An undulator for a free electron laser includes a pipe for an electron beam and one or more periodic magnetic structures extending axially along the pipe. Each periodic magnetic structure includes a plurality of magnets and a plurality of passive ferromagnetic elements, the plurality of magnets being arranged alternately with the plurality of passive ferromagnetic elements in a line extending in an axial direction. Each of the plurality of magnets is spatially separated from the pipe, and each of the passive ferromagnetic elements extends radially from an adjacent magnet towards the pipe. A spacer element may be provided between the magnets and the pipe to provide radiation shielding for the magnets and/or cooling for the pipe.