Simulation of Ion Trajectories

The properties of a wide variety of ion lens configurations have been systematically explored by many research teams and the underlying properties of these lenses are well understood and predictable in terms of the voltage ratios and dimensions of the lens components. However, it is common practice these days to design ion optics with the aid of computer simulations of the ion trajectories. Several programs have been developed for such applications, but the best known and most widely used is SIMION . This is commercial software that has been through a number of revisions over many years and is available for operation on a desktop PC. The user specifies the electrode geometries, separations and applied potentials, from which SIMION can map out the inter-electrode potentials and 

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The other very important function of the ion optics is to shape the ion beam. Voltages on the various lenses should be set to avoid chromatic aherration, which causes energy-dependent transmission of ions in the instrument, and as a result erroneous lEDs [161, 163]. The correct lens settings have been found by simulations of ion trajectories in the EQP using the simulation program SIMION [329], In addition, an experimental method to find the correct settings has been presented [161, 163]. 

Lock, C.M. Dyer, E. Simulation of Ion Trajectories Through a High Pressure RF-only Quadrupole Collision Cell by SIMION 6.0. Rapid Commun. Mass Spectrom. 1999., 75,422-431. 

Forbes, M.W. Sharifi, M. Croley, T. Lausevic, Z. March, R.E. Simulation of Ion Trajectories in a Quadrapole Ion Trap a Comparison of Three Simulation Programs. J. Mass Spectrom. 1999, 34, 1219-1239. 

Simulations. In addition to analytical approaches to describe ion—soHd interactions two different types of computer simulations are used Monte Cado (MC) and molecular dynamics (MD). The Monte Cado method rehes on a binary coUision model and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. As the name Monte Cado suggests, the results require averaging over many simulated particle trajectories. A review of the computer simulation of ion—soUd interactions has been provided (43). 

Figure 11 Simulated Sc+ ion trajectories (a) Ion optic geometry and voltages. Plot shows assumed charge separation function, (b) No space-charge effect included, (c) Total beam current through skimmer of 1 xA (d) Total beam current through skimmer of 1500 xA. (Note that darker trajectories correspond to 1% of the ion beam 99% of the ion beam is lost as indicated by the lighter trajectories.) (From Ref. 105.)...

The resolution of a SIMION model is limited by manory constraints. The accuracy of ion trajectory simulations is highly dependent on the spatial resolution of the PA naturally, higher resolution models provide better approximations of smooth electrode surfaces and hence a better description of the electric field. Unfortunately, high-resolution models are memory-intensive each point in the PA requires 8-10 bytes of dynamic memory. SIMION v. 8.0 has an upper limit of 2x 10 points, which corresponds to ca 1.8 GB of RAM. Thus, the maximum cubic PA allowed is approximately 580x 580x 580 points. However, in order to run efficiently simulations of dynamic... 

Figure 3.8 SRIM simulations of the trajectories of 100, 1 keV Cs ions incident at an angle of 60° with respect to the surface normal in Silicon. In the inset is shown the energy distribution of Silicon recoils relative to the surface normal toward the vacuum. Note, only those with energy greater than the surface binding energy (4.7 eV for Silicon substrates) can escape. The energy of the sputtered population then decreases by this amount.

Classical Ion Trajectory Simulations. Classical ion trajectory simulations were carried out by means of the three-dimensional scattering and recoiling imaging code (SARIC) developed in this laboratory. SARIC is based on the binary collision approximation, uses the ZBL universal potential to describe the interactions between atoms, and includes both out-of-plane and multiple scattering. Details of the simulation have been published elsewhere 11). 

Classical ion trajectory computer simulations based on the BCA are a series of evaluations of two-body collisions. The parameters involved in each collision are tire type of atoms of the projectile and the target atom, the kinetic energy of the projectile and the impact parameter. The general procedure for implementation of such computer simulations is as follows. All of the parameters involved in tlie calculation are defined the surface structure in tenns of the types of the constituent atoms, their positions in the surface and their themial vibration amplitude the projectile in tenns of the type of ion to be used, the incident beam direction and the initial kinetic energy the detector in tenns of the position, size and detection efficiency the type of potential fiinctions for possible collision pairs. 

