Analysis of spectral properties of harmonic undulator radiation of an electromagnet undulator

In this paper we analyze the spectral properties of undulator radiation with an electromagnet undulator for electron injected off the undulator axis. The electromagnet undulator is self bi-harmonic for locations near to the electromagnet. The electrons execute additional betatron oscillation when it injected off the undulator axis. It is observed that the electromagnet undulator can be used for harmonic lasing free electron laser operates at the cost of betatron oscillations for electron injected off the axis.