Device configured to generate image charge / current signal and tuning method thereof

Abstract

The present invention provides a device configured to generate an image charge / current signal and a tuning method thereof. The device is configured to generate an image charge / current signal representing trapped ions undergoing oscillatory motion, and the device includes: an electrostatic ion trap; an image charge / current detector configured to obtain an image charge / current signal representing trapped ions undergoing oscillatory motion in the electrostatic ion trap. The image charge / current detector includes one or more pickup electrodes, and the one or more pickup electrodes are configured to obtain the image charge / current signal. The one or more pickup electrodes are arranged to detect the image charge / current signal generated by ions with a given mass / charge ratio m in each signal period T. sig (m) The one or more pickup electrodes are further arranged such that: the time interval Δt between the two signal pulses sep (m) satisfying a predetermined condition to suppress a predetermined nth harmonic within the image charge / current signal, where n is an integer of 1 or greater.

Description

Technical Field

[0001] The present invention relates to an apparatus configured to generate an image charge / current signal representative of trapped ions undergoing oscillatory motion. Background Art

[0002] Electrostatic ion traps for mass analysis utilizing anharmonic oscillations of ions are known.

[0003] For example, WO 2012 / 116765 A1 discloses various forms of electrostatic ion traps utilizing anharmonic oscillations of ions.

[0004] Ions in an electrostatic ion trap can oscillate harmonically or non-harmonically, depending on the structure of the ion trap. In general, harmonic oscillation can be understood as an oscillation that produces a signal whose amplitude A changes with time t as A(t)=A0sin(ft+a), where f and a correspond to the frequency and phase of the oscillation, respectively. Non-harmonic oscillation can be understood as an oscillation that produces a signal whose amplitude behavior deviates from a sinusoidal function.

[0005] The image charge signal detected in the electrostatic ion trap based on the anharmonic oscillation of the ions produces a complex spectrum including multiple harmonics with a frequency corresponding to the frequency of the ion oscillation. If a relatively wide range of ion masses is being studied, the harmonics corresponding to different ion masses may overlap each other in the spectrum. Therefore, before the frequency of the ion oscillation can be related to the mass-to-charge ratio of the ions, for example, by suppressing unwanted harmonics, one or more harmonic orders of the spectrum usually need to be deciphered or removed. For example, after removing the second harmonic and the fourth harmonic from the spectrum, a spectrum including only the third harmonic corresponding to the triple frequency of each ion mass that can be clearly converted into a mass spectrum can be obtained (as long as the mass range is not so large that other harmonics overlap with the third harmonic). Observing higher harmonics (i.e., H in the spectrum) is not a good idea. n , where n=2 or greater) is that it provides higher mass resolution (compared to the fundamental frequency H1, also called the first harmonic frequency) without increasing the duration of the measured signal.

[0006] Various methods have been proposed to obtain mass spectra from anharmonic signals.

[0007] EP2642508A2 discloses a linear combination method which requires N+1 pick-up electrodes to eliminate N harmonics from the spectrum. The disadvantage is the requirement for several electrodes and respective signal measurements (proportional increase in the number of amplifiers, data acquisition systems and data size). Another disadvantage is that the method cannot handle the frequency of equalized ions. In addition, after performing the linear combination, the signal-to-noise ratio (S / N) may deteriorate.

[0008] EP2779206A2 discloses the following method, which includes: applying a validity test to each of a plurality of peaks in an image charge / current signal in the frequency domain, wherein applying the validity test to a peak in the image charge / current signal in the frequency domain includes: determining whether a phase angle associated with the peak satisfies a predetermined condition. The method also includes: forming a new image charge / current signal, the new image charge / current signal including data representing one or more peaks that have passed the validity test; and excluding data representing one or more peaks that have not passed the validity test.

[0009] WO2017162779A1 discloses directional orthogonal projection of signals. This technique requires substantial post-processing work and one or a set of calibration signals. The method defines ion frequency candidates for each peak from the spectrum, and then uses the calibration signal and a subsequent linear equation solving system that outputs the intensity of each frequency candidate to generate a signal for each candidate. The disadvantage is a large amount of computer resources and time required to obtain a mass spectrum.

[0010] The present invention is designed in view of the above considerations. Summary of the invention

[0011] In a first aspect, the present invention provides a device configured to generate an image charge / current signal representing a trapped ion undergoing oscillatory motion, the device comprising: an electrostatic ion trap, which is configured to trap ions so that the trapped ions undergo oscillatory motion in the electrostatic ion trap; an image charge / current detector, which is configured to obtain an image charge / current signal representing the trapped ion undergoing oscillatory motion in the electrostatic ion trap, wherein the electrostatic ion trap is configured to trap ions so that the image charge / current signal in the time domain is generated for ions of a given mass / charge ratio m with a signal period T sig (m)[s] by frequency f sig (m) [Hz] repetition, wherein the image charge / current detector comprises one or more pickup electrodes, and the one or more pickup electrodes are configured to obtain the image charge / current signal; wherein the one or more pickup electrodes are arranged to detect the ions having the given mass / charge ratio m in each signal period T sig (m) two signal pulses caused within; and wherein the one or more pickup electrodes are further arranged so that: ions having the given mass / charge ratio m are detected in each signal period T sig The time interval Δt between two signal pulses caused by sep (m) is preferably approximately equal to To suppress predetermined n-th harmonics within the image charge / current signal, wherein n is an integer of 1 or greater, and wherein p is an integer of 0 or greater.

[0012] Thus, by careful arrangement of the pick-off electrode or electrodes, predetermined nth harmonics within the image charge / current signal may be suppressed without requiring complex calculation steps.

[0013] This is particularly useful when the ions (eg, in a linear ion trap) undergo anharmonic oscillatory motion, since, as mentioned above, it is the anharmonic oscillatory motion that can be most problematic for second and higher harmonics.

[0014] A given mass / charge ratio m can be expressed in terms of elementary charge unit (e = 1.60217662 × 10 -19 The mass / charge ratio may alternatively be referred to as m / z instead of m (m is actually used as shorthand for m / z).

