WO1989012316A1

WO1989012316A1 - Resolution improvement in an ion cyclotron resonance mass spectrometer

Info

Publication number: WO1989012316A1
Application number: PCT/US1989/002481
Authority: WO
Inventors: Alan L. Rockwood; John Wronka; Ying Pan; Douglas P. Ridge
Original assignee: University Of Delaware
Priority date: 1988-06-06
Filing date: 1989-06-06
Publication date: 1989-12-14
Also published as: EP0419557A1; EP0419557A4

Abstract

In an ion cyclotron resonance mass spectrometer (10), ion cyclotron resonance signals at higher harmonics of cyclotron frequency are employed to increase the resolution of ICR mass spectrometer without increasing the magnetic field. The detection electrodes consist of M (where M is an integer) identical electrodes (A, B, C, D) arranged in M-fold symmetry about the axis of the coherent cyclotron motion of the observed ions. In an ion cyclotron having four points of voltage in space, the cyclotron electrodes are set up in clockwise symmetric fashion. To increase the resolution in signal detection resulting from the potential induced by ions moving in orbits in the spectrometer, the first and third voltages are added and the second and fourth voltages are subtracted from the sum of the first and third voltages.

Description

RESOLUTION IMPROVEMENT IN AN ION CYCLOTRON RESONANCE MASS SPECTROMETER

This invention relates to improvement in the resolution of the spectra in an ion cyclotron mass spectrometer by harmonic detection.

BACKGROUND OF THE INVENTION

Signals are usually detected in ion cyclotron resonance-based mass spectrometry by measuring potential changes induced by the periodic motion of the ions in "antennae" electrodes. Since the induced voltage is not linear with distance for finite electrodes, the potential induced by ions moving in orbits of non-zero radius will not have a perfect sinusoidal variation with time. The signal will, therefore, contain components at higher harmonics (NF_e) of the cyclotron frequency as well as at the fundamental (F_e). This effect does not depend on the inhomogeneity of the trapping field and is, therefore, quite general. The ion cyclotron resonance experiment is usually designed to minimize harmonic signals since they can complicate proper identification of sample ions. In the usual continuous wave (cw) experiment the harmonics are not detected because of the detecting method. Usually a phase sensitive detector is used and the detector is tuned to the fundamental frequency. In the modern Fourier transform spectrometer the harmonics are suppressed by cell design and choice of operating conditions.

SUMMARY OF THE INVENTION It is an object of this invention to increase the resolution of ICR mass spectrometry without inceasing the magnetic field. This is accomplished by detecting the signal at a harmonic of the cyclotron frequency rather than at the fundamental. This may be done in a conventional ICR cell. However, much better performance is obtainable by building unconventional cells. Increased resolution of ICR mass spectroscopy is obtained and also increased sensitivity may result. Ion cyclotron resonance signals at higher harmonics of the cyclotron frequency are described. If dissipation of the charge in an orbiting charge packet depends only on time, the linewidths of the signals at all harmonics are the same. The spacing between mass lines increases with harmonic order, therefore resolution increases linearly with harmonic order. Selection rules are developed for a class of detection schemes that will detect selected harmonics. The detection electrodes for this class of detectors consists of M (where M is an integer) identical electrodes arranged with M-fold symmetry about the axis of the coherent cyclotron motion of the observed ions. The sum of the signals from all the electrodes contains harmonics of order Mk (k is an integer). The difference between the sum of the signals from every other electrode and sum of the signals from the remaining electrodes contains harmonics of order M92k - 1)/2 (in this case M must be even). This suggests that it is possible to detect harmonics of arbitrary order in the absence of harmonic signals of lower order. This could be useful in improving resolution in ion cyclotron resonance mass spectroscopy without increasing data acquisition time or magnetic field strength.

Stated otherwise, the present invention provides in an ion cyclotron that with four points of voltage in space. The electrodes are set up in clockwise symmetric fashion. The effect of the invention can be seen from providing that the first and third voltages are added and the second and fourth voltages are subtracted from the sum of the first and third voltages. Then the first harmonic and all higher odd harmonics disappear by symmetry and only even harmonics remain.

Further, it is noted that with this arrangement of four points of voltage, the intensity of the second harmonic is twice that of the single detector embodiment.

