Characterization of a hybrid ion traplaude.cm.utexas.edu/research/hybrid.pdfCharacterization of a...

Characterization of a hybrid ion trap

C Richard Arkin, Brian Goolsby, D.A. Laude*

Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, TX 78712, USA

Received 8 April 1998; accepted 23 October 1998

Abstract

A new ion trap is constructed of a cylindrical ring electrode and hyperbolic end caps. The premise is to determine the effectring electrode geometry has on the operation of the ion trap. A model for the potential and electric field within the trap isdeveloped. The model is used to show how adjusting the geometric parameters of the cell could be used to reduce the presenceof higher order fields or optimize other desired properties. The stability diagram is mapped experimentally and using thestandard definition forqz, theqejectwas determined to be 0.76. A proposed modification for the definition ofqz, which adjustsfor the shape of the cylindrical ring electrode, results in aqejectof 0.93. The trap is shown to have a linear scanning relationship,resolved isolation and unit mass resolution. (Int J Mass Spectrom 190/191 (1999) 47–57) © 1999 Elsevier Science B.V.

Keywords:Ion trap mass spectrometry; Ion detection; Ion trap design; Mass spectrometry instrumentation; Trapped ion cell

1. Introduction

There have been a variety of radio-frequency iontraps that do not conform to the standard hyperbolicgeometry described in the literature [1–11]. There areseveral reasons to deviate from the standard geome-try, such as increased ion storage [1], rapid ionextraction [2], prolonged ion storage [3], miniaturiza-tion [4], and ease of machining [5]. We consider herea different geometry with which to study the effect ofring electrode geometry on the performance of iontrap operation. The justification is that ion trajectoryin mass selected instability mode is primarily alongthe z axis, and specifically we show that the ringelectrode geometry can be significantly modified withminimal detriment to performance. To test this hy-

pothesis, the standard hyperbolic ring electrode wasreplaced with a cylindrical ring electrode.

The cell under consideration is a hybrid betweenthe standard hyperbolic ion trap and the cylindricalion trap (CIT). Performance in the hyperbolic ion traphas been well characterized [12] and the CIT is also wellunderstood [7–11]. This new hybrid trap is characterizedfirst by the development of a model to describe theelectric potential and electric field within the volume ofthe cell. Second, the stability diagram is experimentallydetermined and related to theaz and qz dimensionlessparameters of a theoretical hyperbolic trap. Last, themass scan and isolation capabilities are discussed.

2. Theoretical

Although numerical solutions to the potential dis-tribution within an ion trap cell is common with the

* Corresponding author. E-mail: [email protected] to J.F.J. Todd and R.E. March in recognition of their

original contributions to quadrupole ion trap mass spectrometry.

1387-3806/99/$20.00 © 1999 Elsevier Science B.V. All rights reservedPII S1387-3806(98)14267-7

International Journal of Mass Spectrometry 190/191 (1999) 47–57

software available today, the derivation of an analyt-ical solution often provides insight unavailablethrough numerical analysis or simulation. For thispurpose a solution to the electric potential and electricfield within the hybrid trap is derived.

2.1. Electric potential

The electric potential produced within the volumeof the trap is developed where a potential is applied tothe ring electrode and the end caps are grounded(applying the potential in this manner is designated asmode II of operation [13]). The trap consists of twohyperbolic end cap electrodes and one cylindrical ringelectrode which are defined by Eqs. (1) and (2),respectively, and illustrated in Fig. 1

z2

z02 2

r2

z02 tan2 u

5 1 (1)

r 5 r1 (2)

The parameters used to define the electrodes are thevertex and asymptotic angle of the end cap electrodes( z0 and u, respectively), the inner radius of the ring

electrode (r1), the radial displacement (r ) and theaxial displacement (z).

A model to describe the electric potential and theelectric field is developed in a method similar toMarch and co-workers [9]. The primary assumptionhere is that both the cylindrical ring electrode and thehyperbolic end cap electrodes extend toward infinity.

Using the method of separation of variables, thegeneral solution to the Laplace equation with noangular dependence (3) is given in Eq. (4):

¹2F 5 ¹2R~r ! Z~ z!

5 F 2

r2 11

r

r1

2

z2GR~r ! Z~ z!

5 0 (3)

F~r , z! 5 R~r ! Z~ z! 5 A cos~cz!I0~cr! (4)

wherec is a constant resulting from the separation ofvariables,A is the accumulation of integration con-stants, andI0( x) is the zero order modified Besselfunction of the first kind [10].

