RESOLUTION IMPROVEMENT IN AN ION CYCLOTRON RESONANCE MASS SPECTROMETER

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 - l)/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 Cr(CO)-5 formed from CR(CO)g at 1.0 x 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 Cr(CO)^ is plotted versus F^/N where F < j 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=l); (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 Ri 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 R]_. The electrode is a distance R Q from the center of the circle and a distance r from Q. The angular poistion of Q is 0, or w c t. The electrode is located at point A at a distance RQ 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 \ / / I Q y Wjr ε„ r where r is the distance between Q and A and £ Q is the permittivity constant. When the particle moves along its fixed circular path with an angular frequency u 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 ( 2 ) 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 =w c l+e 0 . Θ is the arbitrary initial angle at t = 0 which, for simplicity, is set to . 0. Then, Eq. (2) becomes (3) 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 R_ whose center is a distance R Q from A. The potential is given in terms of R = RI/R Q and w c t 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 c t) is a bounded periodic function (for R < 1), this can be shown explicitly by representing it as a Fourier series. ( 4a ) where ( 4b ) (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 in a circle of radius R]_. the center of the circle is RQ from A. The A n are plotted as a function of R = Ri/Ro. 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) R n 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 R n 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 0 = 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 c t. 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 (5) 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 ^ 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 n^ /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, w j) , induced at each single electrode. The potential V(R, $j t ) at each electrode differs only in initial phase angle. This leads to - / J v(κ t n ) - Z ( J V(*> 0j) (6a) '- O ( 6a ) where Θr- i* θ oj ( 6b ) 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. -11- The Fourier transform expression of V(R, 0j) is (7a) ϋ (7b) Since V(R, j,) is a periodic function with period of 27y the identity Ξ fl 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. (9) the nth harmonic signal is thus given by 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. Hhe magnitude of the potential detected by M electrodes can be finally written as (see Appendix B) (11) 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 kM M (even) II M(2k-l)/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) Q V [R,t9) = 4ft fo 0 [R 2 + 1 - 2R cos( ω t)] I 2 can be expanded in Legendre polynomials, P h [cos(ώJ c ) ] yielding (for R < 1) Fourier analysis of this expression yields, in matrix notation 3 {R-tP whereb/ can be generated from the recursion relation (5) where b β ? = 2. . Q J = 0( >0), = 0(Jφ 1) , and b^ = 1. Terms on the right de of Eq. (A-3) of the form jj are replaced by ( ϋ ± f) . All the diagonal elements of .OJ ) are non-zero and all elements with / >/ are zero. This implies that the th harmonic of V is of the form for^ > 0) A ■ v .cos(n.c c, iT) = cos D (A-4) At small R, only the leading term in the summation is significant, so at small R the strength of the th harmonic signal grows as R^. The coefficient b^ is given by i o APPENDIX B - 15 - APPENDIX A b η = 2 IT [2/ + l]/[2( /+ 1)] (A-5) l-O for)-} > 0. Starting with Eq. (10), let the summation over^' be equal to S given by Application of a simple trigonometric identify to Eq. (B-l) yields S = cos ( ± 1) J cos(.2 jTT/M) + , ■ „ • (B-2) sin() oj c l!-)X (± 1) J slι.{2r ϊ 7rj/- J -) 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 S = cos(n.o r ) (± 1) cos(2l7 < '/M) = (1/2)cos (ηcj c ) X SS where SS = 22 (± 1) cos(2r?c /M) (B-3) or SS - + e -'(zη rj/n l (B-4) Type I connection For type I connection, as defined in Fig. 4, SS gives APPENDIX B - 16 - where Let M Si x (B-7) - 1 From Eq. (B-7) Si XSi = X - X M + 1 (B-9) or 51 = X(1 ~ X 1 (B-10) 1 - X Similarly, from Eq. (B-8) 1 - X~ M 5 2 = (B-ll) X - 1 Substituting Eqs. (B-10) and (B-ll) into Eq. (B-5) gives X(l - x ) (1 - χ-M) SS = - i s^- i + • '- (B-12) 1 - X X - 1 SS is zero and thus S is zero unless 1 " X = ° (B-13) and therefore APPENDIX B - 17 - implying that L* - 1 (B-15) w h ere k is an integer. Ohis leads to the first selection rule: = kM. That is, only harmonics of order /^^ /Will be detected by an M-electrode array with type I connection. The limiting value c-f 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 ss -Σ f e ' ( ^/^ + f - ; (2 r CV/M + j l where e t ^rhas been substituted for - 1. A treatment similar to that outlined in Eqs. (B-5)-(B-14) shows that S = 0 unless n-* = (2k - DM (B-16) where k an integer. This is the second selection rule. That is, only harmonics of order (2k - l)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 ΠT is given by Eq. (B-15) for type I connection and Eq. (B-16) for type II connection. V(R, M, η) is zero for n not equal to n"^" .

Claims: 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 i s 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.

Inventors: PAN YING, RIDGE DOUGLAS P, ROCKWOOD ALAN L, WRONKA JOHN, PAN, YING, RIDGE, DOUGLAS, P., ROCKWOOD, ALAN, L., WRONKA, JOHN
Applicants: UNIV DELAWARE, UNIVERSITY OF DELAWARE
Application year: 1989
Main classification: H01J49
IPC codes: H01J49