In general, it has been discovered that for every number of electrodes symmetrically spaced all harmonics are enhanced and some not. This invention will be better understood in view of the following description taken with the following drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, Figure 1 shows an arrangement in block diagram for continuous wave ICR harmonic detection;

Figures 2a and 2b show cyclotron resonance signals;

Figure 3 is a coordinate diagram of a point electrode;

Figure 4 is a plot of the potential function with phase angle;

Figure 5 is a plot of the potential at a point resulting from the motion of a charge; and

Figures 6a and 6b illustrate arrangements of multiple electrodes according to this invention.

DESCRIPTION OF THE EMBODIMENTS

Phase sensitive detectors tuned to a fundamental frequency have been disclosed.

Figure 1 illustrates an arrangement which provides a second harmonic that occurs at twice the fundamental frequency and accordingly the resolution is twice that of the fundamental spectrum. In Figure 1, a cell 10 has plates A, B and C which detect a second harmonic. RF excitation is applied to plate D from a RF generator 11. The output from the plate A smplified at 12 is received by the phase sensitive detector 13 and an output is suitably recorded at recorder 14. A frequency multiplier 15 generates a new reference frequency which is at the harmonic being detected and locked in phase with the original fundamental. Detection on any of the three plates A, B or C gives the same result, that is, relative to the fundamental the resolution is improved by a factor of two.

Figure 2 shows an illustrative example. Plate A was set up to be the detecting plate. The magnetic field strength is 1.1 Tesla. The ion detected is formed from CR(CO)₆ at 1.0 × 10^-6 Torr. the cubic cell of Figure 1 is operated in the continuous trapped mode. The electron beam is continuously on, so ions are formed and drifted to the cell walls resulting in a steady state ion population. With the strongest fields occurring in the corner of the cell between the excite/detect electodes, ions in that region will be the most strongly excited and will contribute most strongly to the signal. Such ions will also reach the walls of the apparatus quickly and have a short life-time. The cyclotron resonance line is, therefore, lifetime broadened. As mentioned before, the resolution obtained by detecting at higher harmonics should be improved. This is shown in Figure 2b. The signal intensity detected at twice the excitation frequency is plotted against the excitation frequency. The width of the resulting peak is half the width of the signal detected at the fundamental shown in Figure 2a. The appearance of the isotope peak dramatizes the improved resolution.

In Figure 2 the cyclotron resonance signal of

is plotted versus F_d/N where F_d is the detection frequency and N is the order of harmonic or harmonic number. Normalizing the detection frequency in this way puts the abscissa on the same scale for all harmonics so they can be directly compared.

(a) First harmonic or fundamental (N=1);

(b) Second harmonic (N=2). Note the narrower linewidth and isotope peak indicating improved resolution.

HARMONICS DETECTED BY A SINGLE POINT ELECTRODE

Figures 1, 2a and 2b illustrate single plate detection in which a second-order harmonic signal was detected.

In the following description of the present invention there is described the constructing of ICR cells geometrically arranged for selective harmonic detection.

The origin of harmonics in the ICR signal is illustrated and described with reference to Figure 3. A packet of ions of total charge Q moving coherently in a circular cyclotron orbit of Radius R₁ is illustrated in Figure 3. The coherent motion of the ions is the result of an excitation step. The ICR signal is detected by monitoring currents or voltages induced in antennae electodes by this coherent ion motion. These induced signals differ significantly from pure sinusoidal waves. This difference increases as the cyclotron radius increases relative to the size of the cell. Hence, they contain high-frequency components, harmonics of the fundamental cyclotron frequency. The occurrence of harmonics in the signal obtained from a cyclindrical cell has been discussed by E. N. Nikolaev and M. V. Gorshkiv, International Journal of Mass Spectrometry and Ion Processes, vol. 64, page 115 (1985). In addition, harmonics are sometimes observed in FT-ICR spectra (see paper presented at 34th Annual Conference on Mass Spectrometry, June 8-13, 1986 in Cincinnati, Ohio by R. E. Shomo and others). Harmonic signals complicate assignment of masses of sample ions and their usefulness for increasing resolution has only recently been recognized. As shown in the following discussion, the problem of spectral congestion can be minimized by selectively detecting harmonic signals.

