Design considerations for a 1 إ SASE undulator

The various technologies available to build a SASE-type undulator for a 1Å wavelength are compared. This includes permanent magnets, superconducting and room-temperature electromagnets for both the planar and helical-field configurations. Following a 3D computation of the magnetic field, general expressions are given for the peak field as a function of the undulator period. The growth length and saturated length of the SASE radiation is computed by means of the simple analytical expressions of the 1D theory and of a 3D numerical simulation for each type of undulator technology and electron beam quality. It is found that the saturated length is almost independent of the electron energy in the 15–40 GeV range of the TESLA linear accelerator project. It is proportional to the undulator period. A reduction of the saturated length is predicted with additional FODO type focusing with an optimum beta function around 20 m. This large beta function allows the placement of the FODO quadrupole outside the undulator in a drift space located between two undulator segments. The tunability of the radiation through the change of undulator field is possible but it requires a longer undulator. The tunability imposes the use of magnetic phasing sections also located between the undulator segments. A method is presented for an absolute monitoring and alignment of the angle of the electron beam in each undulator section. It is based on the observation of the spontaneous emission separately from each undulator section. It has a precision of 1.4 μrad limited by the electron beam divergence.