In order to determine the exact solution for themodel potential within the hybrid trap, the boundaryconditions must be considered. For the ring electrode,the boundary condition is given in Eq. (5) where thepotential at the electrode is the applied potential,V0;Vdc is the direct current component of the appliedpotential, Vrf is the amplitude of the oscillatingcomponent of potential applied,V is the frequency ofthe oscillating potential andt is time.

F~r1, z! 5 V0 5 Vdc 1 Vrf cos~Vt! (5)

For the hyperbolic end caps, which are at groundpotential, the boundary condition is represented byEq. (6), wherer is defined by Eq. (7)

F~r , 6z0r! 5 0 (6)

r ; Î1 1 ~r2/z02 tan2 u ! (7)

Being dependent on two variables, a hyperbolicboundary condition presents a difficulty; therefore, acoordinate transformation is used which will convertthe hybrid cell into a cylindrical cell, by a method

Fig. 1. Pictorial representation of the hybrid ion trap geometry usedin the experiments with the definition of the relevant parameters.

48 CR. Arkin et al./International Journal of Mass Spectrometry 190/191 (1999) 47–57

similar to that used by O and Schuessler [6]. Using thetransformations of Eqs. (8) and (9),

u 5 r (8)

n 5z

r(9)

the general solution to the Laplace equation becomes

F~u, n! 5 A cos~cnr!I0~cu! (10)

Following coordinate transformation, the boundaryconditions become

F~u, 6z0! 5 0 (11)

F~r1, n! 5 V0 (12)

for the end cap and ring electrodes, respectively. Theend cap boundary condition results in cos(cz0) 5 0,giving

cn 52n 1 1

2z0p (13)

The final boundary condition is used, in conjunctionwith Fourier’s theorem, to determine the integrationconstant,An, which is

An 5~21!n2V0

cnz0I0~cnr1!(14)

Thus the solution of the potential in (u, n) space is

F~u, n! 52V0

z0O

n50

` ~21!n

cnS I0~cnu!

I0~cnr1!D cos~cnn!

(15)

Using Eqs. (8) and (9) the potential within the hybridion trap, in cylindrical coordinates is

F~r , z! 52V0

z0O

n50

` ~21!n

cnS I0~cnr !

I0~cnr1!D cosScnz

rD

(16)

The isopotentials resulting from Eq. (16) are shown inFig. 2(a).

2.2. Electric field

The electric field within the hybrid trap can befound by taking the gradient of Eq. (16)

E 5 ¹F 5F

rr 1

1

r

F

uu 1

F

zz (17)

The scalar of the electric field for the hybrid trap is

uEu 5 ÎSF

r D2

1 SF

zD2

, (18)

where

F

r5

2V0

z0O

n50

` ~21!n

I0~cnr1!F I1~cnr ! cosScnz

rD

22r

r3z02 tan2 u

I0~cnr ! sinScnz

rDG , (19)

F

z5

22V0

z0rO

n50

`

~21!nS I0~cnr !

I0~cnr1!D sinScnz

rD (20)

andI1( x) is the first order modified Bessel function ofthe first kind.

2.3. Evaluation of potential and optimization ofgeometry

Using the analytical approximations in Eqs. (16)and (18), the potential and field within the hybrid trapcan be determined. The isopotentials resulting fromEq. (16) are shown in Fig. 2(a). Eqs. (16) and (18) canalso be used to optimize the trap geometry.

The quality of a potential (or electric field) can beevaluated in terms of the extent of poles whichcontribute to the potential. Any potential distributionwith cylindrical symmetry can be described by Eq.(21)

F~r , z! 5 On50

`

An~Îr2 1 z2!nPnS z

Îr2 1 z2D (21)

whereAn are scaling factors for each pole order (e.g.n 5 0–4 corresponds to the monopole, dipole, qua-

49CR. Arkin et al./International Journal of Mass Spectrometry 190/191 (1999) 47–57

Fig. 2. (a) Isopotential plot of Eq. (16), withr1 5 1.4 cm,z0 5 1.0 cm, andu 5 53.6°. The applied potential difference between the ringelectrode and end cap electrodes is ten units. (b) Plot showing how adjustment of the asymptopic angle (u) and the aspect ratio (z0/r1) allowsnot only the octopolar component of the electric potential to be removed (closed circle), but that other parameters, such as the fractionaldodecapolar component (dashed line), can be optimized. The arrow indicates the only aspect ratio which the CIT has a zero octopolar term,which also corresponds to the limit asu approaches 90° for the hybrid trap. (The CIT aspect ratio was calculated to be 0.888, using theequations in [9].)


