This research includes a study to understand the behavior of charged particles beam through consideration of systems of quadrupole triplet reaching to the optimum design of beam transport through a system of triplet quadrupole triplet lenses. In this work, tracing the path of charged particles beam has been within the free field space and quadrupole electrostatic lens system which include the triplet quadrupolelens by using matrices to described particle trajectories throughout the system. Matrix representation deals with ion beam as bunched and representing phase ellipse for both horizontal and vertical planes. The present work investigated the effect of the main parameters of triplet quadruple such as length of quadrupole, the distance between the lenses, voltage applying on lenses,second field free region length. Matlab program built to study these parameters, the results indicated that good focusing properties for both horizontal and vertical plane.

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