[0015] For an ion with a given mass / charge ratio m, the nth harmonic H n will have frequency n×f sig (m). For example, the first harmonic (fundamental harmonic or main harmonic) H1 will have a frequency f1(m)=f sig (m), the second harmonic H2 will have a frequency of f2(m) = 2×f sig (m), etc. Therefore, the above condition equal When this condition is met, the nth harmonic is suppressed because the corresponding Fourier coefficients become zero due to the equality of the positive and negative parts after integration around each signal pulse; see the "Theoretical Description" below for more details.

[0016] Here, it is worth adding that the nth harmonic does not satisfy the above If the above conditions are met, the only harmonic is suppressed. If the condition is satisfied, then the corresponding Fourier coefficient becomes zero because the positive and negative parts are equal after integration near each signal pulse, so each harmonic H (2k+1)n will be suppressed, where k = 0, 1, 2, 3, ...; for more details, please see the "Theoretical Description" below again.

[0017] Thus, for example, if n=2, the individual harmonics H2, H6, H 10 , … (but not H3, H4, H5, H7, etc.) will be suppressed.

[0018] Similarly, if n = 3, then the harmonics H3, H9, H 15 , … (but not H2, H4, H5, H6, etc.) will be suppressed.

[0019] In some embodiments, n is selected to be an integer of 2 or greater.

[0020] In other embodiments, n = 1. It is noted here that by setting n = 1, suppression of H1, H3, H5, H7 (all odd harmonics) can be achieved, effectively doubling the frequency of the peaks in the frequency domain. In an electrostatic ion trap with circular field-forming electrodes (see below), this can be achieved using a pickup electrode of a specific diameter, or using a reflective electrode at high voltage and the center electrode as the pickup electrode (although this latter option may be more complicated to implement).

[0021] Note that despite the above The condition is defined with respect to ions with a given mass / charge ratio, but if it is satisfied for an ion with a given mass / charge ratio, it will apply to ions with all other mass / charge ratios, since the ion motion takes place in an electrostatic field, i.e., it can be explained by scaling the time axis to to transform the trajectory of an ion with mass / charge ratio m1 into a trajectory of another mass / charge ratio m2. This means that if an ion with mass / charge ratio m with an oscillation period of T causes spikes separated by dT in the time domain signal, then the ratio T / dT will always be the same regardless of the value of m. Due to this independence, the ion at 1 / 2nf sig The electrodes at will suppress at the same set of harmonics for any mass / charge ratio.

[0022] Here, "substantially the same" may be considered to mean the same as ±5%, more preferably the same as ±1%, and more preferably the same as ±0.1%.

[0023] Preferably, n=2, so that the second harmonic in the image charge / current signal is suppressed.

[0024] If n=2, then preferably the device is configured for use with a mass / charge ratio range (m min ~m max ) so that the H1 peak in the spectrum of the ions within the mass / charge ratio range does not overlap with the H3 peak in the spectrum of the ions within the mass / charge ratio range. In this way, confusion between the H1 peak and the H3 peak in the spectrum can be avoided. If n=2, then preferably, the device is configured for use with a mass / charge ratio range (m min ~m max ) so that the H1 peak in the spectrum of ions in this mass / charge ratio range does not overlap with the H3 peak in the spectrum of ions in this mass / charge ratio range, but overlaps with the (suppressed) H2 peak in the spectrum of ions in this mass / charge ratio range. In this way, confusion between the H1 peak and the H3 peak can be avoided while taking advantage of the additional spacing in the spectrum created by suppressing the H2 peak.

[0025] In other examples, n=3, so that the third harmonic within the image charge / current signal is suppressed.

[0026] If n=3, then preferably the device is configured for use with a mass / charge ratio range (m min ~m max ) so that the H2 peak in the spectrum of ions within the mass / charge ratio range does not overlap with the H4 peak in the spectrum of ions within the mass / charge ratio range. In this way, confusion between the H2 peak and the H4 peak in the spectrum can be avoided, which can help allow the H2 peak or the H4 peak to be studied.

[0027] As mentioned above, higher harmonics (i.e., H n , where n=2 or greater) is that it provides a higher mass resolution (compared to the fundamental frequency H1, also called the first harmonic frequency) without increasing the duration of the measured signal.

[0028] Preferably, n is less than 10, more preferably, n is less than 5. That is, preferably, the predetermined harmonics to be suppressed are relatively low-order harmonics.

[0029] The two signal pulses may appear as two simple peaks in the time domain signal, or have a more complex form, eg each signal pulse comprising more than one individual peak.

[0030] Typically, for example, as in the following reference Figures 11A-11C As shown, one or more pickup electrodes are preferably arranged so that: each signal period T sig The two signal pulses in (m) are essentially mirror images of each other in the time domain. This helps to minimize the suppression of the predetermined nth harmonic in the image charge / current signal.

[0031] To achieve this, the pickup electrode(s) are preferably selected to be symmetrical with respect to the well geometry (e.g., the axial symmetry or plane symmetry of the well coincides with the axial symmetry or plane symmetry of the pickup electrode) to maximize suppression of the predetermined nth harmonic. Figures 11A-11C Let’s discuss this in more detail.

[0032] It can be used for ions with a given mass / charge ratio m in each signal period T sig The time interval Δt is measured by the corresponding features in the two signal pulses caused by sep (m) These corresponding features may be the maximum values ​​of the two signal pulses, or the weighted centers of the two signal pulses.

[0033] As the skilled person will appreciate, the apparatus configured to generate an image charge / current signal representative of trapped ions undergoing oscillatory motion may take a variety of forms.

[0034] Preferably, the device configured to generate an image charge / current signal representative of a trapped ion undergoing oscillatory motion is an electrostatic ion trap.The electrostatic ion trap may have field forming electrodes configured to generate an electrostatic field that undergoes oscillatory motion.

[0035] Preferably, the / each pickup electrode is embedded within a (respective) field forming electrode of the electrostatic ion trap, for example the / each pickup electrode may be at least partially (preferably fully) embedded within a cavity of the respective field forming electrode.

[0036] The / each pickup electrode embedded in the (corresponding) field forming electrode of the electrostatic ion trap may be configured to be movable within the (corresponding) field forming electrode in which the / each pickup electrode is embedded, preferably the cavity in the (corresponding) field forming electrode is large enough to accommodate the movement of the pickup electrode. In this way, the position of the embedded / each pickup electrode may be changed as required without unnecessarily affecting the electrostatic field, for example, this may help ensure that one or more pickup electrodes are arranged so that the above conditions are satisfied for these pickup electrodes

[0037] Movable electrodes will be most feasible for linear oscillations, but will be more challenging for other geometries where there is drift of the ions perpendicular to their motion (eg, cylindrical geometries).