drupole, hexapole and octopole, respectively), andPn( x) is the Legendre polynomial [15]. TheAn termscan be determined through some simplifications; e.g.thez axis of the electric field with mirror symmetry isrepresented by

F

zr50

5 On51

`

~21!n~2n! A2nz2n21 (22)

In a perfect quadrupole ion trap, only the monopo-lar and quadrupolar terms (A0 andA2, respectively)would be nonzero; however, in practice all realelectrode arrangements have some higher order terms.In order to reduce the presence of higher order terms,the aspect ratio (r1/z0) is optimized to produce theAn

terms near zero (n . 2), as is done with thehyperbolic [16] and cylindrical ion traps [7].

Using Eq. (20), theAn terms for the hybrid trap aredetermined, and as expected an aspect ratio is foundwhere the octopolar term (A4) is zero. However,unlike the CIT which has only one aspect ratio withA4 5 0, the hybrid trap has the advantage of varyingthe asymptotic angle,u [17]. This allows for an aspectratio whereA4 5 0 for each angle. The benefit of thisadded degree of freedom is that the trap can beoptimized for other variables. Some examples includethe optimization of the dodecapolar term, pseudopo-tential well depth, or ion capacity without an octopo-lar term.

Fig. 2(b) shows the relationship between the aspectratio and asymptopic angle whereA4 5 0. Fig. 2(b)also shows how a particular combination of aspectratio and asymptopic angle may be chosen to optimizethe dodecapolar term. For example, if one chose anasymptopic angle of 50°, an aspect ratio of 0.956would produce a potential distribution with no oc-topolar (A4) component, as well as a fractionaldodecapolar (A6/A2) contribution of20.025.

3. Experimental

For these experiments a modified ITMS (Finnigan,San Jose, CA) mass spectrometer was used for thedetermination of the stability diagram. The ring elec-

trode was replaced with a 304 stainless steel cylindri-cal electrode (i.d.5 37.85 mm, width5 12.95 mm,gap5 4 mm). The end cap electrodes were notmodified (z0 5 7.81 mm,u 5 54.2°). The reagent,either dimethylether (DME), carbon tetrachloride orperfluorotributylamine (PFTBA), was used at a pres-sure of 4.03 1026 Torr, uncorrected. Ionization wasachieved via electron ionization (EI) for period of 5.0ms, and no bath gas was used.

Instrument control was performed with softwareassociated with the ITMS system. Data acquisitionwas performed using a LeCroy 9400 dual channeldigital oscilloscope (LeCroy, Chestnut Ridge, NY)and was transferred to a PC via GPIB, usingLabVIEW (National Instruments, Austin, TX) soft-ware. Pressure measurements were made using aBayard–Alpert, hot cathode ionization gauge (MKSInstruments, Boulder, CO). The PFTBA and CCl4

ware degassed through two freeze–pump–thaw cy-cles. The DME was not purified. Samples wereintroduced into the vacuum manifold using a Gran-ville–Phillips (Granville-Phillips Co., Boulder, CO)precision leak valve. Each mass spectrum consists often scans averaged on the oscilloscope. Followingtransfer to PC, each mass spectrum was smoothedwith a ten-point adjacent average [18]. This datamanipulation was performed in order to reduce thenoise associated with circumventing the data process-ing features on the ITMS circuit board.

Stored-waveform inverse Fourier transform(SWIFT) [19,20] waveforms were produced usingLabVIEW software developed in-house. These 32kdata point waveforms used a sampling rate of 5 MHzand were transferred to a Tektronix (Tektronix, Wil-sonville, OR) model AWG 2005 arbitrary waveformgenerator via GPIB interface and triggered by theITMS software.

The dc potential generated by the ITMS wasdetermined by direct measurement with a digitalvoltmeter for each dc offset used. The rf potentialgenerated was measured simultaneously with eachpart of the experimental scan from the 12-bit DACoutput of the ITMS, using the second channel of thedigital oscilloscope. A five-point calibration curvewas produced between the 12-bit DAC output to the rf


output test point of the ITMS, which is assumed tohave a 1:100 ratio in amplitude when compared to theactual potential at the ring electrode.

