Kinetic theory of radio frequency quadrupole ion traps. I. Trapping of atomic ions in a pure atomic gas

A kinetic theory based on the Boltzmann equation is developed for the trapping of atomic ions in a radio-frequency quadrupole ion trap containing enough neutral atoms that ion-neutral collisions cannot be ignored. The collisions are treated at the same level of sophistication and detail as is used to deal with the time- and space-dependent electric fields in the trap. As a result, microscopic definitions are obtained for the damping and stochastic forces that originate from such collisions. These definitions contrast with corresponding phenomenological terms added ad hoc in previous treatments to create damped Mathieu and Langevin equations, respectively. Furthermore, the theory indicates that either collisional cooling or heating of the ions is possible, depending upon details of the ion-neutral mass ratios and interaction potential. The kinetic theory is not dependent on any special assumptions about the electric field strengths, the ion-neutral interaction potentials, or the ion-neutral mass ratio. It also provides an ab initio way to describe the ion kinetic energies, temperatures, and other properties by a series of successive approximations.     

The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study

A theoretical method, the harmonic balance method, was introduced to study the coupling effects of hexapole and octopole fields on ion motion in a quadrupole ion trap. Ion motion characteristics, such as ion motion center displacement, ion secular frequency shift, nonlinear resonance curve and buffer gas damping effects, have been studied with the presence of both hexapole and octopole fields. It is found that hexapole fields have bigger impacts on ion motion center displacement, while octopole fields dominate ion secular frequency shift. Furthermore, the nonlinear features originated from hexapole and octopole fields could enhance or cancel each other, which provide us more space in a practical ion trap design process. As an example, an ion trap with improved performance was designed using a specific combination of hexapole and octopole fields. In this ion trap, a hexapole field was used to achieve efficient ion directional ejection, while an octopole field was added to correct the chemical mass shift and resolution degradation introduced by the hexapole field. Copyright © 2013 John Wiley & Sons, Ltd.     

Prediction of collective characteristics for ion ensembles in quadrupole ion traps without trajectory simulations

Fundamental aspects are presented of a two-temperature moment theory for quadrupole ion traps developed via transformation of the Boltzmann equation. Solutions of the moment equations correspond to changes in the ensemble average for any function of ion velocity, because the Boltzmann equation reflects changes to an ion distribution as a whole. The function of primary interest in this paper is the ion effective temperature and its behavior during ion storage and resonance excitation. Calculations suggest that increases in ion effective temperature during resonance excitation are due primarily to power absorption from the main RF trapping field rather than from the dipolar excitation signal. The dipolar excitation signal apparently serves mainly to move ions into regions of the ion trap where the RF electric field, and thus ion RF heating, is greater than near the trap center. Both ideal and non-ideal ion trap configurations are accounted for in the moment equations by incorporating parameterized variables a and q , which are modified versions of the commonly used forms for the DC and AC ring voltages, and b and d , which are new forms that account for the voltages applied to the endcaps. Besides extending the applicability of the moment equations to non-ideal quadrupole ion traps, the modified versions of the parameterized variables can have additional utility. Calculation of the spatial dependence of ion secular oscillation frequencies is demonstrated as an example.     

Mass selective axial ion ejection from a linear quadrupole ion trap

The electric fields responsible for mass-selective axial ejection (MSAE) of ions trapped in a linear quadrupole ion trap have been studied using a combination of analytic theory and computer modeling. Axial ejection occurs as a consequence of the trapped ions' radial motion, which is characterized by extrema that are phase-synchronous with the local RF potential. As a result, the net axial electric field experienced by ions in the fringe region, over one RF cycle, is positive. This axial field depends strongly on both the axial and radial ion coordinates. The superposition of a repulsive potential applied to an exit lens with the diminishing quadrupole potential in the fringing region near the end of a quadrupole rod array can give rise to an approximately conical surface on which the net axial force experienced by an ion, averaged over one RF cycle, is zero. This conical surface has been named the cone of reflection because it divides the regions of ion reflection and ion ejection. Once an ion penetrates this surface, it feels a strong net positive axial force and is accelerated toward the exit lens. As a consequence of the strong dependence of the axial field on radial displacement, trapped thermalized ions can be ejected axially from a linear ion trap in a mass-selective way when their radial amplitude is increased through a resonant response to an auxiliary signal.     

