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We analyze the collective light scattering by cold atoms in free space of apump laser beam possessing orbital angular momentum. We derive a set of coupledequations for the atomic motion in which the vacuum-mode field is adiabaticallyeliminated. The resulting equations describe collective recoil as due to eithertransfer of linear momentum or orbital angular momentum. For a transverseannular atomic distribution the initial equilibrium with uniform atomic phasesand no scattered field, is unstable. The atoms are set in rotation and bunchedin phase at different harmonics depending on the pump azimuthal index l and onthe ring radius.

Superradiant atomic recoil lasing with orbital angular momentum light