INSTRUMENTATION FOR TXRF AND GI-XRF - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 138

Figure3.6. Instrumental arrangement of an undulator and free-electron laser. An essential part is
the undulator with up to 100 alternating poles at a distance λ u . It is placed between two outer mirrors
in a distance of n λ u , which can be up to several tens of meters. The bending magnets before and
behind the undulator deflect the electron beam right into it and out of it, respectively, so that the
second mirror will not be destroyed. This second mirror is semitransparent or has a small hole so
that the synchrotron radiation can get out. Figure from Ref. [15], reproduced with permission from
the author.

fields force the electrons on sinusoidal curves around their straight-line path,
that is, the electrons weave on a slalom course within the horizontal orbit plane
or vertical to this plane [14,15].
The distance of two neighboring like poles is called undulator wavelength,
λ u . Undulators cause up to 100 oscillations of the electrons around the straight
line with small λ u values and small amplitudes (vertical divergence 1/ γ where γ
is the Lorentz factor), while wigglers cause less deflections at larger λ u values
but higher amplitudes of the electron beam (vertical divergence 1/ γ ). The
spectrum of a wiggler is a broad continuum while the spectrum of an undulator
shows narrow energy bands [15,16]. The so-called undulator parameter, K = λ u /
2 πρ m , differs for multipole wigglers ( K >> 1) with a continuum and undulators
with several discrete energy peaks, so-called harmonics ( K ≈ 1), or with only
the first harmonic ( K

1). The radiation of an undulator is quasi-mono-
chromatic. In comparison to bending magnets of the second generation, the
flux, and moreover the brilliance of the radiation are increased by three to five
orders of magnitude for wigglers and by four to eight orders of magnitude for
undulators. N oscillations give a gain of N 2 for the brilliance; for example, 100
oscillations give 10 000-fold brilliance.
Undulators and wigglers are usually several meters long. If this length is
increased to 10 or even 100 m, the photons of the radiation can interact with the
relativistic electrons and can get“light amplification by stimulated emission of
radiation.”This effect is referred to as free-electron laser (FEL). It is the latest
development in the field of relativistic particles [11,14,17,18].
Such a free-electron laser is also shown in Figure 3.6. It contains an
undulator as the main component between two outer mirrors. The electron
beam replaces the gas or solid medium of a conventional optical laser. Such a
laser is consisting of a gain medium, a mechanism to supply energy to it, and a
device to provide an optical feedback [19,20]. The highly accelerated electrons