Simulation of Unidirectional Ion Ejection in an Asymmetric Half-Round Rod Electrode Linear Ion Trap Mass Analyzer
An asymmetric trapping field was generated from an asymmetric half-round rod electrode linear ion trap (A-HreLIT), and its performance of unidirectional ion ejection was studied. Two different asymmetric structures of A-HreLITs were constructed, one rotating y electrode pairs toward an x electrode with an angle θ, and the other stretching one x electrode with a distance α. The center of trapping field was displaced away from the geometrical center of the ion trap, defined to be the midpoint along the axis of y between x electrodes, which leads to unidirectional ion ejection through one x electrode. Computer simulations were used to investigate the relationship between asymmetric geometric parameter of θ (or α) and analytical performance. Both structures could result in similar asymmetric trapping fields, which mainly composed of dipole, quadrupole, and hexapole fields. The dipole and hexapole fields were approximately proportional to the asymmetric geometric parameter of rotation angle θ (or stretch distance α). In simulation, ion trajectories and ion kinetic energy were calculated. For ions with m/z 609 Th, the simulation results showed that mass resolution of over 2400 (FWHM) and ion unidirectional ejection efficiency of nearly 90% were achieved in an optimized A-HreLIT. Ion detection efficiency of A-HreLIT could be improved significantly with only one ion detector, while maintaining a considerable mass resolution. Furthermore, the A-HreLIT could be driven by a traditional balanced RF power supply. These advantages make A-HreLIT suitable for developing miniaturized mass spectrometer with high performance.
KeywordsUnidirectional ion ejection Asymmetric geometry Ion detection efficiency Miniaturization Odd-order fields
A linear ion trap (also referenced as two-dimensional ion trap) could mainly be divided into an axial ejection linear ion trap (AeLIT) [1, 2] and a radial ejection linear ion trap (ReLIT)  according to ion ejection direction during mass analysis. In recent years, various types of ReLIT with simplified geometry were developed for special purposes, such as a rectilinear ion trap (RIT) [4, 5], an ion trap array (ITA) , a triangular-electrode linear ion trap (TeLIT) [7, 8], a printed circuit board ion trap (PCBIT)  and a half-round rod electrode linear ion trap (HreLIT) , etc. The simplified ReLIT was considered to be more suitable for developing miniaturized mass spectrometer than classical ReLIT, due to its ease of fabrication, compact size, and low cost [11, 12, 13].
The performance of an ion trap, including mass resolution, sensitivity, spectrum scan speed, ion capacity, and collision-induced dissociation (CID) capabilities were studied in many previous works by means of experiment and simulation [3, 14, 15]. Performance improvement was usually achieved by optimizing the geometrical shape and relative position of electrodes. For example, “stretch” of electrodes was a widely used geometry optimizing method of enhancing mass resolution, which has been successfully applied on classical ReLIT , RIT , and HreLIT . There were other methods, which focused on optimizing electrode shape, r/r0 , and slot size , etc.
Computer simulation played a very important role in the process of studying and optimizing an ion trap. Mathematical modeling approaches have been proved useful, especially for deep understanding of some phenomenon observed in experiments, such as the relationship between mass resolution and scan speed [3, 14]. However, numerical simulations are required in study of scanning of RF field and “realistic” ion trap electrode geometries . Especially for simplified structured ion traps, such as a cylindrical ion trap (CIT) [18, 19, 20], RIT, and TeLIT , the internal potential could hardly be expressed by strictly defined mathematical models. In such situations, numerical simulations were used to study ion trajectory, ion ejection process, and ion neutral collisions, and finally to evaluate the performance of these “realistic” ion traps.
Sensitivity is critical for mass spectrometer in real application. Ion capacity, ion ejection efficiency, and ion detection efficiency have great impacts on ultimate sensitivity of an ion trap mass spectrometer. For existed ReLITs, including RIT, ITA, TeLIT, and HreLIT, ions were ejected from both sides along the x-axis, which means that ion detection efficiency would not be higher than 50% if only one ion detector was used, as it usually does in miniaturized ion trap mass spectrometers. To solve this problem, two ion detectors were used in a commercialized LIT mass spectrometer (LTQ, Thermo Finnigan) . However, this configuration requires a large vacuum chamber and high cost, which is undesirable for developing miniaturized mass spectrometers.