A point electrode is a simple model that can be used to illustrate harmonic behavior. The model is defined in Figure 3. Figure 3 is a coordinate diagram for point electode A interacting with a charge Q moving in a circle of radius R₁. The electrode is a distance R_O from the center of the circle and a distance r from Q. The angular poistion of Q is O, or w_ct. The electrode is located at point A at a distance R_O from the center of the cyclotron orbit of ions Q. We take the electrode to be a high-impedance antenna responsive to the field at A. The potential at point A is given by

where r is the distance between Q and A and ε_o is the permittivity constant. When the particle moves along its fixed circular path with an angular frequency ω_c , the potential induced at point A will change periodically. This is made implicit by giving the potential in terms of the angular position of Q

where

In Eq. (2), θ is the angular position of Q as shown in Figure 1. This angle- is modulated by the motion of the particle as θ=w_c1+θ_o. θ is the arbitrary initial angle at t = 0 which, for simplicity, is set to 0. Then, Eq. (2) becomes

This function is plotted through one cycle for R = 0.1, 0.3, 0.5, 0.7 and 0.8 in Figure 4. Figure 4 shows the potential from Eq. (3) of a point A as a result of motion a charge Q around a circle of radius R₁ whose center is a distance R_O from A. The potential is given in terms of R = R₁/R_O and w_ct where w_c is the angular velocity of Q. From the top, R = 0.8, 0.7, 0.5, 0.3 and 0.1. The function is obviously not sinusoidal for large values of R, which corresponds to large values of the radiius of the cyclotron motion. As R grows, the relative importance of harmonics in the signal grows. Since V_a(Rw_ct) is a bounded periodic function (for R < 1), this can be shown explicitly by representing it as a Fourier series.

where

(Because of symmetry, it is only necessary to integrate over half a period.)

The integrals can be done numerically and the results are shown in Figure 5. Figure 5 shows coefficients, A_n, of the expansion in Eq. (4) of the potential at a point, A, resulting from the motion of charge Q in a circle of radius R₁. the center of the circle is R_O from A. The A_n are plotted as a function of R = R₁/R_o. Harmonic order N = 1-10. The coefficients of the various harmonic terms A_n(R) are plotted against r. At small R, the higher harmonic coefficients are small, but they incease dramatically at larger R. Inspection of Figure 5 suggests that A_n(R)~Rⁿ at small R. Appendix A shows that this is true. While the results illustrated in Figures 4 and 5 are for an idealized point electrode, qualitatively similar results apply for real electrodes. The case that has been previously considered in the most detail is the cylindrical cell. In this case, the harmonics also incease linearly with Rⁿ for small R. The harmonics become increasingly important at high levels of excitation. As R approaches 1, the harmonic signals approach equal intensity. In the point electrode case, the filed is unbounded at θ = 0 and R = 1. The signal is a delta function which will have all harmonics equally in its Fourier series. Qualitatively similar effects can be expected to obtain for essentially any practical electrode.

MASS RESOLUTION IN HARMONIC SIGNALS

Representing the signal as a Fourier series makes it possible to specify the peak shape and resolution of the harmonic signal components. Even if the electrode is not a point but has some shape and size, the signal it senses as a result of the cyclotron motion of the ions will be a periodic function of w_ct.

It will note, in general, be perfectly sinusoidal, but it will be expressible as a Fourier series analogous to that of Eq. (4). If the total charge, Q, moving coherently dissipates according to f(t) as a result of collisions, reactions, or other processes, then the signal, S, will be given by

By the convolution theorem (see Modulation, Noise and Spectral Analysis, P. F. Eanter, McGraw-Hill, New York 1965, pages 36-38), this signal in the frequency domain will consist of peaks centered at the harmonic frequencies with line shapes corresponding to the Fourier transform of f(t). If f(t) is an exponential, exp(-kt), for example, the line shapes will be Loretnzian with half-width k. This implies that mass resolution will incease linearly with harmonic order. If two ions have cyclotron frequencies which differ by Δ w, for example, their signals at the nth harmonic will be at frequencies differing by n Δ w. Since the linewidths, k, are the same for all harmonics, then the resolution becomes nΔw/k and increases linearly with harmonic number.