Ion trajectory simulation for electrode configurations with arbitrary geometries

A multi-particle ion trajectory simulation program ITSIM 6.0 is described, which is capable of ion trajectory simulations for electrode configurations with arbitrary geometries. The electrode structures are input from a 3D drawing program AutoCAD and the electric field is calculated using a 3D field solver COMSOL. The program CreatePot acts as interface between the field solver and ITSIM 6.0. It converts the calculated electric field into a field array file readable by ITSIM 6.0 and ion trajectories are calculated by solving Newton's equation using Runge-Kutta integration methods. The accuracy of the field calculation is discussed for the ideal quadrupole ion trap in terms of applied mesh density. Electric fields of several different types of devices with 3D geometry are simulated, including ion transport through an ion optical system as a function of pressure. Ion spatial distributions, including the storage of positively charged ions only and simultaneous storage of positively/negatively charged ions in commercial linear ion traps with various geometries, are investigated using different trapping modes. Inelastic collisions and collision induced dissociation modeled using RRKM theory are studied, with emphasis on the fragmentation of n-butylbenzene inside an ideal quadrupole ion trap. The mass spectrum of 1,3-dichlorobenzene is simulated for the rectilinear ion trap device and good agreement is observed between the simulated and the experimental mass spectra. Collisional cooling using helium at different pressures is found to affect mass resolution in the rectilinear ion trap.     

稳定图的测定与矩形离子阱质谱性能分析

从理论上讲, 离子阱质谱仪的性能是由阱内电场分布决定的,而电场分布又是由组成离子阱的电极几何结构和离子阱工作电压决定的. 对于矩形离子阱, 即使不考虑其几何结构的偏差, 其阱内的电场分布一般也很复杂. 在矩形离子阱内, 除四极电场外, 还包含多种成分的其他各种高阶场, 它们直接影响离子在阱内的运动轨迹和离子阱质谱的性能. 由于各种电场成分对离子阱内离子运动的影响非常复杂, 还很难从数学上给出精确的解析解, 使得目前从理论上还无法预测高阶场成分对质谱性能的影响. 本工作通过测定不同几何结构的矩形离子阱的稳定图, 从实验上比较了不同场半径, 即不同电场分布条件下的离子阱质谱性能的差别. 实验中, 通过改变离子阱的几何比例结构, 详细测定了不同结构的矩形离子阱的稳定图特征, 并与实验测得的质谱分析结果进行比较. 同时, 我们还详细介绍了矩形离子阱质谱的稳定图的测定方法, 并根据得到的不同情况下的稳定图结构分析了离子阱的质谱性能. 研究结果表明： 可以通过比较试验得到的稳定图结构来判断其离子阱质谱仪的性能如质量分辨能力等. 此外, 实验结果还发现： 对于y方向拉伸结构的矩形离子阱, 其实验绘制得到的是不完整的稳定图. 但根据稳定图边界的特点, 通过采用四极直流电压调制的方法, 可以对y方向拉伸结构的矩形离子阱的性能进行改善, 极大地提高了阱的质量分辨能力.     

Dynamically Harmonized FT-ICR Cell with Specially Shaped Electrodes for Compensation of Inhomogeneity of the Magnetic Field. Computer Simulations of the Electric Field and Ion Motion Dynamics

The recently introduced ion trap for FT-ICR mass spectrometers with dynamic harmonization showed the highest resolving power ever achieved both for ions with moderate masses 500?C1000?Da (peptides) as well as ions with very high masses of up to 200?kDa (proteins). Such results were obtained for superconducting magnets of very high homogeneity of the magnetic field. For magnets with lower homogeneity, the time of transient duration would be smaller. In superconducting magnets used in FT-ICR mass spectrometry the inhomogeneity of the magnetic field in its axial direction prevails over the inhomogeneity in other directions and should be considered as the main factor influencing the synchronic motion of the ion cloud. The inhomogeneity leads to a dependence of the cyclotron frequency from the amplitude of axial oscillation in the potential well of the ion trap. As a consequence, ions in an ion cloud become dephased, which leads to signal attenuation and decrease in the resolving power. Ion cyclotron frequency is also affected by the radial component of the electric field. Hence, by appropriately adjusting the electric field one can compensate the inhomogeneity of the magnetic field and align the cyclotron frequency in the whole range of amplitudes of z-oscillations. A method of magnetic field inhomogeneity compensation in a dynamically harmonized FT-ICR cell is presented, based on adding of extra electrodes into the cell shaped in such a way that the averaged electric field created by these electrodes produces a counter force to the forces caused by the inhomogeneous magnetic field.     

