“Integrable accelerator” structure for round beams with a soliton-like force

This work is devoted to finding the integrable systems for accelerators with strong nonlinear fields. Among all the solutions there is one with a soliton-like force; one of the invariants for this system is a quartic in momentum polynomial. Another one is angular momentum, so this system is related with round beams. Such a field can be made by solenoidal focusing field, so the solution presents an example of integrable accelerator with regular nonlinear motion. All this shows the relation of general theory of integrable systems with particular theory of accelerators; it might initiate applications of Lie groups to equations in partial derivatives for finding “integrable” lattices of accelerators