Multiturn injection of an electron beam in a storage ring

In this report, the radial-phase motion of electrons in a storage ring is investigated. The expression for the Hamiltonian, connecting amplitudes of two modes of oscillations is reviewed in view of nonlinear magnetic fields of the third order. The Hamiltonian has a stationary point of a type “limiting cycle”, which in coordinate space defines an equilibrium orbit. The existence “of a limiting cycle” allows one to carry out multiturn injection of the electron beam with final phase volume in a storage ring. The conditions of realization of multiturn injection are reviewed. The results of the research can be used and for stores of particles with large weight