B American Society for Mass Spectrometry, 2018 J. Am. Soc. Mass Spectrom. (2018) 29:2173Y2181DOI: 10.1007/s13361-018-2032-9

RESEARCH ARTICLE

Multi-electrode Harmonized Kingdon Traps

Evgeny Nikolaev,1 Mikhail Sudakov,1,3 Gleb Vladimirov,1

Luis Fernando Velásquez-García,2 Petr Borisovets,1 Anastasia Fursova1

1Skolkovo Institute of Science and Technology, Moscow, Russian Federation2Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, MA, USA3Ryazan Radiotechnical University, Ryazan, Russian Federation

Abstract. Based on the analysis of the results ofthe study of various designs of multi-electrodeharmonized Kingdon traps, we propose a newtype of trap with two merged internal electrodesthat has the ability to capture and accumulateions formed inside. We also investigated the in-fluence of inaccuracies in the manufacture of theelectrodes on the field inside such trap. The four-electrode trap, which actually degenerates into atwo-electrode device with traces of two other

electrodes present at the ends of the internal electrodes (their splitting) has been found as the less sensitive toinaccuracies caused by manufacturing and cutting the ends of trap electrodes. We show that a mass spectrom-eter with a relatively high resolving power can be created on the basis of such a trap. The creation of the trapsrequires the manufacture of complex electrodes with demanded accuracy of their surfaces. This becomespossible with the advent of 3D printers.Keywords: Electrostatic ion trap, Mass analyzer, High resolution, Simulation, Fourier transform, FT-MS

Received: 2 March 2018/Revised: 1 July 2018/Accepted: 3 July 2018/Published Online: 1 August 2018

Introduction

The Kingdon ion trap, invented in the beginning of thetwentieth century, has proved to be of great relevance for

mass spectrometry. The original Kingdon trap [1] is a cylinder(external electrode) with closed ends that have holes to hold awire (internal electrode) stretched along the entire cylinderalong its axis. The cylinder is grounded, and a negative electricpotential is applied to the wire for confining positive ions (apositive bias voltage would be used for confining negativeions). The ions created with some non-zero momentum insidesuch a system do not fall on the wire because of their momen-tum conservation and do not strike the surface of the cylinderbecause their total energy (the absolute value of which isbetween the magnitude of the wire potential and the potentialof the cylinder) is less than the surface potential of the cylinder.The most famous Kingdon trap is a device used in massspectrometers invented by Makarov and manufactured byThermo under the name Orbitrap, which has been extensively

investigated and described [2]. However, very little is knownabout other types of Kingdon traps, although the possibilitiesfor their creation have been investigated by Professor Golikovand his collaborators more than a decade ago [3]. Among them,there are many-electrode Kingdon traps with a quadratic po-tential in one of the directions, which we call in this work theharmonized Kingdon traps. In this terminology, the Orbitraptrap is a one-electrode harmonized Kingdon trap.

The Orbitrap is a further development of Knight’sideas—the first to propose measuring the frequencies of ionsoscillating in a quadratic field to measure their masses, and alsosuggested an electrostatic trap for creating such a field [4]. Afeature of the quadratic field is that the frequency of the motionof the ions does not depend on the amplitude of their oscilla-tions and is inversely proportional to the square root of the ionmass-to-charge ratio. Mass spectrometers based on Kingdontraps could be of great interest as portable devices because thetrap itself is purely electrostatic and low-energy consumingmass analyzer. Nevertheless, if we consider Orbitrap’s trap asa core for such mass spectrometer, we will find two fundamen-tal drawbacks that compelled its creators to propose a more

Correspondence to: Evgeny Nikolaev; e-mail: e.nikolaev@skoltech.ru

complex ion manipulation system for creating a mass spec-trometer, namely (i) the need to trap accelerated ions with ashift from the center of the trap, and (ii) the need for a pulsedhigh-voltage supply to control the electric potential of thecentral electrode. The Orbitrap cannot capture the ions createdinside; therefore, the trap can only be used in conjunction withanother trap (e.g., C-trap in the implemented Orbitrap-basedmass spectrometer [2]) or a pulsed ion source. The use of anadditional radio frequency trap with a complex system ofdeflectors to inject the ions to the Orbitrap, as well as the useof a high-voltage pulsed power supply, significantly increasesthe energy consumption of the device, and also greatly com-plicates its implementation as a portable device or as scientificpayload for space applications.

