  We present a study of the scattering of a monochromatic helical laser beam,
described by a Laguerre-Gauss solution of the Maxwell equations, on an electron
sheet, initially at rest in the focal plane of the laser; the interaction is
described in the framework of a local plane wave approximation. We calculate
the scattered electromagnetic field observed in an arbitrary point at a large
distance from the laser focal spot, by adding coherently the contributions of
each electron in the electron sheet. Due to the interference effects, the
radiation is emitted only into the forward direction, within a narrow cone, and
it has a spatial structure that we analyze theoretically and numerically. For
circularly polarized incident fields, the structure is also helical, with a
helical index which depends on the helical index of the incident radiation and
the harmonic order. These structures can be observed experimentally, as each
harmonic order is emitted with a different frequency, and within cones of
different opening angles. Our findings are in agreement with experimental
results in the literature which demonstrate the generation of OAM carrying
photons by radiation scattering on electrons.
