1. SRL
Simulations of High Resolving Quadrupoles with Collisional Cooling Interface and Fringing Fields.
Michael Sudakov
Shimadzu Research Laboratory (Europe) Ltd., Manchester, UK
Fringing Fields in Quadrupole
Single Quadrupole Model
Overview.
Complete simulation of a single quadrupole device with fringing fields and collisional cooling interface is presented. True initial conditions for ions inside essentially 2D section of quadrupole is obtained. It was found that collisional cooling interface allows to prepare a cold beam of ions, while delayed DC ramp allows transmitting the beam into analytical quadrupole without heating the cloud. Peak shape and transmission of quadrupoles with hyperbolic electrodes and with cylindrical rods are investigated. Results indicate that resolving power of quadrupoles with circular rods is limited by nonlinear distortions. In contrast quadrupole with hyperbolic electrodes shows high transmission up to resolving power of
Introduction
Quadrupole Mass Filter is probably the oldest device of radio-frequency mass spectrometry. It is widely used in applications which require selection of ions of particular mass-to-charge ratio by discarding ions of other mass. Over the years passed from an invention of rf-quadrupole by W.Paul [1], the device was thoroughly investigated by theory and well characterized by experiment. Since that time a number of technological advances was made in quadrupoles. Among them is a method of preparation of the ion beam with a help of collisional cooling [2] and delayed DC ramp [3].
Objective of present poster is to investigate the influence of quadrupole geometry and initial conditions of ions on the ultimate performance of quadrupoles by means of simulations.
2D simulations of Quadrupoles
Fringing field calculation for quadrupoles can be performed by a number of methods, but accuracy of calculation should be carefully considered in every case. SIMION field solver can provide accuracy of field interpolation better than 10ppm suggesting that voltages of electrode points are accurate [7]. Potential arrays for fringing field models were prepared using accurate 2D solutions with grid step of 0.01ro (45mm). A special program for calculating multipole expansions was developed. Program allows calculating up to 24 multipoles. It was found, that fringing field has an exponential decay for both DC and Quadrupole fringing fields. Multipole expansions obtained from these analysis were used to perform particle tracing in fringing field. Such kind of simulation requires negligible RAM for complete 3D simulation as compared to SIMION.
Simulation model of a single quadrupole device includes PreFilter section with fixed RF voltage (no resolving DC) and a MainQuadrupole section with variable parameters of the RF and DC voltages. PreFilter section is based on a quadrupole with cylindrical rods (R/ro=1.145) because high quality of the field is not required in this section. PreFilter length (40mm) is sufficiently long in order to avoid influence of fields both from Q0 and Q1.
Usually simulation of ion transmission in quadrupole is performed using 2D fields [6] without account for fringing field. In such kind of simulation cloud of ions is injected directly into 2D field with certain spread of initial positions and energy. Ions that have passed down to the back end of field region are counted as if they have reached detector. Similar simulation for quadrupoles with hyperbolic and circular electrodes was prepared using AXSIM software. Analytical formulae was used for potential distribution of pure quadrupole field. A. B.
Fig 2. Two dimensional simulation for pure quadrupole (ro=5mm, rf frequency 1MHz). Ion beam parameters: diameter 0.24mm, radial energy spread 0.025eV, axial energy 5eV, entry phase of RF = 0.
Methods
Fig 8. Single Quadrupole Simulation Geometry.
Ions start from the middle of PreFilter section with initial conditions obtained from previous simulation of collisional cooling quadrupole. Main Quadrupole has inscribed radius ro=4.5mm and operates at a frequency of 2MHz. Two different models of analytical quadrupole Q1 were prepared. First features perfect geometry with hyperbolical rods (hQuad). Another one is based on cylindrical rods with ratio R/ro=1.127, which is frequently used by quadrupole manufactures. This ratio is believed to provide optimised performance in terms of peak shape and transmission. Results of peak shape simulation for both quadrupoles are presented below. C.
Position of the boundaries of a tip of stability of a mass filter were computed using analytical expressions for b parameter [4]. Equations were used for calculation of RF and DC voltages in simulation for a given theoretical resolution R.
Fig. 5. Potential distributions and dimensions for DC (A) and quadrupole (B) models for fringing fields. (C) Axial dependence of multipole components Ao(z) for DC field from a plate and A2(z) for a quadrupole field in logarithmic scale.
For quadrupoles with circular electrodes potential distributions were obtained with 10 digits accuracy from effective charge method [4]. Important question of quadrupole design is – the optimum ratio of rod radius R with respect to the inscribed radius of the quadrupole ro. From the point of view of minimum dodecapole distortion A6 the optimum ratio equals R/ro= [5]. However best peak shape is reached at smaller R/ro. Simulation for quadrupoles with different ratio R/ro in a range from to shows no definite optimum (fig.3B). Peak shape for all of these quadrupoles is equally distorted and shifted, although ratio R/ro produces slightly better peaks with maximum resolving power of 3000.