[0038] The electrostatic ion trap is preferably configured to generate an image charge / current signal representative of trapped ions undergoing anharmonic oscillatory motion.

[0039] The skilled person will appreciate that various forms of electrostatic ion traps are capable of producing image charge / current signals representative of trapped ions undergoing anharmonic oscillatory motion.

[0040] For example, the electrostatic ion trap may be a linear electrostatic ion trap. The linear ion trap may have field forming electrodes configured to generate an electrostatic field that causes linear oscillatory motion. The linear ion trap may be configured to generate an image charge / current signal representing a trapped ion that undergoes linear oscillatory motion at a predetermined position of ion oscillation, whereby the ion moves back and forth in the direction of ion motion (e.g., around a reference axis that may be determined by the electrostatic field).

[0041] As another example, the electrostatic ion trap may be of the form described in WO 2012 / 116765 A1.

[0042] In a particularly preferred example (referred to herein as an "electrostatic ion trap with circular field-forming electrodes"), the device is an electrostatic ion trap having a first set of concentrically arranged circular field-forming (i.e., circular plate) electrodes centered about a reference axis and arranged on a first side of a midplane and a second set of concentrically arranged field-forming (i.e., circular plate) electrodes centered about the reference axis and arranged on a second side (opposite side) of the midplane, wherein the field-forming electrodes (in the first and second sets) are configured to generate an electrostatic field in which ions undergo linear oscillatory motion in the midplane (e.g., around a predetermined center position) while precessing about the reference axis. Such an apparatus is disclosed herein and, for example, also disclosed in WO2012 / 116765A1 (e.g., see Fig. 10A ) is disclosed in the .

[0043] In an electrostatic ion trap with circular field forming electrodes, one or more pickup electrodes may include a first circular pickup electrode centered on a reference axis. The first circular pickup electrode may be located on a first side of a midplane in a first set of field forming electrodes. The first pickup electrode may be embedded in one of the first set of field forming electrodes. The first circular pickup electrode may be arranged such that: by appropriately configuring the radius of the first circular pickup electrode (e.g., the innermost radius), an ion with a given mass / charge ratio m is picked up in each signal period T sig The time interval t between two signal pulses caused by sep (m) is roughly equal to

[0044] The first circular pickup electrode may be the only pickup electrode.

[0045] However, preferably, one or more pickup electrodes further include a second pickup electrode centered on the reference axis. The second pickup electrode may be located on a second side of the midplane in the second set of field forming electrodes. The second pickup electrode may be embedded in one of the second set of field forming electrodes. The second pickup electrode preferably has a shape and size that matches the shape and size of the first pickup electrode. The second circular pickup electrode may be arranged such that: by appropriately configuring the radius of the second circular pickup electrode (e.g., the innermost radius), ions with a given mass / charge ratio m are picked up in each signal period T sig The time interval t between two signal pulses caused by sep (m) is roughly equal to Thus, the radius of the second circular pickup electrode may be the same as the radius of the first circular pickup electrode.

[0046] Although an electrostatic ion trap with circular field forming electrodes is a preferred geometry of the present invention, other geometries are possible. For example, the device may be an electrostatic ion trap utilizing a sector field as disclosed in, for example, US9082602 or an orbital trap or Fourier transform ion cyclotron resonance device. An orbital trap or Fourier transform ion cyclotron resonance device is not preferred because both are typically used to trap ions for harmonic oscillation motion.

[0047] By configuring the device to additionally apply any one or more of the methods of EP2642508, EP2779206A2 or WO2012 / 116765A1, further suppression of harmonics in the image charge / current signal may be achieved.

[0048] For example, the apparatus may be configured to generate a plurality of image charge / current signals representative of ions undergoing oscillatory motion, wherein the apparatus is configured to:

[0049] A linear combination of the plurality of image charge / current signals is generated using a plurality of predetermined coefficients that have been selected to suppress at least one xth harmonic component of the image charge / current signal within the linear combination of the plurality of image charge / current signals.

[0050] Here, x may be an integer of 1 or greater. Here, x may be the same as n (i.e., a linear combination of the image charge / current signals may suppress harmonics that are suppressed by the arrangement of one or more pickup electrodes, which may be useful, for example, in situations where one or more pickup electrodes are not precisely positioned, so that optimal suppression cannot be achieved).

[0051] It is also possible that x may be different from n (ie, a linear combination of the image charge / current signals may suppress harmonics other than those suppressed by the arrangement of one or more pickup electrodes, which may be useful, for example, to suppress additional harmonics).

[0052] EP2642508 teaches techniques for suppressing predetermined harmonics using linear combinations of image charge / current signals, the contents and techniques of which are incorporated herein by reference.

[0053] A first aspect of the present invention may provide a mass spectrometer, comprising:

[0054] Equipment as described above; and

[0055] A processing device is configured to process the image charge / current signal obtained by the image charge / current detector.

[0056] The processing device is preferably configured to convert the image charge / current signal from the time domain into the frequency domain (eg using a Fourier transform) to obtain a spectrum. In this case, the mass spectrometer may be a Fourier transform mass spectrometer.

[0057] As is known in the art, a spectrum obtained in this way can effectively be regarded as a mass spectrum.However, for reasons discussed, for example, in EP2642508, it is preferred to avoid overlapping of harmonics within such a spectrum, in order to avoid spurious peaks.

[0058] According to a second aspect of the present invention, there is provided a method for tuning an apparatus according to the first aspect of the present invention.

[0059] The method may include:

[0060] By varying the position of the pickup electrode / electrodes, for ions of a given mass / charge ratio m, the suppression of the predetermined nth harmonic relative to the fundamental harmonic, ie the H1 harmonic, is increased in the spectrum obtained from the image charge / current signal.

[0061] As mentioned above, the / each position-varying pickup electrode may be embedded within a field forming electrode.

[0062] The method may include:

[0063] By varying the shape of the / each pickup electrode, the suppression of the predetermined nth harmonic relative to the fundamental, ie H1, harmonic is increased in the spectrum obtained from the image charge / current signal for ions of a given mass / charge ratio m.

[0064] According to a third aspect of the present invention, there is provided a method for operating an apparatus according to the first aspect of the present invention.

