Calculation and analysis of the magnetic field of a transverse focusing undulator

The transverse focusing undulators can be used for electron beams of low energy and smaller function. At present, there are some designs on transverse focusing undulators at home and abroad. This paper proposes several transverse focusing undulators of different magnetic structures which are based on the inclined surface of permanent magnet or/and pole blocks. Using the three-dimensional program Radia, the characteristics of focusing field of these undulators were calculated, the relationship between the focusing characteristics with the main parameters was studied, and performance of these undulators were also compared with other existing transverse focusing undulators. The results show that, for both the weak and strong focusing, several undulator schemes with better and simpler structures than the existing transverse focusing undulators were proposed. In addition, the average focusing gradient of weak focusing undulators does not increase significantly with the center magnetic field whereas the average focusing gradient of strong focusing undulators increases obviously with the center magnetic field.