However, it is possible to create harmonized Kingdon trapsthat hold the ions created inside them and allowmeasuring theirmasses. While analyzing the solutions of the Laplace equationwith the goal of creating time-of-flight mass spectrometers withtime focusing of infinitely high order, Golikov found a familyof Kingdon traps with several internal electrodes [3, 5].Golikov’s work shows that there can be any number of internalelectrodes stretched parallel to the axis of the external electrodewithout interfering with the creation of a quadratic potential inthe space between them along the direction of their extension.Of course, in order to create such a quadratic potential, thegeometry of the external electrode is more complex than acylinder of fixed radius, which was found by Golikov for arange of traps with different numbers of internal electrodes. Inthis work, we use modeling and simulations to investigate aplurality of four-electrode harmonized Kingdon traps to deter-mine their sensitivity to the manufacturing and assembly errorsof electrodes, as well as to the fringing fields caused by thetruncation of the trap. From this effort, we identified that theharmonized Kingdon traps with two merged internal electrodeshave the lowest sensitivity to these distortions in geometry. Wesynthesized a design of such a trap, investigated its ability tocapture and accumulate ions formed inside, and explored theuse of such a trap as a mass spectrometer.

Modeling and Design of Four--Electrode Harmonized Kingdon TrapsIn the work of Golikov’s group, e.g., [6], and also in the paperof Klaus Köster [7], variants of the Kingdon ion trap withmultiple internal electrodes and harmonic potential on a givendirection are described. These traps were first described in thepapers and dissertations of the Golikov’s group, which unfor-tunately are not available to a broad international audiencesince they are written in Russian. Köster, apparently indepen-dently, proposed a Kingdon trap with two internal electrodes,which he named Cassinian trap because its electric field can bedescribed in part by the Cassinian equation. Köster modeled,implemented, and characterized experimentally his Cassiniantrap, obtaining resolution values close to those demonstrated on

Orbitrap prototypes; he also indicated ways to increase theresolving power and other characteristics of the instrument.

In the multi-electrode harmonic Kingdon traps, as in theOrbitrap, the distribution of the field is quadratic in one of thedirections (usually along the axis of the electrodes, i.e., the z-axis). The motion of ions in this direction is a harmonicoscillation in which the oscillation frequency exclusively de-pends on the mass-to-charge ratio of the ions; therefore,through the measurement of the oscillation frequency, it ispossible to determine the mass of ions, which makes possibleto use such traps asmass spectrometers (in suchmulti-electrodeharmonized Kingdon traps, the signal induced by the oscillat-ing ions on the external electrode is measured, as is done inOrbitrap, to obtain the mass spectra via a Fourier transform).The electric potential distribution of a four-electrode harmo-nized Kingdon trap (Fig. 1), i.e., φ(x, y, z), is obtained bysolving the Laplace equation using as constraint the quadraticdependence of the potential on one of the coordinates; the resultis the expression:

φ x; y; zð Þ ¼ c z2−cx2 þ dy2

2

� �þ ln xþ að Þ2 þ yþ bð Þ2

� �xþ að Þ2 þ y−bð Þ2

� �h iþ

ln x−að Þ2 þ yþ bð Þ2� �

x−að Þ2 þ y−bð Þ2� �h i

ð1Þ

where x and y are directions perpendicular between them and tothe axis of the trap, i.e., z, and a, b, c, and d are constants. Here,we use formalism and ideas of Golikov’s group [6]. In this kindof trap, in addition to the orbital rotation of ions around theinternal electrodes, orbital rotations around subsets of the in-ternal electrodes are possible, as shown in Fig. 2. After

Figure 1. An example of a harmonized Kingdon trap with fourinternal electrodes. In this example, a = 0.9, b = 0.9, c = 0.2, andd = 0.5, the external electrode is biased at Uhigh = 7, and theinternal electrodes are biased at Ulow = 1