[0065] The method may comprise any method step implementing or corresponding to any of the apparatus features described in connection with any of the above aspects of the invention.

[0066] The present invention includes combinations of the described aspects and preferred features unless such combinations are expressly impermissible or explicitly avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Embodiments and experiments illustrating the principles of the present invention will now be discussed with reference to the accompanying drawings, in which:

[0068] Figure 1 An example Fourier transform mass spectrometer is shown.

[0069] Figure 2 An example simulated time domain signal during one period of oscillation caused by an ion with a test mass / charge ratio m is shown.

[0070] Figure 3 Show Figure 2 The first 20 μs of the image charge signal with and without added noise.

[0071] Figure 4 The Fast Fourier Transform (FFT) algorithm is used to Figure 2 Spectrum (amplitude only) obtained by transforming the analog test signal.

[0072] Figure 5 Show implementation and Figure 1 The linear electrostatic ion trap 210 is simulated based on the same principle as the electrostatic ion trap 110 .

[0073] Figure 6 The suppression ratios of H2 and H6 depending on the positional offset of the pickup electrodes E5A, E5A′ in the direction of the mid-plane are shown.

[0074] Figure 7 Show the use Figure 5 Shown is an example spectrum obtained using a test ion for the E5A electrode.

[0075] Figure 8 Another method for determining the position of a pickup electrode according to the invention is shown.

[0076] 9A to 11C is provided to assist the theoretical explanation provided below.

[0077] FIG. 12A to FIG. 15 Provided to illustrate various symmetrical arrangements. DETAILED DESCRIPTION

[0078] Aspects and embodiments of the present invention will now be discussed with reference to the accompanying drawings. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned herein are incorporated herein by reference.

[0079] In general, the following discussion sets forth a method for eliminating harmonics in the spectrum of image charge / current signals representing trapped ions undergoing oscillatory motion, particularly non-harmonic oscillatory motion. The method enables certain harmonics to be suppressed or even eliminated in the spectrum of such signals by positioning one or more pickup electrodes at one or more specific locations. As a result, certain harmonics in the spectrum of these signals can be significantly suppressed without additional post-processing, compared to signals obtained from other pickup electrodes located elsewhere. This enables certain higher harmonics of non-harmonic signals to be eliminated without the need for additional signal processing.

[0080] The method can be used to obtain a simplified spectrum of a non-harmonic periodic signal generating more than one harmonic component, for example using a pick-up electrode in a Fourier transform mass spectrometry (FTMS) instrument using image charge detection.

[0081] Unlike the aforementioned methods such as those disclosed in EP2642508A2, EP2779206A2, WO2017162779A1, etc., the method does not require additional post-processing and can eliminate certain harmonics for any set of masses (including aliquots) without unnecessarily involving degradation of the S / N ratio.

[0082] In more detail, the inventors have found that arranging one or more pickup electrodes according to the present invention can suppress a predetermined nth harmonic H in the image charge / current signal. n (where n is an integer of 2 or greater), and more generally, such that the harmonics H (2k+1)n , where k = 0, 1, 2, 3, ...

[0083] For example, if n = 2, then the harmonics H2, H6, H 10 , … (but not H3, H4, H5, H7, etc.) will be suppressed.

[0084] For example, if n=3, then the harmonics H3, H9, H 15 , … (but not H2, H4, H5, H6, etc.) will be suppressed.

[0085] In an example where one or more pickup electrodes are arranged according to the present invention (where n=3), the third harmonic H3 can be significantly suppressed, for example more than 100 times, compared to other non-suppressed harmonics (e.g., H1). This will enable the second harmonic H2 spectrum to be converted into a mass spectrum even if the mass range is so large that the third harmonic H3 frequency range overlaps the second harmonic H2 frequency range. Thus, a mass spectrometer configured to utilize the second harmonic H2 frequency range will be able to have an expanded mass range without encountering problems caused by the overlap of the second harmonic H2 frequency range with the third harmonic H3 frequency range. However, note that unless the fourth harmonic H4 frequency range is suppressed by some other method (e.g., the method taught by EP2642508A2), the mass range should be selected here so that the fourth harmonic H4 frequency range does not overlap the second harmonic H2 frequency range. These requirements can be met by appropriately configuring the mass spectrometer settings.

[0086] In the example where one or more pickup electrodes are arranged according to the invention (where n=2), it enables the first (fundamental) harmonic H1 spectrum to be converted into a mass spectrum even if the mass range is so large that the second harmonic H2 frequency range overlaps the first harmonic H1 frequency range. Note, however, that the mass range should be selected here so that the third harmonic H3 frequency range does not overlap the first harmonic H1 frequency range, unless the third harmonic H3 frequency range is suppressed by some other method (e.g., the method taught in EP2642508A2). These requirements can be met by appropriately configuring the mass spectrometer settings.

[0087] In general, the pickup electrode(s) are preferably selected to be symmetrical with respect to the well geometry (eg, the axisymmetry or symmetry of the well coincides with the axisymmetry or symmetry of the pickup electrodes) to maximize suppression of a predetermined nth harmonic.

[0088] Various symmetrical arrangements are discussed below, among which:

[0089] ● For planar geometry: the symmetry plane or reference plane is located in the middle of the line connecting the opposite ion mirror (reflection) points (i.e., the points where the ions stop and reflect). The pick-up electrode arrangement that generates one set of said symmetric peaks on the time domain signal should be symmetric with respect to the axis (plane) to another set of electrodes responsible for another set of peaks on the time domain signal, both types of peaks being within one period of the signal.

[0090] • For cylindrical geometry: the symmetry axis or reference axis is located at the axisymmetric of the well. The axis of the circular pickup electrode that generates the two sets of said symmetric peaks on the time domain signal should coincide with the axis of the well.

[0091] In some embodiments, the shape of the pickup electrode can be arbitrary as long as it is positioned correctly.

[0092] The required position of the electrodes to achieve suppression can be determined as follows. If it is desired to suppress the second harmonic H2 (n=2), then for ions of a given mass / charge ratio m, a signal with a period T sig The time distance interval t between adjacent peaks in the time domain signal of the test ion (m) sep (m) is preferably equal to where f2 is the frequency of the second harmonic H2 of the ion, and f sig (m) is the frequency with which the image charge / current signal repeats in the time domain for an ion of a given mass / charge ratio m (note that f2 = 2f sig (m)).

