Frank A. Londry

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.

Resonance excitation of ions stored in a quadrupole ion trap. Part 1. A simulation study

Abstract Preliminary findings are presented of a simulation study of resonance excitation of gaseous ions stored within a quadrupole ion trap. The ion trap was operated in the common mode wherein a radio-frequency drive potential was applied to the ring electrode while the end-cap electrodes were grounded or held at a small potential. The arrangement chosen for computer simulation of resonance excitation discussed here is that in which an auxiliary potential is applied to both end-cap electrodes such that these electrode potentials are in phase with each other. The effects of resonance excitation are manifested in the following ways: temporal variation of ion kinetic energy; temporal variations of axial and radial displacements from the trap centre; direction of ion ejection; and emergence of new frequency components of ion motion. The extent of resonance excitation has been examined as a function of ion mass, trapping parameters a u and q u , ion initial position and velocity, drive and auxiliary potential phase angles, delayed imposition of auxiliary potential, auxiliary potential amplitude and frequency, and mass of an inert collision gas. Four principal findings are reported. Irradiation of trapped ions at the two fundamental secular frequencies, axial and radial, does not lead exclusively to ejection of ions in the axial and radial directions, respectively: there is clearly a degree of perturbation of ion radial motion upon irradiation at the axial fundamental secular frequency, and vice versa, which can become dominant under certain conditions and lead to a change in direction of ion ejection. Excitation at theoretically predicted secular frequencies other than the fundamental frequencies is virtually negligible, as expected from the magnitudes of the C 2 n coefficients. Strong resonance absorption occurs at a series of frequencies which are not present in the motion of the unexcited ions; these frequencies are designated as new frequencies. The motion of ions subjected to resonance excitation often becomes characterized by additional frequency components which we have designated as induced frequencies.

Computer simulation of single-ion trajectories in paul-type ion traps

The computer simulation of single-ion trajectories using a number of computer programs is described together with associated theory. The programs permit calculation of ion trajectories while the ion is subjected to collisions with buffer gas of variable pressure, resonance excitation in any of three modes, and static or ramped DC and radiofrequency levels. Initially, the programs were designed for the calculation of ion trajectories in a quadrupole ion trap. The programs now permit such calculations for ions confined in traps having electrodes shaped to include percentages of hexapole and octupole components in the electric field as well as electrode surface geometries for which there is no closed-form expression. The Langevin collision theory is reviewed and a theoretical treatment of the multipole trap is presented.

A new model for the effective thermal conductivity of packed beds of solid spheroids : alumina in helium between 100 and 500°C

Abstract An analytical model is given for the thermal conductivity of a bed of solid spheroidal particles in static gas, when the conductivity of the solid is substantially greater than that of the gas. It has two fitting parameters, the width and average radius of the narrow gaps that exist between the irregularly shaped particles and which contribute significantly to the thermal conductivity. Since both parameters are physically measurable, the model holds the potential for calculating the thermal conductivity without any adjustable parameters. Agreement is excellent with measurements on alumina particles in helium at 100–500°C up to 100 kPa pressure.

Resonance excitation of ions stored in a quadrupole ion trap Part II. Further simulation studies

Abstract Further simulation studies have been carried out on the behaviour of ions stored in a quadrupole ion trap and subjected to small auxiliary potentials oscillating at frequencies related to the secular frequencies of ion motion. Quadrupolar excitation at frequencies of β r Ω and β z Ω, that is, twice the fundamental radial and axial secular frequencies, respectively, results in parametric resonance which induces rapid excitation of ion motion. Frequency analysis of ion axial and radial motions has been carried out to determine the effects of collisions on ion motion, and of auxiliary potential amplitude and frequency for several working points in the stability diagram. A systematic survey was carried out of the variation, as a function of working point, of ion kinetic energy averaged over the final three r.f. cycles prior to ejection. The chosen working points lay on the locus of β r Ω = β z Ω, the two main areas of the stability diagram for which β z Ω r Ω and β r Ω z Ω, the q z axis, and working points for which a z was varied at constant q z . Ion kinetic energies averaged over the final three r.f. cycles are interpreted in terms of potential well-depths, while the irradiation times required for ion ejection indicate relative efficiencies for energy absorption by the subject ion from the resonance radiation.

Resonant excitation in a low-pressure linear ion trap.

It has been shown that through the process of resonant excitation the fragmentation of ions confined in a low-pressure (<0. 05 mTorr) linear ion trap (LIT) can be accomplished while maintaining both high fragmentation efficiency and high resolution of excitation. The ion reserpine, 609. 23 Da, has been fragmented with efficiencies greater than 90% while a higher mass ion, a homogeneously substituted triazatriphosphorine of mass 2721. 89 Da, has been fragmented with 48% efficiency. This was accomplished by extended resonant excitation by low-amplitude auxiliary RF signals. Computer modelling of ion trajectories and analysis of the trapping potentials have demonstrated that a reduction in neutralization of ions on the rods (or losses on the rods) and increased fragmentation is a consequence of higher order terms in the potential introduced by the round-rod geometry of the LIT.