Ion detection efficiency could be greatly improved by unidirectional ion ejection even if only one detector was used. Splendore et al.  employed an asymmetric trapping field on a traditional three-dimensional ion trap by adding an alternating voltage out of phase to the endcap electrodes at the same frequency as the ring electrode. In this case, the center of ion vibration was displaced away from the geometrical center of the trap. Experiment results showed that unidirectional ion ejection occurred and the absolute ion abundance was doubled. Remes et al.  created several models of hyperbolic ReLITs with asymmetric geometry and studied their performance using numerical simulation approaches. These asymmetric ion traps were highly comparable to an ideal quadrupole ion trap in mass resolution. Wang et al.  studied the ion motion characteristics in a quadrupole ion trap coupling with hexapole and octopole fields using mathematical modeling approach. It was found that hexapole field leads to unidirectional ion ejection and degradation of mass resolution, while octopole field could compensate nonlinear effects and enhance mass resolution. In summary, it could concluded that asymmetric electric fields (odd-order fields) were the key to unidirectional ion ejection, and proper components of even-order fields were necessary for compensating the nonlinear effects and enhance mass resolution. The asymmetric electric fields could be added to an ion trap by applying unbalanced RF trapping voltage on electrodes or by constructing an ion trap with asymmetric geometries.
In the present study, two types of “realistic” models of A-HreLITs were created, and their performances including unidirectional ion ejection efficiency and mass resolution were studied using numerical simulation approaches. The impact of geometric parameters on performance was also studied.
Structure of a -HreLIT
The modeled ion trap electrode profiles were created using the SIMION 8.0 geometry file scripting language. A two-dimensional model was used in the simulation and was defined in cross-section with an 800-by-800 point grid array with a grid step of 0.05 mm. The radius of the half-round rod r = 4.0 mm, the width of slots d = 0.6 mm, the gap between the x and y electrodes g = 2.0 mm and the width of the rectangular rod for mounting m = 4.0 mm.
Field and Ion Trajectory Simulation
The performance of ion trap was mainly determined by its internal electric field distribution. Until now, there have been many studies focusing on quadrupole and high-order fields of ion trap . In this study, the internal electric field of A-HreLIT was also studied.
In ion trajectory simulations, ion motion was simulated with random collisions of ions with helium buffer gas at a pressure of 1.0 mTorr and temperature of 300 K using a hard sphere collision model.
Simulation of Mass Analysis
In this study, the HreLIT was operated using the technique of mass selective instability scan and resonance ejection. The main RF power supply was sine wave with fixed frequency (1.0 MHz), and mass analysis was performed by scanning the amplitude of RF signal (with a scan speed of 1500 Th/s). During mass analysis, an excitation signal AC of sine waveform with a particular frequency was applied to excite ions having the same secular frequency. In this case, the amplitude and frequency of AC were critical for the performance of A-HreLIT.
In simulation, the modeled ion populations were comprised of 300 ions (m/z 609 Th, 610 Th, 611 Th, each type with a number of 100). The initial position of ions was randomly chosen from a Gaussian distribution around the geometric center of ion trap with a 0.1-mm standard deviation, and the initial energy of ions was around 0 eV with a 0.1-eV deviation. During mass analysis, the termination time and location of ions were recorded and, consequently, mass spectrum and conditions of ion ejection could be obtained. The mass resolution was estimated from the spectrum peak width, unidirectional ion detection efficiency equaled the ratio between number of ions that ejected to one of detection planes and total number of ions (i.e., 300).
Results and Discussion
Geometry Optimization of HreLIT
The two types of A-HreLITs in this work were designed from the corresponding HreLIT, respectively. So the electrode geometry of two types of HreLITs were first optimized, and then A-HreLIT based on the optimized HreLIT were built, and the changed parts of the structure and asymmetric geometric parameters were both marked in red in Fig. 1(c), (d).
For both types of HreLITs, the slots for ion ejection created some serious nonlinear electric fields because of field penetration inside the slots . To compensate for this serious nonlinear electric fields, a classical method called “stretch”  was used in the two types of HreLITs.
Potential Distribution in A-HreLIT
Unidirectional Ion Ejection in A-HreLIT
It was expected that unidirectional ion ejection of A-HreLIT arrived at about 90%, while maintaining a considerable mass resolution. Thus, when ion unidirectional ejection efficiency and mass resolution were both taken into account, a compromise should be made and the optimum frequency of AC would be 0.328 MHz.
In this work, asymmetric trapping fields were generated in two types of A-HreLITs for unidirectional ion ejection. In this case, the center of ion vibration was displaced away from the geometrical center of A-HreLITs and ions were ejected predominantly through one of x electrode pairs. The current investigation has demonstrated that ion detection efficiency could be improved significantly in A-HreLIT mass spectrometer with only one detector, while maintaining a considerably high-mass resolution, which made the A-HreLIT suitable for developing miniaturized mass spectrometer with good analytical performance. Yet, all results in this work were achieved using computer numerical simulation approaches. Constructing real A-HreLIT mass spectrometer and test the performance of unidirectional ion ejection and mass resolution in experiment would be our next work.
This study is supported by and funded by the Natural Science Foundation of China (61601314).