Electron with orbital angular momentum in a strong laser wave

Electrons carrying orbital angular momentum (OAM) have recently been discovered theoretically and obtained experimentally, which opens up possibilities for using them in high-energy physics. We consider such a twisted electron moving in the external field of a plane electromagnetic wave and study how this field influences the electron's OAM. Being motivated by the development of high-power lasers, we focus our attention on a classically strong-field regime for which e²A²̄/(me²c ⁴)≳1. It is shown that, along with the well-known "plane-wave" Volkov solution, the Dirac equation also has the "non-plane-wave" solutions, which possess OAM and spin-orbit coupling and generalize the free-electron's Bessel states. Motion of an electron with OAM in a circularly polarized laser wave reveals a twofold character: the wave-packet center moves along a classical helical trajectory with some quantum transverse broadening (due to OAM) existing even for a free electron. Using the twisted states, we calculate the electron's total angular momentum and predict its shift in the strong-field regime, which is analogous to the well-known shifts of the electron's momentum and mass (and to a less-known shift of its spin) in intense fields. Since the electron's effective angular momentum is conserved in a plane wave, as well as in some more general field configurations, we discuss several possibilities for accelerating nonrelativistic twisted electrons by using focused and combined electromagnetic fields.