[0093] In the following reference Figure 1 In the case where the pickup electrode is a ring electrode, this means that the ring must have a specific radius as follows, which is selected to satisfy the condition tsep (m) is roughly equal to This results in suppression of H2, H6, H 10 、…。

[0094] Note that the time interval for ions of a given mass / charge ratio m can be determined by simulating the motion of ions in an electrostatic field with the desired geometry and potential to obtain suitable focusing characteristics. This can alternatively be determined experimentally, for example by moving the pickup electrode until the desired time interval is achieved.

[0095] If you want to remove H3, the time distance requirement is This will result in suppression of H3, H9, H 15 、…。

[0096] Figure 1 An example of a Fourier transform mass spectrometer 101 is shown, which includes:

[0097] an electrostatic ion trap 110; and

[0098] A processing device is configured to process the image charge / current signal obtained by the image charge / current detector.

[0099] In this case, the processing device is a computer 130 .

[0100] The electrostatic ion trap 110 is an electrostatic ion trap having a first group of concentrically arranged circular field-forming plate electrodes 111-113 centered on a reference axis 108 and arranged on a first side of a midplane 109, and a second group of concentrically arranged circular field-forming plate electrodes 111'-113' centered on the reference axis 108 and arranged on a second side (opposite side) of the midplane 109, wherein the field-forming electrodes 111-113, 111'-113' are configured to generate an electrostatic field in which ions undergo linear oscillating motion in a midplane 109 (e.g., approximately a predetermined center position where the axis 108 intersects the midplane 109) while precessing around the reference axis 108.

[0101] The ion trap 110 implements the principle described in WO 2012 / 116765 A1.

[0102] In this example, electrodes 111, 111' are grounded or low potential pick-up electrodes. These pick-up electrodes are configured to produce image charge / current signals representative of trapped ions undergoing linear oscillatory motion about reference axis 108, which are generated by ions passing through pick-up electrodes 111, 111'. As described in more detail below, these pick-up electrodes 111, 111' are arranged / positioned to eliminate H2, H6, H10 wait.

[0103] In this example, the electrodes 112, 112' are high potential electrodes configured to generate trapping and focusing electrostatic fields.

[0104] The electrode groups 111 , 112 and 111 ′, 112 ′ have the same shape and positions corresponding to each other, and are positioned symmetrically with respect to the midplane 109 .

[0105] In this example, the electrodes 113, 113' are reflective electrodes configured to reflect oscillating ions.

[0106] Here, the electrodes 111 - 113 , 111 ′ - 113 ′ take the form of annular plates, but in an extreme case they may be cylindrical.

[0107] In the ion trap 110, the pickup electrodes are arranged to suppress the harmonics H2, H6, H 10 wait.

[0108] One of the possible ion trajectories is indicated by line 104. The image charge signal generated by the (electrically connected to each other) pickup electrodes 111, 111' is amplified by amplifier 105 and sent to acquisition system 106 which transmits the measured data to computer 130 for recording, visualization and further processing.

[0109] In this case, although both electrodes 111 , 111 ′ are used as pick-up electrodes, it is also possible that only one of the electrodes 111 , 111 ′ is used as pick-up electrode 111 , although this would mean a weaker signal.

[0110] Figure 2 An example simulated time domain signal during one cycle of an oscillation caused by an ion with a test mass / charge ratio m is shown.

[0111] Here a signal period T is shown sig (m), but note that this period actually corresponds to half a period of the ion oscillation, since the signal will repeat itself twice within one oscillation (note that the ions will pass through each ring electrode 111, 111' twice on their way from one side of the device to the other, and then again twice on their way back). The signal is generated by sig The image charge signal of (m) consists of two peaks that occur repeatedly.

[0112] In this example, the pickup electrodes 111, 111' are positioned so that ions with a test mass / charge ratio m are detected in each signal period T. sig The time interval t between two signal pulses caused by sep(m) is roughly equal to To suppress the second harmonic in the image charge / current signal.

[0113] In this example, Figure 2 The signal shown is generated with a sampling rate of 50 ns, a duration of 400 ms, and a period of T sig (m) = 4.45 μs (f = 224.7 kHz). The test signal is generated independently of mass, and for any given mass / charge ratio the electric field can be adjusted so that the signal will have the desired oscillation frequency. For example, the mass may be a test mass of 200 Th.

[0114] Figure 3 The results show the difference between the two images with and without noise added (simulated normal distribution noise with a standard deviation of 2). Figure 2 The first 20μs of the image charge signal.

[0115] Figure 4 The Fast Fourier Transform (FFT) algorithm is used to Figure 2 Spectrum (amplitude only) obtained by transforming the analog test signal.

[0116] Notice, Figure 4 Results are shown only for the test mass / charge ratio m.

[0117] In this example, only H1-H are shown. 10 , although usually the harmonics continue until H n <f max So far, among which f max is the maximum measurement frequency determined by the sampling rate. From this figure, it can be seen that the amplitude of H2 is more than 1 million times smaller than that of H1, and similar statements apply to H6 and H 10 The noisy signal causes H2, H6 and H 10 This effectively means that these harmonics are completely removed from the spectrum (note that Figure 4 with logarithmic scale).

[0118] Note that suppressing H2 for test mass m will also result in suppressing H2 for other masses, for reasons described below.

[0119] Figure 5 Show implementation and Figure 1 The linear electrostatic ion trap 210 is simulated based on the same principle as the electrostatic ion trap 110 .

[0120] exist Figure 5 In the example, electrodes E5A, E5A' are used as pickup electrodes.

[0121] Note that each pickup electrode E5A, E5A' is embedded within the corresponding field forming electrode E5, E5' by being located within a cavity included in the field forming electrode E5, E5'.

[0122] Here, the position of the E electrode is adjusted to have a maximum H2 suppression ratio relative to H1 (ie, maximum H1 / H2).

[0123] Figure 6 The H2 and H6 suppression ratios are shown depending on the radial offset of the middle radius (middle radius = (R1 + R2) / 2, where R1 is the inner radius of the ring electrode and R2 is the outer radius of the ring electrode) of the pickup electrodes E5A, E5A'.