The fractal behavior of diffusion trajectories of ions has been studied in the molten phase of Agl as well as in the a-phase. The Devalues for an MD system with 250 Ag and 250 I" at 900 K were calculated from Fig. 21 to be 2 and 2.17, respectively. The mean-square displacements are shown in Fig. 22 in comparison with those of the a-phase at 670 K. As results of supplementary MD simulations, these authors obtained Dj = 1 for Ag and D = 2.17 at 1000 K and Df = 2 for both ions at 2000 K. Thus, they have concluded that (1) at an extremely high temperature above the melting point, the system is in a completely liquid state, which leads to a... 

Fig. 1. Schematic diagram of the multimass ion imaging detection system. (1) Pulsed nozzle (2) skimmers (3) molecular beam (4) photolysis laser beam (5) VUV laser beam, which is perpendicular to the plane of this figure (6) ion extraction plate floated on V0 with pulsed voltage variable from 3000 to 4600 V (7) ion extraction plate with voltage Va (8) outer concentric cylindrical electrode (9) inner concentric cylindrical electrode (10) simulation ion trajectory of m/e = 16 (11) simulation ion trajectory of rri/e = 14 (12) simulation ion trajectory of m/e = 12 (13) 30 (im diameter tungsten wire (14) 8 x 10cm metal mesh with voltage V0] (15) sstack multichannel plates and phosphor screen. In the two-dimensional detector, the V-axis is the mass axis, and V-axis (perpendicular to the plane of this figure) is the velocity axis (16) CCD camera.

The direct simulation of P(z) is possible in principle by following the motion of the ion in a long molecular dynamics trajectory and binning the observed values of the ion position. This method will give reasonable... 

Once the initial and boundary conditions are specified, the classical equations of motion are integrated as in any other simulation. From the start of the trajectory, the atoms are free to move under the influence of the potential. One simply identifies reaction mechanisms and products during the dynamics. For the case of sputtering, the atomic motion is integrated until it is no longer possible for atoms and molecules to eject. The final state of ejected material above the surface is then evaluated. Properties of interest include the total yield per ion, energy and angular distributions, and the structure and... 

Fig. 4.36. Projection of a 3D trajectory simulation of a stable ion onto the x- and y-coordinate. Reproduced from Ref. [110] with permission. Elsevier Science, 1998.

Ion trajectory simulations allow for the visualization of the ion motions while travelling through a quadrupole mass analyzer (Fig. 4.36). Furthermore, the optimum number of oscillations to achieve a certain level of performance can be determined. It turns out that best performance is obtained when ions of about 10 eV kinetic energy undergo a hundred oscillations. [110]... 

Odelius and co-workers reported some time ago an important study involving a combined quantum chemistry and molecular dynamics (MD) simulation of the ZFS fluctuations in aqueous Ni(II) (128). The ab initio calculations for hexa-aquo Ni(II) complex were used to generate an expression for the ZFS as a function of the distortions of the idealized 7), symmetry of the complex along the normal modes of Eg and T2s symmetries. An MD simulation provided a 200 ps trajectory of motion of a system consisting of a Ni(II) ion and 255 water molecules, which was analyzed in terms of the structure and dynamics of the first solvation shell of the ion. The fluctuations of the structure could be converted in the time variation of the ZFS. The distribution of eigenvalues of ZFS tensor was found to be consistent with the rhombic, rather than axial, symmetry of the tensor, which prompted the development of the analytical theory mentioned above (89). The time-correlation... 

Analytical treatment of the diffusion-reaction problem in a many-body system composed of Coulombically interacting particles poses a very complex problem. Except for some approximate treatments, most theoretical treatments of the multipair effects have been performed by computer simulations. In the most direct approach, random trajectories and reactions of several ion pairs were followed by a Monte Carlo simulation [18]. In another approach [19], the approximate Independent Reaction Times (IRT) technique was used, in which an actual reaction time in a cluster of ions was assumed to be the smallest one selected from the set of reaction times associated with each independent ion pair. 

SIMION, "Simulated Ion Trajectories" is a computer program developed by D. McGilvery, LaTrobe University. This Program has been refined and expanded by the group (D.A. Dahl and J.E. Delmore) at Idaho National Laboratory, Department of Energy. 

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