Approximate multipole coefficients of RF ion traps as functions of aperture size

In this study we present approximate analytical expressions for estimating the variation in multipole expansion coefficients as a function of the size of the apertures in the electrodes in axially symmetric (3D) and two-dimensional (2D) ion trap ion traps. Following the approach adopted in our earlier studies which focused on the role of apertures to fields within the traps, here too, the analytical expression we develop is a sum of two terms, A(n,noAperiure), the multipole expansion coefficient for a trap with no apertures and A(n,dueToAperture), the multipole expansion coefficient contributed by the aperture. A(n,noAperture) has been obtained numerically and A(n,dueToAperture) is obtained from the n th derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A(2) to A(12), estimated by our analytical expressions, were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap dimension. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be largely in the range of 10-15%. The leading multipole expansion coefficient, A(2), however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and the LIT for large aperture sizes. (C) 2010 Elsevier B.V. All rights reserved.

Coplanar Capacitively Coupled Probe Fed Microstrip Antennas for Wideband Applications

The design and analysis of a coplanar capacitive fed microstrip antenna suspended above the ground plane is presented. It is demonstrated that the proposed approach can be used for designing antennas with impedance bandwidth of about 50% and a good gain to operate in various microwave bands. The model of the antenna incorporates the capacitive feed strip which is fed by a coaxial probe using equivalent circuit approach, and matches simulation and experimental results. The capacitive feed strip used here is basically a rectangular microstrip capacitor formed from a truncated microstrip transmission line and all its open ends are represented by terminal or edge capacitances. The error analysis was carried out for validity of the model for different design parameters. The antenna configuration can be used where unidirectional radiation patterns are required over a wide bandwidth.

Optimization of ion energy spread in inductively coupled plasma source designed for focused ion beam applications

The ion energy distribution of inductively coupled plasma ion source for focused ion beam application is measured using a four grid retarding field energy analyzer. Without using any Faraday shield, ion energy spread is found to be 50 eV or more. Moreover, the ion energy distribution is found to have double peaks showing that the power coupling to the plasma is not purely inductive, but a strong parasitic capacitive coupling is also present. By optimizing the various source parameters and Faraday shield, ion energy distribution having a single peak, well separated from zero energy and with ion energy spread of 4 eV is achieved. A novel plasma chamber, with proper Faraday shield is designed to ignite the plasma at low RF powers which otherwise would require 300-400 W of RF power. Optimization of various parameters of the ion source to achieve ions with very low energy spread and the experimental results are presented in this article. (C) 2010 Elsevier Ltd. All rights reserved.

Optimum aperture distributions in the presence of blockage

A method is presented for optimising the performance indices of aperture antennas in the presence of blockage. An N-dimensional objective function is formed for maximising the directivity factor of a circular aperture with blockage under sidelobe-level constraints, and is minimised using the simplex search method. Optimum aperture distributions are computed for a circular aperture with blockage of circular geometry that gives the maximum directivity factor under sidelobe-level constraints.

Convergence feedback and unstable low frequency oscillations in a simple coupled ocean‐atmosphere model

The role of convergence feedback on the stability of a coupled ocean‐atmosphere system is studied using model III of Hirst (1986). It is shown that the unstable coupled mode found by Hirst is greatly modified by the convergence feedback. If the convergence feedback strength exceeds a critical value, several new unstable intraseasonal modes are also introduced. These modes have very weak dependence on the wave number. These results may explain the behaviour of some coupled models and to some extent provide a mechanism for the observed aperiodicity of the El‐Nino and Southern Oscillation (ENSO) events.

Dipolar cross-correlation effects in the nuclear overhauser experiments of weakly and strongly coupled spins

The effect of dipolar cross correlation in 1H---1H nuclear Overhauser effect experiments is investigated by detailed calculation in an ABX spin system. It is found that in weakly coupled spin systems, the cross-correlation effects are limited to single-quantum transition probabilities and decrease in magnitude as ωτc increases. Strong coupling, however, mixes the states and the cross correlations affect the zero-quantum and double-quantum transition probabilities as well. The effect of cross correlation in steady-state and transient NOE experiments is studied as a function of strong coupling and ωτc. The results for steady-state NOE experiments are calculated analytically and those for transient NOE experiments are calculated numerically. The NOE values for the A and B spins have been calculated by assuming nonselective perturbation of all the transitions of the X spin. A significant effect of cross correlation is found in transient NOE experiments of weakly as well as strongly coupled spins when the multiplets are resolved. Cross correlation manifests itself largely as a multiplet effect in the transient NOE of weakly coupled spins for nonselective perturbation of all X transitions. This effect disappears for a measuring pulse of 90° or when the multiplets are not resolved. For steady-state experiments, the effect of cross correlation is analytically zero for weakly coupled spins and small for strongly coupled spins.