2174 E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps

calculating the potential and shape of the electrodes (whichfollow equipotential surfaces), the solution can be normalizedso that the external electrode has a potential of zero, and thebias voltage of the internal electrode is equal to − 1. The choiceof the equipotentials for positioning the internal and externalelectrodes was made on the bases of two demands: first, not tocreate electric field on the surface of these electrodes strongenough to cause autoemission of electrons and second, to createspace to trap enough ions for high dynamic range. Therefore,the actual solution is the normalized solution multiplied by therequired voltage of the internal rods, which in this example was4 kV. In Fig. 2, the trajectories of the ions were estimated usingthe SIMAX program (www.mssoft.pro), which can receive asinput electric potential solutions from the SIMION program(http://simion.com) and produce accurate particle tracing inthese fields. In Fig. 2, left, a 500-Da ion starts from the pointxo = 20 mm, yo = 20 mm, and zo = 0 mm with energy 2000 eValong the y-axis; similarly, on Fig. 2, right, the same ion startsfrom the point xo = 13.5 mm, yo = 13.5 mm, and zo = 0 mm,having an initial energy of 500 eV along the y-axis and 500 eValong the x-axis. Note that the oscillations along the z-axis areharmonic and strictly isochronous, with a frequency that de-pends only on the mass-to-charge ratio of the ions.

Four-electrode harmonized Kingdon traps can also be ob-tained as a superposition of two Cassinian traps. The internalelectrodes of the 2 two-electrode traps can be rotated relative toeach other at an arbitrary angle around the z-axis. At smallangles between the planes in which the pairs of Cassinian trapslie, the electrodes will merge, resulting in a trap with twointernal electrodes with more complex shapes than the elec-trodes of the original Cassinian traps (in the next section suchtraps will be described in more detail). We investigated a

variety of four-electrode Kingdon traps, primarily to determinetheir sensitivity to the manufacturing and assembly errors ofelectrodes, as well as to the fringing fields caused by thetruncation of the trap; such investigations are necessary be-cause the non-ideality of the electric field (i.e., its differencefrom the quadratic term and (x,y) dependence of the coefficientthat multiplies the quadratic term in the polynomial equationthat describes the dependence on z of the electric potential inthe volume in which the ionmotion takes place) leads to a rapiddephasing of the harmonic oscillations along the z-axis, whichleads to loss of resolving power. Investigations of the influenceof electrode roughness can be done in the following way. InSIMION software, a uniform grid is used to present fielddistributions and electrodes are presented by this grid with thesame voltage across the electrode. With curved electrodes, thegrid points do not fall exactly on the boundaries of electrodes.This can be treated as electrode with not even, distorted shape.We produced such potential arrays with a grid step 0.075 mmfor both Cassinian trap with two rods and for our geometry andrefined them. Those arrays were used further in simulation withmeasurement of induced ion current. According to our simula-tions, dephasing of the ion clouds due to mechanical roughnessof electrodes of 75 μm happens within 10 ms for Cassinian iontrap with two rods and within more than 20 ms for our geom-etry with merged rods. The ion trap with merged electrodeshave additional degree of freedom to change the shape of therods in order to make geometry less sensitive to mechanicaldistortions of electrodes. Our trap could be optimized further incase of necessity.

Our simulation results show that the traps with two internalmerged electrodes have the lowest sensitivity to these distor-tions in geometry. The parameters used in the optimal solution

Figure 2. An example of ion orbital rotation around all the internal electrodes (left) and around two internal electrodes (right) in a four-electrode harmonized Kingdon trap; the ions also oscillate along the z-axis due to a quadratic potential in z. The figures showprojection of ion trajectories on the transverse cross-section of the trap at z = 0. When the ions are introduced from the outside, it isnecessary to momentarily increase the bias voltage at the internal electrodes with a pulse to reduce their kinetic energy to therequired value for orbital capture—otherwise, the ions will collide with the outer electrode due to energy conservation. The ions arenot introduced into the trap at the center (z = 0), but at some distance from the center along the z-axis, which initiates the oscillationsof the cloud along the z-axis. The location of ion injection along the z-axis defines the amplitude of the oscillations

E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps 2175

are a = 0.1, b = 0.73, c = 2, and d = 0; the shape of the externalelectrode (which is determined by the shape of the equipoten-tial surface for the selected potential) was given by the condi-tion Uhigh = 2.0, and the bias voltage acting on the internalelectrodes is Ulow = −2.8. The trap has a dimension along thez-axis of 66 mm—all the electrodes are extended 3 mm at bothends using cylinders with diameters that coincide with theelectrode diameters at their cutoff point to correct the fringingfields near the ends. A 3D view of such a trap is given in Fig. 3.In this design, the openings at the ends of the traps, formedbecause of its cutting, are close to the minimum possibledimensions; therefore, the influence of the penetration of fieldsfrom external structures through these holes is minimal.

