1. Simulations of High Resolution Resonance Ejection Scan in a Digital Ion Trap .
Michael Sudakov and Sumio Kumashiro
Shimadzu Research Laboratory (Europe) Ltd., Manchester, UK
Overview
Recently a prototype of Digital Ion Trap (DIT) was developed in SRL [1]. This ion trap is driven by square wave supply and uses a novel method of frequency scan with a linear mass scale, which theoretically does not have limitations of mass range from high mass side. Unlike all existing commercial ion traps, DIT uses theoretical geometry of electrodes. Instead of deliberate modification of electrode geometry a novel Field Adjusting method is used in DIT. DC field penetration from an external electrode trough the entrance hole allows making the secular frequency of ion oscillation almost independent of amplitude thus providing conditions of high-resolution resonance excitation. A new approach for building ion trap instrumentation requires investigation both by means of experiment and simulations.
Methods
Simulation Model
A simulation was performed with the use AXSIM-2 software. AXSIM uses fields refined by SIMION-7.0 for the actual electrode geometry of DIT prototype. In preliminary study [2] it was found that potential arrays with a grid step of 50mm and with a grid step of 25mm give similar results, hence the grid step of 25mm was used all over this study. Like in SIMION, AXSIM uses linear interpolation for electrical vector from the grid. An RKF4 integration procedure was used with a fixed integration step. Consequently, present simulation is equivalent to SIMION simulation with fixed integration step (“trajectory quality” zero). AXSIM-2 is optimised for multi-particle ion trap simulations. It features accurate hard sphere model of ion collisions with buffer gas particles [3], which was tested in separate simulations for correct Maxwell distributions of particles in absence of electrical fields and for correct values of mobility and diffusion coefficients. AXSIM-2 allows fast and accurate simulation of ion motion in RF fields with conventional RF voltage scan or Square Wave with frequency scan under digital control, allows simulating of complicated resonance excitations and DC signals. User interface of AXSIM allows visualizing the particle motion in a real space and investigating the nonlinear motion by Phase space and Fourier transform analysis. All this makes AXSIM-2 a powerful tool for simulations of RF ion traps, quadrupoles and other ion optics devices.
For optimisation of resonance ejection scan a simulation of DIT was prepared with all signals which may affect resolving power (see numbers of corresponding electrodes on fig.1):
1) RF supply on the ring electrode: +/-1000V Digital Square Wave (frequency scan)
2) Pulsed dipole excitation, each 4th period of RF 0/-1.2V (pulse width variable)
3) Field Adjusting voltage: DC signal (variable)
4) Focusing Electrode Voltage: DC singal –100V
5) Detector Entrance Voltage: DC signal –1.5kV
Fig.1. DIT schematic with major power supplies x
14.14mm FA
+1kV
-1kV
Digital SQW
-100V
-1.5kV
Pulsed Dipole and
Waveform Generator
-2kV…
+2kV
7bit
to Detector
from
Ion Source 1 2 3 4 5
Ions of mass 1562Da (singly charged) were used for present simulation study. Cross section of ions was taken 500sq.A. Ion trap is filled with He buffer gas at temperature 300K.
Buffer Gas pressure optimisation
Field Adjusting Voltage optimisation and comparison with Experiment
In first series of simulations the gas pressure inside the trap was optimised for best resolving power in a scan with speed 1000Da/s. In this simulation 1000 ions are flown until they hit detector. Detector has a fixed sampling time of 50ms. Each ion contributes into a peak shape according with it’s time of flight. Parameters of the scan was adjusted in such a way, that ejection of ions starts approximately 30ms from the beginning of scan. Typically 10ms is sufficient for complete cooling. Consequently all ions loose any memory of initial conditions far before the ejection. Simulation was repeated many times with different pressure of the buffer gas, while all other simulation parameters were fixed as well as initial conditions of ions. Results are presented in fig.2, fig.3, fig.4.
In a second series of simulations the scan was further optimised for best resolution at constant buffer gas pressure of 0.1mTorr. Variable parameter in this simulation was the voltage of Field Adjusting electrode (FAE). Results are presented in fig.5, fig.6.
Fig.5
Fig.6 Comparison with experiment
Fig.2
Fig.3
Fig.4
It was found that the peak shape and peak position is sensitive to a FAE voltage. With non optimised FAE voltage the resolving power of the scan is only At certain value of FAE voltage resolution suddenly improves by an order of magnitude. Optimum value of FAE voltage according with present simulation lies between 1100V and 1400V.
Simulation was confirmed by the experiment on DIT prototype [1] with Glu-fibrinopeptide B ions. Comparison of experimentally measured resolution (FWHM) with simulation is presented in fig.6. Experiment shows nice agreement with simulations, although the maximum resolving power is slightly smaller. Optimum value of FAE voltage for best resolution slightly varies depending on scan speed. Higher resolution can be achieved by reducing the scan speed. Resolving powers over was achieved on DIT prototype for very slow scans (39Da/s).
Peak position is sensitive to buffer gas pressure and resolving power is improved at lower pressures. Not all ions are ejected with dipole excitation of 1.2V at pressures over 0.3mTorr. They will be ejected at the boundary of stability contributing to “ghost” peaks. In further simulations He pressure of 0.1mTorr was used.
Fourier Transform analysis of Ion Vibrations (Frequency Shift Correction).
Phase Space Analysis of ion motion (Attractive Cycles).
In order to reveal the mechanism of field adjustment the ion motion at the point of ejection was investigated. Ejection of 1562Da ions happens at 33ms from the beginning of frequency scan with present simulation settings. Period of square wave at 33ms was calculated to be ms. Secular frequency of ions can be calculated using Fourier transform method [4] depending on amplitude of ion vibrations in Z direction. Results of such calculations with and without FAE voltage are presented in fig. 7.
