Orbital angular momentum radiation and polarization of relativistic electrons in magnetic fields

While spin polarization from synchrotron radiation is well established, the polarization of orbital angular momentum (OAM) in such radiative processes remains elusive. We study radiation and polarization of relativistic electrons in a uniform magnetic field, focusing on OAM polarization radiation for vortex electrons which carry intrinsic OAM. The results illustrate that transition rates are asymmetric in the low-photon-energy regime, favoring OAM decrease, analogous to the spin-flip asymmetry in the Sokolov-Ternov effect. Under these conditions, synchrotron radiation can polarize the OAM. The characteristic relaxation time and stationary-state OAM distribution are obtained analytically. The polarization of spin about $\mathcal{P}_{\text{spin}}$ reaches $92.38\%$, while that of $\mathcal{P}_{\text{OAM}}$ can even approach almost unity for a large OAM; however, their polarization behaviors are different. For typical storage ring parameters, the OAM polarization time is orders of magnitude shorter than the spin polarization time. Thus, synchrotron radiation offers a mechanism for controlling vortex electron beams which carry OAM for high-energy accelerator applications.