  Classical theories of radiation reaction predict that the electron motion is
confined to the plane defined by the electron's instantaneous momentum and the
force exerted by the external electromagnetic field. However, in the quantum
radiation reaction regime, where the recoil exerted by individual quanta
becomes significant, the electron can scatter `out-of-plane', as the photon is
emitted into a cone with finite opening angle. We show that Monte Carlo
implementation of an angularly resolved emission rate leads to substantially
improved agreement with exact QED calculations of nonlinear Compton scattering.
Furthermore, we show that the transverse recoil caused by this finite beaming,
while negligible in many high-intensity scenarios, can be identified in the
increase in divergence, in the plane perpendicular to the polarization, of a
high-energy electron beam that interacts with a linearly polarized,
ultraintense laser.
