Self-extraction in a Positive Ions // Proc. 14th Int. <...> The proton therapy system for the Compact High-Intensity H+ Cyclotron at IBA // Proc. of EPAC 2000. <...> New Design Issues of the EXCYT Project // Proc. of EPAC’96. 7. <...> Project of the DC-60 Cycltron with Smoothly Ion Energy Variation for Research Center at L. N. Gumilev Euroasia State University in Astana (Kazakhstan) // Proc. of the Cyclotrons’2004. <...> Preliminary Structure Design of the Main Magnet for the 100 MeV Cyclotron// Ibid. 71 10. <...> Development and Status Report of Medical Cyclotron at KIRAMS // APAC 2004. <...> New Design of the KIRAMS-13 Cyclotron for Regional Cyclotron Center // Proc. of APAC 2004. <...> Study of transverse beam size evolution in cyclotrons acceleration simulation S. A. Kostromin, E. V. Samsonov, S. G. Shirkov Joint Institute for Nuclear Research 6 Joliot-Curie str., Dubna, Moscow region, 141980, Russia E-mail: kostromin@jinr.ru Technique of beam dynamics simulation by means of numerical integration of the equations of motion is described. <...> Estimations of the transverse beam size can be done by analysis of the amplitudes of free radial and vertical oscillations of the particles in the accelerating beam. <...> Examples of transverse beam motion study is considered. <...> Представлена методика организации расчета ускорения пучка в циклотроне на основе численного интегрирования уравнений движения. <...>