Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2291910.22363/2658-4670-2019-27-4-378-385Research ArticleEfficient computational scheme for ion dynamics in RF-field of Paul trapMelezhikVladimir S.melezhik@theor.jinr.ruBogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear ResearchDubna State University1512201927437838519022020Copyright © 2019, Melezhik V.S.2019<p>We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom 10 2/ defined by the atomic trap frequency 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.</p>cold atoms and ionsPaul trapradio-frequency fieldclassical Hamilton equationscomputational schemeхолодные атомы и ионыловушка Паулярадиочастотное полеклассические уравнения Гамильтонавычислительная схема[M. Tomza, K. Jachymski, R. Gerritsma, A. Negretti, T. Calarco, Z. Idziaszek, and P. S. Julienne, “Cold hybrid ion-atom systems,” Reviews of Modern Physics, vol. 91, no. 3, p. 035 001, 2019. DOI: 10. 1103 / RevModPhys.91.035001.][V. S. Melezhik, Z. Idziaszek, and A. Negretti, “Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps,” Physical Review A, vol. 100, no. 6, p. 063 406, 2019. DOI: 10.1103/PhysRevA. 100.063406.][V. S. Melezhik and P. 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