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Two dimensional (2D) trap Boundary element method (BEM) Electric field in the vicinity of aperture Multipole a b s t r a c t 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 formwhere 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.

<p class="DefaultParagraphFont1">This paper represents a comparative study of three different types of DC-DC converter that can be used for reduction of Total Harmonic Distortion (THD) in stator current, back electromotive force (EMF) and torque of brush less DC motor. In addition, the topologies of these converters are analysed, and the THD of the output characteristics have also been studied. In this work, SEPIC, Zeta and Flyback converters are considered and their outputs are fed to the BLDCM with the help of universal bridge or six step inverter. Moreover the THD of the output voltages are not only measured for three converters but also reduced by tuning the parameters. At first these three converters are modeled in MATLAB/ Simulink based simulation platform and studied the performance individually and further executed with hardware circuitry. Finally the output parameters from both software simulation and real time hardware are compared for these three converters separately and got satisfactory similar results. Again we studied the performance with these converters in terms of efficiency while fed in the commutation drive circuitry of BLDCM by considering minimum THD. From this comparative simulation results, it has been observed that Zeta converter showed maximum efficiency. Therefore, in real time hardware implementation, the commutation drive circuitry of BLDCM is studied with Zeta converter. With this configuration, a comparatively low THD of stator current, back EMF and electromagnetic torque have been achieved in BLDCM with PID controller.</p>

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