Surface-induced dissociation of molecular ions in a quadrupole ion trap mass spectrometer

A method is reported by which surface-induced dissociation is used to activate ions stored in a quadrupole ion trap mass spectrometer. The method employs a short (< 5 μs), fast-rising (< 20-ns rise time), high voltage direct current (dc) pulse, which is applied to the endcaps of a standard Paul-type quadrupole ion trap. This is in contrast to the application of an alternating current (ac) signal normally used to resonantly excite and dissociate ions in the trap. The effect of the dc pulse is to cause the ions rapidly to become unstable in the radial direction and subsequently to collide with the ring electrode. Sufficient internal energy is acquired in this collision to cause high energy fragmentations of relatively intractable molecular ions such as pyrene and benzene. The dissociations of limonene are used to demonstrate that high energy demand processes increase in relative importance in the dc pulse experiment compared with the usual resonance excitation method used to cause activation. The fragments are scanned out of the ion trap using the conventional mass-selective instability scan mode. Simulations of ion motion in the trap provide evidence that surface collisions occur at kinetic energies in the range of tens to several hundred electronvolts. The experiments also demonstrate that production of fragment ions is sensitive to the phase of the main radiofrequency drive voltage at the point when the dc is initiated.     

Asymmetric rectilinear ion trap with unidirectional ion ejection capability

In this paper, the shapes of the electrodes are modified based on a rectilinear ion trap to achieve unidirectional ejection of ions. The designed asymmetric rectilinear ion trap (ARIT) analyzer adds convex and concave circular structures with a height of 0.5 mm on the two X‐electrodes, so that the electric field center of the ion trap is inclined to the concave side. The electric field lines of the convex side are compressed to the concave side. Both simulations and experimental results show that ions are more likely to emit from the slit on the concave side plate when performing ion resonance ejection. The mass spectrum signal intensity can reach more than twice that of the original rectilinear trap when using only one detector. Calculations of the electric field components in the trap show that the even‐order higher field proportion in the ion trap has not been significantly affected. Combined with the experimental test results, the study further confirmed that the developed ARIT has no significant loss in mass resolution, tandem mass spectrometry capability, and quantitative analysis capability. The proposed asymmetric structure modification scheme can achieve single‐side ejection without significantly affecting other performances of the analyzer, which provides a new idea for the structural optimization of the subsequent ion trap analyzers.     

Evidence of isomerization during ion isolation in the quadrupole ion trap

Evidence of ion isomerization during isolation in an ion trap mass spectrometer is presented. An ion-molecule reaction that is specific for the tolyl cation was used to monitor the relative abundance of this species. In particular, it has been observed that ion isolation in the ion trap can impart sufficient energy to the tolyl cation to cause it to isomerize to a form (presumably either the benzyl or the tropylium ion) that is not reactive with the neutral reagent. These results are important to consider in ion trap applications involving ion species having activation barriers for isomerization lower than the activation barriers for dissociation.     

阶梯电极离子阱质量分析器的结构与性能

本研究从理论上优化了一种新型结构的线型离子阱质量分析器-阶梯电极离子阱质量分析器,它是由2对阶梯电极与1对端盖电极组成。与传统平板电极矩形离子阱长阶梯电极离子阱相比,具有调节电场分布的优点,同时在几何结构设计上更接近于双曲面电极结构,但比双曲面电极更容易加工。通过改变阶梯电极结构的高度、宽度、场半径比例等几何参数,实现了对离子阱内部电场分布的优化,从而实现离子阱性能的优化。理论模拟研究结果表明,根据几何结构和电场分布优化获得的阶梯电极离子阱质量分析器(X0×Y0=9 mm×5 mm),可以在225 Da/ s 扫速下获得10150的质量分辨率。阶梯电极离子阱结构简单,分辨能力明显高于矩形离子阱。初步的实验结果表明,阶梯电极离子阱具有较好的串级质谱分析性能。     

An electrically compensated trap designed to eighth order for FT-ICR mass spectrometry

We present the design, guided by theory to eighth order, and the first evaluation of a Fourier transform ion cyclotron resonance (FT-ICR) compensated trap. The purpose of the new trap is to reduce effects of the nonlinear components of the trapping electric field; those nonliner components introduce variations in the cyclotron frequency of an ion depending on its spatial position (its cyclotron and trapping mode amplitudes). This frequency spread leads to decreased mass resolving power and signal-to-noise. The reduction of the spread of cyclotron frequencies, as explicitly modeled in theory, serves as the basis for our design. The compensated trap shows improved signal-to-noise and at least a threefold increase in mass resolving power compared to the uncompensated trap at the same trapping voltage. Resolving powers (FWHH) as high as 1.7 x 10(7) for the [M + H](+) of vasopressin at m/z 1084.5 in a 7.0-tesla induction can be obtained when using trap compensation.     