This incease in resolution makes harmonic detection very useful. It does not require an increase in either the magnetic field strength or the signal acquisition time. DESCRIPTION OF THE PREFERRED EMBODIMENT

MULTIPLE POINT ELECTRODES

Using more than one electrode for detection gives a stronger signal at a selected harmonic and eliminates lower harmonics. Consider, for example, the case of M point electrodes evenly distributed around the complete circle (m-fold symmetry) about the center of cyclotron motion of the ion. If M = 2 then the difference between the signal from the two electrodes contain the harmonics of order n - 1, 3, 5, 7, etc. If M = 4 and the sum of the signals of the other opposing pair, the resulting signal will contain harmonics of order n = 2, 6, 10, 14, etc. This is illustrated in Figure 6. Figure 6 shows an arrangement of multiple electrodes to detect harmonics of the ion cyclotron resonance signal. The electrodes have M-fold symmetry about the center of the cyclotron motion. In type I connection, the signals from all electrodes are summed. In type II connection, the signals from alternate electrodes are summed and subtracted from the sum of the signals of the remaining electrodes. M = the number of electrodes. Similar rules apply for electrode arrays with higher symmetry. The rules apply to three-dimensional electrodes as well as point electrodes. All that is required is that the M electrodes have M-fold symmetry about the central axis of the cyclotron motion.

These selection rules for the multiple harmonic detection can be derived as follows. Consider M = 4 electrodes arranged to have 4-fold symmetry about the central axis of the coherent cyclotron motion of the ions to be observed. The total potential, V(R, M), induced by the circular motion of the charged, particles will be the summation of the potentials, V(R, wθj), induced at each single electrode. The potential V(R, θj , ) at each electrode differs only in initial phase angle. This leads to

where

In Eq. 6a, the plus sign is taken when the signal from all the electrodes are summed (type I connection) and the minus sign is taken when the sum of signal from every other electrode is subtracted from the sum of the signal from the remaining electrodes (type II connection). Type II connection requires, of course, that M be even. The Fourier transform expression of V(R, θj) is

(7a)

(7b)

Since V(R, θj,) is a periodic function with period of 2 the identity

holds by variable substitution.

Combining Eqs. 6-8 gives the total potential induced by the cyclotron motion of the ions at relative radius R at all M electrodes.

the nth harmonic signal is thus given by

(10) By examining the summation over j in Eq. 10, the selection rules can be derived. These are summarized in Table 1. The detailed algebra of deriving the selection rule is given in Appendix B. The magnitude of the potential detected by M electrodes can be finally written as (see Appendix B)

where *n is determined by the selection rules summarized in Table 1. V (R, M, n) is zero for n values other than n*.

TABLE I

Selection rules for the detection of harmonics by multipole ICR cells

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Number of Connection electrodes type ^a n^*b

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

M I kM

M (even) II M(2k-1)/2

^a Defined in Figure 6 b Observed harmonic orders, k = integer The means for differentiating the voltages between the electrodes and the means for subtracting voltages between groups of electrodes are illustrated by the following representative description in relation to the representative illustrations in Figs. 6a and 6b. Referring to Fig. 6b, one subtracts one voltage from another using standard electronic signal processing methods including but not limited to standard methods of using linear operational amplifiers, see for example differential amplifier described and illustrated in Linear IC/OP AMP Handbook, 2nd edition, by Joseph J. Carr published by Tab Books, Inc., Blue Ridge Summit PA, 1983, at pages 35 et seq. The output of the multiple electrodes of Fig. 6b is placed on the input of the differential amplifier and the detection described above is effected.

Referring to Fig. 6a, one adds one voltage to another using similar standard technologies, see for example the summing amplifier described in Linear IC/OP AMP Handbook, at pages 12 et seq. The output of Fig. 6a is placed on one of the inputs of the basic summing amplifier. The outputs are added by taking a different voltage from each electrode and applying the voltages to the input of the summing amplifier.

In summary, the important points addressed here are:

(1) a symmetrical multipole arrangement of detecting electrodes can selectively detect any order of harmonic signal with an intensity M times stronger than a single electrode;

(2) the selection rules are generally applicable for any shape of electrode since the only term the shape of the electrode is the A_n(R) term, which is absent in the derivation of the selection rules.