[0124] like Figure 6 As shown, the H2 and H6 suppression ratios strongly depend on the position accuracy. For example, a slight inaccuracy in the position of the pickup electrodes E5A, E5A' may result in only a 100-fold suppression at H2, for example, and this may not be enough, because the H2 peak with an amplitude well above the noise level may be mistakenly regarded as another mass of small intensity.

[0125] A position accuracy of about ~50 μm may be required to obtain sufficient suppression to avoid aliasing between different harmonics.

[0126] Achieving such high precision may be difficult and expensive unless the position of the pickup electrodes E5A, E5A' can be moved within the field forming electrodes E5, E5', as is the case here.

[0127] If the pickup electrodes are not set up accurately to achieve suppression, the suppression of unwanted harmonics can be overcome by any one or more of the methods of EP2642508, EP2779206A2 or WO2012 / 116765A1 (e.g., a linear combination with another pickup signal as taught in EP2642508). The linear combination enables any desired harmonic (e.g., H2) to be excluded without degrading the signal-to-noise ratio S / N, as long as the desired harmonic in the spectrum of another pickup electrode is not suppressed.

[0128] like Figure 2 As shown, the suppression ratios of different harmonics are the same for an ideal symmetrically shaped time domain spike. However, in reality, real electrode shapes may produce asymmetrical peaks that will result in different suppression ratios.

[0129] Figure 7 Show the use Figure 5 An example frequency (FT) spectrum obtained using a test ion for the E5A electrode is shown, where it can be seen that: H2 has the smallest intensity of suppressed harmonics, H6 is suppressed but greater than H2, and H 10In other words, the inhibition of H6 is not as effective as that of H2, and H 10 The suppression of H6 is not as effective as that of H6. For example, the suppression of H6 and H 10 (For example, as determined by the ratio H6 / H1 and H 10 Thus, two adjustments to the suppression ratio can be made by offsetting the entire pickup electrode to obtain maximum suppression of H2 (i.e., lowest H2 / H1 ratio), and by changing the shape / geometry of a portion of the electrode to tune the ratio of other higher harmonics to be suppressed.

[0130] Figure 8 Another method for determining the position of a pickup electrode according to the invention is shown.

[0131] exist Figure 8 In FIG. 1 , the y-axis shows the distance (“radius”) of a simulated test ion of mass / charge ratio m from the reference axis 208 in mm as a function of the flight time (TOF) of the simulated test ion in μs. Figure 8 Also shown are the radius r0 of the pickup electrode E5A which can be changed in the simulation, and t1 and t2 which are the time required for the test ion to travel from the reflection point until the first time (t1) and the second time (t2) the test ion passes through the pickup electrode E5A.

[0132] exist Figure 8 , one possible E5A electrode shape and position is shown for illustration purposes.

[0133] In order to obtain suppression of the harmonic H2 in the spectrum, the radius r0 of the pickup electrode E5A is varied until t sep (m) = t1-t2 satisfies For example, for H2, H6, H 10 , ... inhibition (n = 2), according to Figure 8 , the flight time should be considered equal to the following (where p = 0):

[0134]

[0135]

[0136] The time of flight is related to the time it takes for the ions to reach the reflection point.

[0137] Theoretical explanation

[0138] A theoretical explanation useful for understanding the present invention is now provided.

[0139] like Fig.9Aand 9B As shown, the underlying core idea of ​​the present invention is to position the electrodes so that the signal pulses (marked as P1 and P2) Fig.9A and 9B The peaks in the image (the peaks in the image) fall into the maxima and minima of the sinusoid (Fourier harmonics).

[0140] Since the Fourier coefficient C n Calculated as C n =∫S(t)e -2πint dt, where S(t) is the signal and C n The time interval between signal pulses is equal to T sig (m) / 2 or in general equal to When , it is zero.

[0141] Therefore, among them

[0142] C n =∫S(t)e -2πint dt=I1+I2=0, where I1 and I2 are the integrals obtained near the P1 and P2 peaks, respectively.

[0143] Fig.9A The time domain signal and the Fourier harmonic signal of the third harmonic (H3) are shown, where the time interval Δt sep (m) is configured to suppress the third harmonic (n=3). As shown here, the time domain signal pulses P1 and P2 are aligned with the maximum and minimum values ​​of the H3 Fourier harmonic, so the Fourier coefficient C3 is zero (C3=I1+I2=0). For H (2k+1)n Harmonics (i.e. H9, H 15 The same is true for harmonics, etc.), where k = 0, 1, 2, 3.

[0144] Fig. 9B The time domain signal and the Fourier harmonic signal of the second harmonic (H2) are shown, where the time interval Δt sep (m) is configured to suppress the third harmonic (n=3). As shown here, the time domain signal pulses P1 and P2 are not aligned with the maximum and minimum values ​​of the H2 Fourier harmonic, so the Fourier coefficient C2 is not zero (C2=I1+I2≠0). (2k+1)n The same is true for all other harmonics of the harmonic split (ie, H1, H4, H5 harmonics, etc.).

[0145] The skilled person will appreciate that the time domain signal pulses do not have to fall into adjacent peaks / troughs of the Fourier harmonic signal in order for the Fourier coefficients to be zero. This is due to Fig. 10A and 10B It is shown that it satisfies the Fourier coefficient C n The general case of cancellation, where where p is an integer of 0 or greater (for these purposes, 0 is considered an integer).

[0146] Fig. 10A (i)-(iii) show the locations of (where n = 3 and p = 0) at H3, H9 and H 15 Fourier harmonic signals and time domain pulses to correspond to H3, H9 and H in the spectrum 15 The harmonics will be suppressed (note that here, the signal peaks fall within the respective maxima and minima of these Fourier harmonic signals).

[0147] Fig. 10B (i)-(iii) show the locations of (where n=3 and p=1) at H3, H9 and H 15 Fourier harmonic signals and time domain pulses to correspond to H3, H9 and H in the spectrum 15 The harmonics will be suppressed (note that here, again, the signal peaks fall within the respective maxima and minima of these Fourier harmonic signals).

[0148] Figures 11A-11C The following table shows the signal of an ion with a given mass / charge ratio m in each signal period T. sig (m) How to measure the time interval Δt sep (m). The double arrows indicate that The interval time between the dashed lines to be adjusted. For clarity, only the shaded cross-sections of the pickup electrodes that generate the corresponding signal pulses are placed.

