Design and optimization of planar undulators for X-ray free-electron lasers: Comparative analyses considerations on magnetic structures

A comparative design and magnetic performance analysis of planar undulator configurations is presented using the 3D magnetostatics simulation code RADIA. Three representative structures are investigated: a pure permanent magnet undulator, a hybrid configuration with Vanadium Permendur poles, and a hybrid configuration with iron poles. The designs are assessed in terms of achievable magnetic field strength, undulator parameter, harmonic content, field uniformity, and overall magnetic field quality. Numerical results obtained from RADIA are systematically compared with theoretical estimates based on established empirical models. Results indicate that the Vanadium Permendur-based hybrid configuration achieves the highest peak magnetic field and improved harmonic purity, thereby satisfying the requirements for high-brilliance synchrotron radiation sources and free-electron laser applications. The iron-based hybrid design provides a cost-effective alternative with competitive performance, while the pure permanent magnet configuration, despite its structural simplicity, shows limited field strength and increased harmonic distortions. These results confirm the reliability of RADIA as a predictive tool for planar undulator design and optimization.