New hybrid permanent magnet undulator schemes were analysed with the g
oal to find a magnet configuration providing electron beam focusing in
both transverse directions. Numerical simulations with the 2D code PA
NDIRA and the 3D code TOSCA were completed. It is demonstrated that us
ing either side magnet arrays, satellite magnets or poles profiled by
rectangular holes one could provide an effective focusing field profil
e of the undulator. A complex magnet configuration appearing as 3D hyb
rid undulator was also found which enables strong enhancement of the u
ndulator field as well as transverse focusing.