[0149] exist Fig.11A In the example, the pickup electrode is located at the coordinates corresponding to the time when the signal pulse occurs. In this example, each signal pulse is a single peak. In this example, the time interval Δt between the signal pulses can be measured for the maximum value of each signal pulse (i.e., the maximum value of the two peaks). sep (m).

[0150] exist Fig. 11B In the example, each signal pulse has a more complex form, which in this case is a doublet. The signal pulses are mirror images of each other. In this example, the time interval Δt between the signal pulses is measured for the weighted center of each signal pulse, i.e., the weighted center of each doublet (dashed line). sep (m).

[0151] exist Fig. 11CIn the example, each signal pulse has a more complex form, which in this case is a continuous function of time A=A(t). The signal pulses are mirror images of each other. In this example, the time interval Δt between the signal pulses is measured for the weighted center of each signal pulse, i.e., the weighted center of each continuous function (dashed line). sep (m).

[0152] The weighted center is defined as follows. In the discrete case, when each pulse is a group of similar shape peaks, the center position is Among them, A i -The maximum value of each peak in the pulse, t i - The time position of the corresponding maximum. The pulses must be mirrored with respect to the reference axis.

[0153] In the non-discrete case, in A(t) is the time domain pulse function and the integration is performed around the pulse. The pulse must be mirrored with respect to the reference axis.

[0154] NOTE: The form of pickup electrode being used is not particularly important here, only the position of the pickup electrode is important.

[0155] Symmetrical layout

[0156] As mentioned above, in general, the pickup electrode(s) are preferably arranged such that: sig The two signal pulses in (m) are essentially mirror images of each other in the time domain.

[0157] Figures 12A-12C , Figures 13A-13C , Figures 14A-14C and Fig.15 Electrodes are shown which are arranged to produce image pulses within one cycle of the oscillation and which are arranged to produce either symmetrically shaped pulses in the time domain or not symmetrically shaped pulses in the time domain for various ion trap geometries. In detail:

[0158] Figures 12A-12C A linear ion trap geometry (multi-mirror type) is shown, where the ion trajectory 121 is isochronous along the direction of ion motion, and drifts in a direction perpendicular to that direction, where:

[0159] · Fig. 12A Electrodes arranged to produce symmetrically shaped mirror peaks and mirror pulses are shown because the pickup electrode sections 122-123 and 124-125 have symmetrical shapes and the electrodes are positioned symmetrically with respect to symmetry planes 126 and 127. The pickup electrodes are mirrored with respect to symmetry plane 127 which preferably maintains isochronous motion of the ions.

[0160] · Fig. 12B Electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirrored pulses because the pickup electrode sections 122-123 and 124-125 do not have symmetrical shapes and the electrodes are positioned symmetrically with respect to symmetry planes 126 and 127. The pickup electrodes are mirrored with respect to symmetry plane 127 which preferably maintains isochronous motion of the ions.

[0161] · Fig. 12C The electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirror image pulses because the pick-up electrode sections 122-123 and 124-125 do not have symmetrical shapes and the electrodes are positioned symmetrically with respect to the symmetry planes 126 and 127. The pick-up electrodes are not mirrored with respect to the symmetry plane 127 which is not preferred because it may be difficult to maintain isochronous motion of the ions. Note that as Figures 12A-12B The symmetry shown is more preferred because it also preserves z-symmetry.

[0162] Figures 13A-13C A cylindrical ion trap geometry (multi-mirror type) is shown, where the ion trajectories 131 are isochronous along the direction of ion motion and drift around an axis of symmetry 132, where:

[0163] · Fig.13A The electrodes are shown arranged to produce symmetrically shaped peaks as well as mirrored pulses because the electrodes 133 and 134 have symmetrical shapes in cross section and the electrode axes coincide with the trap axis of symmetry 132. The pickup electrodes are mirrored with respect to a symmetry plane 135 which preferably maintains isochronous motion of the ions.

[0164] · Fig. 13B Electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirrored pulses because electrodes 133 and 134 do not have symmetrical shapes in cross section and the electrode axes coincide with the trap axis symmetry 132. The pickup electrodes are mirrored with respect to a symmetry plane 135 which preferably maintains isochronous motion of the ions.

[0165] · Fig. 13C The electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirrored pulses because the pickup electrode 134 cross section does not have a symmetrical shape and the electrode axis coincides with the trap axis symmetry 132. The pickup electrode is not mirrored with respect to the symmetry plane 135 which is not preferred because it may be difficult to maintain isochronous motion of the ions. Note that as Figures 13A-13B The symmetry shown is more preferred because it also preserves z-symmetry.

[0166] Figures 14A-14C A cylindrical ion trap geometry (orbital trap type) is shown, in which the ion trajectory 141 rotates about a symmetry axis 142 and undergoes isochronous motion along this axis, wherein:

[0167] · Fig.14AThe electrodes are shown arranged to produce symmetrically shaped peaks as well as mirrored pulses because the electrodes 143 and 144 have symmetrical shapes in cross section and the electrode axes coincide with the trap axis symmetry 142. The pickup electrodes are mirrored with respect to a symmetry plane 145 which preferably maintains isochronous motion of the ions.

[0168] · Fig. 14B Electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirrored pulses because electrodes 143 and 144 do not have symmetrical shapes in cross section and the electrode axes coincide with the trap axis symmetry 142. The pickup electrodes are mirrored with respect to a symmetry plane 145 which preferably maintains isochronous motion of the ions.

[0169] · Fig. 14C Electrodes are shown not arranged to produce symmetrically shaped peaks but to produce mirrored pulses because the pickup electrodes 143 and 144 do not have symmetrical shapes in cross section and the electrode axes coincide with the trap axis symmetry 142. The pickup electrodes are not mirrored with respect to the unpreferable symmetry plane 145 which may be difficult to maintain isochronous motion of ions.

[0170] Fig.15 A multi-turn TOF-like ion trap geometry is shown, where the ion trajectories are isochronous along the ion motion direction 151, and there is a drift in the direction perpendicular to this direction, where:

[0171] · Fig.15 Electrodes arranged to produce symmetrically shaped mirror peaks and mirror pulses are shown because the pickup electrode cross sections 152-153 and 154-155 have symmetrical shapes and the electrodes are positioned symmetrically with respect to the symmetry plane 156. The pickup electrodes are mirrored with respect to the ion motion direction 151 which preferably maintains isochronous motion of the ions. Similar to the previous geometry, the electrode shape may not be mirrored with respect to the ion motion direction 151, but should be symmetrical with respect to the symmetry plane 157 or other symmetry planes (if present).