3.1. Determination ofbr 5 0 andbz 5 0

The experimental timing diagram (scan function)in determining thebr andbz boundaries is illustratedin Fig. 3(a). During the trapping event of the experi-ment, the trapping rf was set and dc potential wasapplied to the ring electrode. After a delay of 5.0 ms,the rf potential was linearly ramped and the ejectedions were detected. A plot of ion abundance versus dcpotential was generated and is illustrated in Fig. 3(b).As theb line was approached, a sharp reduction in ionabundance was observed. This sharp portion of thecurve was linearly extrapolated to determine thexintercept. Thisx intercept was defined as the dcpotential for instability for the specific storage rfpotential. Thebz 5 0 ejection line was determinedwith a positive dc offset and thebr 5 0 ejection linewas determined with a negative dc offset. This pro-cedure was repeated for several rf storage potentials.

3.2. Determination ofbz 5 1

The bz 5 1 line was determined simultaneouslywith the other lines. The points were determined bythe dc and rf potentials at which the ion was detectedvia instability mode detection [21].

3.3. Calculation of isobeta lines

The isobeta lines, used to compare with the exper-imental data, were calculated from theb 5 0 andb 5 1 curves, described elsewhere [22]. Each poly-nomial was truncated at the eighth order of thepolynomial.

4. Results and discussion

4.1. Stability diagram

Using the procedures outlined to determine thebr 5 0, bz 5 0 and bz 5 1 lines, a stability dia-

gram [Fig. 4(a)] was developed using the followingequations [23] to calculateaz andqz, respectively,

az 5216Udc

~m/e!~r12 1 2z0

2!V2 (23)

qz 58Vrf

~m/e!~r12 1 2z0

2!V2 (24)

where, Udc is the dc potential applied to the ringelectrode,Vrf is the rf potential amplitude applied tothe ring electrode,r1 is the inner radius of the ringelectrode (18.92 mm),z0 is the vertex of the hyper-bolic end caps (7.81 mm), andV is the angularfrequency of the rf potential (6.93 106 rad s21) and(m/e) is the mass-to-charge ratio of the ion.

The experimentally determined stability diagramsfor both fragments of DME have the same generalshape, yet appear condensed when compared to thetheoretical diagram for a hyperbolic trap. The reasonfor the reduced diagrams is related to the equationsused to defineaz andqz. If one considers the effect acylinder has on the potential at a fixed point whencompared to a hyperboloid, the cylinder will producea larger potential. In order for the potential to be thesame at this fixed point, the hyperbola would need tobe closer to the point. Since Eqs. (23) and (24) are fora hyperbolic ring electrode, there should be a scalingfactor (k , 1) introduced into these equations whichaccounts for this effect. When the scaling factor isintroduced to correct the radial parameter, the stabilitydiagram approximates the theoretical hyperbolic sta-bility diagram quite well. This is demonstrated in Fig.4(b) in which Eqs. (25) and (26) are used to calculateaz andqz, respectively, and with a value ofk 5 0.74.

az 5216Udc

~m/e!~kr12 1 2z0

2!V2 (25)

qz 58Vrf

~m/e!~kr12 1 2z0

2!V2 (26)

The scaling factor ofk 5 0.74 isinaccurate in twoprimary respects: the determination of the rf ampli-tude used an approximation to relate true amplitude atthe cell to a test point on the rf generator circuit board


Fig. 3. Determination of thebr 5 0 andbz 5 0 isobeta lines for the hybrid trap. (a) Timing diagram for experiment used to determine thestability diagram. (b) Plot of ion abundance as the dc potential is decreased, at a constant storage trapping rf potential of 570Vop, showingdecay in ion signal as thebr 5 0 stability boundary is approached.


Fig. 4. Experimentally determined stability diagram (a)m/z 5 47 DME fragment using the standard definitions ofaz andqz. (b) m/z 5 47DME fragment using the modified definitions ofaz andqz, wherek 5 0.74. (The stability diagrams for them/z 5 45 DME fragment wereessentially identical.)


and the adjusted experimental stability diagram [Fig.4(b)] does not correspond to the boundaries of thetheoretical stability diagram. However, the fact thatthe experimental boundaries have a similar shape andnearly the same values as the theoretical boundaries,suggests that one could use a proportionality factor of0.74 with equations previously developed [12] for thetheoretical hyperbolic ion trap to estimate a number ofdesired variables such as secular ion frequency orpseudopotential well depth.

