion signal intensity per irradiated area is not constant, but rather increases with increasing area. This is in contrast to results found with AP-MALDI PDF applied to a Thermo Finnigan LCQ ion-trap and described by Tan et al., Anal. Chem., in press, where a linear dependence of spot size (at constant laser fluence) with total ion current was found. By curve fitting a power law dependence to the data,FIG. 13shows that the following approximate dependence of ion signal intensity with area ratio: I=I0(A/A0)2. This result is consistent with effects known for a Z-spray interface associated with the Micromass/Waters QTOF mass spectrometer, where greater ion currents result in disproportionately higher sensitivity. Moreover, the result suggests that significant improvement factors are attainable with larger irradiation areas in the particular case of AP-MALDI PDF with the QTOF MS configuration. In one embodiment of the present invention, laser spot sizes as large as 2 mm diameter can be effectively applied (i.e., having area of 3.14 mm2). Spot sizes greater than 2 mm in diameter are also suitable for the present invention.

As for throughput differences between the tapered design and the various ion collection devices of the present invention, for sharper inlets, throughput is expected to level off at larger laser spot sizes. However, at the irradiation chosen and for the spot sizes evaluated, both the tapered configuration and the non-tapered configurations showed significant increases in ion signal intensity with laser spot size. Further, for larger spot sizes described above, higher throughput capacity and better off-axis ionization are expected.

Accordingly, an advantage of the present invention is that it permits larger spot sizes in MALDI, thereby reducing the spot-to-spot variations that arise due to sample inhomogeneity. Indeed,FIG. 14shows the decline in the standard deviations from replicate analyses when larger irradiation areas are applied.

FIG. 15shows the result of applying a disk18to a capillary8. A sensitivity improvement in the base peak was realized with the application of a disk18in comparison to a capillary8without a disk18. The results inFIG. 15indicate a general improvement with the present invention, i.e. producing ion signal intensity levels that were previously unattainable using tapered capillaries.

Various embodiments of the present invention have also been demonstrated on an quadrupole ion trap mass spectrometer (ITMS) such as for example a LCQ Classic Thermo Finnigan mass spectrometer with an AP/MALDI source (Model 111, MassTech, Inc.) which includes a capillary extender. The PDF module employed in this demonstration was the commercially-available MassTech Inc. PDF Module, Model 1×2. In the ITMS experiments, the PDF module was set to pulse the HV electric field to zero 15 μs after the laser irradiation pulse. The sample preparation for the ITMS experiments were the same as previously described for the QTOF. A laser spot size of ˜1.1 mm2and a laser energy of ˜220 μJ/pulse were applied.

In the setup for the ITMS, the commercial capillary, which has a significantly larger inner diameter of 0.75 mm (vs. 0.44 mm in results fromFIGS. 10–15), was used. To increase the ion collection, a disk18was once again attached to the capillary8. Comparing the capillary8with the disk18to a capillary without a disk showed that adding a disk18allowed improved performance at lower applied voltages (FIG. 16). Obtaining 3 kV performance (best without the disk18) at a 2 kV setting makes the AP-MALDI PDF system safer to operate, without compromising performance.

The improvement factors at 2 kV and 4 kV settings for the disk18attachment were measured to be +35% and +15%, respectively. Differences in the improvement factors between the ITMS and QTOF systems at the same 4 kV setting may be attributed to differences in the capillary-to-target plate distances between the two AP-MALDI models. This would result in the systems being tested at different electric fields. Despite the differences, the benefits of the invention in both ITMS and QTOF systems have been demonstrated.

One aspect of the present invention, owing to the reduction in the peak electric field which in conventional sampling orifices occurs near the inlet to the orifice (seeFIG. 8), permits application of higher voltages than allowed in prior AP-MALDI PDF configurations. Although 4 kV over a ˜2 mm target plate-to-sampling inlet distance was the highest voltage setting applied in the demonstrations disclosed herein, even greater voltages can be applied, according to the present invention, without premature electric field breakdown.

In another embodiment of the present invention, the electric field near the sample surface is increased due to the presence of metallic structures (e.g. tapered metallic structures) on the surface of the sample plate10. As shown inFIG. 17, the sample plate10can include a metallic backing22and an insulator24. In this embodiment, tapered metallic structures26are formed in the metallic backing22. Other designs of metallic protruding structures which serve to concentrate the electric filed near the sample plate10are likewise suitable for this embodiment of the present invention. This configuration reverses the configuration shown inFIG. 8, where instead of the electric field peaking to a maximum near the sampling inlet location, the electric field would peak to a maximum near the sample surface. In this embodiment of the present invention, the electric field strength is increased about a region in which sample ionization occurs, and thus reduces the above-described gas-phase recombination problem by having the electric field strength the highest where the negative and positive ions are created. As shown inFIG. 17, an insulator24can be provided over the metal protrusions to provide a surface upon which sample material can be deposited for ionization such as for example with laser desorption/ionization.

