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In this paper, a simple analytical approach for obtaining user-defined axial magnetic field profile of a periodic permanent magnet (PPM) structure used for focusing the electron beam in linear beam tubes is presented. Axially magnetized permanent ring magnet and single cell of a PPM structure are represented by equivalent solenoids, and their equivalent parameters are obtained from the dimensions and material properties of these magnet structures. Axial magnetic field for the finite-length PPM structure is obtained using the superposition of equivalent solenoids of all PPM cells. Finally, a methodology is presented to obtain a user-defined axial magnetic field profile in a PPM structure. Analytically computed axial magnetic field is compared with finite-element-method simulation and measured results and found to show a very good agreement.
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Santra et al. (2011) studied this question.
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