Although not evaluated in this study it is importantto point out that evaluating the interior of the stabilitydiagram can be as important as the determination ofthe stability boundaries. Since no real ion trap canproduce a perfect quadrupolar potential, some higherorder potentials will be present. The existence of thesehigher order potentials gives rise to a variety ofnonlinear effects [24]. The superposition of higher

order potentials on the quadrupolar potential canresult in ion ejection when an ion resides on certainiso-b lines, such asbz 5 2/3 for hexapole andbz 5

1/ 2 for octopole. Such iso-b lines which result in ionejection are commonly called black canyons, andhave been experimentally observed [25,26]. Blackcanyons generally reduce the retention of daughterions in MS/MS and MSn experiments and the efficienttrapping of externally generated ions.

Higher order potentials are present in the hybridtrap, and one would predict that not only do blackcanyons exist for this geometry, but that their effectshould be greater than for a hyperbolic geometry.However, through the choice of appropriate geometricparameters, such as aspect ratio and asymptopicangle, and experimental parameters, such as trappingpotential, one could reduce the effects of these non-linear resonances.

Fig. 5. (a) Mass spectrum of PFTBA. (b) Linearity of the applied rf potential, in terms of the D/A converter value, versus the mass-to-chargeof the PFTBA fragment ion.


4.2. Mass scan

A sample of PFTBA was used to determine thelinearity of the mass scale relative to the rf potential.Fig. 5 shows the resulting PFTBA spectrum and thelinear relationship between the rf potential applied tothe ring electrode and the mass-to-charge ejected aspredicted by both Eqs. (24) and (26). Using Eq. (24)the averageqeject 5 0.76. With ak value of 0.74, theaverageqeject is 0.93 using Eq. (26).

As the PFTBA spectrum indicates, the mass rangeis only 350 Da. This is a result of the large ringelectrode radius (r1 5 18.92 mm)chosen [27] forthis experiment and is not a result of the geometry.

4.3. Resolution and isolation

Two important practical features for a quadrupoleion trap are the ability to resolve peaks of closem/zand the ability to isolate one for further ion manipu-lation. A sample of carbon tetrachloride, which pro-duces three significant ion peaks with nominalm/z of117, 119 and 121 Da/e, is used to demonstrate theseproperties in the hybrid trap. Fig. 6(a) shows, with theaddition of a 440 kHz dipolar signal across the endcap electrodes, that not only are the chlorine isotopepeaks baseline resolved, but that the average resolu-tion is 390 (FWHM). Using the SWIFT isolationtechnique the isolation capabilities of the hybrid trapare demonstrated in Fig. 6(b). Both the 117 and 121peaks are absent and the retention of the 119 ions is83%, in abundance when compared to the Fig. 6(a).

5. Conclusion

The hybrid ion trap is capable of performing someof the same tasks as the standard hyperbolic ion trap.A model has been developed to describe the electricpotential and field within the ion trap cell. The upperportion of the stability diagram was experimentallydetermined and shown to have the same general shapeas that for the hyperbolic geometry. When a propor-tionality factor,k, was added to the equations definingthe az and qz values, the stability diagram approxi-

mated that of the hyperbolic model. This proportion-ality factor could be applied to estimate importantparameters, such as secular ion frequency or pseudo-potential well depth. A linear mass scale relative toapplied rf potential was demonstrated. With the addi-tion of a supplementary dipolar signal across the endcap electrodes, the useful technique of SWIFT isola-tion was shown with greater than 80% efficiency andunit mass resolution was demonstrated. Our conclu-sion is that modification of the ring electrode geom-etry affects theaz and qz parameters describing theion stability boundary, yet has no apparent effect onthe basic properties of the ion trap of linear mass scan,effective isolation and unit mass resolution. Currentlythe hybrid ion trap is being studied as a candidate forin situ image current detection [28,29]. Future work

Fig. 6. (a) Resolution of the chlorine-35/chlorine-37 isotopes of theCCl3

1 ion with axial modulation at 440 kHz and 5.9 Vop. The 117,119, and 121 nominalm/z ions have a resolution (FWHM) of 343,408, and 418, respectively. (b) SWIFT isolation of them/z 5 119ion, under the same conditions as in (a) except with the addition ofa broadband SWIFT waveform of 180 to 300 kHz with a singlenotch at 2256 5 kHz, 5 Vop.


includes the optimization of the cell geometry forincreased ion capacity.

Acknowledgements

CR.A. would like to thank Dr. Jennifer Brodbeltfor use of the ITMS and Grady Rollins for the qualitymachine work. This work was supported by the NIHand The Welch Foundation.

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