Figure 4 shows the difference in the distribution of theelectric potential along the z-axis from the ideal (i.e.,

calculated analytically using Eq. (1)) for different valuesof the z coordinate at which the trap is cut off. It isnoticeable that, in all cases, the addition of extensions onboth ends of the trap reduces the difference; the lowest ofthe graphs in Fig. 4 (corresponding to the cutoff at 33 mmfrom the center of the trap with 3 mm added extensions)indicates a nearly complete suppression of the fringingfields near the center of the trap. Although the graphs inFig. 4 show the behavior of the deviation of the potentialfrom the ideal along the z-axis, the curves are not entirelyinformative in terms of evaluating the nonlinear distor-tions. The deviations calculated in Fig. 4 contain a constantcomponent that does not change the motion of ions at all, aquadratic component that only slightly changes the qua-dratic potential (and hence only the absolute value of theoscillation frequency), and higher-order terms that carryinformation about nonlinear deviations (the dependenceof the oscillation frequency on their amplitude). To calcu-late the latter, we can use the method of polynomial re-gression, but before proceeding to this, we calculate theamplitude of the quadrupole component for the unper-turbed field. To this end, we represent the potential alongthe z-axis, i.e., φ(z) in the form

φ zð Þ ¼ U rodsA2z

zo

� �2

ð2Þ

where Urods is the bias voltage on the internal electrodeswith a grounded external electrode, zo = 33 mm, i.e., thedistance from the center of the trap to the cut ends, and A2

is the amplitude of the quadrupole field. The equation ofmotion of ions with mass m and charge e in such apotential has the form

md2

dt2z ¼ −e∙U rodsA2

2z

z2o; ð3Þ

Figure 3. 3D schematic of a four-electrode harmonizedKingdon trap with two merged internal electrodes

Figure 4. Difference between the distribution of the actual electric potential along the z-axis (for x = 0, y = 0) and that of the ideal trapfor different truncation variants (see the legend). The internal electrodes are biased at a potential of 4 kVwhile the external electrode isgrounded. Here, Bsides^ are additional 3mm2D sections that are added fromboth sides of the trap at the place of truncation. Shapeof electrodes in those 2D sections repeat the shape of truncated electrodes

2176 E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps

which describes harmonic oscillations with an angularfrequency Ω equal to

Ω ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2e∙U rodsA2

mz2o

sð4Þ

The simulation of this system showed that for singly-charged ions of mass 500 Da, the frequency of axial oscilla-tions is f = 186,690 Hz. From this value, we can calculate theamplitude of the quadrupole field as

A2 ¼ mz2o2e∙U rods

2πfð Þ2 ¼ 0:971; ð5Þ

the value is close to unity and it will serve us as a basis forcomparison with the amplitudes of nonlinear distortions, whichare calculated below.

As already mentioned above, it is convenient to use apolynomial regression to calculate the amplitudes of nonlineardistortions. In this case, it is necessary to take into account twocircumstances. First, the interpolation should be built in theregion where the ions move while being trapped (in the nextsection, it will be shown that this is the region near the center ofthe trap − 6 mm< z < 6 mm). Secondly, we should not usehigher-order polynomials for interpolation, since the ampli-tudes of higher polynomials increase rapidly. In this study,we used polynomials up to the sixth-order inclusive. Thus,the interpolation polynomial for the potential distribution alongthe z-axis has the form

φ zð Þ ¼ ∑6

n¼0Un

z

zo

� �n

ð6Þ

At the line starting at the point x = 0, y = 0, the interpolationpolynomial contains only even powers of z because of thesymmetry of the distribution with respect to the center of thetrap. The calculations using the MathCad 13 program (https://www.ptc.com/en/products/mathcad/) yielded the amplitudesgiven in Table 1. The amplitudes are not significant, but thechange in the amplitudes of the higher distortions shows thatthe best trap of the set is trap number 3. Here, numbering ofgeometries of traps in the first column of the table correspondto Fig. 4, namely 1st and 2nd rows are traps truncated at thedistance 31 and 33 mm from the trap center and without 2Dsections added from both sides of truncation. Rows 3 and 4 are

the same traps as 1 and 2, but with additional 2D sections addedfrom both sides of truncation. The fifth row corresponds to atrap truncated at 33 mm from trap center and with coarseelectrode surfaces of accuracy of 0.075 mm.

