Results of design calculations for the modulator of the crossed field undulator device

The modulator is a five pole wiggler with a fixed 5 cm gap. In the current design, the modulator is oriented so that the magnetic field in the device is parallel to the field in one of the undulators. The two end poles have no coil and are only half as thick as the inner poles. The end poles serve as field clamps that reduce the stray field of the modulator and the sextuple coefficient of the field integral. The center pole and the two side poles can be energized with coils. As long as the permeability is large enough within the steel the current in the center coil should be twice the current in a side coil to avoid steering the electron beam. Therefore, if the center coil has twice as many turns as the side coil, the magnet can be driven by one power supply. The design of the modulator is based on theoretical work done by K. Halbach. The highest magnetic flux density occurs at the base of the center pole where the average flux density should be well below the saturation field of vanadium permendur. Assuming infinite permeability, the average flux density at the base of the pole can be calculated as a function of pole height and phase shift. This design was checked with the 2D-Magnet Code POISSON using a measured B-H curve for vanadium permendur. The computer calculations showed that at up to 80% of the design current, the steering of the electron beam is small (<30μrad) compared with the minimum width of the first harmonic radiation cone of UA (∼ 28Oμrad). The phase shift at 80% of the design current is 2π for a wavelength of 1300 angstrom. Due to the beginning of saturation, the steering of the electron beam increases to 140μm at 100% of the design current (600A)