What Are Undulators?

Undulators are periodic magnetic devices used in particle accelerators to generate intense, tunable beams of electromagnetic radiation. They consist of alternating arrays of permanent or superconducting magnets arranged in rows along the path of a relativistic electron beam, with the magnetic poles alternating in polarity from one row to the next. As electrons pass through the undulator, they experience transverse Lorentz forces that cause them to oscillate perpendicular to their direction of travel, emitting synchrotron radiation with each oscillation. Unlike bending magnets, which deflect electrons along a curved arc, undulators produce interference between the radiation emitted at each oscillation, concentrating the output into a narrow cone with a nearly monochromatic spectrum.

The central emitted wavelength follows the relation lambda equals P divided by 2 times gamma squared times one plus K squared over two, where P is the magnet period, gamma is the relativistic Lorentz factor, and K is the undulator parameter proportional to the peak magnetic field. By adjusting the magnet gap and therefore the peak field, operators can tune the emission wavelength across a wide range from the infrared to the hard X-ray regime. This tunability distinguishes undulators from wigglers, which are stronger-field relatives that produce a broader, less coherent spectrum.

Synchrotron Radiation Sources

Undulators are the primary photon-producing elements at modern synchrotron light sources, where they are inserted into straight sections of the storage ring between bending magnets. A detailed treatment of synchrotron radiation and X-ray free-electron lasers describes how the interference of radiation from successive oscillation periods gives rise to peaks in the energy spectrum called harmonics, with the fundamental wavelength and its odd harmonics determined by the undulator equation. High-brightness undulator beams drive experimental stations in X-ray diffraction, spectroscopy, imaging, and lithography, providing photon fluxes many orders of magnitude greater than conventional X-ray tubes.

Free-Electron Lasers

In free-electron lasers (FELs), the undulator plays a dual role. It both forces radiation emission and, through the interaction of the radiation field with the electron beam, causes the electrons to self-organize into periodic microbunches spaced at the radiation wavelength. This microbunching amplifies the emitted power coherently through a process called self-amplified spontaneous emission (SASE), producing laser-like X-ray pulses with peak brightness billions of times higher than that of storage-ring undulators. The X-Ray Free Electron Laser overview from SLAC National Accelerator Laboratory details how FELs such as the Linac Coherent Light Source operate through a single-pass amplification scheme in which the electron bunch traverses a long undulator once before being discarded. More recent developments, described in Physical Review Accelerator Beams research on attosecond X-FEL schemes, explore optical undulators and advanced phasing methods to push FEL pulses into the attosecond range.

Undulator Design and Technology

Practical undulator design requires precise control of the magnetic field profile to maintain the electron trajectory on axis and minimize field errors that would degrade beam quality. Conventional permanent-magnet undulators use NdFeB (neodymium iron boron) blocks arranged in Halbach arrays. Superconducting undulators, which use niobium-titanium or niobium-tin wire cooled to cryogenic temperatures, achieve higher peak fields at shorter periods, enabling shorter emission wavelengths at a given beam energy. The undulator parameter K scales directly with peak field and magnet period, so superconducting designs expand the tuning range significantly. Electromagnetic undulators with copper-wound coils offer fast wavelength switching at the cost of lower peak field.

Applications

Undulators have applications in a range of fields, including:

• Structural biology, for determining protein and virus structures via X-ray crystallography and cryo-electron microscopy
• Materials science, for studying thin-film interfaces and nanostructured surfaces with X-ray scattering
• Industrial lithography and nanofabrication using extreme ultraviolet and soft X-ray beams
• Ultrafast science, for probing chemical reaction dynamics at femtosecond and attosecond timescales
• Medical imaging research using phase-contrast and fluorescence X-ray techniques