A simulation study of ion kinetic energies during resonant excitation in a stretched ion trap

The trajectories of ions confined individually in a commercial quadrupolar ion trap of stretched geometry and subjected to resonant excitation have been calculated. During resonant excitation, the average ion kinetic energy increases when the ion secular frequency motion is in phase with the resonant excitation and decreases when the phases are opposed. The temporal variation of ion kinetic energy when subjected to resonant excitation exhibits two cyclical forms, one with low ion kinetic energy and one with relatively high ion kinetic energy. The low ion kinetic energy cyclical form is characterized by smoothly rounded profiles at time intervals of ca. 2 ms; the high ion kinetic energy cyclical form is characterized by sharply pointed crests at time intervals of ca. 1 ms. In the low ion kinetic energy cyclical form, the maximum instantaneous ion kinetic energy attained is ca. 16 eV and corresponds to axial excursions of up to 3 mm. In the high ion kinetic energy cyclical form, the maximum instantaneous ion kinetic energy attained increases in value to in excess of 70 eV, with an axial excursion of 6.2 mm, as the resonant excitation frequency is increased. At a critical frequency, ec, there is a discontinuous change from the high to the low ion kinetic energy cyclical form. The maximum instantaneous ion kinetic energy, KEmax, varies as a simple quadratic function of the axial excursion of the ion, so that ion kinetic energy is derived from the main storage field within the ion trap. The asymmetric form observed in the experimental resonance absorption curve, obtained as a function of resonant frequency, has been reproduced qualitatively and the asymmetry can be ascribed to the transition between the two cyclical forms of the temporal variation of ion kinetic energy.

Linear Quadrupoles with Added Hexapole Fields

Linear quadrupoles with added hexapole fields are described. The shifts in ion oscillation frequency caused by the addition of a hexapole field are calculated within the effective potential model. Methods to construct linear quadrupoles with added hexapole fields with exact electrode geometries and with round rods are discussed. A quadrupole with added hexapole field can be constructed with round rods by rotating two rods (say the y rods) towards an x rod. Computer simulations are used to investigate the possibility of mass analysis with quadrupoles with added hexapole fields. We find that a quadrupole with an added hexapole field in the range 2–12% can provide mass analysis provided the dc is applied with the correct polarity and value. When a rod set is constructed with round rods, other multipoles in the potential degrade the peak shape, resolution and transmission. The largest of these after the quadrupole and hexapole are a dipole and octopole term. With round rod sets, the peak shape can be improved by using different diameters for the x and y rod pairs to minimize the octopole term in the potential and by injecting ions at the field center where the dipole term is zero. Calculations of the boundaries of the stability diagram for this case show the boundaries move out, relative to those of a pure quadrupole field, but remain sharp.

Resonance excitation of ions stored in a quadrupole ion trap. Part IV. Theory of quadrupolar excitation

Abstract A new theoretical treatment is presented for quadrupolar resonance excitation of ions stored in a quadrupole ion trap. When the ratio of the tickle voltage amplitude to that of the drive potential is small, the equation of ion motion can be expressed in the form of a perturbation series. Exact and approximate solutions to the first-order perturbation eqations are presented. Ion trajectories calculated from these solutions are compared with those calculated by numerical integration. The resonance conditions were found to correspond to a series of angular frequencies given by ω u,n = | n + β u | − ∞ n z Ω, (1 + β z )Ω(1 − β z )Ω β,Ω, had been observed previously in simulation studies.

Resonance excitation of ions stored in a quadrupole ion trap Part III. Introduction to the field interpolation simulation method

Abstract Additional simulation studies have been carried out on the behaviour of single ions stored in a quadrupole ion trap and then subjected to auxiliary potentials of small amplitude oscillating at frequencies related to the secular frequencies of ion motion. The ion trap was operated in the common mode wherein an r.f. drive potential was applied to the ring electrode while the end-cap electrodes were grounded or held at a small potential. A new method of field interpolation has been developed for the calculation of ion trajectories; this method has been tested by direct comparison with the analytic solution of the Mathieu equation. The field interpolation method has been employed to calculate trajectories of ions excited resonantly by application of an auxiliary oscillating potential in each of three possible modes. Each ion trajectory is calculated to the point of ejection from the ion trap or for a pre-selected time period. The continual absorption of resonance radiation by an ion stored within a trap leads to increasing ion kinetic energy until the trapping potential is exceeded and the ion is ejected from the trap. It has been shown earlier that ion ejection requires a constant fluence, where fluence is the product of auxiliary potential amplitude and the duration of irradiation. At a given frequency, where the absorption of energy over a period of time is proportional to the coefficient of absorption at that frequency, a small coefficient of absorption will require a large fluence for ion ejection. Thus the coefficient of absorption is proportional to the reciprocal of the fluence required, at a given frequency, for ion ejection. Relative absorption coefficients have been obtained in this manner for the three types of irradiation mode and at a number of auxiliary potential frequencies; these relative absorption coefficient are compared with experimental results of the abundance of ions ejected under conditions of constant fluence.