Comparison of equilibrium ion density distribution and trapping force in penning, Paul, and combined ion traps

Starting from the classical Boltzmann distribution, we obtain the ion density distribution in the limit of either high temperature/low density (Coulomb interaction energy much less than ion kinetic energy) or low temperature/high density (kinetic energy much less than Coulomb interaction energy), and the trapping force for an ion cloud in Penning ion cyclotron resonance, Paul (quadrupole), and combined (Paul trap in a uniform axial static magnetic field) traps. At equilibrium (total angular momentum conserved), the ion cloud rotates at a constant frequency in Penning and combined traps. In a Penning trap, the maximum ion density is proportional to B ²/m (B is magnetic field and m is the mass of ions), whereas the maximum ion density in a Paul trap is proportional to (V _rf ² /mΩ² r ₀ ⁴ ), with Mathieu equation axial q value <0.4 to satisfy the pseudopotential approximation. Ion maximum densities in both Penning and Paul ion traps depend on the trapping field (magnetic or electric) and ion mass, but not on ion charge. In a Penning trap at maximum ion density (zero pressure), the radial (but not the axial) trapping potential is mass dependent, whereas both radial and axial potentials in a Paul trap at maximum ion density are mass dependent.     

Properties of matrix-assisted laser desorption. Measurements with a time-to-digital converter.

Some properties of matrix-assisted laser desorption have been studied using single-ion-counting methods and a time-to-digital converter. The methods allow examination of the process for irradiances near the reported threshold for observation with a transient recorder. All measurements were made using bovine insulin as a test compound. We present direct evidence that an irradiance threshold near 10(6) W cm-2 exists for ion production, and that the process is a collective effect, either involving a large number of molecular ions (approximately 10(4) in a successful event or none at all. Above the threshold, the yield is found to scale with a high power (4th to 6th) of the irradiance. Measurements of initial velocity distributions indicate an axial velocity spread corresponding to approximately 50 eV and a radial velocity spread corresponding to approximately 2.4 eV. Thus the ejection or extraction mechanism appears to be strongly asymmetric.     

Dynamically Harmonized FT-ICR Cell with Specially Shaped Electrodes for Compensation of Inhomogeneity of the Magnetic Field. Computer Simulations of the Electric Field and Ion Motion Dynamics

The recently introduced ion trap for FT-ICR mass spectrometers with dynamic harmonization showed the highest resolving power ever achieved both for ions with moderate masses 500?C1000?Da (peptides) as well as ions with very high masses of up to 200?kDa (proteins). Such results were obtained for superconducting magnets of very high homogeneity of the magnetic field. For magnets with lower homogeneity, the time of transient duration would be smaller. In superconducting magnets used in FT-ICR mass spectrometry the inhomogeneity of the magnetic field in its axial direction prevails over the inhomogeneity in other directions and should be considered as the main factor influencing the synchronic motion of the ion cloud. The inhomogeneity leads to a dependence of the cyclotron frequency from the amplitude of axial oscillation in the potential well of the ion trap. As a consequence, ions in an ion cloud become dephased, which leads to signal attenuation and decrease in the resolving power. Ion cyclotron frequency is also affected by the radial component of the electric field. Hence, by appropriately adjusting the electric field one can compensate the inhomogeneity of the magnetic field and align the cyclotron frequency in the whole range of amplitudes of z-oscillations. A method of magnetic field inhomogeneity compensation in a dynamically harmonized FT-ICR cell is presented, based on adding of extra electrodes into the cell shaped in such a way that the averaged electric field created by these electrodes produces a counter force to the forces caused by the inhomogeneous magnetic field.     

Analytical theory for field induced periodic equilibrium structures in nematic and cholesteric films

Planar films of cholesteric liquid crystals exhibit an instability in electric or magnetic fields. Depending on a special choice of the elastic constants and the helix pitch either a striped texture appears at a threshold field or an ordinary Freedericksz transition is observed. The type of field-induced transition can be predicted by a simple criterion.     

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.     