[0172] Final Statement

[0173] Features described in the foregoing description, or in the appended claims, or in the drawings in a specific form, or in terms of components for performing the disclosed functions or methods or processes for obtaining the disclosed results, may be appropriately used in separate forms or in any combination of these features to implement different forms of the present invention.

[0174] Although the present invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art given the present disclosure. Therefore, the exemplary embodiments of the present invention described above should be considered illustrative rather than restrictive. Various changes may be made to the described embodiments without departing from the spirit and scope of the present invention.

[0175] In order to avoid any doubt, any theoretical explanations provided here are provided to enhance the reader's understanding. The inventor does not wish to be bound by any of the theoretical explanations in these theoretical explanations.

[0176] Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0177] Throughout this specification including the appended claims, unless the context requires otherwise, the words "comprise" and "include", and variations such as "comprises", "comprising" and "including", will be understood to imply the inclusion of stated integers or steps or groups of integers or steps but not the exclusion of any other integers or steps or groups of integers or steps.

[0178] It must be noted that, as used in the specification and the appended claims, the singular forms "a", "an", and "the" include plural references unless the context clearly dictates otherwise. Ranges may be expressed herein as from "about" one particular value and / or to "about" another particular value. Where such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Likewise, where values ​​are expressed as approximations, the antecedent "about" is used, it will be understood that the particular value forms another embodiment. The word "about" in relation to a numerical value is optional, and means, for example, + / - 10%.

[0179] References

[0180] A number of publications have been cited above to more fully describe and disclose the present invention and the state of the art to which the present invention belongs. The complete citations of these references are provided below. Each of these references is incorporated herein in its entirety.

[0181] WO2012 / 116765A1

[0182] EP2642508A2

[0183] EP2779206A2

[0184] ·WO2017162779A1

Claims

1. An apparatus configured to generate an image charge / current signal representative of a trapped ion undergoing oscillatory motion, the apparatus comprising: an electrostatic ion trap configured to trap ions such that the trapped ions undergo oscillatory motion in the electrostatic ion trap; An image charge / current detector is configured to obtain an image charge / current signal representing a trapped ion undergoing an oscillatory motion in the electrostatic ion trap, wherein the electrostatic ion trap is configured to trap ions so that the image charge / current signal in the time domain is transmitted for an ion of a given mass / charge ratio m with a signal period T sig (m)[s] by frequency f sig (m)[Hz] repetition, Wherein, the image charge / current detector comprises one or more pickup electrodes, and the one or more pickup electrodes are configured to obtain the image charge / current signal; The one or more pickup electrodes are arranged to detect ions having the given mass / charge ratio m in each signal period T. sig (m) two signal pulses caused by The one or more pickup electrodes are further arranged so that: ions with the given mass / charge ratio m are picked up in each signal period T sig The time interval Δt between two signal pulses caused by sep (m) is equal to to suppress predetermined n-th harmonics within the image charge / current signal, where n is an integer of 1 or greater, and where p is an integer of 0 or greater.

2. The device according to claim 1, wherein: The apparatus is configured to generate an image charge / current signal representative of trapped ions undergoing anharmonic oscillatory motion.

3. The device according to claim 1 or 2, wherein: n is less than 5.

4. The device according to claim 1 or 2, wherein: n=2 or n=3.

5. The device according to claim 4, wherein: n=2, and the device is configured for use with mass / charge ratios in the range m min ~m max ions so that the H1 peak in the spectrum of ions within the mass / charge ratio range does not overlap with the H3 peak in the spectrum of ions within the mass / charge ratio range.

6. The device according to claim 4, wherein: n=3, and the device is configured for use with mass / charge ratios in the range m min ~m max ions so that the H2 peak in the spectrum of ions within the mass / charge ratio range does not overlap with the H4 peak in the spectrum of ions within the mass / charge ratio range.

7. The device according to claim 1 or 2, wherein: The one or more pickup electrodes are arranged so that each signal period T sig The two signal pulses in (m) are essentially mirror images of each other in the time domain.

8. The device according to claim 1 or 2, wherein: The device is an electrostatic ion trap.

9. The device according to claim 8, wherein: The / each pickup electrode is embedded within a respective field forming electrode of the electrostatic ion trap.

10. The device according to claim 9, wherein: The / each pickup electrode embedded within a respective field forming electrode of the electrostatic ion trap is arranged to be movable within the respective field forming electrode in which it is embedded.

11. The device according to claim 8, wherein: The electrostatic ion trap has a first set of concentrically arranged circular field-forming electrodes centered on a reference axis and arranged on a first side of a midplane, and a second set of concentrically arranged circular field-forming electrodes centered on the reference axis and arranged on a second side of the midplane, wherein the field-forming electrodes are configured to generate an electrostatic field in which ions undergo linear oscillatory motion in the midplane while precessing around the reference axis.

12. The device according to claim 11, wherein The one or more pickup electrodes include: A circular first pickup electrode is centered on the reference axis, wherein the circular first pickup electrode is located on the first side of the midplane in the first set of field-forming plate electrodes.

13. The device according to claim 12, wherein: The first pickup electrode is embedded in one of the first set of field-forming plate electrodes.

14. The apparatus according to claim 12 or 13, wherein: The one or more pickup electrodes include: A second pickup electrode centered about the reference axis, wherein the second pickup electrode is located on the second side of the midplane in the second set of field forming plate electrodes, wherein the second pickup electrode is optionally embedded in one of the second set of field forming plate electrodes.

15. A method for tuning a device according to any one of claims 1 to 14, wherein: The method comprises: increasing the suppression of the predetermined nth harmonic relative to the fundamental harmonic, i.e. the H1 harmonic, in the spectrum obtained from the image charge / current signal for ions of a given mass / charge ratio m by changing the position of the pickup electrode / electrodes; and / or By varying the shape of the / each pickup electrode, the suppression of the predetermined nth harmonic relative to the fundamental, ie H1, harmonic is increased in the spectrum obtained from the image charge / current signal for ions of a given mass / charge ratio m.

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