We also investigated the influence of inaccuracies in themanufacture of the electrodes on the field inside the trap. Thesestudies were performed using the SIMION program. The sur-face of each electrode is an equipotential; given that inSIMION the electrode is set on a uniform grid, the nodes ofwhich do not fall on the curved surface of each electrode can betreated as an unevenness of the electrode surface. Figure 5shows the difference between the exact potential and the po-tential given by SIMION using its finest mesh size for mappingelectrodes (a grid spacing of 75 μm); the amplitudes of thenonlinear distortions for this case are given in the fifth row ofTable 1—the result not only reflects the effect of the inaccuracyin the manufacture of electrodes, but also the edge effects dueto electrode cutoff. The non-linear amplitudes in this case arequite large compared with the other cases examined; however,considering that the electrodes can be manufactured with ac-curacy not worse than 5 μm using precision machining, thesevalues will be an order of magnitude smaller and should notsignificantly affect the parameters of the device.

For the final design of the trap, shown in Fig. 5, we carriedout a more detailed study of the deviation of the axial distribu-tion of the potential from the ideal case due to the cutoff of thetrap along the ends. In this case, the difference in the potentialdistribution along the z-axis was calculated for the ideal trap andtruncated along the lines at constant (x,y) values; these functionswere then subjected to polynomial interpolation (i.e., Eq. (6)).The study showed that at distances from the axis of the trap inthe x-direction over 20 mm, the difference between the distribu-tions of the ideal trap and the cutoff trap is negligible. This isunderstandable since the edge effects in this region are negligi-ble as well. For other lines, the results are shown in Table 2.

The calculations given in Table 2 show a rather significantchange in the value of U2, which changes the frequency of theaxial oscillations of the ions. However, this would happen if themotion of ions along the z-direction would occur at constantvalues of x and y; in reality, as what follows from the z-oscillation frequency spectra (see next section), when the ionmoves along z, oscillations along the x- and y-directions alsooccur. In this case, the values of U2 and the values of the othernonlinear amplitudes Un leverage. As a result, the dependenceof the ion oscillation frequency along the z-direction weaklydepends on the initial position of the ion. This was proved by

Table 1. Dimensionless amplitudes of the distortions of the axial electric potential for traps of the four types of four-electrode harmonized Kingdon traps described inFig. 4 (the fifth row corresponds to a trap with coarse electrode surfaces, as described in the text)

Trap type Z0 (mm) U0 U2 U4 U6

1 31 0.097 4.185 14.661 95.3952 32 − 0.019 2.403 3.105 128.5463 31 − 0.031 1.184 − 0.586 96.2974 32 − 0.032 0.733 − 3.671 100.5975 32 − 8.552 20.869 − 403.341 7207

E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps 2177

calculating the oscillation frequencies of ions with a mass of50 Da started from the position z0 = 6 mm and different posi-tions (x,y) having zero initial energy, which resulted in har-monic oscillations of the ions along the z-direction in the − 6- to6-mm range. The frequencies were calculated by Fourier anal-ysis of the signal produced by these oscillations. We did notfind any differences in the frequency of the ion oscillationwithin an error of 1 Hz.

Multi-electrode Harmonized KingdonTraps with Merged Internal ElectrodesA practical multi-electrode harmonized Kingdon trap has elec-trodes of finite dimensions with surfaces that coincide, as muchas possible, with equipotential surfaces of the ideal electric fieldsolution; evidently, the shape and size of these electrodes aredetermined by the choice of the potential that is applied tothem. When selecting their geometry, the electrodes must bepositioned so that they do not interfere with the motion of the

trapped ions, that is, they should not be in the regions of stableion motion. In the case of multi-electrode harmonized Kingdontraps, when these conditions are met, the electrodes can mergeand, as already mentioned, instead of four internal electrodes,two electrodes of a more complex geometric shape result(Fig. 3). The four-electrode trap actually degenerates into atwo-electrode device with traces of two other electrodes presentat the ends of the internal electrodes (their splitting). Theadvantage of this design is that the cut ends of the outerelectrode practically cover the inner region of the trap and thepenetration of the field from the external electrodes, resulting inminimal distortions of the fields. At the same time, the internalelectrodes are of sufficient thickness to be technically feasibleto anchor them outside the trap.