3D Monte Carlo simulations of a magnetic disk-like particle dispersion

We have investigated the aggregate structures of a colloidal dispersion composed of ferromagnetic disk-like particles with a magnetic moment normal to the particle axis at the particle center, by means of 3D Monte Carlo simulations. Such disk-like particles have been modeled as a circular disk-like particle with the side section shape of spherocylinder. We have attempted to clarify the influences of the magnetic field strength, magnetic interactions between particles and volumetric fraction of particles. In order to discuss quantitatively the aggregate structures of clusters, we have focused on the radial distribution and orientational pair correlation functions, etc. For no applied magnetic field cases, long column-like clusters come to be formed with increasing magnetic particle–particle interactions. The internal structures of these clusters clearly show that the particles incline in a certain direction and their magnetic moments alternate in direction between the neighboring particles in the clusters. For applied magnetic field cases, the magnetic moment of each particle inclines in the magnetic field direction and therefore the column-like clusters are not formed straightforwardly. If the magnetic field is much stronger than magnetic particle–particle interactions, the particles do not have a tendency to form the clusters. As the influence of magnetic particle–particle interactions is significantly strong, thick chain-like clusters or column-like clusters or brick-wall-like clusters come to be formed along the magnetic field direction.     

Diffusioosmosis of electrolyte solutions in a fine capillary tube

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.     

Kieselgelstandards für die Bestimmung von Spurenelementen in pulverförmigen Proben mit leichter Matrix durch Röntgenfluorescenzanalyse

The paper deals with homogeneous magnetic fields and added chemical substances both affecting the spectrochemical results obtained in arc excitation studies. The influence of a homogeneous magnetic field on the total intensity of lines of various analysis elements (Hg, Zn, Ga, Tl) in graphite has been examined. Furthermore, the axial and radial distributions of line intensities in arc plasma were determined. Parameters used were the magnetic field strength (0, 0.01, 0.02, 0.04 T) and the physical data of the analysis elements. It was found that the effect of the magnetic field varies with the ionization potential of the elements involved, their atomic mass and the strength of the magnetic field applied. A non-destructive method of measuring was introduced for studying the effects of a homogeneous magnetic field on the rates of evaporation. The results showed increased evaporation rates in presence of magnetic fields as a function of the evaporation heat of the elements involved. Effects of Ga₂O₃ additive on the line intensities of impurity elements are governed by the Ga₂O₃ concentration and the ionization potential of the elements examined.     

Magnetic properties of nickel and zinc double hydroxides

Magnetic properties of nickel and zinc double hydroxides were studied using an axial extraction apparatus and a Faraday balance. Measurements were taken mainly between 4.2 and 40 K for applied fields 50-45 000 Oe.The results confirm the existence of two types of structure α and β, which were previously determined by X-ray analysis.The β solids, i.e., with a low zinc concentration, are essentially antiferromagnetic at 4.2 K for fields smaller than 45 kOe. They are compared with the hydroxide β-Ni(OH)₂. The α solids are metamagnetic with a low threshold field. The magnetization isotherms obtained for the α solids at 4.2 K show magnetic viscosity phenomena.This difference in magnetic behaviour is useful for attributing the α or β structure to samples in which the phase containing the double hydroxide is not detected by X-ray analysis.     

Computer simulation of a nitrogen ICP discharge

A theoretical model for calculating radial and axial temperature profiles in a nitrogen ICP discharge was improved to include the normal distribution of magnetic flux density and a three-gas flow pattern commonly used in spectrochemical applications. Calculated radial temperature and particle velocity distributions for nitrogen ICP discharges compare well with experimentally obtained data.     

Influence of cylindrical submicrometer confinement on the static and dynamic properties in nonyloxycyanobiphenyl (9OCB)

Broadband dielectric spectroscopy (10(2)-1.9 x 10(9) Hz) and specific heat measurements have been performed on nonyloxycyanobiphenyl (9OCB) in the isotropic (I), nematic (N), and smectic A (SmA) phases confined to 200 nm diameter parallel cylindrical pores of Anopore membranes. Untreated and HTBA-treated membranes have been found to obtain axial and radial confinements, respectively. However, structural or configurational transitions in untreated membranes have been reported to exist in the SmA-mesophase of 9OCB. Both confinements clearly affect the N-I and SmA-N phase transitions. In the axial confinement, the analysis of the specific heat and static dielectric permittivity data leads to a second order SmA-N phase transition, which is known to be weakly first order for bulk 9OCB. Dynamic dielectric measurements have accounted for the different molecular motions in both confinements. On both mesophases, either N or SmA, the relaxation processes in axial configuration are faster than in the bulk. However, in radial confinement, they are either equal or slower than in the bulk. Additionally, there are no differences in the energy barrier hindering the molecular motions between the axial and radial confinements and even in relation to bulk. Likewise, dielectric results suggest that the extension inside the pores of the surface pinned molecular layer (proved to be temperature-dependent) persists at high enough temperature as a residual-thin layer adjacent to the pore wall.     

