undulator

An undulator is a device in accelerator-based light sources that uses a periodic magnetic field to force relativistic electrons to follow a transverse sinusoidal path as they travel through it. The emitted radiation, produced by constructive interference from many wiggles, is highly collimated and exhibits sharp spectral lines at harmonics of a fundamental wavelength.

An undulator consists of a linear array of magnets with alternating polarity embedded in a vacuum chamber. The magnetic period, lambda_u, and the number of periods, N, determine the total length and spectral properties. Planar undulators produce a planar wiggle and linearly polarized light, while helical undulators produce circularly polarized radiation.

Key parameters include the undulator parameter K = e B0 lambda_u / (2 pi m_e c), where B0 is the peak magnetic field, and the fundamental wavelength lambda = lambda_u / (2 gamma^2) [1 + K^2/2 + gamma^2 theta^2]. For small observation angles, theta ~ 0, the on-axis wavelength is lambda ≈ lambda_u / (2 gamma^2) (1 + K^2/2). When K < 1 the device is typically called an undulator; for larger K the device behaves more like a wiggler.

Applications include generation of hard and soft X-ray beams at storage rings, and the production of intense, coherent X-ray pulses in free-electron lasers. In FELs, the undulator interacts with a high-brightness electron beam to amplify radiation through the FEL process; SASE and seeded variants are common operation modes.

Modern advances include short-period, high-field undulators and superconducting undulators, which extend reachable photon energies and brightness. The choice of period, K, and the number of periods is guided by the desired photon energy, flux, and polarization.