Experimental investigation of three-layer electromagnetically coupled circular microstrip antennas

The broadband behaviour of a three-layer electromagnetically coupled circular microstrip antenna is investigated experimentally. The effects of interlayer spacings and the thickness of the parasitic layers on the impedance bandwidth, 3 dB beamwidth and pattern shape, are studied. Experiments show that this structure can provide a frequency bandwidth as high as 20% with a low crosspolarisation level and a moderately high gain.

MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

Solitons of Coupled Scalar Field Theories in Two Dimensions

This work offers a method for finding some exact soliton solutions to coupled relativistic scalar field theories in 1+1 dimensions. The method can yield static solutions as well as quasistatic "charged" solutions for a variety of Lagrangians. Explicit solutions are derived as examples. A particularly interesting class of solutions is nontopological without being either charged or time dependent.

Demixing of severely overlapped H-1 NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A(3) spins in a weakly aligning medium

We report a single C-13 spin edited selective proton-proton correlation experiment to decipher overcrowded 13C coupled proton NMR spectra of weakly dipolar coupled spin systems. The experiment unravels the masked C-13 satellites in proton spectrum and permits the measurement of one bond carbon-proton residual dipolar couplings in I3S and for each diastereotopic proton in I2S groups. It also provides all the possible homonuclear proton-proton residual couplings which are otherwise difficult to extract from the broad and featureless one dimensional H-1 spectrum, in addition to enantiodifferentiation in a chiral molecule. Employment of heteronuclear (C-13) decoupling in the evolution period results in complete demixing of overlapped signals from enantiomers. The observed anomalous intensity pattern in strongly dipolar coupled methyl protons in methyl selective correlation experiment has been interpreted using polarization operator formalism. (C) 2010 Elsevier Inc. All rights reserved.

Coupled substitution of niobium and silicon in potassium titanyl phosphate and arsenate (KTiOPO4 and KTiOAsO4. Synthesis and nonlinear optical properties of KTi1-xNbxOX1-xSixO4 (X = P, As)

Coupled substitution of Nb(V) and Si(IV) for Ti(IV) and P(V)/As(V) in KTiOP04 (KTP) and KTiOAsO4 (KTA) giving new series of nonlinear optical materials, KTi1-xNbxOX1-xSixO4 (X=P,As), has been investigated. Substitution up to x = 0.40 readily occurs, the members retaining the orthorhombic (Pna2(1)) structure of KTP. The second harmonic generation (SHG) property of the parent KTP and KTA is not adversely affected by the coupled substitution. SHG intensity of the powder samples of the X = P series shows a slight increase with x up to x = 0.15; for 0.15 < x less-than-or-equal-to 0.40, there is a decrease in SHG intensity as compared to that for KTP. A similar trend in SHG intensity is seen for the arsenic analogs.

Mechanisms of variability and predictability of the tropical coupled ocean-atmosphere system

A conceptual model is proposed to explain the observed aperiodicity in the short term climate fluctuations of the tropical coupled ocean-atmosphere system. This is based on the evidence presented here that the tropical coupled ocean-atmosphere system sustains a low frequency inter-annual mode and a host of higher frequency intra-seasonal unstable modes. At long wavelengths, the low frequency mode is dominant while at short wavelengths, the high frequency modes are dominant resulting in the co-existence of a long wave low frequency mode with some short wave intra-seasonal modes in the tropical coupled system. It is argued that due to its long wavelength, the low frequency mode would behave like a linear oscillator while the higher frequency short wave modes would be nonlinear. The conceptual model envisages that an interaction between the low frequency linear oscillator and the high frequency nonlinear oscillations results in the observed aperiodicity of the tropical coupled system. This is illustrated by representing the higher frequency intra-seasonal oscillations by a nonlinear low order model which is then coupled to a linear oscillator with a periodicity of four years. The physical mechanism resulting in the aperiodicity in the low frequency oscillations and implications of these results on the predictability of the coupled system are discussed.