Hence, one apparatus of the present invention, as illustrated by the above embodiments, can include an ion transfer device configured to connect to a sampling orifice (or inlet flange) of a mass spectrometer. The ion transfer device has an entrance inlet configured to accept ions. The inlet has an end member whose surface extends in a direction from an axis of the ion transfer device. The ion transfer device extends in a direction from the sampling orifice of the mass spectrometer preferably a distance of at least 10 times an inner diameter of an entrance orifice of the mass spectrometer. In one preferred embodiment of the present invention, the surface is parallel to a surface of a sample plate holding a sample to be ionized. The ion transfer device can include a capillary having a gas passage, with the capillary having a wall thickness that is in a range of 2–5 times a diameter of the gas passage. The ion transfer device can include a capillary having a gas passage and a disk at an inlet of the gas passage, with the disk having a diameter that is in a range of 2–5 times a diameter of the gas passage.

In another embodiment of the present invention, the apparatus includes a sample plate configured to locate a sample to be ionized. The capillary of the ion transfer device can, in that embodiment, have a wall thickness greater than a distance between the sample plate and the entrance to the ion transfer device. Likewise, the capillary of the ion transfer device in this embodiment can include a disk at an inlet of the capillary, with the disk having an outer diameter greater than a distance between the sample plate and the entrance to the ion transfer device. The sample plate can have metallic protrusions extending in a normal direction from the sample plate and can include a dielectric covering the metallic protrusions.

In still another embodiment of the present invention, the apparatus of the present invention can include a conical ion transfer device configured to transfer ions to a mass spectrometer. The conical ion transfer device includes an inlet to accept ions, with the inlet constituting an end member whose surface extends in a direction from an axis of the ion transfer device. The surface, in one embodiment, preferably extends to a diameter greater than a distance between a sample plate locating the sample and the inlet of a conical ion transfer device. In one preferred embodiment of the present invention, the surface is parallel to a surface of a sample plate holding a sample to be ionized.

In either of the above-noted embodiments, the apparatus can include a pulse modulator configured to provide an electric field between the sample plate and the inlet of the ion transfer device. The pulse modulator can be configured to reduce a field strength of the electric field prior to the ions drifting in the electric field arriving at the inlet of the ion transfer device.

In either of the above-noted embodiments, the apparatus can include an ion generator configured to produce the ions. The ion generator can include the above-noted sample plate locating a sample to be ionized and a laser source configured to produce the ions for example by matrix-assisted laser desorption/ionization.

FIG. 18is a flowchart illustrating a method according to various embodiments of the present invention. As shown inFIG. 18, at step100, ions are produced from a sample in an ion source. At step102, an electric field is provided that is more uniform in an area adjacent the sample than in an area adjacent an inlet of the ion transfer device (step102a) and/or that is larger in field strength at the sample than at a point removed from the sample towards an inlet of the ion transfer device (step102b). At step104, the ions are received into the electric field and transferred through the ion transfer device to a sampling orifice of the mass spectrometer.

In step100, the ions can be produced at atmospheric pressure or at pressures above 100 mTorr. The ions can be produced by laser desorption/ionization including matrix-assisted laser desorption/ionization. In step102, the electric field can be provided such that the electric field that is directed to an end member of the ion transfer device (e.g. an inlet of the ion transfer device) whose surface extends in a direction from an axis of the ion transfer device. The electric field can be directed to an inlet of a capillary, with the capillary having a wall thickness greater than a distance between the sample plate and the entrance to the ion transfer device. The electric field can be directed to a disk at an inlet of a capillary, with the disk having an outer diameter greater than a distance between the sample plate and the entrance to the ion transfer device. The electric field can be directed to an inlet of a non-concentric capillary, with the capillary having a wall thickness greater than a distance between the sample target plate and the entrance to the ion transfer device.

In step104, the ions can be transported in a gas passage of a capillary having a wall thickness that is in a range of at least three times a diameter of the gas passage. The transferring can utilize a pulsed dynamic focusing or a timed-extraction technique. During pulsed dynamic focusing, laser spot areas larger than six times an area of the entrance orifice can be applied. During pulsed dynamic focusing, a laser position that is offset from an entrance axis of the ion transfer device by a distance greater than six times a diameter of the entrance orifice can be applied. During pulsed dynamic focusing, a field strength of the electric field can be reduced prior to the ions drifting in the electric field arriving at the inlet of the ion transfer device. The transferring can occur by flowing a gas into the ion transfer device, by flowing a gas into a capillary tube, by flowing a gas into a non-concentric capillary tube, and/or by flowing a gas into a gas passage of a capillary having a wall thickness that is in a range of at least three times a diameter of the gas passage.