As a result of this invention increased resolution is obtained in an ICR mass spectrometer. Also increased sensitivity can be obtained. APPENDIX A & B - 14 -

The function in Eq. (2)

_f can be expanded in Legendre polynomials , P_h[cos (ω_ct ) ] yielding (for R < 1 )

Fourier analysis of this expression yields, in matrix notation

whereb/jr can be generated from the recursion relation (5)

where b_∞ = 2. b_oj = 0(j>0), = 0 (j≠1), and b₁₁ = 1. Terms on the right side of Eq. (A-3) of the form b_ij are replaced by b i. ( 0+ 1) .

All the diagonal elements of (bij) are non-zero and all elements with j>i are zero. This implies that the th harmonic of V is of the form (for n> 0)

At small R, only the leading term in the summation is significant, so at small R the strength of the 77th harmonic signal grows as Rⁿ. The coefficient b_nn is given by APPENDIX B - 15 - APPENDIX A

n

Starting with Eq. (10), let the summation over j be equal to S given by

Application of a simple trigonometric identify to Eq. (B-1) yields

The second summation can be shown to be zero by methods completely analogous to those we now use to evaluate the first sum. Therefore, Eq. (B-2) can be further reduced to

t where

or

Type I connection

For type I connection, as defined in Fig. 4, SS gives APPENDIX B - 16 -

where

From Eq. (B-7)

or

Similarly, from Eq. (B-8)

Substituting Eqs. (B-10) and (B-11) into Eq. (B-5) gives

SS is zero and thus S is zero unless

1 - X = 0 (B-13) and therefore APPENDIX B - 17 -

implying that

where k is an integer. Ohis leads to the first selection rule: = kM. That is, only harmonics of order n* will be detected by an M-electrode array with type I connection. The limiting value of S canb e obtained by applying L'Hospital's rule to Eq. (B-12) and is found to be M. Type 11 connection

For type II connection, as defined in Fig. 4, Eq. (A-2) becomes

where e iπ has been substituted for - 1.

A treatment similar to that outlined in Eqs. (B-5)-(B-14) shows that S = 0 unless

where k an integer. This is the second selection rule. That is, only harmonics of order (2k - 1)M/2 will be detected by an M-electrode array with type II connection. The limiting value of S is again M.

From Eq. (10) and selection rules, the overall potential induced at all M electrodes by the coherent motion of the ions can be finally expressed as

whre n* is given by Eq. (B-15) for type I connection and Eq. (B-16) for type II connection. V(R, M, n) is zero for n not equal to n"^" .

Claims

1. In a method of detection in an ion cyclotron resonance mass spectrometer in which signals are detected by measuring potential changes the steps of exciting ions in an ion cyclotron cell having a plurality of electrodes to provide a fundamental frequency, producing in said excited ions a harmonic of said fundamental frequency, and detecting on an electrode of said cell a harmonic signal.

2. In a method as claimed in claim 1 the step of exciting ions in a cell of an even number N of electrodes symmetrically spaced, providing potential differentiation between said electrodes suppressing all harmonics less than N/2, and enhancing harmonics of N/2 or above.

3. An ion cyclotron mass spectrometer having multiple electrodes symmetrically placed so as to provide orbiting ions with fundamental frequency and symmetrically placed with respect to each other, means for differentiating a voltage between said electrodes to suppress a selected set of harmonics in the spectrometer and to enhance a selected set of harmonics.

4. An ion cyclotron mass spectrometer having multiple electrodes symmetrically placed so as to provide orbiting ions with fundamental frequency wherein said multiple electrodes are symmetrically placed with respect to each other, means for adding voltages of first and third electrodes and subtracting voltages of second and fourth electrodes from the sum of the first and third electrode voltages, whereby the odd harmonics are reduced and the even harmonics predominate in detection of signals.

5. An ion cyclotron mass spectrometer having an even number N of electrodes, symmetrically spaced with respect to each other, means for exciting ions in said spectrometer to produce a fundamental frequency, means for detecting harmonics of N/2 or above on electrodes of said spectrometer.

6. an ion cyclotron mass spectrometer having two pairs of electrodes symmetrically placed so as to provide orbiting ions with a fundamental frequency, and symmetrically placed with respect to each other, means for adding voltages of first and third electrodes and subtracting voltages of second and fourth electrodes from the sum of the first and third electrode voltages, whereby the odd harmonics are reduced and the even harmonics predominate in detection of signals.