Undulators are ALP Factories

Axion-like particles (ALPs) are known to be produced through axion-photon conversion in the presence of a stationary external magnetic field. Devices such as undulators and wigglers, which are used widely for photon production, e.g., in synchrotron radiation facilities, inherently possess strong magnetic fields, making them potential sources for ALP production. In this paper, we establish formalisms and formulas for studying ALP production in the ALP-photon-charged current system based on quantum field theory. We demonstrate that ALP production is inevitable in any undulator with the standard designs due to the electron Coulomb potential as well as a resonance effect depending on the ALP mass. In particular, ALPs are predominantly produced in a direction slightly misaligned with the photons' main direction. We propose placing detectors in the desired directions during operations of the originally planned experiments as an efficient approach to simultaneously probing ALPs. The calculation methods and formulas developed in this study are applicable to ALP production from other environments and productions of other particles beyond the standard model relevant to synchrotron radiations.