Undulator magnets

Figure 2. Synchrotron X-ray source (schematic). The electrons execute circular motions in the storage ring and emit intense X-rays along the tangent of the orbit. This radiation is enhanced by undulator magnets that are often placed inside the vacuum vessel for enhanced performance. The storage ring has a number of straight sections for undulators and wigglers (not shown).

The fact that Ac is proportional to the bending radius is used in so-called insertion devices such as wiggler and undulator magnets.t Although a description of these is beyond the scope of this chapter, the basic principle behind these is to make the electron beam undergo sharp serpentine motions (thereby having a very short radius of curvature). The net effect is to increase the flux and the critical energy (see topmost curve in Fig. 5). 

Fig. 6. Photon field relative to electron trajectory in an undulator magnetic field illustrating the resonance condition (cf eqn. 8). The boldface arrow in the electromagnetic field is a reference.

Theoretical analysis of free-free transitions of electrons moving in undulating magnetic fields has much developed since the original work of Ginzburg (34) and Motz (13). Its renewed importance is related to the development of Free-Electron Lasers using free-free... 

Figure 4 Integrated spectral flux for Advanced Photon Source (APS) undulator. The position of the peaks is adjustable by varying the undulator magnetic gap.

Helical undulators build on this principle by using two orthogonal magnetic field arrays [82, 83]. These permit transverse excursions in perpendicular x and y directions. If the arrays have a relative longitudinal shift, this introduces a phase to the induced perpendicular excursions and when the phase is 90° the electron trajectory can follow left- or right-handed corkscrew paths The emitted radiation is correspondingly right- or left-handed CPL. 

Accurate experimental determinations require that not only the handedness of the produced light, but its exact degree of polarization, are known. The theoretical performance of an undulator may be in practice be degraded by magnetic defects, and the optical beam can be further depolarized by reflections along the beamline. Again, the dephasing on optical elements can in principle be... 

Bulk and micro-XAFS analyses were performed at the PNC-CAT s bending magnet (20-BM) and undulator (20-ID) beamlines of the Advanced Photon Source (APS), Argonne, IL, USA. Other microanalytical and mineralogical characterization studies were conducted at CANMET. Details of the methodology can be found in Paktunc (2008) and other publications by the author. 

The spectmm from an undulator is very different, and numerous peaks result from interference effects within the undulator. When the electron acceleration is confined to the orbit plane and the emission angle very low, the radiation is strongly elliptically polarised and, in the orbit plane itself, it is to within a few per cent linearly polarised. Use of a sequence of permanent magnets with magnetisation arranged in a spiral sequence enables circularly polarised radiation to be extracted from such a helical undulator and this radiation is particularly important for magnetic studies. 

S)mchrotron X-ray sources include both bending magnets and insertion devices. For protein crystallography, an undulator insertion device is preferred because it provides greater intensity at a specific wavelength and has lower beam divergence. This latter property results in smaller X-ray reflections. 

The X-ray source may be a conventional sealed tube or rotating anode generator or bending magnet synchrotron radiation and more recently the exploitation of multipole insertion devices such as wigglers and undulators represent great gains in source intensity. 

Undulator parameters as of October 2003. Ef is the undulator fundamental, Ec the critical energy of the bending magnet radiation in the "slalom" motion. ... 

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