Investigation of ion motion in a phase space (z,vz) further reveals the dynamics of resonance ejection scan. Motion of a single ion 1562Da was simulated for a long time ( cycles) without dipole excitation and random collisions. Weak damping was introduced in order to reduce kinetic energy of vibrations slowly without modifications to the phase-space structure. Ion position was sampled in the middle of negative pulse on the ring electrode and plotted in configuration space (z,vz). Results are presented in fig.9 a,b.
Fig.7. Frequency shift in the ion trap with holes
Fig.8. Field Adjusting potential
Fig.9
Phase space motion of ion at conditions of best resolution in DIT.
A) Small amplitude of vibrations.
B) Big amplitude of vibrations. A. B.
Small and medium vibrations
High amplitude vibrations:
Negative frequency shift due to holes
Map: 1V
+1200V 0V
It was found that ion with small amplitude of vibrations gradually loose energy and approach the middle of the trap (fig.9.A). In contrast ion with big amplitude appears to be “trapped” in a regions of phase space that correspond to a stable nonlinear motion (fig.9.B). Frequency of ion vibrations in such state exactly equals to ¼ of the RF frequency. Ion can not escape from this state unless trapping conditions will change (RF period or FAE voltage). Existence of these regions was confirmed by simulations of resonance ejection scan for a triplet of ions with masses 1561Da, 1562Da and 1563Da (500 ions of each mass) Results are presented in fig.10.
It follows that in the ion trap with holes the secular frequency of ions shifts to lower values at high amplitude of ion vibrations when ion approaches hole regions (see red line in fig.7). The shift can be as big as several percent. Due to this ejection of ions is delayed and resolving power is poor because ion fall out of resonance with excitation field just on the verge of ejection. Simulations show that ion approaches hole region many times prior to ejection. Oscillation of ion with high amplitude in presence of buffer gas results in heating of the internal degrees of freedom and subsequent fragmentation. Fragments become immediately unstable in RF field and hit detector. In this case, peak position depends on ion fragility. Ions of the same mass-to-charge ratio but different collision cross-section appear at slightly different position in a spectrum. This phenomena is know as “chemical mass shifts” [5] and all commercial ion traps have deliberately distorted geometry in order to avoid this problem. In a DIT a method of field adjusting was used to overcome this effect. Positive voltage from FAE penetrates into the volume of the ion trap like shown on fig.8. DC field modifies the shape of the potential well so as to produce frequency shift to higher values (positive frequency shift) when ions approach hole regions. Although the negative frequency shift can not be removed completely, appropriate voltage on FAE provides conditions of high-quality resonance all the way to ejection hole (see blue line on fig.7). As a result ions are ejected almost simultaneously and mass spectra features high resolution and negligible chemical shifts. Thus FAE appears as a general new method of achieving high resolution spectra in ion traps with theoretical geometry and inevitable distortions from ejection holes and slits.
A ms beginning of ejection for 1561Da ions
B ms ejection of 1562Da ions.
C ms – end of ejection for 1561Da ions
D. 33ms – ejection of 1562Da ions.
Ions on the verge of ejection
Ions trapped in a cycle
One can see from fig. 10.D, that some ions of 1561Da appear to be trapped near the regions of nonlinear stability after ejection of the main group. These ions will contribute to the noise floor in the spectrum or they will produce “ghost” peaks. Existence of nonlinear cycles is specific for resonance ejection at ¼ frequency of the RF and it follows that this is not the best solution for resonance ejection scan in a nonlinear ion traps. Better result can be achieved at higher ejection q values.
References.
Conclusions
[1] Li Ding, M. Sudakov, F. Brancha, R. Giles and S. Kumashiro, A digital ion trap mass spectrometer coupled with atmospheric pressure ion sources, J. of Mass Spectrometry, vol.39, p , 2004
[2] Li Ding, M. Sudakov and S. Kumashiro, A Simulation study of the digital ion trap mass spectrometer, Int. J. of Mass Spectrometry, v.221, No.2, pp , 2003
[3] J.H. Parks and J Szoke, Simulation of Collisional Relaxation of Trapped ion Clouds in presence of Space Charge Effects, J. Chem. Phys., v. !03, pp , 1995
[4] M.Sudakov and S.Kumashiro, Theory and Simulations of Resonance Excitation in Nonlinear and Pure Quadrupole Traps. Part II., 16 Int. MS Conference, Edinburgh, September 1-5, 2003
[5] W. Plass, H. Li and R.G.Cooks, Theory, simulation and measurement of chemical mass shifts in RF quadrupole ion traps, Int. J. of Mass Spectrometry, v.228, pp , 2003
A Simulation model of a Digital Ion trap was developed with the use of SIMION potential arrays, Square Wave RF with possibility of frequency scan, Pulsed dipole excitation at ¼of the main trapping frequency, and accurate Monte-Carlo modelling of ion-buffer collisions using hard-sphere approximation.
Resonance ejection of 1562Da ions using frequency scan under digital control was optimised for best resolution. Experiment on DIT prototype shows good agreement with simulation.
Ion motion under conditions of best resolution was investigated using Fourier Transform and Phase Space analysis. It was found that Field Adjusting is a general method to correct for negative frequency shift in ion traps with holes. Areas of stable nonlinear vibrtions (cycles) in phase space were observed at high amplitude of vibration at optimum conditions for resolution. Cycles correspond to ion vibration with frequency exactly equal to ¼ of the main trapping frequency.
Existence of attractive cycles was found to be unfavourable for resonance ejection scan. The use of resonance ejection at higher q values (higher resonance frequencies) is proposed.