Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  175

either if electrons bunch together over a length scale, which is significantly shorter than the

wavelength of their emitted radiation bunch that is short with respect to the radiation wave­

length, or if the electron density in a given bunch of electrons is modulated with the same

frequency as the emitted synchrotron radiation wavelength. For x-​rays, it is too challenging

currently to directly produce sufficiently small electron bunches; however, electron bunch

modulation is now technically feasible and is the basis of the XFEL.

In essence, a linear electron beam is generated using high voltage to give relativistic

speeds, either from an output port of a conventional synchrotron or from using a linear

accelerator (LINAC) design. LINACs have a disadvantage over synchrotrons in requiring

greater straight-​line distances over which to operate (e.g., the Stanford LINAC, which cur­

rently operates as the world’s only superconducting LINAC, is ~3 km in length), but have

an advantage in that less energy from accelerated particles is unavoidably lost as synchro­

tron radiation. The accelerated electron beam is propagated through an undulator consisting

FIGURE 5.3  X-​ray applications. (a) Undulator, used in a LINAC, x-​ray free-​electron laser, or as a module in a synchrotron,

which generates a periodic wiggle in the electron beam resulting in an amplified x-​ray emission. (b) Schematic of a typical

SAXS spectrum of a protein complex in a solution, which allows quantitative discrimination between, for example, two

different molecular conformational states. (c) Fresnel zone plate that acts as a “lens” for x-​rays and can be used in (d) and

x-​ray transmission microscope, as well as (e) and x-​ray absorption spectrometer.