On the Couette-Taylor instability in ferrohydrodynamics

A theory for the stabilizing influence of an axial external magnetic field on a magnetic colloid engaged in cylindrical Couette flow is presented. For the case of a narrow gap, analytical expressions which predict the magnetic field dependences of the critical wavelength and the critical Taylor number at the onset of cellular Taylor flow are obtained.     

Nucleation Mechanism of Iron in an External Magnetic Field

In this work, the solidification of liquid iron with or without external magnetic field was investigated by using two molecular dynamics methods, namely direct cooling and two-phase simulation. The influence of external magnetic field on the solidification is characterized by the critical temperature and radial distribution functions. Our computational results show that under external magnetic field, the solidification point tends to decrease significantly. By further analyzing the diffusion coefficients and viscosity, we attribute the effect to the stronger fluctuation of liquid iron atoms driven by the external magnetic field.     

Reduction of axial kinetic energy induced perturbations on observed cyclotron frequency

With Fourier transform ion cyclotron resonance (FTICR) mass spectrometry one determines the mass-to-charge ratio of an ion by measuring its cyclotron frequency. However, the need to confine ions to the trapping region of the ion cyclotron resonance (ICR) cell with electric fields induces deviations from the unperturbed cyclotron frequency. Additional perturbations to the observed cyclotron frequency are often attributed to changes in space charge conditions. This study presents a detailed investigation of the observed ion cyclotron frequency as a function of ion z-axis kinetic energy. In a perfect three-dimensional quadrupolar field, cyclotron frequency is independent of position within the trap. However, in most ICR cell designs, this ideality is approximated only near the trap center and deviations arise from this ideal quadrupolar field as the ion moves both radially and axially from the center of the trap. To allow differentiation between deviations in observed cyclotron frequency caused from changes in space charge conditions or differences in oscillation amplitude, ions with identical molecular weights but different axial kinetic energy, and thus amplitude of z-axis motion, were simultaneously trapped within the ICR cell. This allows one to attribute deviations in observed cyclotron frequency to differences in the average force from the radial electric field experienced by ions of different axial amplitude. Experimentally derived magnetron frequency is compared with the magnetron frequency calculated using SIMION 7.0 for ions of different axial amplitude. Electron promoted ion coherence, or EPIC, is used to reduce the differences in radial electric fields at different axial positions. Thus with the application of EPIC, the differences in observed cyclotron frequencies are minimized for ions of different axial oscillation amplitudes.     

Off-resonance excitation in a linear ion trap

Off-resonance excitation coupled with mass-selective axial ejection of ions in a linear ion trap is shown to allow coherent control of a trapped ion population. Oscillations of the detected ion current have been found to correspond to the degree of detuning of the excitation field from the resonance frequency. Under appropriate excitation conditions coherent oscillations at the excitation frequency are seen that evolve into the ions’ secular frequency on termination of the excitation field. Termination of the excitation field at various points during the off-resonance excitation profile leaves the ions with different degrees of radial excitation. The degree of radial excitation can be controlled by the coherent excitation field and is demonstrated to be useful for collision-induced dissociation.     

Effect of an axial magnetic field on the performance of a quadrupole mass spectrometer

We consider the case of a quadrupole mass spectrometer (QMS) in which a static magnetic field is applied axially in the z-direction along the length of the mass filter. The theoretical approach assumed in the model is that the QMS contains hyperbolic rods as electrodes and that the magnetic field acts over the full length of the mass filter assembly. Initial experimental results with argon and helium for a low-resolution instrument confirm the predicted theoretical trends. The analysis also predicts for which values of operating parameters an enhancement of the instrument resolution is achieved when an axial magnetic field is applied. The model predicts instrument resolution R > 3000 for a QMS with a 200 mm long mass filter via application of an axial magnetic field.     

