Composite field approximations for ion traps with apertures on electrodes

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E = E-noaperture + E-aperture. where E-noaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and E-aperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis, of the trap can in this way be well approximated for any aperture that is not too large. To derive E-aperture. classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.E-noaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact(though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once Computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics Studies than have been hitherto attempted. (C) 2009 Elsevier B.V. All rights reserved.

Off-axis field approximations for ion traps with apertures

In recent work (Int. J. Mass Spec., vol. 282, pp. 112–122) we have considered the effect of apertures on the fields inside rf traps at points on the trap axis. We now complement and complete that work by considering off-axis fields in axially symmetric (referred to as “3D”) and in two dimensional (“2D”) ion traps whose electrodes have apertures, i.e., holes in 3D and slits in 2D. Our approximation has two parts. The first, EnoAperture, is the field obtained numerically for the trap under study with apertures artificially closed. We have used the boundary element method (BEM) for obtaining this field. The second part, EdueToAperture, is an analytical expression for the field contribution of the aperture. In EdueToAperture, aperture size is a free parameter. A key element in our approximation is the electrostatic field near an infinite thin plate with an aperture, and with different constant-valued far field intensities on either side. Compact expressions for this field can be found using separation of variables, wherein the choice of coordinate system is crucial. This field is, in turn, used four times within our trap-specific approximation. The off-axis field expressions for the 3D geometries were tested on the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT), and the corresponding expressions for the 2D geometries were tested on the linear ion trap (LIT) and the rectilinear ion trap (RIT). For each geometry, we have considered apertures which are 10%, 30%, and 50% of the trap dimension. We have found that our analytical correction term EdueToAperture, though based on a classical small-aperture approximation, gives good results even for relatively large apertures.

Multiphase models for simulating hot and slightly miscible DNAPL (dense non-aqueous phase fluids) in a saturated rock fracture under deformation

In the present study a two dimensional model is first developed to show the behaviour of dense non-aqueous phase liquids (DNAPL) within a rough fracture. To consider the rough fracture, the fracture is imposed with variable apertures along its plane. It is found that DNAPL follows preferential pathways. In next part of the study the above model is further extended for non-isothermal DNAPL flow and DNAPL-water interphase mass transfer phenomenon. These two models are then coupled with joint deformation due to normal stresses. The primary focus of these models is specifically to elucidate the influence of joint alteration due to external stress and fluid pressures on flow driven energy transport and interphase mass transfer. For this, it is assumed that the critical value for joint alteration is associated with external stress and average of water and DNAPL pressures in multiphase system and the temporal and spatial evolution of joint alteration are determined for its further influence on energy transport and miscible phase transfer. The developed model has been studied to show the influence of deformation on DNAPL flow. Further this preliminary study demonstrates the influence of joint deformation on heat transport and phase miscibility via multiphase flow velocities. It is seen that the temperature profile changes and shows higher diffusivity due to deformation and although the interphase miscibility value decreases but the lateral dispersion increases to a considerably higher extent.

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.

Escape of high mass ions due to initial thermal energy and its implications for axially symmetric RF ion trap mass analyzer design

This paper investigates the loss of high mass ions due to their initial thermal energy in ion trap mass analyzers. It provides an analytical expression for estimating the percentage loss of ions of a given mass at a particular temperature, in a trap operating under a predetermined set of conditions. The expression we developed can be used to study the loss of ions due to its initial thermal energy in traps which have nonlinear fields as well as those which have linear fields. The expression for the percentage of ions lost is shown to be a function of the temperature of the ensemble of ions, ion mass and ion escape velocity. An analytical expression for the escape velocity has also been derived in terms of the trapping field, drive frequency and ion mass. Because the trapping field is determined by trap design parameters and operating conditions, it has been possible to study the influence of these parameters on ion loss. The parameters investigated include ion temperature, magnitude of the initial potential applied to the ring electrode (which determines the low mass cut-off), trap size, dimensions of apertures in the endcap electrodes and RF drive frequency. Our studies demonstrate that ion loss due to initial thermal energy increases with increase in mass and that, in the traps investigated, ion escape occurs in the radial direction. Reduction in the loss of high mass ions is favoured by lower ion temperatures, increasing low mass cut-off, increasing trap size, and higher RF drive frequencies. However, dimensions of the apertures in the endcap electrodes do not influence ion loss in the range of aperture sizes considered. (C) 2010 Elsevier B.V. All rights reserved.

A Layered Zinc Phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2], Formed by One-Dimensional Tubes

An open-framework zinc phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2] (I), with alternating inorganic and organic layers has been synthesized hydrothermally from a starting mixture of ZnO, HCl, H3PO4, H2C2O4, and triethylenetetramine. Single-crystal data for I: monoclinic, space GROUP =P21/c (No. 14), a=9.881(1), b=16.857(1), c=8.286(1) Å, β=96.7(1)°, V=1370.8(1) Å3, Z=2, R1=0.06, and wR2=0.13 [1408 observed reflections with I>2σ(I)]. The structure of I comprises a network of ZnO4, PO4, and PO3(OH) tetrahedra forming one-dimensional tubes. The tubes, in turn, are linked via oxygen atoms forming macroanionic inorganic layers with eight-membered apertures. The one-dimensional tube-like architecture in I is a novel feature worthy of note.

Photo-Defined Electrically Assisted Etching Method for Metal Stencil Fabrication

Metal stencils are well known in electronics printing application such as for dispensing solder paste for surface mounting, printing embedded passive elements in multilayer structures, etc. For microprinting applications using stencils, the print quality depends on the smoothness of the stencil aperture and its dimensional accuracy, which in turn are invariably related to the method used to manufacture the stencils. In this paper, fabrication of metal stencils using a photo-defined electrically assisted etching method is described. Apertures in the stencil were made in neutral electrolyte using three different types of impressed current, namely, dc, pulsed dc, and periodic pulse reverse (PPR). Dimensional accuracy and wall smoothness of the etched apertures in each of the current waveforms were compared. Finally, paste transfer efficiency of the stencil obtained using PPR was calculated and compared with those of a laser-cut electropolished stencil. It is observed that the stencil fabricated using current in PPR waveform has better dimensional accuracy and aperture wall smoothness than those obtained with dc and pulsed dc. From the paste transfer efficiency experiment, it is concluded that photo-defined electrically assisted etching method can provide an alternate route for fabrication of metal stencils for future microelectronics printing applications.

The Behaviour of Two-Phase Flow of DNAPL and Water through a Fractured Rock under Confining Pressure

This study presents the characterization of DNAPL and water flow in a fracture under confining pressure. A comprehensive mathematical model and the conditions under which DNAPL will enter an initially water-saturated deforming rock fracture are discussed. A numerical model with which to predict the quantity of each phase in terms of their saturations in deforming rock joint is developed. The effect of varying confining stresses on the traverse time of DNAPL across a fractured aquitard is studied. The sensitivity analysis for physical and hydraulic properties like initial fracture apertures, fracture dips, equivalent fracture aperture and confining pressures are performed and discussed.

Dual band(WLAN & WiMAX) suppressed harmonic microstrip filter with perturbed ground

Design of a dual band pass filter employing microstrip line with defected ground is presented in this paper. A dual band filter at 2.45GHz and 3.5GHz (covering WLAN and WiMAX) with 6% bandwidth has been designed at each frequency. Apertures in ground plane were used to improve the stop band rejection characteristics and coupling levels in the filter. Measured results of the experimental filter were compared against the simulation results for the purpose of validation.