It is straightforward to show that the trap in question canworkin the mode of both the Orbitrap and the Cassinian trap. How-ever, most importantly, the trap with merged internal electrodescan hold ions near its center (z = 0) that were not necessaryintroduced from the outside; ions can be created directly insidethe trap and accumulated there on oscillatory trajectories (Fig. 6).

Figure 5. x–y (a), x–z (d), and y–z (c) sections (not in scale) of the difference between the electric potentials of an ideal trap and atrap with electrodes with coarse surface (due to the discretization of the shapes using a 75-μm pitch grid). The external electrode isgrounded, the bias voltage on the internal electrodes is − 4 kV. Notice that the color bar resets for values larger than 100 and 200 V

Table 2. The values of the amplitude of the deviations of the ideal trap field from the truncated along various straight lines (x, y) in the regions where ions move

x (mm) y (mm) Uo U1 U2 U3 U4 U5 U6

0 0 − 1.70E−02 0.00E+00 5.78E−01 0.00E+00 3.27E+00 0.00E+00 8.92E+0115 0 − 6.50E−02 0.00E+00 6.95E−01 0.00E+00 − 7.00E+00 0.00E+00 1.02E+0215 15 − 6.30E−02 1.80E−03 7.82E−01 − 2.72E+00 1.22E+01 − 2.69E+01 1.97E+01

2178 E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps

This feature is significant, it obviates the need to create a com-plex system of deflectors to input the ions from the outside;instead, ions can be created directly inside the trap by electronimpact or photoionization. After creation, the ions begin to make

stable oscillations between the internal electrodes in the directionof the coordinate perpendicular to the z-axis.

In order to measure the signal from the ions in a trap of thistype, it is necessary to excite ion oscillations along its z-axis.

Figure 6. (a) Initial ion positions in the mid cross-section (z = 0) of a four-electrode harmonized Kingdon trap with mergedelectrodes as shown in Fig. 5 and (b) their positions after 5 ms of flight (right). Ions have masses in the range from 50 to 2000 Da

Figure 7. Amplitude versus time of the frequency-sweep signal (a) and position of the ions in the z-Ez phase plane at the end of thefrequency sweep excitation (b). As initial conditions for ions, the coordinates and velocities obtained from the previous simulation ofthe ion accumulation process were used (Fig. 6). It can be seen that the ions oscillate with an amplitude of 5–6 mm, forming fairlycompact groups based on their mass-to-charge ratio, which is a prerequisite for the successful registration of induced currents

E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps 2179

The ions are not excited automatically, as is the case in theOrbitrap and in the Cassinian traps, in which ions are intro-duced from the outside across the z-axis with z ≠ 0, where thepotential value is not minimal and the ions begin to bouncealong z immediately after their introduction. It is possible tointroduce ions from the outside of the merged two-electrodetrapwith a shift of the input point some distance from the centeralong the z-axis. However, in the mode of operation consideredby us, the ions are formed in the center of a trap with zeropotential energy; therefore, a radiofrequency field resonantwith respect to the harmonic oscillations along z should beapplied. Mass spectra measurement using the four-electrodetrap with two merged electrodes can work as follows:

(i) First, ions are created by electron impact or photo ionization inthe gap between the electrodes (z= 0) and begin tomake stableoscillations in the effective potential well in the z = 0 plane;

(ii) Then, when a sufficient number of ions are accumulated,their motion along the z-axis is excited by a broadbandfrequency-sweep signal [8] covering the whole range offrequencies of axial oscillations of trapped ions. To gener-ate the dipole field frequency sweep, each of the internalelectrodes is divided into two parts.

(iii) The outer electrode is used to measure the induced cur-rents, followed by its Fourier transform to obtain the massspectrum. The external electrode is also divided into twoparts insulated by radio frequency voltages, having thesame electrostatic potential (0 V in this example).

A simulation of the first stage of operation of the merged-electrode trap as a mass spectrometer (ion accumulation) wasconducted. The ions used in this simulation had a mass-to-charge ratio between 50 and 2000 Da with homogeneousrandom distribution of initial positions in the range 0 mm< x< 25 mm and 0 mm< y < 2 mm; in addition, the ions had athermal distribution of initial energies with an average value of0.025 eV. The simulations predict that around 13.5% of theions got trapped and have stable oscillations in x–y plane.