Ion excitation in a linear quadrupole ion trap with an added octopole field

Modeling of ion motion and experimental investigations of ion excitation in a linear quadrupole trap with a 4% added octopole field are described. The results are compared with those obtained with a conventional round rod set. Motion in the effective potential of the rod set can explain many of the observed phenomena. The frequencies of ion oscillation in the x and y directions shift with amplitude in opposite directions as the amplitudes of oscillation increase. Excitation profiles for ion fragmentation become asymmetric and in some cases show bistable behavior where the amplitude of oscillation suddenly jumps between high and low values with very small changes in excitation frequency. Experiments show these effects. Ions are injected into a linear trap, stored, isolated, excited for MS/MS, and then mass analyzed in a time-of-flight mass analyzer. Frequency shifts between the x and y motions are observed, and in some cases asymmetric excitation profiles and bistable behavior are observed. Higher MS/MS efficiencies are expected when an octopole field is added. MS/MS efficiencies (N(2) collision gas) have been measured for a conventional quadrupole rod set and a linear ion trap with a 4% added octopole field. Efficiencies are chemical compound dependent, but when an octopole field is added, efficiencies can be substantially higher than with a conventional rod set, particularly at pressures of 1.4 x 10(-4) torr or less.     

印刷线路板分压离子阱的离子单向出射性能研究

印刷线路板(Printed-Circuit-Board,PCB)分压离子阱是一种新型质量分析器,其突出优点在于内部电场可通过调节射频分压比进行优化.本实验在PCB分压离子阱离子出射方向的两组离散电极上配置了非对称的射频分压,以引入奇次阶场成分,使得射频电场的场中心(即离子运动中心)发生偏移,从而实现离子单向出射.通过数值计算软件SIMION和AXSIM分析了射频分压比差值与其内部电场分布的关系,并模拟离子运动轨迹,得到离子出射情况和模拟质谱峰.模拟结果表明,当两组离散电极的射频分压比差值为20％时,在合适的AC频率条件下,对于m/z=609 Th的离子,PCB分压离子阱的离子单向出射率可达90％以上,且质量分辨率大于2500.本研究可使PCB分压离子阱在基本不损失质量分辨率和使用单检测器模式下,大幅提高离子检测效率,因而在小型化质谱仪应用中具有显著优势.     

Structure and Performance of Polygonal Electrode Linear Ion Trap

The polygonal electrode linear ion trap (PeLIT) can produce quadrupolar electric field plus some higher order field, which balances the relationship between mass resolution and electrode manufacturing difficulties. The electrodes of PeLIT are relatively simple, but have a good mass resolving power. This study investigated the relationship between the electric field distribution and the ion trap structures, and the performances of PeLIT through theoretical simulation and experimental study. Research results of simulation showed that the polygonal electrode linear ion traps with different structures had different electric field distributions and mass analysis performances. The negative decapole field distorted the performances significantly. The experimental results showed that the mass resolution of reserpine ions (m/z 609) was more than 2500 using a polygonal electrode ion trap. At the same time, mass selective excitation and tandem mass spectrometry experiments were also carried.     

Optimization of a quadrupole ion storage trap as a source for time‐of‐flight mass spectrometry

Designs of a quadrupole ion trap (QIT) as a source for time‐of‐flight (TOF) mass spectrometry are evaluated for mass resolution, ion trapping, and laser activation of trapped ions. Comparisons are made with the standard hyperbolic electrode ion trap geometry for TOF mass analysis in both linear and reflectron modes. A parallel‐plate design for the QIT is found to give significantly improved TOF mass spectrometer performance. Effects of ion temperature, trapped ion cloud size, mass, and extraction field on mass resolution are investigated in detail by simulation of the TOF peak profiles. Mass resolution (m/Δm) values of several thousand are predicted even at room temperature with moderate extraction fields for the optimized design. The optimized design also allows larger radial ion collection size compared with the hyperbolic ion trap, without compromising the mass resolution. The proposed design of the QIT also improves the ion–laser interaction volume and photon collection efficiency for fluorescence measurements on trapped ions. Copyright © 2011 John Wiley & Sons, Ltd.     

