Orbital angular momentum of Liénard–Wiechert fields

We derive a general expression for the electromagnetic field radiated by a relativistic charged particle with arbitrary periodic orbit, in the form of multi-pole expansion of the Liénard–Wiechert potential, which explicitly includes the charged particle motion. Using this expression, we discuss the orbital angular momentum radiated from a relativistic charged particle. It has recently been indicated that the radiation emitted by circularly orbiting charged particles carries well-defined orbital angular momentum. We show that, even for the general cases of arbitrary periodic orbits, the radiation field possesses well-defined orbital angular momentum.