A simulation of the second stage of operation of the merged-electrode trap as a mass spectrometer (excitation of axial oscil-lations of the ions) is shown on Fig. 7. The excitation isachieved with the help of a broadband frequency-sweep signalthat is applied to the halves of the internal rods, for which theyare cut in half as said previously. The frequency-sweep signal isa poly-harmonic signal containing the frequencies of trappedions. In this simulation, the frequency-sweep signal was creat-ed by a special application, which first calculates the signalsimply as a harmonic signal with a varying frequency andamplitude; the application then performs Fourier transform ofthe signal and removes all components of the spectrum that donot correspond to any of the captured ions. In the simulation,only the frequency range from 60 to 600 kHz remains. Next,the application performs an inverse transformation of the re-ceived signal and saves its temporary implementation as a textfile. The resultant frequency-sweep signal does not contain anyunnecessary harmonics. For this simulation, the resulting fre-quency sweep signal had a duration of 13 ms and an actual

Figure 8. Top, current induced on the halves of the external electrode as a function of time. Bottom, mass spectrum of trapped ionsin the range from 50 to 2000 Da after conducting a Fourier transform (magnitude mode). For some of the peaks, the resolving poweris indicated

2180 E. Nikolaev et al.: Multi-electrode Harmonized Kingdon Traps

maximum amplitude of 20 V (Fig. 7, top). As can be seen fromthe figure, with an increase in the frequency of the signal itsamplitude decreases; this is necessary for a more uniformexcitation of ions of different masses to the same amplitudeof oscillations along the z-axis. The clustering of the ions basedon their mass-to-charge ratio is shown in Fig. 7, bottom.

At the end of the frequency-sweep signal, the ions begin toperform harmonic oscillations along the z-axis, inducing a signalin the other pair of the external electrodes of the trap (third stageof operation of the merged-electrode trap as a mass spectrome-ter). Figure 8 shows the dependence of this signal on time duringthe first second. It can be seen that the signal of the inducedcurrent decreases somewhat with time; this is probably due toerrors in integrating the equations of ion motion—neither colli-sions with gas nor field distortions in this simulation were takeninto account in the simulations.

Figure 8 shows the mass spectrum of the trapped ionsobtained by the Fourier transformation of the induced currentas a function of time. For a mass-to-charge ratio of 50 Da, theresolving power is 609,000; this is a very high value—note thatit was obtained without any apodization and other commonlyused methods of Fourier spectrum processing. Using theexisting techniques for processing spectra, the resolution canbe doubled. As already mentioned, in this simulation, the exactanalytical field of the trap, calculated by a special applicationand stored in the PA format of the SIMION program files, wasused. That is, the effects of truncation of the trap along the z-axis and the unevenness and inaccuracy of the electrode as-sembly were not taken into account. Of course, taking intoaccount these factors, the result will not be so high, but webelieve that with the development of technology, these limitingparameters can be achieved.

ConclusionsBased on the analysis of the results of the study of variousdesigns of multi-electrode harmonized Kingdon traps, we pro-pose a new type of trap with two merged internal electrodesthat has the ability to capture and accumulate ions formedinside. We show that a mass spectrometer with a relativelyhigh resolving power can be created on the basis of such a trap.The creation of such traps requires the manufacture of complexelectrodes, which is very expensive and time consuming ifstandard precision machining is used. However, with the

advent of 3D printers [9], this becomes possible at a low costand short production time. Additive manufacturing of ourproposed trap with merged electrodes will require high-resolution manufacturing processes with associates materials(metals) that have high electrical conductivity, high-temperature compatibility (for system baking), and ultra-high-vacuum compatibility—among other characteristics. Althoughthe current accuracy and resolution of making metal electrodesvia 3D printing is still not high enough [10, 11] to reach thelimit values of the resolution of such devices as mass spec-trometers, the technologies are constantly evolving and, un-doubtedly, in the near future traps with curved electrodes, theprinciple of creation of which was first proposed by Golikov,will be fully realizable and affordable.

AcknowledgementsAuthors are acknowledging Skoltech-MIT grant BNext Gener-ation Program

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