Orbital motion in generalized static fields of FELs accounting for axial magnetic field, beam forces, undulator and external focusing

Orbital motion of electrons in generalized static fields of FELs is studied. Terms linear with both transverse coordinates and their derivatives are taken into account, thus allowing to include axial magnetic field, undulator and external focusing and beam forces. The undulator field is described as a superposition of fields of two plane undulators with mutually orthogonal fields and an arbitrary axial shift between them. The general solution allows to analyse particular cases of planar or helical undulators (or a superposition of several undulators) combined with the axial magnetic field in studying orbits, gyroresonance, polarization, limiting beam current etc.