On the analytic representation of periodic magnetostatic fields

A generalized form is considered in a source-free region for the magnetic scalar potential in focusing planar undulators and insertion devices. A number of particular cases is outlined: periodic quadrupole and sextupole focusing, combined-function nonlinear wigglers, twisted undulator, alternating longitudinal field focusing system, an adjustable phase insertion device. A special attention is paid to quadrupole type intrinsic fields including strong periodic focusing. The generalised formalism can be used in particle tracing codes or 3D codes for free electron lasers simulation