There remain magnetic errors that cause trajectory wandering beyond a few micrometer, additional focusing effects and other dynamic effects. They are compensated using shims. Shims are small pieces of permanent magnets or ferromagnetic material strategically placed within the undulator. The effect of permanent magnet shims depends on the size and positions, while the effect of ferromagnetic shims also depends on the magnetic field at the shim position. The latter effect is used in BESSY undulators to compensate shift dependent effects. Shims are also used to compensate dynamic multipoles due to the naturally occurring and omnipresent edge focusing. In fact, undulators consist of nothing but edges. On top of the natural focusing there is beam distortion due to magnetic field imperfections. The focusing varies according to the operational status of the undulator. It is localized in the storage ring at the position of the undulator. This modifies the electron beam cross section all around the storage ring unless compensated by slightly different powering of adjacent magnetic focusing elements of the storage ring as done at BESSY.
The dynamic apertures as measured by kicking the electron beam with different amplitudes show the expected increase of the dynamic aperture due to shimming. A further increase of the dynamic aperture for all undulators will improve the lifetime of the stored beam. It also will increase the injection efficiency with operating undulators as needed for topping-up operation of the BESSY storage ring.
Fig. 2: Bench for local and integrated magnetic field measurements: The system consists of a slide on air cushions on a 6 m long granite (maximum travel 5.5 m). A Hall probe is located on an extender reaching into the magnetic gap of the undulator. The position of the Hall probe is reproducible by better than 5 μm and is measured using a laser interferometer. The system is also used to verify the mechanical straightness of completely assembled. Additionally, a moving wire system is used to characterize the integrated multipoles with a high accuracy. It consists of two xyz positioning systems at either end of the undulator. A wire is stretched between them through the active volume of the undulator. The voltage induced in the wire is recorded. First and second field integrals are obtained as function of the transverse and vertical position inside the gap. The wire is also part of a pulsed wire set-up.