Planar undulator schemes with strong focusing properties for the VUV-FEL at the TESLA test facility

At DESY in Hamburg a free electron laser for the VUV spectral range at 6.4 nm using self amplified spontaneous emission is under construction. It will use the electron beam of the TESLA test facility. One of the main components is an undulator of 30 m length. In order to keep the electron beam-size small over the length of the undulator an alternating quadrupole field has to be superimposed. In this paper three different planar undulator schemes with these properties are described. Their characteristics are studied and compared using the 3D code MAFIA.