Characterization of an Electron Ionization Source Trap Operating in the Presence of a Magnetic Field Through Computer Simulation

We explore the feasibility of conducting electron ionization (EI) in a radio-frequency (rf) ion source trap for mass spectrometry applications. Electrons are radially injected into a compact linear ion trap in the presence of a magnetic field used essentially to lengthen the path of the electrons in the trap. The device can either be used as a stand-alone mass spectrometer or can be coupled to a mass analyzer. The applied parallel magnetic field and the oscillating rf electric field produced by the trap give rise to a set of coupled Mathieu equations of motion. Via numerical simulations, electron trajectories are studied under varying intensities of the magnetic field in order to determine the conditions that enhance ion production. Likewise, the dynamic behavior of the ions are investigated in the proposed EI source trap and the fast Fourier transform FFT formalism is used to obtain the frequency spectrum from the numerical simulations to study the motional frequencies of the ions which include combinations of the low-frequency secular and the high-frequency micromotion with magnetron and cyclotron frequencies. The dependence of these motional frequencies on the trapping conditions is examined and particularly, the limits of applying a radial magnetic field to the EI ion trap are characterized.

Effects of magnetic field and geometrical size on the interband light absorption in a quantum pseudodot system

We study in this paper the direct interband transitions in quantum pseudodot system under the influence of an external magnetic field. We obtain the analytical expressions for the light interband absorption coefficient and threshold frequency of absorption as the functions of applied magnetic field and geometrical size of quantum pseudodot system. We study the absorption threshold frequency (ATF) at small and high applied magnetic field and also as a function of size of quantum pseudodot. According to the results obtained from the present work, we find that (i) the ATF is linear at large magnetic field. (ii) It is nonlinear at small magnetic field. (iii) The ATF depends on the geometrical size of quantum pseudodot and decreases when the size of quantum pseudodot increases. Therefore, the magnetic field and quantum pseudodot size play important roles in the ATF.     

On the stability of two rigidly rotating magnetic fluid columns in zero gravity in the presence of mass and heat transfer

The stability of two rigidly rotating magnetic fluids separated by a cylindrical interface and stressed by a timely oscillating axial magnetic field is investigated. Only axisymmetric disturbances are considered. The interface admits both mass and heat transfer. Weak viscous effects on the interface are taken into account so that their contributions are demonstrated in the boundary conditions. The solution of the boundary value problem leads to a transcendental differential equation. It includes a periodic coefficient together with modified Bessel functions of operators involved as their arguments. In the absence of rotation and under the assumption of small amplitude of the harmonic magnetic field, the characteristic equation is analyzed by means of Whittaker's perturbation technique to determine the transition curves which separate stable from unstable solutions. While in the presence of rotation, the method of multiple-time scales is adopted to investigate the necessary and sufficient conditions for stability. The analysis results in the resonance cases as well as the nonresonance cases. In order to simplify the analysis, the periodic solutions are only considered. Therefore, stability is discussed through the marginal state. Furthermore, the rotation is considered as small. The analytical results are numerically confirmed.     

Excitation modes for fourier transform-ion cyclotron resonance mass spectrometry

Various geometric configurations for the excitation of coherent ion motion in Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR/MS) are analyzed (in some cases for the first time) with unified notation. The instantaneous power absorption, F v, in which v is ion velocity and F the force produced by the applied excitation electric field (harmonic, single frequency, on-resonance, in-phase), is time averaged and then set equal to the time rate of change of ion total (cyclotron + magnetron + trapping) energy, to yield a differential equation that is readily solved for the (time-dependent) amplitude of each of the various ion motions. The standard FT-ICR excitation (namely, radial dipolar) is reviewed. The effects of quadrature and radial quadrupolar excitation on ion radial (cyclotron and magnetron) motions are also reviewed. Frictional damping is shown to decrease the ion cyclotron orbital radius and trapping amplitude but increase the magnetron radius. Feedback excitation (i.e., excitation at the simultaneously detected ion cyclotron orbital frequency of the same ion packet) is introduced and analyzed as a means for exciting ions whose cyclotron frequency changes during excitation (as for relativistically shifted low-mass ions). In contrast to conventional radial dipolar excitation, axial dipolar excitation of the trapping motion leads to a mass-dependent ion motional amplitude. Parametric (i.e., axial quadrupolar) excitation is shown to produce an exponential increase in the ion motional amplitudes (hyperbolic sine and hyperbolic cosine amplitude for cyclotron and magnetron radii, respectively). More detailed consideration of parametric excitation leads to an optimal ion initial radial position in parametric-mode FT-ICRjMS.