Fig 1. Definition of (a,q) parameters with account for quadrupole field strength A2 and calculation of parameters for a given theoretical resolving power R.
Fig 9. Result of peak shape and transmission simulation. (A) Main Quadrupole base on perfect hyperbolic electrodes. (B) Main Quadrupole is a quadrupole with cylindrical rods and ratio R/ro= Actual resolving power obtained from simulations is provided in a legend. Note different mass scale.
Collisional Cooling Quadrupole Model A. B.
To simulate collisional cooling interface a model of quadrupole Q0 (100mm long, circular electrodes R/ro=1.145, ro=4.5mm) with elevated pressure (2mTorr, was prepared. Ions are confined within Q0 due to oscillating RF potential of 3kV at frequency 1.8MHz, and repulsive voltages +10V on the entrance plate and on the exit orifice. A. B. C.
References.
W. Paul, In Les Prix Nobel, Almqvist and Wiskell International; Stokholm, 1989
D.Douglas, J.French, US Patent 4,963,736
W.M. Brubaker, Advan. Mass. Spectrom., vol.4, 1968, p.293
P.H. Dawson, “Quadrupole Mass Spectrometry and its Applications”, Elsiver, 1976, Chapter III.
D.J. Douglas, Glebova T.A., Konenkov N.V., Sudakov M.Yu., Technical Physics, V44, 1999, pp
Douglas D.J., Konenkov N.V., RCM, v.!6, 2002, p.1425
M.Sudakov, 9th Seminar “Recent trends in CPO”, 12 July-16 July 2004, Brno, Czech Republick
After cooling for 10ms potential on the exit orifice is dropped to –2.5V and ions are released into pre-rods and accelerated by potential difference of 5eV. Ions are stopped inside pre-rods sufficiently far away from fringing field and this distribution of ions is used in further simulation as true initial conditions. A.
Simulation was performed using a home built software AXSIM. The software allows performing simulations with potential arrays from SIMION and also features a new method of field calculation from 3D multipole expansions, which significantly reduces memory requirements for simulation with fringing fields. Additional advantage of the software is an imbedded model of stochastic hard-sphere collisions, which allows simulating equilibrium distributions of ions in RF quadrupole devices.
In case of 2D simulations (for quadrupole with cylindrical rods) potential distribution was calculated using effective charge method, which provides accurate solution within 10 digits [5]. For simulation with fringing fields a multipole expansions were used. Later was obtained with the help of a special program for field analysis. Source field for this program was created by SIMION with specially designed 3D potential arrays, so as to produce a fringe field solution with correct asymptotic behaviour inside quadrupole.
For peak shape simulation a mass filter is operated with a fixed RF and DC voltages. Ions of different mass are injected and a total number of ions of each mass that reached detector is calculated. It worth mentioning that such simulation produces a reversed peak shape as compared to experiment – longer tail is observed on a high mass side. Real quadrupole is operated by scanning the voltage, while mass of ions is not changed. Details of each simulation is explained in the following sections. B.
Fig 3. (A) Geometry of quadrupole with circular rods and potential distribution. (B) Peak shape for quadrupoles (ro=5mm, W=2MHz) with different ratio R/ro at theoretical resolving power (C) Peak shape for a quadrupole with R/ro=1.120 at different theoretical resolving power.
Fig.6 Geometry of quadrupole (A) and power supply for simulation of collisional cooling interface. Plot (B) shows distribution of ion velocities for Reserpine ions 609Da during ejection into pre-rods.
Ions stopped here
Discussion & Conclusion
Presented results indicate, that quadrupoles with cylindrical rods have limitation of resolving power due to nonlinear fields. Peak shape is shifted and distorted and transmission is lost at resolution over In contrast quadrupole with perfect geometry exhibits high transmission up to resolving powers of There is still a room for improvement of quadrupole performance providing that mechanical design will reach higher level of accuracy, that electronics can stand higher voltages at higher frequencies. Modern methods of ion beam preparation such as collisional cooling and delayed DC ramp provide means for improvement of quadrupole performance to such an extend that a Single-Quad instrument can compete with ToF and Ion Trap in resolving power.
Fig 4.
Transmission curve obtained from such simulation shows that quadrupole with circular electrodes has a limit of resolving power near Quadrupole with perfect geometry exhibits high transmission up to resolving power of 10k, but is it possible to obtain such resolving powers in a real instrument? Answer can be obtained from a 3D simulation.
Fig.7. Phase space distributions of ions in a middle of PreRods at the RF phase 00 (maximum positive voltage on X rods). Used as initial conditions for further simulations of quadrupole transmission.