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TY - CONF AU - Barminova, H.Y. AU - Chikhachev, A.S. ED - Eshraqi, Mohammad ED - Trahern, Garry ED - Schaa, Volker RW TI - Analytical Approach for Achromatic Structure Study and Design J2 - Proc. of HB2016, Malmö, Sweden, July 3-8, 2016 C1 - Malmö, Sweden T2 - ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams T3 - 57 LA - english AB - The analytical approach is proposed to study the various achromatic structures. The method is based on the self-consistent time-dependent models, which allow to describe the dynamics of both continuous and bunched beam in external magnetic fields. The fully kinetic models are implemented in this approach. The kinetic distribution functions dependent on the motion integrals allow to obtain accurate Vlasov equation solutions as KV-model does it. The method allows to solve the envelope equation both analytically and by ODE system numerical integration, and to predict the beam phase portrait behavior in magnetic fields of the structure. The advantages of the method are the possibility of easy scaling and the wide physical generality, which is important for the multi-parameter problem of the high-intensity high-brightness beam formation. The results of the method application for the bending magnets and the quadrupoles are presented. PB - JACoW CP - Geneva, Switzerland SP - 203 EP - 206 KW - quadrupole KW - emittance KW - dipole KW - cyclotron KW - factory DA - 2016/08 PY - 2016 SN - 978-3-95450-185-4 DO - 10.18429/JACoW-HB2016-MOPL009 UR - http://jacow.org/hb2016/papers/mopl009.pdf ER -