Field-modulated selective ion storage in a quadrupole ion trap

A new method of selective ion storage in a quadrupole ion trap is described. Broadband waveforms were applied to the endcaps of an ion trap to eject unwanted ions by resonance excitation, which enhanced the storage of selected target ions. A unique trapping field amplitude modulation technique allowed the use of waveforms with fewer frequency components. The requirements and methods of calculations for frequency-optimized wave-forms are discussed. Advantages of this method include the reduction of target ion loss that results from collision-activated dissociation. In other applications, equivalent performance, relative to methods that use nonmodulated trapping fields combined with waveforms that have a higher frequency density, was shown.     

A two-dimensional quadrupole ion trap mass spectrometer

The use of a linear or two-dimensional (2-D) quadrupole ion trap as a high performance mass spectrometer is demonstrated. Mass analysis is performed by ejecting ions out a slot in one of the rods using the mass selective instability mode of operation. Resonance ejection and excitation are utilized to enhance mass analysis and to allow isolation and activation of ions for MS(n) capability. Improved trapping efficiency and increased ion capacity are observed relative to a three-dimensional (3-D) ion trap with similar mass range. Mass resolution comparable to 3-D traps is readily achieved, including high resolution at slower scan rates, although adequate mechanical tolerance of the trap structure is a requirement. Additional advantages of 2-D over 3-D ion traps are also discussed and demonstrated.     

Development and Investigation of a Mesh-Electrode Linear Ion Trap (ME-LIT) Mass Analyzer

A mesh-electrode linear ion trap (ME-LIT) mass analyzer was developed and its performance was primarily characterized. In conventional linear ion trap mass analyzers, the trapped ions are mass-selected and then ejected in a radial direction by a slot on a trap electrode. The presence of slots can strongly affect the electric field distribution in the ion trapping region and distort the mass analysis performance. To compensate for detrimental electric field effects, the slot is usually designed and fabricated to be as small as possible, and also has very high mechanical accuracy and symmetry. A ME-LIT with several mesh electrodes was built to compensate for the effects caused by slots. Each mesh electrode was fabricated from a plate electrode with a relatively large slot and the slot was covered with a conductive mesh. Our preliminary experimental results show that the ME-LIT could considerably diminish the detrimental electric field effects caused by slots, and increase the mass resolving power and ion detection efficiency. Even with 4-mm-wide slots, a mass resolution in excess of 600 was obtained using the ME-LIT. Mass resolution could be remarkably improved using mesh electrodes in ion traps with asymmetric electrodes. The stability diagram of the ME-LIT was mapped, and highly efficient tandem mass spectrometry was demonstrated. The ME-LIT was qualified as a LIT mass analyzer. The ME-LIT can improve the mass resolution and decrease the requirements of mechanical accuracy and symmetry of slots, so it shows potential for a wide range of practical uses.

Characterization of an Electron Ionization Source Trap Operating in the Presence of a Magnetic Field Through Computer Simulation

We explore the feasibility of conducting electron ionization (EI) in a radio-frequency (rf) ion source trap for mass spectrometry applications. Electrons are radially injected into a compact linear ion trap in the presence of a magnetic field used essentially to lengthen the path of the electrons in the trap. The device can either be used as a stand-alone mass spectrometer or can be coupled to a mass analyzer. The applied parallel magnetic field and the oscillating rf electric field produced by the trap give rise to a set of coupled Mathieu equations of motion. Via numerical simulations, electron trajectories are studied under varying intensities of the magnetic field in order to determine the conditions that enhance ion production. Likewise, the dynamic behavior of the ions are investigated in the proposed EI source trap and the fast Fourier transform FFT formalism is used to obtain the frequency spectrum from the numerical simulations to study the motional frequencies of the ions which include combinations of the low-frequency secular and the high-frequency micromotion with magnetron and cyclotron frequencies. The dependence of these motional frequencies on the trapping conditions is examined and particularly, the limits of applying a radial magnetic field to the EI ion trap are characterized.