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TY - CONF AU - Vinogradova, E.M. AU - Starikova, A.V. ED - Kuzin, Maxim ED - Schaa, Volker RW TI - The Multipole Lens Mathematical Modeling J2 - Proc. of RuPAC2016, St. Petersburg, Russia, November 21-25, 2016 C1 - St. Petersburg, Russia T2 - Russian Particle Accelerator Conference T3 - 25 LA - english AB - In the present work the mathematical model of the multipole system is presented. The multipole system is composed of arbitrary even number of the uniform electrodes. Each of the electrodes is a part of the plane. The potentials of the electrodes are the same modulus and opposite sign for neighboring electrodes. The variable separation method is used to solve the electrostatic problem. The potential distribution is represented as the eigen functions expansions. The boundary conditions and the normal derivative continuity conditions lead to the linear algebraic equations system relative to the series coefficients. PB - JACoW CP - Geneva, Switzerland SP - 535 EP - 537 KW - multipole KW - electron KW - vacuum KW - cathode KW - controls DA - 2017/02 PY - 2017 SN - 978-3-95450-181-6 DO - 10.18429/JACoW-RuPAC2016-THPSC001 UR - http://jacow.org/rupac2016/papers/thpsc001.pdf ER -