“…The questions of electromagnetic fields modeling and simulation in different focusing and accelerating systems, and corresponding beam dynamics investigation and optimization, are widely discussed. Electromagnetic fields analytical representation is often used in scientific research, in particular, [Ovsyannikov, 2012;Ovsyannikov and Altsybeyev, 2013;Rubtsova, 2014a,b;Rubtsova, 2016a;Rubtsova and Ovsyannikov, 2018;Vinogradova, Starikova and Varayun ′ , 2017;Altsybeyev et al, 2018]. Analytical field description makes possible beam dynamics optimization theory developing on the basis of analytical methods, including trajectory ensemble control methods [Ovsyannikov, 1997;Ovsyannikov et al, 2006;Ovsyannikov, 2012;Ovsyannikov and Altsybeyev, 2013;Rubtsova and Suddenko, 2012;Rubtsova, 2016b;Rubtsova and Ovsyannikov, 2018;Balabanov, Mizintseva, Ovsyannikov, 2018;Nikolskii and Belyaevskikh, 2017;Nikolskii and Belyaevskikh, 2018].…”